Talking Circuits. The Development and Assessment of a Digitally-Scaffolded, Collaborative Method for Teaching and Learning Electrical Circuits in Early Secondary Schools

Studien zum Physikund Chemielernen M. Hopf und M. Ropohl [Hrsg.] 394 Thomas Sean Weatherby Talking Circuits The Development and Assessment of a Digitally-Scaffolded, Collaborative Method for Teaching and Learning Electrical Circuits in Early Secondary Schools λογος Studien zum Physikund Chemielernen Herausgegeben von Martin Hopf und Mathias Ropohl Diese Reihe im Logos Verlag Berlin l¨ adt Forscherinnen und Forscher ein, ihre neuen wissenschaftlichen Studien zum Physikund Chemielernen im Kontext einer Vielzahl von bereits erschienenen Arbeiten zu quantitativen und qualitativen empirischen Untersuchungen sowie evaluativ begleiteten Konzeptionsentwicklungen zu ver¨ offentlichen. Die in den bisherigen Studien erfassten Themen und Inhalte spiegeln das breite Spektrum der Einflussfaktoren wider, die in den Lehrund Lernprozessen in Schule und Hochschule wirksam sind. Die Herausgeber hoffen, mit der F¨ orderung von Publikationen, die sich mit dem Physikund Chemielernen befassen, einen Beitrag zur weiteren Stabilisierung der physikund chemiedidaktischen Forschung und zur Verbesserung eines an den Ergebnissen fachdidaktischer Forschung orientierten Unterrichts in den beiden F¨ achern zu leisten. Martin Hopf und Mathias Ropohl Studien zum Physikund Chemielernen Band 394 Thomas Sean Weatherby Talking Circuits The Development and Assessment of a Digitally-Scaffolded, Collaborative Method for Teaching and Learning Electrical Circuits in Early Secondary Schools Logos Verlag Berlin λογος Studien zum Physikund Chemielernen Martin Hopf und Mathias Ropohl [Hrsg.] Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet ¨ uber http://dnb.d-nb.de abrufbar. Dieses Werk ist lizenziert unter der Creative Commons Lizenz CC BY-SA (https:// creativecommons.org/licenses/by-sa/4.0/). Die Bedingungen der Creative-Commons-Lizenz gelten nur f¨ ur Originalmaterial. Die Wiederverwendung von Material aus anderen Quellen (gekennzeichnet mit Quellenangabe) wie z. B. Schaubilder, Abbildungen, Fotos und Textausz¨ uge erfordert ggf. weitere Nutzungsgenehmigungen durch den jeweiligen Rechteinhaber. Logos Verlag Berlin GmbH 2025 ISBN 978-3-8325-6008-9 ISSN 1614-8967 DOI 10.30819/6008 Logos Verlag Berlin GmbH Georg-Knorr-Str. 4, Geb. 10 D-12681 Berlin Tel.: +49 (0)30 / 42 85 10 90 Fax: +49 (0)30 / 42 85 10 92 https://www.logos-verlag.de Talking Circuits The Development and Assessment of a Digitally-Scaffolded, Collaborative Method for Teaching and Learning Electrical Circuits in Early Secondary Schools Thesis for the award of the Degree of Doctor of Natural Sciences presented to the Faculty of Physics of the Goethe University, Frankfurt am Main, Germany by Thomas Sean Weatherby Born in Oxford, England, United Kingdom. Frankfurt am Main, 2025. (D30) The open access publication of this book was funded by the Open Access Publication Fund of Goethe University Frankfurt am Main. Accepted as a thesis by the Faculty of Physics at the Goethe University Frankfurt. Dean: Prof. Dr. Roger Erb Reviewer: Prof. Dr. Thomas Wilhelm Date of Viva Voce: 16th April 2025 iii Heartfelt thanks to everyone who has helped along the way. To Mum and Dad, my deepest gratitude, for all the chats, proofreading and heavy lifting, without which I could never have completed this project. To my mentor, Thomas, whose trust, responsiveness and assistance supported my work and, moreover, made it worth doing. To Jan-Philipp, whose openness and enthusiasm made both starting in Frankfurt and starting a doctorate a much less of a daunting task. To all of my colleagues in Frankfurt, with whom the jokes, chats and shared purpose made eating the Mensa food worth it. To BERA-BJET, for the funding. To the teachers, with whom I worked during my intervention, who took me in with open arms and made me feel part of the team within days. And lastly, to the learners, for taking it in their stride. x 4.2Units in “An Introduction to Electricity Using Potential Difference” 145 4.3National Curriculum for England - Circuit Electricity 156 4.4Bridging vs. Scientific Vocabulary 164 4.5Estimated Vocabularies of School Children in the USA 170 4.6Table showing Intrinsic Motivational Inventory Items 189 5.1Summary of Learner and Class Numbers 193 5.2Preand Post-Test Scores for Both Experimental Groups 195 5.3ANOVA Summary for Preand Post-Test Scores 197 5.4Score Gains for Both Experimental Groups 197 5.5Cronbach’s Alpha for Each IMI-Subscale 198 5.6 Means and Standard Deviations for Each Measurement Point of the IMI 200 5.7ANOVA Summary for Preand Post-Test IMI Results 202 5.8p-Statistics and Effect Strengths for IMI-Differences 203 5.9 Means and Standard Deviations for Each Measurement Change of the IMI 203 5.10 Mean and Standard Deviations for Concept Scores in Classes Taught by a Single Teacher 207 5.11 ANOVA Summary for Single Teacher Preand Post-Test Scores 207 5.12 Occurrences of each coded Alternative Conception 208 5.13 p-values for Z-Tests for each Alternative Conception 210 A.1Alternative Conceptions in Answer Combinations 264 B.1 List of Possibly Unknown Words used in “An Introduction to Electric Circuits” 268 1Foreword Perhaps the most remarkable aspect of evolution is its ability to generate cooperation in a competitive world. Thus we might add “natural cooperation” as a third fundamental principle of evolution beside mutation and natural selection. – Martin Novak Five Rules for the Evolution of Cooperation 1.1Motivation I firmly believe that the best way to get on is by cooperation. The story of science is often told through the triumph of great geniuses or singular breakthroughs. But, most science is done in teams. This could be in projects like the LHC in CERN, involving thousands of different scientists and engineers from all over the world, or several teams working on small aspects of the same research or in the team of largely uncredited deaf women who were responsible for tracking and cataloguing stars under Edwin Hubble. Even above being a “team game”, science is in itself a great shared reality, based on observations and measurements. This, in turn, is based on a shared philosophy, the scientific method: hypothesis, testing and falsification. To construct this shared reality and effectively share their ideas and receive feedback, scientists share their work through written publications and spoken presentations, containing diagrammatic representations of data and 2 talking circuits concepts 1 . However, scientists working in teams mostly communicate by talking to each other within their research communities2. When talking to one another about science, a specific vocabulary is needed. This vocabulary too is co-constructed. This was made very apparent to me when I joined a largely German-speaking laboratory in Munich during my Master’s studies. When laser beams in the laboratory needed to be aligned, the German speaking members of the team would not use the German word “ausrichten” to talk about alignment. Instead, as there were a large number of non-native speakers in the international team, the made-up word “alignen” 3 would be used by the whole team, to facilitate understanding. Depending on who was operating the laser, they would need to align something specific, for their experiment. So, depending on who was saying they were going to align the laser, it would mean a different concrete set of actions achieving the same thing: alignment. This throwaway example allows us to see the adopted use of a specific word in a single context, used to mean subtly different things. Not to mention if I was talking to the same people about different topics, then the word alignment could mean something totally different, e.g. politically aligned or alignment in a role-playing game4. However, it is not always the case that scientific language enables accessibility. In fact, it can have quite the opposite effect. The everyday word that is used to discuss household electricity in English and German are “power” and “Strom” respectively, the literal translation of “Strom” into English is “current”. Learners continue to use both “power” and “Strom” in the context of science lessons when they are not appropriate and associate them with similar misconceptions 5 . For this reason we 1 There are of course other incentives to do these things, as they garner prestige and a kind of scientific social capital. 2 There is often considerably less social capital at stake in these kinds of interactions, which can indeed make them more informal and more effective! 3Simply the English verb align with German conjugation rules 4For the uninitiated, whether your character is good or evil or follows the rules or not. 5 A discussion of what misconceptions are, how they work, other names for them and foreword 3 need to make our scientific vocabulary accessible to our learners, if we want to strive for equal and effective education. Science educators cannot also ignore the fact that they are introducing learners to a culture of science. This includes its language and despite the temptation to have a separate scientific language that engages with abstract thought, learners must be exposed to all given words in a variety of contexts and meanings must be made explicit and related to their context. Using this language in productive classroom talk comes with its own benefits. Students participating in a talk rich curriculum have improved outcomes across the core subjects in primary school 6 . A famous example of the power of student talk to improve learning progress in Physics, comes from the world of higher education with Peer Interaction 7 . Here, undergraduate students engaged in discussions during their contact time, increasing their conceptual understanding. An example of this kind of intervention in lower secondary electricity, however, was not as successful in increasing learning outcomes8. With these thoughts in mind, I wanted to go about designing and assessing learning materials that would benefit practitioners and learners alike and be confident in making my recommendation (or otherwise!) of them, but not be solely driven by testing outcomes. Things did not go exactly to plan. Working across borders in schools, during a global pandemic, as the UK tries to figure out how to leave a customs union that you want to bring 30 iPads from, is not an experience I would recommend. Nonetheless, the following is the collection of ideas, results and analysis collected over those very enjoyable, nearly six years. how to try and combat them see Chapter 2. 6Jay et al. [2017] 7Mazur [1997] 8Ruthven et al. [2017] 2Theory and Measurement of Learning and Knowledge You see my physics students don’t understand it... That is because I don’t understand it. Nobody does. – Richard Feynman QED: The Strange Theory of Light and Matter 6 talking circuits Chapter Contents 2.1Models of Learning and Knowledge 7 2.1.1Piaget’s Mental Representations 8 2.1.2Vygotsky’s Social Learner 8 2.1.3Rogoff’s Learning in Cultural Context 10 2.1.4The Learner as Agent of Change 12 2.1.5Self Determination Theory 13 2.1.6Representations, Analogies and Models both Mental and Scientific 14 2.2Conceptual Change 18 2.2.1Rational Conceptual Change 19 2.2.2Theory Theory 20 2.2.3Framework Theory 21 2.2.4Ontological View 22 2.2.5Knowledge Analysis and Knowledge in Pieces 25 2.2.6How Theory Informs Practice 29 2.3A Summary of Alternative Conceptions on the Subject of Circuit Electricity 31 2.3.1The Physical Model for Lower Secondary 32 2.3.2The Cluster Concept Electricity†33 2.3.3Misconceptions Relating to Current and possibly to wider Electricity†34 2.3.4Misconceptions Relating to Voltage 38 2.3.5Other Difficulties 41 2.3.6Considering Underlying Schemata 46 2.3.7Language Resulting in Alternative Conceptions 46 2.4Measuring Alternative Conceptions and Learning Gains 49 2.4.1Alternative Conceptions as Distractors and Something Measurable 50 2.4.2Tests on the Topic of Electricity 51 theory and measurement of learning and knowledge 7 In this Chapter, I will begin by giving an overview of relevant learning theories, paying special attention to definitions needed in this chapter and beyond. As is generally the case, the chapter will develop from general to specific, from descriptions of knowledge and learning intended for general use to specific learning challenges faced in the teaching of science, specifically physics, and then even closer, on the topic of electricity, the topic of the intervention study in this thesis. The chapter concludes with a review of the literature on the specific alternative conceptions on the topic and the available concept knowledge test on the topic of electricity. 2.1Models of Learning and Knowledge Models of learning and knowing within Western philosophy date back to Aristotle’s analogy of the mind as a blank slate waiting to have ideas etched upon it 9 . These have been developed throughout history and have become progressively more complex with focus on different aspects of the learners’ development, with key contributions, that will be discussed in the opening to this chapter from developmental and cognitive psychologists such as Piaget, Vygotsky and Rogoff. Furthermore, there are science education specific contributions to models of mental organisation and cognitive change from educational specialists, such as Vosniadou and diSessa. The idea in this chapter is not to evaluate and critique these models of learning and cognition, but to introduce definitions 10 and use the ideas present within them to inform thinking about how to best support teaching and learning within the context of lower secondary physics, on the topic of electricity. These ideas go on here and in later chapters to inform the rationale and decision making processes involved in developing materials as discussed in Chapter 4. Where models, however, may might make contrary suggestions for practice, this is discussed. 9Smith [2014] 10 Those who read this with a background in the learning sciences will probably be familiar with the ideas contained in this section. I present this here to be an introduction to those with background in physics, from a more “practical” teaching background or for readers who come from a different cultural context. 8 talking circuits 2.1.1Piaget’s Mental Representations Schemata describe “figurative representations” 11 , suggesting a type of mental image, for clustering and discriminating objects into particular classes or groups. These groupings have underlying rules and rest upon generalisations. The schema are constructed and adjusted by attempted assimilation of new ideas into pre-existing schemata and the accommodation of small changes to these schemata 12 where inconsistencies lead to cognitive dissonance13. Schemes are, similarly, mental representations, but this time for procedural knowledge, i.e. how to do certain tasks. This study is primarily concerned with developing figurative knowledge, however the scheme of work implemented introduces some procedures for analysing electric circuits. More nuanced descriptions of the way learners’ mental structures are conceptualised are given in Section 2.1.6, as developing and measuring these is the centre of my study. However, just conceptualising them in this primarily rational way ignores the social dynamics important for an intervention centred around peer work. 2.1.2Vygotsky’s Social Learner The importance of social interaction is central to Vygotsky’s work and, although Piaget does not ignore its importance 14 , it is not central in his writings. As the current study will implement discussion work in pairs, exchange in this intermental space 15 is central. Learners too not only construct ideas together, but in expressing their ideas through externalisation 16 , mediated by psychological or cultural tools, they develop whatever (nascent) thoughts are present 17 . Learners then have the 11 Siraj-Blatchford and Siraj-Blatchford [2010, p. 209] 12 Piaget [1929] in Goddu and Gopnik [2022] 13 Piaget [1929] in Adcock [2012] 14 DeVries [1997] 15 A social space for ideas between people. 16 Piaget also illustrates an internalisation/externalisation dynamic, but on an operational level, with the identification of object surface features being mapped onto how the object may be used and causal constructions, for more see Martí [1996]. 17 Vygotsky [1986] theory and measurement of learning and knowledge 9 opportunity to become aware and reflect on their own ideas before interacting with externalisations from their partners, which, in turn, they may internalise, in a transformative process 18 , after their negotiation in the intermental space19. Another key idea that will be important throughout this work, with regards to both technology and language, is the mediated nature of thinking and idea exchange through psychological or cultural tools, also called signs or symbols under which Vygotsky includes: “language; various systems for counting; mnemonic techniques; algebraic symbol systems; works of art; writing; schemes, diagrams, maps, and mechanical drawings; [and] all sorts of conventional signs” 20 . The idea of a psychological tool when looking at language, diagrams and technology will be especially key in my study. Vygotsky argues that usage of psychological tools result in new ideas, so in developing tools for classroom use it is important to ensure that these are conducive to the knowledge we wish to construct. For example, through careful use of language and analogy or in the production of diagrams or learning workflows, as discussed in Chapter 4. It is also of note that these tools are not inherent, and must too be learnt. The Zone of Proximal Development defines the difference in what a learner may achieve when engaged in an activity alone, and when “under adult guidance or in collaboration with more capable peers” 21 . Their partner or guide enables the learner to generate and co-construct novel ideas and solve previously unsolvable problems. Learners can then internalise this and then be able to tackle similar activities alone. This, however, beyond Vygotsky, is also possible when the peer is not “more capable”, i.e. neither peer can solve the problem alone. For 18 Vygotsky and Luria [1930/1994] in Lawrence and Valsiner [1993] 19 Vygotsky [1981b] in translation from Vygotski, Lev Semnoviq. Razvitie vysxih psihiqeskih funkci: iz neopublikovannyh trudov. Moskva: Izdatelstvo Akademii pedagogiqeskih nauk RSFSR, 1960. 20 Vygotsky [1981a, p. 137] in translation from the same Russian source. 21 Vygotsky [1978, p. 86] 16 talking circuits Figure 2.1:Three Boats with Surface and Structural Similarities: Shown left to right are a real boat, a model boat that moves and a realistic looking model boat. Real and realistic model boat images uploaded to Wikimedia by Tim Reynaga and licenced under CC BY 2.5. is a familiar phenomenon and a model is developed post hoc to give reasons as to why it is happening. Analogies can be drawn between model and physical object 36 or between multiple models. In order to make teaching a given model easier, an analogy may be introduced, linking to a familiar or more intuitively understood model with that of a more abstract one. It is here the ideas of structural and functional similarity become useful again. For something to be a good analogy, for the purposes of teaching, there needs to be sufficient similarity between the source (the well known) and target (the to be taught) domain 37 . Importantly, all of the primary concepts to be taught must have an analogue that appears in the source domain. The way these concepts relate must also be analogous in both domains. Taken together this is appropriate relational matching. Learners also make connections between domains with mere-appearance (surface level) matching 38 . Furthermore, it can also be shown that superficial similarities are important for learners to connect the two domains 39 , making it a desirable attribute for teaching analogies. As in Figure 36 Kircher et al. [2015] 37 Gentner [1983] 38 Gentner and Markman [1997] 39 Gentner et al. [1993], Gick and Holyoak [1980], Keane [1987] in Blanchette and Dunbar [2001] theory and measurement of learning and knowledge 17 Source Domain Target Domain Analogy Figure 2.2:An analogy represents the relationship of objects and attributes (represented through different shapes) between the source and the target domain. As illustrated, both domains do not necessarily match in every respect. Author’s work, published in Burde et al. [2021]. 2.2 40 , we can see the blue and red shapes represent the source and target domains respectively. There are specific features of the concepts represented by the square, circle and triangle in the target domain, that we want to teach, represented by their number of sides and patterns. We also want to teach the ways they relate to each other, represented by the arrows. To make this more concrete using ideas from the domain of electricity and its mapping to pressure, these three concepts could be current, resistance and potential difference, and the relations R=V I , or the equivalent in words. In the domain of pressure, these are represented by airflow, blockages and pressure difference and the fact that a higher pressure difference results in a higher airflow and that blockages with reduce airflow. These relations and the teaching of them will be more explicitly addressed in Chapter 4. Note too, that 40 Interestingly, an analogical structure for explaining analogies! 18 talking circuits there are some features that are not the same, such as the colours of the objects or the shapes not linked by arrows. Of course, some of the features of the system will be different and this is to be expected. For example, to return to the previous examples that what flows changes between electrons and air, or that a battery works on a different basis to a normal air pump. As long as these do not represent core differences within our model to be taught, they can be addressed for interested learners, but do not impact our central learning objective. How one goes about effectively connecting these two domains, i.e. facilitating analogical learning, will be discussed also in Chapter 4. 2.2Conceptual Change The idea of conceptual change is useful in science teaching as it contrasts with learning of declarative or procedural knowledge, for which the routes of acquisition are relatively well established. Conceptual Change is deeper and more elusive and to examine it in this section we will draw on and extend the historical review by diSessa [2022]. Conceptual Change Theory’s roots lie in two historical-philosophical works from Kuhn [1962] and Toulmin [1972] whose differences underpin the divergence in subsequently discussed theories within this section. In short, Kuhn [1962] discusses scientific theories 41 shifting in a period of radical change, switching between one theory and a new, incommensurable theory. Incommensurable meaning that the new theory’s claims are unable to be expressed in terms of its predecessor. The transition between these theories happens rapidly, which Kuhn likens to Gestalt switches 42 . Toulmin [1972] undermines this, examining the lack of systematicity actually present in science. He uses the term conceptual ecology, looking at wider contexts as well as interaction between developing concepts. This describes a more complex types of knowledge and transitioning between concepts, contrasting with Kuhn’s “binary” Gestalt switch. 41 This is a discussion of scientific theory more broadly, not at the level of a learner. 42 Like the immediate transition from seeing one image in an optical illusion to another. theory and measurement of learning and knowledge 19 2.2.1Rational Conceptual Change Posner et al. [1982] drew from both of the aforementioned works (among others) to define a set of four rational preconditions that must be met to engender accommodative43 conceptual change: 1. There must be dissatisfaction with existing conceptions. 2. A new conception must be intelligible. 3. A new conception must appear initially plausible. 4. A new concept should suggest the possibility of a fruitful research program. Their writings are heavily influenced by the history and philosophy of science, asserting that the learning process is “rationally based”, looking to engender cognitive conflict through “anomalies” that do not fit learners’ initial conceptions. They reflect that doing this, however, is difficult, as learners may not recognise the conflict the “anomalies” present to their own implicit ideas. They also question, that even if “anomalies” are presented and the theory understood, it remains “at best only intelligible and partially plausible, but never fully persuasive to students who are firmly committed to a set of conflicting metaphysical beliefs and epistemological commitments” 44 . They do not, however, expect such an “anomaly” to be rejected outright. For example, in an intervention where experiments were used to create cognitive dissonance in learners, learners said that the experiment was wrong or broken in several ways, or even “accused [the teacher] of “falsing”[sic] the experiment” 45 , perhaps indicating the need for the inclusion of affective factors into the description. Posner et al. [1982] formulate a set of further recommendations, for content as well as teaching strategy and teacher role. Logically, ensuring learning has first taken place, before trying to cover more content and that learners be taught “observational theory” along side to enable 43 in the Piagetian sense (defined in 2.1.1) 44 Posner et al. [1982, p. 224] 45 Johsua and Dupin [1985, p. 336] 20 talking circuits engagement with the included “anomalies” are advised as ways to structure content necessary for this style. The teacher’s role is envisioned as quite combative, they confront learners with anomalies, diagnose and deal with errors diagnosed, as well as, regularly challenge “ad hoc-ness” or inconsistencies in learners’ thinking, in order to engender the desired cognitive change. Interestingly, they also recommend uses of “metaphors, models, and analogies... [to] ... make a new conception more intelligible and plausible”, which could be seen as an assimilation (as opposed to the accommodation-al style of learning they are outlining) into an existing schema. Because, for analogical learning to be successful, a good source domain, i.e. an existing schema, needs to exist in order to be extended (see previous section). There is no detailed description of the internal representations or to the mechanism, other that it is a piecemeal, but complete, overhaul of the concept. The mechanistic description happens at a concept and claim level, the process of conceptual change being described as learners’ “process of taking an initial step toward a new conception by accepting some of its claims and then gradually modifying other ideas, as they more fully realize the meaning and implication of these new commitments” 46 . This does not, however, look at finer granularities of representations and does not reflects upon learners’ historical or classroom context. 2.2.2Theory Theory The conceptions here seem to be treated as monolithic and not strongly context-specific, with a certain direction of travel 47 seemingly built in. This is sometimes referred to as the theory theory; a detailed example of which, in the field of physics, can be seen in the “impetus theory” 48 . This again references historical developments and the persistent nature of the theories, linking it closely to the structure of formal knowledge. 46 Posner et al. [1982, p. 223] 47 From non-scientific learner conceptions to normative, scientific conceptions. 48 McCloskey [1983] theory and measurement of learning and knowledge 21 In “The Origin of Concepts” 49 , Carey argues that (even) infants innately possess concept-like internal representations and mechanisms, that allow them to identify these from perceptual inputs. This is called core cognition and is used for evolutionarily important survival tasks. Innately is taken to mean without having to learn any of those aspects and this idea is pushed beyond the field of core cognition, to representations not perceptual in nature, such as something having a cause, explicitly defined as non-domain-specific. Interesting for this work is, how Carey interprets the conceptual change between two qualitatively-different representational systems CS1(an initial system) and CS2(a new system). The ideas within CS2cannot be expressed in terms of ideas from CS1, and for this reason there is a “discontinuity” that represents a true cognitive change. Carey cites the consistency of answers across multiple stimuli from learners with either of the representational systems, underlying the fact they are “theory-like”. The ideas were developed by Carey that instead of a Gestalt-like switch, theory change takes place through a process known as Quinian Bootstrapping. To begin, a set of mental, explicit, “placeholder” symbols are constructed, partially interpreted from previous concepts. It is important to show that this is necessarily partial, as the learners do not yet have the means to express the new system. Then, a series of processes such as “analogy construction and monitoring, limiting case analyses, thought experiments and inductive inference” 50 are used to build out the definitions and define the relationships between the once placeholder concepts. Although this account provides a nice mechanism for cognitive change to occur, the lack of evidence for underlying theories being applied in the context of pre-(or even post-instruction) physics learners, as will be evidenced in Section 3.1. 2.2.3Framework Theory Vosniadou [2012] divides learners’ preconceptions and misconceptions clearly. For her, learners’ preconceptions are present pre-instruction and 49 Carey [2009] in Carey [2011] 50 Carey [2011, p. 120] 22 talking circuits form a “coherent, although relatively narrow, explanatory framework theory” 51 , where the “term theory is used loosely to denote a network of interrelated beliefs that can be used to provide explanations and form predictions and not a fully developed scientific theory”. The contrast here with a scientific theory comes in that learners are not “metaconceptually aware of their beliefs and they do not understand they represent hypotheses to be falsified.” Another way in which preconceptions differ from scientific theories, are in their ontology 52 and epistemology 53 . Physical objects/ideas must be reassigned slowly and gradually to different ontological categories, i.e. “electricity” from a manner of “energy source” to a domain of physics. These recategorisations, if successful, come with “epistemological sophistications” to interweave perceptual, everyday knowledge with a new conceptual model, reconciling the both. Misconceptions, on the other hand, are what may occur after instruction, when learners extend their preconceptions with material presented to them. This results in an internally inconstant so called synthetic model 54 , in other words, not true conceptual change. This theory, although related to the previous “Theory-Theory” style, gives more flexibility. This results in a perspective that, although more inline with what is seen from learners, only adds another level of abstraction in accessing some underlying “theory”, rather than attempting to describe spontaneous interpretation and problem solving more generally. 2.2.4Ontological View Chi [1992] places the core of cognitive change on meaning change. Ontological Categories are arranged in a tree-like structure, getting more specific at each level. For example, a sample ontological category for a bee might be “Matter → Natural Kind → Living → Animal”. The bee has certain ontological attributes, like mass and colour. It would be wrong to say that you had a bee with a mass of 1kg or a pink bee, as they misdescribe the category. Another kind of error is a 51 Vosniadou [2012, p. 122] 52 Nature of being 53 Nature of knowing 54 Vosniadou et al. [2008, p. 28] theory and measurement of learning and knowledge 23 category error, assigning an ontological attribute that an object cannot have. This would be like saying “the bee is an hour long”, as the bee does not have the “length of time” attribute - as an event, for example the “bee’s lifespan”, does. Of interest to us, Chi [1992] lists “electrical circuits” under “Events → Constraint based → Artificially Constructed” 55 and as we will see from Section 2.3, learners tend to see “electricity”, before introductory teaching, as a kind of “material substance” 56 or “quasi-material” 57 , thus requiring an ontological shift. A category error can be seen here in the statement “electricity/current flows” rather than “charge flows”. It shows an incorrect or at least a too broad assignment of “electricity/current” implying that they are a material that can flow, rather a branch of science and the rate of flow of charge respectively. This category error, between the categories of “matter” and “process” in particular, is investigated by Chi et al. [1994a], where physics experts used predicates associated with processes much more, and with materials much less, than novices when explaining physics problems. Lee and Law [2001], assessing the same predicates, evidence that higher process predicate use is associated with higher physics test scores on the topic of electricity. Chi makes some distinctions of non-radical and radical conceptual change. For radical conceptual change to occur, learners must58: 1. Learn the new ontological category’s properties via acquisition processes; 2. Learn the meaning of individual concepts within this ontological category via acquisition processes; 3. Reassign a concept to this new ontological category: (a) actively abandon the concept’s original meaning and replace it with the new meaning; (b) allow both meanings to coexist and access both meaning depending on context; (c) replace automatically via coherence and strength of new meaning. 55 Chi [1992, p. 131] 56 Chi [1992, p. 136] 57 von Rhöneck [1981] 58 Chi [1992, p. 144] 24 talking circuits There is a (perhaps incongruent with constructivism) reliance on blankslate style learning in the first two points here; there is no accounting for learning to interact with already known material. Apart from in the third point, which occurs when the new ontological structure is already in place. Examples of processes from non-radical conceptual change are: 1. Revision of Part-Whole Relations 2. Formation of New Superordinate or Subordinate Categories 3. Reclassification of Existing Categories 4. Spreading Associations in Insight Problems 5. Direct Reassignment within Ontological Categories If we are able to map a learners’ ontological structure, or infer which ones might be common from the literature, we can see whether any of these operations listed would contribute to producing the normative ontology. For example the division of the categories of “current” and “voltage” when the two are merged in the case identified by Maichle [1981]. Chi eschews the debate as to whether learners’ prior conceptions are theory-like. Defining “theorylike” to refer to a psychological coherence rather than a strict scientific definition, but ultimately calls the debate a “digression that has been misleading for the research agenda” 59 , a statement with which I agree, to a large extent, as outlined in the discussion of impact on practice to come in Section 2.2.6. The structures offered here can provide a way to think through what content is necessary to achieve learning goals, and the steps needed to attain it based on learners’ prior knowledge. The strictly formalised and constrained structure of the theory, however, seems to under emphasise the flexibility and context dependence of learners’ reasoning and knowledge60 and, for this, we turn to our next and final theory. 59 Chi [1992, p. 161] 60 diSessa [2017] theory and measurement of learning and knowledge 25 2.2.5Knowledge Analysis and Knowledge in Pieces DiSessa’s idea of how systems of knowledge hang together is called knowledge in pieces 61 , situated more widely in the study of Knowledge Analysis 62 . He considers learners’ ideas not as monolithic, instead they are thought to consist of a large number of knowledge 63 elements. This knowledge may be inarticulate, contradictory and, crucially, highly dependant on the context in which they are applied. These properties make measuring and deciphering prior knowledge difficult and imply that even in domains that are highly abstract and removed from every day situations, ways of thinking are informed by learners’ prior experiences and their invocations of phenomenological primitives, discussed later. It is precisely this issue of contextuality that is lacking in conventional conceptual change theories. Knowledge Analysis research practice, as defined by diSessa et al. [2015], has six principles (positive integers) and three counter-principles (negative integers)64: 1. Knowledge is constituted in mental representations. With this diSessa states the knowledge and cognition focus of the research, aiming to produce complete and precise descriptions of the learners’ understanding. 2. Knowledge can be non-propositional and encoded in various modes. Non-propositionality can be thought of as tacit or non-articulable knowledge. Encodings, in this sense, are types of (psychological) representations, and may be attained from the senses rather than the more “formal” semantic representation, integrating ideas and concepts. 3. Studying the mental representations of individuals requires highly nuanced accounts of content. Here, the speci61 diSessa [1988] 62 diSessa et al. [2015] 63 Referred to throughout in diSessa et al. [2015] as knowledge⋆(knowledge star), to differentiate their ideas from other definitions of knowledge, dropped here for convenience. 64 Each (counter-)principle is listed verbatim in print script from page 36-39 of diSessa et al. [2015], but a conciser explanation is then given than in the source. 32 talking circuits every circumstance, not exclusively held by students or learners, persist after instruction 80 and are not necessarily seen as pre-existing thought patterns transferable by learners between contexts and may be spontaneously generated. As discussed in section 2.1.6even physical models have their boundaries and limits, as (in counterpart) many alternative conceptions have situations in learners’ prior experiences where they are applicable, otherwise they might not be quite as compelling. These alternative conceptions have long since been of interest to educational researchers, as teachers try in various ways to usher learners towards correct scientific understanding and away from these common erroneous ways of thinking. Here, I will summarise and build upon the works of Wilhelm and Hopf [2018] and Driver et al. [2014] as well as the bibliography from Duit [2009]. 2.3.1The Physical Model for Lower Secondary Before we begin discussing alternative conceptions, I wish briefly to show what they are alternative to. In this section I present a simplified scientific concept, for teaching in lower secondary. There is didactic idealisation within this description, in that I ignore electronic band structure and electron scattering. In this description wires and voltage sources are treated as being resistance free. Charge is a property of materials. Materials can be positively or negatively charged. Atoms are made of positively charged cores and negatively charged electrons. In insulators these electrons cannot move from their cores, but in conductors it is possible for them to move. In order for them to move there needs to be a potential difference and a pathway to a lower potential. A battery or other voltage source provides a potential difference. A closed circuit provides a pathway. A flow of charges is called acurrent. Certain components are harder for current to flow through; the harder a material is to flow through, the higher its resistance. 80 They may even be induced by instruction! theory and measurement of learning and knowledge 33 2.3.2The Cluster Concept Electricity† Alternative conceptions are not to be thought of as having well defined objects with well defined interrelations as a scientific theory does. The division between any of the following ideas: “electricity”, “current”, “charge”, “voltage”, “power” and “energy”, may not be clear to a learner 81 . So many of these conceptions are general ideas that learners will seemingly transfer between these different physical quantities, so I will use electricity†82, when referring to this nebulous concept. Such a collection of related and undifferentiated ideas can be described as a “Cluster Concept” 83 . The fact that a given alternative conception can be assigned to a range of physical properties can be seen as a transferral of ideas from a “deep structure” onto a current situation 84 , for examples see Section 2.3.6, commensurate with the idea of knowledge in pieces. The German everyday word for electricity † is “Strom”, the word for current 85 , and it is used in the same way as power in English in the phrase “Power Consumption” → “Stromverbrauch”, so many of these misconceptions in the German literature are seen to have to do with current. This culminates in an “dominating concept” 86 of Current/Electricity † that dominates German learners’ other conceptual understandings 87 . In English speaking learners, Shipstone [1985, p.35] makes explicit the lack of coherence in the words children use when talking about electricity † and interviews show the use of “it”, “electricity” or, even vaguer, “something”, to refer to electrical concepts 88 . This also seems to be the case for French speaking learners 89 for “électricité”. Electricity † is therefore used where any of the learners refer vaguely to an undifferentiated concept in their respective languages. 81 Shipstone [1984], Psillos et al. [1988], von Rhöneck [1981] 82 This is typeset as “electricity dagger”, feel free to read it as just “electricity”, but the “dagger” is used to make us mindful of the change in meaning from standard use. 83 German original: “Clusterbegriff”, cf. Wilhelm [2005], Schecker [1985]. 84 Niedderer et al. [1992] 85 Although “Stromstärke” would be more correct, it is very commonly shortened. 86 German original: vorherrschender Begriff 87 von Rhöneck [1986a, p. 87] 88 Osborne and Freyberg [1985], Cohen et al. [1983] 89 Ben Hamida [1980] in Tiberghien [1984] 34 talking circuits 2.3.3 Misconceptions Relating to Current and possibly to wider Electricity † Electricity † “use” is a widespread and resilient conception that comes in multiple forms and is shown in various ways. It is often divided into two key ideas a learner can hold regarding current: a complete usage of current and a partial usage of the current in a load. These ideas can present themselves when learners are given the task “make this lightbulb glow” or, alternatively, when asked “in which of these arrangements does the lightbulb glow?”. These conceptions have been referred to as “conceptions in introductory lessons” 90 , however, even advanced learners can show these conceptions after secondary school instruction 9192 . Even when learners have internalised the fact or piece of declarative knowledge that “a circuit needs to be closed to work”, they have different explanatory models for why this might be. There is an overlap here with the idea of electricity as a fuel or even as an industrial commodity 93 , a kind of quasi-material 94 within the circuit, to be used up in different ways, as displayed in Figure 2.3. Figure 2.3A shows a simple unipolar model, where the electricity † is transported to the lightbulb along the single wire and used up. Even if learners recognise the need for a second wire or a closed circuit, it is described as not having an active role, perhaps as a “safety wire” 95 . In the model shown in Figure 2.3B both wires carry electricity from the battery to the bulb. Existence of a second wire may be justified with the idea that the second wire is there “to bring more (or enough) electricity” 96 or that there are “two electricities a plus and a minus” 97 . The “partial usage” model is shown in 2.3C, which gains in popularity as learners age (and perhaps see the need for a closed circuit), only to be 90 From the German “Vorstellungen im Anfangsunterricht” from Wilhelm and Hopf [2018] 91 Fredette and Lochhead [1980] 92 Andersson and Kärrqvist [1979] in Driver et al. [1985] 93 Muckenfuß [1980, p. 33] 94 von Rhöneck [1981] 95 Driver et al. [2014] 96 Johsua and Dupin [1987, p. 124] 97 Dupin and Johsua [1985, p. 334] theory and measurement of learning and knowledge 35 A B C D Figure 2.3:Four Models of Current beginning with a simple unipolar model (A), a “Clashing Current” model with two wires (B), a “partial usage” model (C) and finally the “scientific model” (D) as first measured in Osborne and Freyberg [1985]. Green arrows represent current: the direction and the size. overtaken at sixth-form level 98 by a physical model of current 99 , shown in 2.3D. These models, first established by Osborne and Freyberg [1985] in New Zealand have since been found many times over in other countries: the UK (England, Wales and Northern Ireland) 100 , Australia 101 , Greece 102 , Sweden 103 , and France 104 . An interesting illustration of the fragility of such alternative conceptions is that if the students are given a lanternor 3R12-battery 105 , instead of a round battery, most can con98 British Advanced school leavers opting for physics and studying it from the ages of sixteen to eighteen. 99 Shipstone [1984] 100 Shipstone [1985], Gott [1984] 101 Butts [1985] 102 Psillos et al. [1987] 103 Andersson [1984] 104 Dupin and Johsua [1985] 105 Called a “flat battery” in Tiberghien [1984] presumably a “Flachbatterie” rather than a spent battery as in English. 36 talking circuits nect it correctly 106 . These are 4.5 V batteries with two elongated metal plates as terminals, common in mainland European science classrooms, comparable with the use of 9 V batteries in U.K. science classrooms, before battery holders became common. Possibly, as the battery has two clearly visible terminals, the unipolar model is not even triggered. As mentioned, if learners see electricity as something that gets “used up”, it may follow to regard current as a fuel 107 or as energy 108109 , with batteries as a store of electricity †110 . English speaking learners, when asked about bulbs with power ratings, said “something”, perhaps power or electricity † , is used up in proportion with the power rating 111 . Energy, although not physically getting “used up”, is converted, which learners also regard as being “used up”. This is a common conception, especially in German, where a circuit component is often referred to as a “Verbraucher”, roughly translated as “user”. Usage conceptions are even present when learners are asked about voltage and not in the close to physical way that one may describe Kirchhoff’s voltage law 112 . This kind of usage may be seen as being dependent on the value of resistance, a larger resistance (or perhaps resistor) using more electricity † . This is shown in implicit thinking alongside sequential reasoning, when learners analyse a series circuit with changing or variable resistors 113 and I will call it resistance proportional to usage, following Burde [2018, p. 48]. In parallel circuits, as discussed in von Rhöneck [1986b, p. 13], increasing current with increasing resistance must be interpreted as a different idea to that previously, as the current use and sequential reasoning cannot be assumed in this case. The idea, that more current flows through a larger resistance is named the inverse resistance conception by Burde [2018, p. 49]. 106 Delacote and Tiberghien [1976] in Tiberghien [1984] 107 von Rhöneck [1986b] 108 Osborne and Freyberg [1985] 109 von Rhöneck [1981] in Tiberghien [1984] 110 Maichle [1981] in Tiberghien [1984] 111 Cohen et al. [1983] 112 von Rhöneck [1980, p. 25] 113 Shipstone [1984,1985] theory and measurement of learning and knowledge 37 Heller and Finley [1992] saw in an interview with a learner the idea that “more current is used in travel[l]ing the extra distance to the bulbs” 114 , this leaves it slightly up to interpretation as to whether this is because the learner thinks that the wires “use up” the current sequentially to the bulbs or whether the distance is the deciding factor, compare Johsua and Dupin [1987, p. 123], dubbed the “current wearing out” conception. The pure distance conception, as in the interpretation by Morris [2018, p. 8] will be referred to as the current-distance relation. “Electricity † is supplied” or in German “Strom wird geliefert” 115 is evidenced through a forum post in Wilhelm and Hopf [2018] and this phrase and related ones were common in German language text books according to Stork and Wiesner [1981][p. 219]. I will call this idea current is delivered to contrast it with the everyday phrase. The learners in Stork and Wiesner [1981], however seem to attribute agency to the load on the circuit: “pick up/grab something” 116 . This idea is similar to the physical idea of “current draw” in English, but can be harmful if a causative characteristic is given to the pulling or “sucking” of current from the battery. I will call this idea current is taken to contrast it with the idea of current draw. Related to this is the idea that current is the same regardless of the resistance or that the battery provides or delivers a constant current 117 , rather than a constant potential difference, i.e. battery gives constant current. Electricity † can also be shared. Shipstone [1985, p. 37] describes a reasoning based on identical components and reasoned at the level of the whole circuit, but current is not regarded as being conserved. This is perhaps unsurprising as sharing is a key societal theme prevalent cross culturally and central to most children’s socialisation. 114 Heller and Finley [1992, p. 272] 115 The German word “geliefert” is more closely translated as “delivered”, but the full phrase is closer to the English everyday equivalent given here. However, “delivered” implies a more active role for the voltage supply in this instance 116 German original: “Das Birnchen hat sich [...] was geholt.” in Stork and Wiesner [1981] [p. 227] 117 Cohen et al. [1983], McDermott and Shaffer [1992], Licht and Thijs [1990], Dupin and Johsua [1987] 38 talking circuits Although not quite as omnipresent as in German, English speaking learners too tend to use current as their primary concept to reason through a problem more often than voltage and sometimes inappropriately 118 . This may overlap with other ideas, notably sequential reasoning and local argumentation, but will be categorised separately as arguing from current. To summarise, there are a few key concepts which can be invoked when learners reflect on electricity † or later current, both of which can be the physical idea of a flow of charge or a kind of quasi-material used in making electric circuits function. Learners associate this with certain actions it can do, the primary of which is use, i.e. something getting used up while moving around or within the circuit. Whether the electricity is used fully or partially and under what circumstances, i.e. whether a complete circuit is necessary or how it gets used, either in the wires or just the components, makes this idea flexible and possibly therefore resilient. Sharing is another keyword that can be used together or apart from the use term. The next is deliver, both may be accompanied by giving the current/charge agency and resulting in placing current at the core of explanations of the nature of circuits. The latter two have a tendency to personify components or the charges themselves. 2.3.4Misconceptions Relating to Voltage Voltage has a comparative nature, making it essential to tell the difference between potential and potential difference, something that learners find difficult. This shows itself, for example, in learners viewing components at a higher potential being a defining factor, rather than the potential difference over them 119 . Some learners may remember the need for connecting to the plus and minus poles of a battery when measuring its potential difference, but not apply this “pole rule” consistently over other components or appreciate why120. 118 Cohen et al. [1983, p. 409] 119 McDermott and Shaffer [1992] 120 von Rhöneck [1980, p. 20] theory and measurement of learning and knowledge 39 Some learners (both preand post-instruction, years eight and nine 121 in German technical school 122 ) see no connection between voltage and current in their role in a circuit 123 . On the opposite extreme, for some learners voltage and current are so closely linked they do not differentiate them at all 124 , perhaps a way in which learners’ cluster concept is expressed. This carries through to post-instruction in onein-five learners as is shown in the fourth and final statement in Table 2.1. Jung [1985] measured that 19% and 40% of German Year eights (n= 70) and Year tens (n=73)125 view voltage as a property. However, cautions the reader to not put too much store by this as according to unpublished work by Ulla Maichle, even few adults have switched from verb usage from “is” to “have” when discussing properties 126 . Maichle [1980] defines a “TRANSFER-Schema” 127 to reflect learners’ understanding pre-instruction, within this voltage is assigned as a property of current/electricity†. Statement Agree Disagree Every electricity†/Current has a Voltage Jeder elektrische Strom hat eine Spannung 90% (10%) Electricity consists of a Current and a Voltage Der elektrische Strom besteht aus Stromstärke und Spannung 65% (35%) A Voltage can also exist without a Current Eine elektrische Spannung kann auch ohne elektrischen Strom vorkommen (30%) 70% You can call electricity†/Current a Voltage Den elektrischen Strom kann man auch Spannung nennen 20% (80%) Table 2.1:True or False answers to statements about electrical circuits post instruction from Maichle [1980][p. 10]. The italicised German language versions are the original. Percentages in brackets are calculated from learners answering the opposite. 121 Aged 13-14 Years and 15-16 Years, respectively. 122 Realschule 123 von Rhöneck [1980] 124 von Rhöneck [1980], Maichle [1981] 125 Aged 13-14 Years and 15-16 Years, respectively. 126 Jung [1985, p. 201] 127 German original: “Verteilen-Schema”, translated in Engelhardt [1997] as “TRANSFERSchema”. 40 talking circuits Looking at the results from Table 2.1, this way of thinking seems persistent after instruction. However, if we exercise the same caution Jung [1985] advises about learners discussing properties, although the first statement is false in the sense that a current does not “have a voltage”, it does, for example, “have a voltage” as its cause. The nuances of such semantic differences make answers to such a question difficult to interpret. However, with the pre-instruction interviews, the known resilience of pre-instruction thinking as additional evidence and such a high proportion agreeing with the statement, it seems the most likely outcome that at least the voltage as property of current part of the TRANSFER-Schema is also present in some learners after instruction. The second statement in this table is more explicit in referring to the property nature. Also, calling attention to the fact electricity and current are not the same thing, by explicitly using both nouns. However, from my (albeit unsystematic) teaching experience with undergraduates, learners misuse the verbal phrase besteht aus 128 , when they have a developing idea of the system and wish to link concepts together. I also find it less easy to say this question has a definitive answer. The web of ideas in the domain of electricity does consist of 129 the concepts current and voltage, but they are not “ingredients” of electricity in the same way a cake consists of flour, butter and sugar. For this reason, this question seems to have a too large a room for interpretation to make the answer reliable and no additional interview evidence is provided. As in the first statement, the third statement lacks a clear division between current and electricity † , which may make interpretation difficult for the learners. The clearest interpretation would be that learners see voltage as only possible when current is present. This idea is dubbed No voltage in absence of current 130 , which some students reason using, and overgeneralising, Ohm’s Law, V=IR131 . The fourth statement is discussed above. 128 German for consists of. 129 Contains as essential and core components. 130 von Rhöneck [1981,1984] 131 Johsua [1982] in Tiberghien [1984] theory and measurement of learning and knowledge 41 Although a resistance is a necessary condition for establishing a potential difference, some learners struggle to differentiate the properties, using concepts that indicate one to refer to another, for example talking of a “resistance drop” or a “2Volt Resistor” 132 . Learners also seem to struggle to reason how the constance of potential difference from a voltage source relates to a varying resistance 133 . Although it is unclear from the examples given where the origin of this difficulty is, i.e. whether it is the overgeneralisation of a constancy rule or whether the idealisations of Ohmic resistors, when compared to the resistance characteristics of a light bulb, are not clearly compartmentalised. Voltage seems to be able to illicit a wide range of misconceptions from our learners in a much more varied and complex way than current seems to. This be because of its more abstract, comparative nature and the fact it is often introduced after and in relation to current and resistance. This will be reflected in the teaching material developed in later chapters. 2.3.5Other Difficulties The fact that resistance has not been afforded its own subsection here may be quite telling, as it is often seen only in its relation to the other key physical quantities. Muckenfuß [1980, p. 35] notes the lack of conceptions of resistance related to science, only those related to social issues i.e. “non-violent resistance”, “resistance to progress/reform” and “resistance from parents”. These ideas can prove helpful, as they do not overlay with the dominant electricity † use key idea, where a resistor may be seen to consume rather than hinder 134 . All the above social ideas map onto the idea of a hindrance nicely. Other difficulties regarding resistance are its relation to length and cross-sectional areas of the material, whereby the former seems relatively intuitive135. 132 Riley et al. [1981] in Tiberghien [1984] 133 Johsua [1982] in Tiberghien [1984] 134 This extension of the usage key idea can be seen for example in von Rhöneck [1984, p. 5]. 135 Johnstone and Mughol [1978, p. 49] 48 talking circuits categories will be dependent on the learning objectives of the teaching sequence. Structural features define how to use this newly learnt word: the function it serves in a sentence (what part of speech, i.e. noun or verb, it is), or the verbs or other parts of speech it may interact with. This denotative or logical content is not the extent of language, however. The connotative meaning of the way we speak about electricity in the everyday sense, stands in direct contrast to how we use it in physics. Additionally, whether the conceptual content that is intended by the speaker/writer is understood by the audience, will be focussed through an associative lens, i.e. what does the word mean from a speaker or listener’s reference point. Duit [1984b] uses the example of “the sun rises”, being a true observation going against a scientific, heliocentric view of our solar system. An example from electric circuits might be “switch the electricity on”, which although perfectly acceptable in everyday speech, does not acknowledge the processes of a switch closing, creating a pathway for current, over which must be a potential difference, but instead imbues the “electricity” with a kind of “power” of its own. In fact, even experts will use these kinds of phrases in their everyday speech, fully aware of the true denotative content behind them, perhaps encoding using social meaning markers that they no longer in their role as scientist, commonly called code switching but more precisely referred to in linguistics as register shifting 146 . We see here the difference between the conceptual meaning as a kind of philosophical/logical object and the connotative meaning as a more psychological object. Duit [1984b] argues that the subject-predicate-object structure leads to cause and effect thinking, structural importance related to Leech’s thematic meaning. The tendency to use these simple structures, lead to local argumentation and sequential reasoning, suggests Duit [1984b]. As well as seeing quantities with unclear meanings as “quality of an object” as with the idea that voltage is a property of current, leading to a false schema and categorisation of contrastive or structural features. 146 Bullock and Toribio [2009] theory and measurement of learning and knowledge 49 The final point is the borrowing or overlap between scientific vocabulary and everyday vocabulary. These misinterpretations occur as a result of reflective and collocative meanings. The word “current”, for example, refers not just to the flow of electricity, but that of rivers and oceans. The word has multiple possible conceptual meanings that are then reflected in each other, meaning ideas about one can be transferred to the other, which can be both useful and disadvantageous in teaching about a topic, again reflective of the learning outcomes. Collocative meanings are transferral of meanings from words that often go together. This again can be both advantageous or disadvantageous. The phrase “electricity usage” can support a current use misconception and within an interview shown in section 3.1a pre-instruction learner reasoned the meaning of resistance being to do with hindrance with reference to the phrase ‘resisting arrest’. Duit [1984b] belies a difficulty of translating the understanding of physical concepts across language barriers. He uses examples that are not entirely comprehensible in the translated English, as they would be if the author was writing in his native German. For example, he references the phrase “the weightlifter has force” from a German publication of his “der Gewichtheber hat Kraft” 147 . The phrase in English sounds unconvincing and is better translated with “the weightlifter has (the) strength”, showing the perils of translating phrases literally and how that the words “force” and “Kraft” may carry different associations, based upon the usage of the words in their respective everyday conversations. This functions as an illustrative example to justify the validation of any instrument across languages, as will be illustrated in section 3.1. 2.4Measuring Alternative Conceptions and Learning Gains The standard graded school test is ubiquitous and familiar to everyone, however the goal of a knowledge test can be multifarious. Considering why one is using a given test, the intended audience and additional information that one can extract, allows teachers and researchers alike 147 Duit [1984a] in Duit [1984b] 50 talking circuits to make better use of tests than just for summative assessment 148 . Much more information can be extracted from a test than just a percentage mark. 2.4.1 Alternative Conceptions as Distractors and Something Measurable Rather than simply marking a given test right or wrong (scientific or unscientific thinking), the distractors of a test can be developed and assigned to alternative conceptions, providing richer information. If performed as a pre-test, the researcher can learn what ideas are prevalent in the population and for a teacher this might be a useful tool to plan for addressing these ideas, allowing teachers to ‘know their competition’. Additionally, richer information can provide a better insight as to the progress of learners over and above a dichotomous true or false. When comparing preto post-test, as learners’ ideas can be organised hierarchically in closeness to the scientific conception. This can be seen, for example, in Hadenfeldt et al. [2016] on the particle theory of matter, systematising the complexity of thinking into 5“levels of understanding” and compare progress that way. Such hierarchical levels can be conceptualised more generally as “everyday”, “school informed” and “scientific” ways of thinking, where there may be multiple examples of each way of thinking, even compounding. 149 However, it is important to not consider these levels as a natural or even expected progression, as learners often “regress” 150 to previous ways of thinking, even misremembering evidence presented in order to address their “everyday” ways of thinking.151 148 This is the kind of assessment that asks “What has been learnt?” at the end of a topic and refers more to an assessment paradigm rather than a given method, but is often synonymous with the graded test. For more about summative assessment’s counterpart, formative assessment, see Section 4.4.2. 149 Hericks [1993] 150 Cosgrove and Osborne [1985] 151 Gauld [1986] theory and measurement of learning and knowledge 51 As the conceptions often lie at an underlying explanatory level 152 these tests are often two-tiered - with a ‘what’ level and a ‘why’ level 153 . Learners may also recall a rule correctly but still have an underlying misconception - for example, know that current is the same at all points in a simple loop circuit, but say current/electricity † is split evenly among the components in the circuit 154 . In such cases we can measure more closely whether a deeper level cognitive change has occurred. The second tier also has a secondary effect in that it reduces the amount of false-positive diagnoses for a given alternative conception. For example, when a diagnosis is made on the basis of selecting one of five singletier answer choices, there is a false-positive chance of 20% when a learner is picking randomly. The diagnosis made on the basis of answer combinations on a two-tiered test reduces the likelihood of the answer simply being chosen at random. For example, five answer options followed by five answer options, reduces this likelihood from 20% to 4%. 2.4.2Tests on the Topic of Electricity There are many single choice test instruments for testing understanding within the domain of physics, probably the most well known of which being the Force Concept Inventory 155 . This test, among others, is designed to measure whether learners have understood an underlying concept, for example, that “constant acceleration [results in] a parabolic orbit” 156 and distractors may or may not be based upon supporting research on learners’ alternative conceptions. This review looks at tests created after 1997, for those created before that date “statistics associated with the reliability and validity [...] are almost non-existent”157. However, for a review of those produced before this time, there is a thorough review in Engelhardt [1997]. 152 Items do not simply ask ‘What do you think?’, but set the learners a task to apply their knowledge and the conception is deduced from those answers. 153 Burde [2018], Urban-Woldron and Hopf [2012], Ivanjek et al. [2021] 154 Maichle [1980, p. 12] 155 Hestenes et al. [1992] 156 Hestenes et al. [1992, p. 1] 157 Engelhardt [1997, p. 64] 52 talking circuits Within the topic of electricity there are several tests in the English language 158 and beyond 159 . The tests on the topic of electricity vary in intended age and ability of learners, as well as learning outcomes tested. Questions within a test are often referred to as “items”. Such tests are not often freely shared as researchers are concerned that teachers in their interventions will “teach to test”, rendering the point of checking underlying understanding useless, by the repetition of rote answers 160 . Sangam and Jesiek [2010] discuss four English language concept inventories on the topic of electricity, one is intended exclusively for electrical engineering undergraduates, the Circuits Concept Inventories (CCI) 161 . This is apparent by the fact it contains networks of resistors and the inclusion of capacitors, as well as alternating currents and graphical interpretations of transient voltages unsuitable for an introduction to the topic in lower secondary. Although Sangam and Jesiek [2010] class it as a “quantitative assessment”, this is only strictly the case with items 17-22, with 17 asking for an equation and 18-22 testing the ability to read specific physical quantities from a graph. Therefore, not matching what would be most commonly understood by a “quantitative assessment” of students abilities, among physicists, despite the numerical answers to many items. Secondly, Sangam and Jesiek [2010] introduce the Electric Circuits Concept Evaluation (ECCE) 162 with 45 single-tiered, single-choice items, pitched at undergraduates in the United States of America. 4items ask, in addition, “Briefly explain [...] how you arrived at your answer [...]” to a selection of questions. Multiple questions are asked for a given circuit. Six items have capacitors (Questions 17-20) or inductors (Questions 21-22) included in the questions and the questions 39-45 158 Sangam and Jesiek [2010], Halloun [2007] 159 Burde [2018], Urban-Woldron and Hopf [2012], Ivanjek et al. [2021] 160 A fear, I personally find unfounded, as considering the prevalence of the researchpractice gap, teachers and learners seem unlikely to seek out specific tests from science education or didactic literature. 161 Kindly provided to me through personal communication with the author, Prof. David P. Rancour. 162 Sokoloff [1996] theory and measurement of learning and knowledge 53 ask about alternating current, so beyond the scope of lower secondary. This leaves 32 items that possibly have a use in lower secondary, the learning outcomes of which are summarised in Table 2.4. The questions contain up to 10 answer possibilities and references to diagrams stretch beyond a page requiring learners to keep a lot of information in their short term memory. This test, despite having some good situations for developing items for lower secondary, on the whole is not applicable. Thirdly, the Electric Circuits Concept Evaluation (DIRECT) 163 is a 29 item, single-tiered single choice test, each with 5answer options. In her doctoral thesis Engelhardt [1997] gives an account of how the test was developed and then re-developed, both with statistics and interviews, with specific reference to misconceptions. There are a set of objectives clearly defined (p. 72) and linked with specific items. Only three of the learning objectives (6,7and 9) are not applicable to the learning objectives of the cohort under investigation. Using the mapping of objectives to items on page 136, items 2,3,11,12,20 and 21 could be omitted to form the basis of a suitable test. Although the internal consistency measures are only “moderate” 164 , the test fulfils a range of other quantitative tests, only narrowly failing to have a high enough discrimination index. Qualitative interviews were collected with a subsection of the questions and the results of which, when analysed, “indicated that, in general, students were interpreting the questions correctly and that the exam was eliciting their misconceptions” 165 . The high school learners completing this test were all 18 years-old, making much of the analysis and development less applicable to our target group of twelveand thirteen-year-olds, despite having a reasonable overlap in learning objectives. For these reasons and with the aforementioned caveats, I consider this test the most appropriate English language electricity concept test, for my purposes, available at the time of writing. A version with revised wording (Ver 1.2) is available as used by Sangam and Jesiek [2012]. 163 Engelhardt and Beichner [2004] 164 Engelhardt [1997, p. 80, p. 85] 165 Engelhardt [1997, p. 154] 54 talking circuits Q Learning Objective Tested Situation 1Current Conservation Simple Loop 2Current in Parallel Circuits Two bulbs in Parallel 3Current in Parallel Circuits 4Brightness-Current Relation 5Potential Difference in Parallel Circuits 6Current in Series Circuits Two bulbs in Series7Potential Difference in Series Circuits 8Brightness-Current Relation 9Current in Branching Circuits & Brightness-Current Relation Bulbs in Mixed Circuit with Switch 10 Current in Branching Circuits 11 Potential Difference in Branching Circuits 12 Function of Switches & Analysis of Voltage and Current in Network of Resistors 13 14 15 Identifying Resistors in Parallel 16 Identifying Resistors in Series and Parallel 17 Capacitance20 21 Inductance 22 23 Identifying Resistors in Series Mixed Circuit with Resistors 24 Identifying Resistors in Parallel 25 Identifying Resistors in Series Series, Parallel and Short Circuits with Resistors 26 Identifying Resistors in Parallel 27 Current Conservation Three identical Resistors in Series 28 29 Current Conservation Three non-identical Resistors in Series 30 31 Current in a Network of Resistors Three identical Resistors, two in Parallel, one in Series 32 33 Three non-identical Resistors, two in Parallel, one in Series 34 35 Three all different Resistors, two in Parallel, one in Series 36 37 Series, Parallel and Short Circuits with Resistors 38 39 Alternating Current - 45 Table 2.4:Summary of learning objectives and contexts from the Electric Circuit Concept Evaluation developed by Sokoloff [1996]. theory and measurement of learning and knowledge 55 Finally, the AC/DC Concepts Test (ACDCCT) 166 is a single-tiered, single choice, 20 item test intended for use with undergraduates. Despite reaching out to the authors, I was not able to obtain a copy for further analysis. There are, however, two considerations in Holton et al. [2008] worth developing in a further discussion on test development: test-wiseness and temporality. Learners can search the question text for information that can lead them to answer correctly despite not knowing the answer to the question. We call the ability to do this test-wiseness. Holton et al. [2008, p. 8] develop a list of eleven cues that are taken into account when redeveloping the test used in the intervention in Section 3.1. Learners are shown to perform significantly worse on questions that have a temporal nature, i.e. what happens in a circuit over time 167 . Holton et al. [2008, p. 14] also note that misconceptions are prevalent throughout the cohort and the major difference in test scores comes from knowledge of circuit invariants. Other tests available in English and in this case French include the Inventory of Basic Concepts - Direct Circuits (IBCDC) 168 . It is a 33 item single-tiered test, testing a wide range of concepts in DC Circuits in school age and undergraduate learners and tested with a large number of participants. The test has undergone multiple iterations and redevelopments. It is successful in covering a lot of material succinctly in relatively few five option items, see Table 2.5for an overview. The test has a focus on “real world” visualisations of circuit problems and correct connections to batteries and bulbs, which should be considered if wanting to use the test. The separation of bulb brightness and current is a nice feature, not assuming that learners see the relation. Furthermore, there are items regarding internal resistance as well as abstract “black box” problems, which may not be desirable difficulties in such a test. Furthermore, the English used is somewhat non-standard and at some points difficult to read, even for an academic native speaker. Finally, the answers to some items seem ambiguous, rest on conventions or 166 Holton et al. [2008] 167 Holton et al. [2008, p. 13] 168 Halloun [2007] 56 talking circuits differing levels of pedagogic idealisation 169 . For example, Item 14 has multiple possible answers (each with different caveats) and similarly Item 16 (with the “black box”) has different correct answers depending on the components inside, but would not be known to a learner who has only studied DC Circuits. This may be considered to be intended, as a hierarchy of models is discussed in Halloun [2007, p. 4], although this is explicitly stated to be not the case on page 13 of the same document. In general, evaluation of learners’ conceptions from the test are never explicated upon. Some items on this test would offer a good basis for further development. However, due to more promising examples covering the same ground, I do not carry out further work on this basis. Originally in Turkish, the Simple Electric Circuits Diagnostic Test (SECDT) also has an (not verified) English language translation 170 . This test has twelve items trialled with Turkish fourteen to sixteen year-olds and each is three-tiered, the third tier of which is a binary choice: “Are you sure about your answers given to the previous two questions?”, with learners being able to answer “Sure” and “Not Sure”. The test would require rewriting in English. The first two items follow the typical “what”, “why” pattern with an open “why” answer. A Cronbach’s α of 0.69 (close to the 0.7recommended by Nunnally and Bernstein [1994]) is given for the three tiered test. Point-biserial coefficients for nine of the twelve items show medium positive correlations (>0.3) 171 , pointing to the test measuring an underlying understanding well. Results for the two-tiered test are not published 172 , as the learners must be “Sure” of their answer to be marked correct. The two-tiered score and number of “Sure” answers are correlated, meaning that the results for the two-tiered test would likely be less reliable. Although the number of false-positives may be reduced using this method, increasing the number of false-negatives feels ethically and theoretically 169 Simplifying a situation or explanation of a phenomenon, so that learners get a simplified understanding that explains the core actions. For a more in depth discussion of idealisation, with use of physical examples, see Weisberg [2007]. 170 Pe¸sman and Eryılmaz [2010] 171 Cohen [2013] 172 Pe¸sman and Eryılmaz [2010] contains analysis at the three-tiered level only. theory and measurement of learning and knowledge 57 Q Learning Objective Tested Situation 1Models of Current Simple Loop 2Material Properties and Brightness 3Internal Resistance Brightness Simple Loop with Internal Resistance 4Internal Resistance Power 5Internal Resistance Voltage 6Internal Resistance Current 7Voltage Brightness Simple Loop with Different Batteries8Conditions for Bulb Burning Out 9Summing Voltages in Series Batteries in Parallel and Series 10 Identifying Resistors in Series Two Bulbs (with fittings) 11 Identifying Resistors in Parallel 12 Identifying Resistors in Series Series, Parallel and Short Circuits with Resistors 13 Identifying Resistors in Parallel 14 Physical Analogues for a Resistor 15 Conditions for Current Flow Black Box Device Attached to a Resistor16 17 Properties of Current and Potential Simple Loop18 Charge Carrier and Flow Speed 19 Charge Flow Model 20 Brightness Comparison Between Situations Simple Loop, Two Bulbs in Parallel and Series 21 22 Current Comparison Between Situations23 24 Potential Difference Comparison Between Situations25 26 Kirchoff’s Voltage Law 27 Kirchoff’s Current Law 28 Ammeter Usage 29 Voltmeter Usage 30 Open Circuit in Series 31 Open Circuit in Parallel 32 Bulb Brightness in a Mixed Circuit Mixed Circuit with Switch and Bulbs33 Function of a Switch Table 2.5:Summary of learning objectives and contexts from the Inventory of Basic Conceptions in DC Circuits developed by Halloun [2007]. 64 talking circuits Chapter Contents 3.1Test Validation 65 3.1.1Taught vs Tested Content Validity 65 3.1.2A Pre-Use Critical Reflection on the Urban-Woldron Test 67 3.1.3Ensuring Translation Robustness 67 3.2Examining Student Conceptions in a Cognitive Laboratory Interview 68 3.2.1Method 69 3.2.2Typical Examples of Interview Responses 72 3.2.3Measured Alternative Conceptions 76 3.2.4Explanations Unrelated to the Physical Situation 81 3.2.5Unmeasured Alternative Conceptions 83 3.2.6Coded Interview Results vs Question Codings 101 3.2.7Linguistic Mismatches 103 3.2.8Problems with Parallel Circuits 106 3.2.9A Critical Evaluation of the Interview Method for Evaluating Alternative Conceptions 108 3.2.10 Ensuring Usability 110 3.2.11 Questions and Diagnoses Added 112 3.3Statistical Methods for Questionnaire Analysis 117 3.3.1Examining Sub-Scales with Factor Analysis 117 3.3.2Test Internal Consistency 120 3.3.3Instrument Quality with Rasch Analysis 122 3.3.4Using Confirmatory Factor Analysis to Assess Misconceptions 130 3.3.5Summary of Quantitative Results 138 verifying testing materials 65 3.1Test Validation The concept of validity is typically subdivided into four, with each part addressing a different methodological consideration 189 . Trochim et al. [2016, p. 28] summarises them as follows: • “Conclusion Validity - The degree to which conclusions you reach about relationships in your data are reasonable. • Internal Validity - The approximate truth about inferences regarding cause-effect or causal relationships. • Construct Validity - The degree to which inferences can legitimately be made from the operationalizations in your study to the theoretical constructs on which those operationalizations are based. • External Validity - The degree to which the conclusions in your study would hold for other persons in other places and at other times.” In this section, the concept test used for evaluating learners’ learning gains is evaluated. This concept test is the way in which we operationalise the measurement of learners’ conceptions, i.e. how we elicit what we theoretically consider learners to think and make it measurable. In other words, here I examine the construct validity of the concept test in several ways: reviewing the content validity through the overlap of tested and taught material, pre-operationally critiquing the test using collected literature, examining usability through a interview study, using methodological triangulation to examine the matching rates of spoken and selected answers in a Cognitive Interview study, as well as, a range of quantitative post-hoc tools examining validity and reliability. 3.1.1Taught vs Tested Content Validity The tested outcomes are mostly in line with the National Curriculum for England 190 , outlined in Table 3.2. The test is concept based, so is difficult to match onto the knowledge statements of the Curriculum and ideally the views of experts and practitioners would have been sought to ensure a sufficient overlap. However, in order to justify the use of 189 Cook et al. [1979] in Trochim et al. [2016] 190 Department for Education [2014] 66 talking circuits Item No Cur. Point Imp. Exp. 2-1,2,8 3-1,8 4-1 6 8 1,2 7 8 1,4 9-3 10 1 2,8 13 -1,2,8 14 -3 15 1 2,8 16 8 3,4 20 -3 21 1 2 22 -1,2 23 -1,2,8 24 1,925 1 2,8 26 1 2,8 27 -1,8 28 -1 29 1 2,8 30 -3 31 2,6 5 32 2,6,9 5 Table 3.1:Urban-Woldron and Hopf [2012] and Burde [2018] Items Coded with Key Stage 3“Current Electricity” National Curriculum for England contents as shown in Table 3.2. the test without such evidence, I include a table in which I map these outcomes to Items in the test, shown in Table 3.1. The only curriculum point missing in test is “bulb ratings”, this is also absent from the resources used in the intervention, outlined in Section 4.3.1 191 . With this one absence from both taught and tested content, we have good agreement, broadly inline with the National Curriculum for England. 191 The reason for this piece of content being missing is also outlined there. verifying testing materials 67 Code Content 1(1) electric current, measured in amperes, in circuits, 2(1) series... 3(1) ... and parallel circuits, 4(1) currents add where branches meet and current as flow of charge 5(2) potential difference, measured in volts, 6(2) battery... 7(2) ... and bulb ratings 8(2) resistance, measured in ohms, as the ratio of potential difference (p.d.) to current 9(3) differences in resistance between conducting and insulating components (quantitative). Table 3.2:A table showing the Key Stage 3content points for “Current Electricity” from the National Curriculum for England. Numbers in brackets indicate original number of the bullet-point shown in Department for Education [2014, p. 66]. 3.1.2A Pre-Use Critical Reflection on the Urban-Woldron Test 70% of learners do not see the relationship between current and brightness 192 , so measuring the understanding of current through the proxy of the brightness may not be reliable. This proxy is used in Items 10, 15,21,24,25,26 and 29. However, there are also items that directly ask for current in similar situations, these being Items 2,3,6,13,22, 23,27 and 28. Having these two groupings allows for a comparison, enabling investigation into whether the relationship between brightness and current is seen by the learners or whether the words trigger other alternative conceptions. 3.1.3Ensuring Translation Robustness The original test items in German were translated in parallel by myself, a native speaker of English and a fluent speaker of German; and a colleague, a native speaker of German and a fluent speaker of English. These two translations were then compared and the final translation produced, in line with the parallel translations model using the TRAPD approach, as described in Harkness [2003, p.38], however without of 192 Maichle [1980, p. 13] 68 talking circuits the use of a third-party adjudicator. Expertise of both translators was established inline with ISO17100 193 that establishes the following six essential competencies: 1. Translation competence 2. Linguistic and textual competence in both the target and the source language 3. Domain competence 4. Competence in research, information acquisition, and processing 5. Cultural competence 6. Technical competence Competency one is met by both translators as they had a good knowledge of the intended use of the translation and that although neither are qualified translators both use both languages professionally, also fulfilling competency two. Both translators have competency in physics, both academically and in a teaching setting, with experience doing both in both languages. Both translators are academics and are required to use competency four on a daily basis. As both translators have spent extended amounts of time in teaching institutions in both German and English speaking countries, competency five, cultural competence is also established. Translations were produced in Microsoft Word Tables and communicated via Email, so no technical competencies beyond that were needed, both translators met this level of technical competence. 3.2 Examining Student Conceptions in a Cognitive Laboratory Interview To examine the operationalisation of learners’ conceptions to test results, a Cognitive Laboratory Interview 194 study, close to the principles of athinking aloud study, was conducted using the translated testing materials. In this study, learners were asked to externalise their thoughts while answering a subset of the questions on the test. This enables learners’ reasoning to be observed verbally, alongside their selected answer options. Comparing these provides a way to perform a reliability 193 Behr [2018] 194 Leighton [2017] verifying testing materials 69 check, ensuring convergent validity, that two methods give correlated results when attempting to measure an underlying variable, in this case learners’ conceptions. Furthermore, this acts as a pilot for the use of the questionnaire in the main study and provides an opportunity to remove any usability barriers from the questions, as well as, extending the test in order to get a better idea of how our learners think. The following two research questions form the focus of this section: TA-RQ1: Do the learners’ spoken explanations match coded alternative conceptions from their written answers? TA-RQ2: Are an adequate number of alternative conceptions coded? 3.2.1Method The full questionnaire consists of 24 items. To reduce fatigue three questionnaires of 12 questions were constructed. To ensure that questions were answered a comparable amount of times, even if learners did not finish the whole test, those questions at the end of “Question Packs 1 and 2” were included at the beginning of “Question Pack 3”. Care was taken ensuring a range of question difficulties and topics were included in each set, the breakdown of the items including question difficulties (given as percentage of correct answers aggregated and weighted by number of learners preand post-test in both control and treatment groups) from Burde [2018, pp. 201 -203] can be seen in table 3.3. Interviewed learners were from a variety of schools: one rural British selective-school ( nSelective =17 , ¯ tSelective =10 m 37 s) and three metropolitan British comprehensive schools ( nComprehensive =14 , ¯ tComprehensive = 18 m 08 s). Learners were a mix between years 7to 9(ages 11 to 14) as well as preand post-instruction, an overview can be seen in Table 3.4. Learners self selected for participation and their parents or guardians provided consent to participate. They received positive feedback regardless of the correctness of their answers and were encouraged to provide an explanation or some underlying thoughts when none were given. This is of course different to how feedback would be given during normal teaching and on reflection, always providing positive feedback 70 talking circuits Item No. Topic Difficulty (%) In Question Pack: 1 2 3 2I/R 51 ✓ ✓ 3I/R 38 ✓ ✓ 4I58 ✓ ✓ 6I/R 16 ✓ ✓ 7I39 ✓ 9P27 ✓ 10 I/R 49 ✓ 13 I/R 46 ✓ ✓ 14 P23 ✓ ✓ 15 I/R 46 ✓ 16 I24 ✓ 20 P24 ✓ ✓ 21 I36 ✓ ✓ 22 I58 ✓ 23 I/R 19 ✓ 24 I28 ✓ ✓ 25 I49 ✓ ✓ 26 I39 ✓ 27 I/R 16 ✓ 28 I43 ✓ 29 I/R 47 ✓ 30 P22 ✓ ✓ 31a V 14 ✓ ✓ 31b V 10 ✓ ✓ 32a V 11 ✓ 32b V 5✓ Table 3.3:Table showing the breakdown of items into sub-questionnaires for validation through thinking-aloud. Topics are Voltage (V), Current (I), Resistance (R) and Parallel Circuits (P). Difficulties given as percentage of students that correctly answered aggregated across both preand post-test in the interventional study from Burde [2018]. Selective Year 8(Pre-Instruction) 8 Year 9(Post-Instruction) 9 Comprehensive Year 7(Pre-Instruction) 7 Year 8(Post-Instruction) 7 Table 3.4:Table showing the number of learners preand post-instruction in each school type. verifying testing materials 71 may result in the learners adhering to their first answers. This is not necessarily negative in this situation where alternative conceptions are under investigation, as it is these initial responses that are of interest. To begin each interview, the following passage was read and some demographic questions were asked to the learner: Hello, (insert learner name), My name is Tom and I work at a University. It’s my job to try and understand how people think about science. Anything we talk about today won’t be used by your teacher and is not a test. I’m interested in how you think, not what you know. I’ll be recording the sound from our talk, so that I don’t forget anything you said. Is that okay with you? If you want to stop at anytime, you can tell me and we’ll stop straight away and when I write my research you’ll be able to look at it too, if you want to. 1. What school year are you in? 2. Have you learnt anything about electricity in school before? Let’s practice thinking aloud. Say aloud everything that goes through your mind, whilst finding an answer to the question. Could you please try and estimate how many seats there are in your science classroom? Now, I am going to show you some questions on electricity. Don’t worry if you don’t know how to answer them. Like I said, I’m not here to test you, just understand how you think. So, if you could read the first question aloud and then you can try and solve it. If you don’t understand the diagrams, I will help you by telling you what each of the symbols mean. Whilst you are solving the questions, try and say everything that goes through your mind out loud. Although the learner was asked to “think aloud” this is technically not a “thinking aloud” study, as defined by Leighton [2017], as in addition to positive feedback for displaying their thoughts, I also asked processoriented probes 195 , a reflection on this style of interviewing will be given later in 3.2.9. 195 Defined in Willis [2015] as questions intended “to uncover the rationale underlying a given response (e.g., “Can you please tell me how you arrived at your answer?”)” 72 talking circuits All interviews were audio recorded and then transcribed using an AItool, otter.ai 196 , then being manually checked. Each utterance was then coded by myself in a first pass using the alternative conceptions coded by the test. Then on a second pass with a larger range of possible alternative conceptions from wider literature and inductively from the arguments learners made. Special attention was paid that conceptions are coded beyond superficial factors such as use of physical vocabulary, as despite the use of subject specific vocabulary and referral to physical rules, post-instruction learners display the same ideas as are present in the pre-instruction learners 197 . However, these can be harder to detect due to the superficial factors previously mentioned. 3.2.2Typical Examples of Interview Responses The following is an example of a coded section of interview from a preinstruction learner (Taken Day 1, Interview 1, hence 1-1) answering Item 22 198 . I am interviewing and am identified in all transcripts as “Tom”. Item 22 asks about a simple loop circuit with a light-bulb, points A and B are marked on the wire are directly (and equidistantly) either side of the bulb. The learner answers both items correctly on the sheet and their final statements in both cases show the physical idea of current conservation, coded here in green. As the concluding statement here in both cases is a physical idea, the learner is marked as showing a physical conception in the end, despite the preceding set of statements showing four alternative conceptions: Current-Distance Conception, Current is Taken, Current Use and Sequential Reasoning 199 . No codes are given for uncommented reading of answer options. Text read aloud is shown in curly brackets: { }, as in the example overleaf: 196 Liang and Fu 197 von Rhöneck [1980, p. 25] 198 Shown in App. A on page 235. 199 For an overview of these alternative conceptions, see Table 2.2. verifying testing materials 73 Time Speaker Transcript 03:39 1-1: {The light bulb in the circuit below is glowing. What can we say about the current points A and B? The current is bigger at A than B. The current is bigger B than A, the current is the same at B, A and B.} 1-1: If we’re measuring them, they will be at the same distance. So they’ll capture the same current from the battery. So I think the current is the same as [sic] A and B. 04:08 Tom: Thanks very much. 04:10 1-1: {Give a reason for your answer. The current is the same in the whole circuit.} Yes, I think some of the current gets used up in the light bulb. Yeah, but if they’re the same going around the current will still be the same on both sides. Or if the current gets used up in the lightbulb. I think it’s measured before the light-bulb. This current is the same in the whole circuit. This section of the transcript shows the alternative conceptions exceptionally clearly and presents a rich and explicit account of the learner’s reasoning weighing up given answer options and then deciding on an answer displaying physical reasoning. This results in Item 22 for Interview 1-1being coded, referred to as summative codes here, as that the learner displays a physical conception. Some statements are more difficult to code directly. For example an answer to Item 24 200 , comparing the brightness of two bulbs attached with wires to batteries, one short-circuited with a bulb in a simple loop. The same learner offers this as explanation: Time Speaker Transcript 07:09 1-1: Their cell is passing through having to go down and also around to enter both lightbulbs which take up some current as well. Firstly, the word “cell” is not mentioned in the question and it cannot “pass through”, so it is assumed that hear the learner has confused this with current or a more nebulous electricity † ; this part of the utterance 200 Shown in App. A on page 236. 80 talking circuits Time Speaker Transcript 05:06 3-1: Um, I1and I2share the same er starting branch. Well, they all do, but then they split off. So ha..., if I halve the 1.2I get 0.6for both of the two branches that split off. For I1and I2I have got to split that again to, to even out so, going to say for L1 0.60 and the same for I2and then I3it’s going to be, oh wait sorry, 0.3for these. Then I3is 0.6, I2 0.3and the same for I1. The conception, battery provides constant current occurs across a range of items: 8occurrences over 7different items across a range of question types. Sometimes it is used to justify current being conserved in a circuit, for example this question with two ammeters either side of a lightbulb in Item 28210: Time Speaker Transcript 03:27 6-3: (...) {What current does the ammeter A2show?} They’ll show the same. 03:52 Tom: Okay... and why would they show the same? 03:54 6-3: Because they have the same like, um, battery, I’m pretty sure, yeah. Other times it is used to justify current not changing when the load is changed, in this example looking at a second motor being added to a series circuit in Item 6211: Time Speaker Transcript 08:54 3-2: (...) (pause) If the current would to stay the same because the battery’s still the same. 09:31 Tom: Okay. 09:32 3-2: So the current wouldn’t change. Inverse Resistance is used by two learners and only one of these uses it to justify their final answer to a question, but repeats this on three occasions. This learner is post-instruction so this likely results from the rule being misremembered as “the higher the resistance, the higher the current” 212 and either directly quoted or paraphrased in their answers. 210 Shown in App. A on page 241. 211 Shown in App. A on page 244. 212 Interview 7-5at 11:16 verifying testing materials 81 Current is independent of resistance was not encoded once, as in every answer the resistance is identified as changing something. Even in the cases where current was stated as staying the same, this was despite not because of the resistor changing, either using sequential reasoning or aclashing currents justification. Higher Resistance-Higher Current Use is also uncoded, as current use is only invoked in relatively few cases and in only once where there is a resistance change. Arguably this code is implicit in this one case, as shown below, even though the link that adding a second resistor in series results in a higher resistance is not explicitly stated and the conception could be more resistors use more current - rather than an underlying concept relating to the physical constant. This statement, in answer to Item 32 213 , lacks any proportional, explicitly comparative nature, so remains, I would argue, ambiguous enough to justify not coding it: Time Speaker Transcript 08:26 Tom: Okay. What does the ammeter to show us? 08:30 1-4: Er, it shows us the current. 08:34 Tom: Uhuh. 08:35 1-4: The resistor uses some the current, it will be lower, I think 3.2.4Explanations Unrelated to the Physical Situation On occasion, learners justified their answers in ways unrelated to the physical situation. One pre-instruction learner, with the longest and most complex (in terms of most unique and varied reasoning) transcript, justified ticking multiple boxes. They similarly identified missing knowledge two other times when the question asked about resistance. In this following segment, the learner assesses the logical consequences of two possible definitions of resistance, reflecting on Item 29214: 213 Shown in App. A on page 243. 214 Shown in App. A on page 241. 82 talking circuits Time Speaker Transcript 07:29 7-2: It could get brighter depending on what resistance is. If resistance, if resistance, if resistance equals ... um.. it multiplies, 07:39 Tom: Mmm. 07:40 7-2: ... then the light bulb gets dimmer, but if the resistance diminishes, then light bulb gets brighter. 07:45 Tom: Right. 07:46 7-2: I might tick both. 07:39 Tom: Okay. 07:40 7-2: Because it really depends on what it means. Three learners, for a total of three occurrences, also took the only numbers given and proceeded to give an answer on that basis, similar to the unwillingness to reason qualitatively difficulty outlined on page 44. This is shown where the learner is looking for a calculation that can be done, but justifies their answer with the lack of information meaning that the situation cannot be more complex. As illustrated by this excerpt from an answer to Item 4215: Time Speaker Transcript 01:12 5-1: Uh, I’m trying to see if there’s a way that I could figure out maybe one of the currents or something? 01:19 Tom: Ahuh. 01:19 5-1: ...and then I would have a look for the other one, or just see if they’re the same. 01:25 Tom: Ahuh. 01:25 5-1: (pause) I probably would have a guess that it’d be both ammeters share the same current. 01:41 Tom: Okay, great. 01:42 5-1: ... because they’re not saying a number. All of these codes are counted and tabulated with the diagnosis answer options given in Urban-Woldron and Hopf [2012] and used as a convergent validity measure discussed in Section 3.2.6. 215 Shown in App. A on page 234. verifying testing materials 83 3.2.5Unmeasured Alternative Conceptions 35 29 15 13 12 12 10 655443 2 2 2 1 1 1 1 11 Sharing Switch as Current Toggle Geometry-Symmetry-Distance Argument from Power Electricity†Issues Clashing Currents Voltage Halving–Dividing Argument from Utility Resistor as Power–Source Current vs Resistance Constant Global Reasoning Current-Distance More LightbulbsMore Brightness (Non-Current) Usage Voltage Punctual Giving-Taking-Requiring Verbal Reasoning Open Circuit-No Voltage Personification Current Speed as Important Ammeter as Energy Giver Figure 3.2:Pie Chart Showing Occurrences of Unmeasured Summative Codes: exploded segments denote ideas not present in the literature. 84 talking circuits In this section I will discuss the alternative conceptions or broader difficulties that learners showed that were not diagnosed by the test, some of which are found in previous literature, to varying degrees, and some not. An overview of all 22 codes, or code groups are shown as a pie chart in Figure 3.2, exploded segments show concepts not found in the literature. Concepts are listed from high to low occurrence rates. Of note is that the sum of occurrences in Figure 3.2does not match “Other” in Figure 3.1, due to removal of explanations not related to the physical situation, discussed in 3.2.4. Sharing was seen as a key idea in thirty-five occurrences in 22 of the 31 interviews, excluding the times sharing is used to explain a physical idea. Many physical quantities were argued to be shared: current (13 occurrences plus 1as charge), voltage (11 occurrences), power (3 occurrences) and energy (2occurrences). Alternatively, learners argued ambiguously with the idea of something being shared (6occurrences). All but one reference to voltage sharing were in answers to Items 31 and 32. These answers were from both preand post-instruction learners. Sometimes the voltage sharing conception is used in a close to physical way, as in this response to Item 31216: Time Speaker Transcript 07:49 6-3: {We now put another of the same light bulbs between point 3and 4. How high is the voltage in the circuit with two light bulbs?} (pause) It’s the same between 1and 2, because there’s no lightbulbs but between 2and 3, I’d say it’s 3because it needs to share out the diff.... for 2. The spoken answer here seems physical, but the learner has already said that voltage is constant in the previous part, meaning it is initially seen as 6 V, then drops to 3 V when “share[d] out” between the additional light bulbs. In some answers learners ignore whether there is a circuit component and simply share the voltage over the markers. Again in response to Item 31217: 216 Shown in App. A on page 238. 217 Shown in App. A on page 238. verifying testing materials 85 Time Speaker Transcript 06:22 4-2: {For the following circuit, how high is the voltage potentially different [sic]?} (pause) 06:45 4-2: Would it be three? 06:47 Tom: Why do you think it would be three? 06:48 4-2: It’s shared. 06:49 Tom: It’s shared, right, yeah. 06:55 4-2:3again. 06:56 Tom: Ahuh. 07:00 4-2: Three. 07:03 Tom: So, why, you say it’s three because why? 07:06 4-2: They’re all shared. Some learners also state that the voltage should be “shared evenly” and yet gave numerical answers that do not support that, as in this response to Item 32218: Time Speaker Transcript 05:46 6-3: (reading) The following current [sic] is made from two identical lightbulbs and a closed switch. How high is the voltage potential difference? (pause) The circuit is 6 so 0.1 . The difference between point 1 and 2 will be (pause) 5 (raises voice). 06:32 Tom: How did you get there? 06:33 6-3: I suppose because it’s on the same circuit, they have to all share the same amount of, um, voltage. 06:41 Tom: Right. 06:44 6-3: So this one will be .7. 06:50 Tom: Ahuh. 06:53 6-3: This one will be 3. 06:56 Tom: Okay, how did you get to those numbers? 06:58 6-3: Because we would have to share equally around, when you go around the circuit, so equally you have to share around the same amount of, um, voltage. When looking at cases where physical properties other than current and voltage were discussed, nine of the eleven occurrences were in answers to Item 24 219 . Learners argued that something determining the brightness of the bulb (be it energy, power or undifferentiated) was being shared, and around half stated this explicitly, as in the following example: 218 Shown in App. A on page 243. 219 Shown in App. A on page 236. 86 talking circuits Time Speaker Transcript 08:53 5-3: {Compare the brightness of the light bulbs, L1, L2and L3in both circuits. Which of the light bulbs glow the brightest?} (pause) L3 because all of the energy is going to it and it’s not being shared. And it was implicit in other learners’ statements, remarking that it was only “one bulb”, as opposed to two in the other circuit: Time Speaker Transcript 03:01 5-4: {Compare the brightness of the light bulbs L1, L2and L3in both circuits. The (inaudible) bulbs are the brightest.} I’d say L3would glow the brightest as it’s one bulb and it’s a series circuit. When looking to the literature, it is possible that such statements may have been interpreted as usage conceptions by other researchers. However, this kind of argument with “one bulb” would imply the contrast to the other circuit with two and that some resource responsible for the brightness is therefore divided between them, presenting an implicit sharing conception. For a discussion of the overlap of the usage,sharing and sequential reasoning linguistic mismatch and an analysis of the differences across languages and question format, see Section 3.2.7. The code group, Geometry-Symmetry-Distance, is constructed from three codes: Geometric Considerations (20 occurrences), Symmetry Identified (5occurrences) and Distances Important (4occurrences). Geometric Considerations is a varied code showing when the geometry (as opposed to the topology) of the circuit is seen as important, with a marked overlap with the codes regarding parallel circuit identification, shown in Section 3.2.8.Geometric Consideration was also given as a code, where learners showed some obviously geometric reasoning, but it was difficult to identify a clear argument, shown here in a response to Item 9220: 220 Shown in App. A on page 237. verifying testing materials 87 Time Speaker Transcript 08:09 7-1: {In which of the circuits are R1and R2connected in parallel to the battery?} (pause) Circuit 2. 08:31 Tom: Circuit 2. Great. Thank you. And why did you choose Circuit 2? 08:34 7-1: Er, these ones, er, like, it’s just right next to it. 08:40 Tom: Yeah. 08:42 7-1: These ones you have to go all the way around. This one is just ... they’re just everywhere. This quote shows a general geometric justification, followed by a learner pointing out (an absence of) symmetry in one of the circuits. Referring to symmetry in circuits ranged from this rather vague statement to “they’re not the same place on either half of it” 221 , clearly referencing a symmetry (breaking) to the use of the word “symmetry” itself in: “The current would be the same since that since it’s symmetric.” 222 . Other than these, distances were also shown to be important by learners counting squares 223 or estimating distances from the diagrams 224 . There is a wide range of questions in which reasoning in this way was carried out. Electricity † Issues indicates an undifferentiated or unphysical use of vocabulary, indicating a diffuse understanding of the underlying physical concepts. These are broadly under the category of Undifferentiated Quantities (6occurrences), as well as three codes where the confused quantities are discernable as Current-Voltage (3occurrences), Current-Energy (5 occurrences) and Current-Power (1occurrence). These confusions show themselves as the usage of incorrect vocabulary, in this case resistance instead of current or, more correctly, charge, shown in this response to Item 29225: Time Speaker Transcript 04:16 3-4: Because the resistance will go through R2... 221 Interview 8-5at 3:08 222 Interview 5-1at 8:34 223 Interview 8-4at 14:26 224 Interview 7-1at 7:18 225 Shown in App. A on page 241. 88 talking circuits Another way would be to jump between two separate quantities in the same explanation, as in this response to Item 6226: Time Speaker Transcript 09:23 2-4: Like the (pause) voltage, I guess, or... 09:28 Tom: Okay. 09:30 2-4: ...like power. Or in this case, in reply to Item 2 227 , flatly stating resistance and current are “the same quantity”: Time Speaker Transcript 29:31 7-2: Ah, I don’t think that makes a difference because they’re the same quantity. In Voltage Halving-Dividing, split into Voltage Halving (8occurrences in 2pre-instruction, 4post-instruction learners) and Voltage Divides Evenly (5occurrences in 3pre-instruction learners), we see a similar conception to sharing. All occurrences are in answers to Items 31 and 32, specifically asking about voltage. The use of the word “halving” could be seen as the application of a learnt rule. However, seeing as it occurs in both preand post-instruction learners and the similarity to sharing, a common concept outside of this topic, it seems that the conception is also informed by pre-instruction experiences. Their use of the word “halving”, as in this answer to Item 31 228 , sometimes implies that passing through the components seems to half a value sequentially: Time Speaker Transcript 10:15 6-1: So then 1.5here, 1.5here, but you would half it to make 7.25 here. So, yeah, that’s 1.5, then you get another 1.5that would be the current down here, but instead it’s 0.75. This previous segment shows the learner, when asked about voltage, discussing current halving (within the same answer voltage and power 226 Shown in App. A on page 244. 227 Shown in App. A on page 243. 228 Shown in App. A on page 238. verifying testing materials 89 are referenced). For other learners the halving happens more in the sharing sense, as with the six volt cell in Item 31229: Time Speaker Transcript 08:47 2-3: Okay, 6because it’s still the same cell and the battery. 08:48 Tom: Ahuh. 08:51 2-3:3because it’s like, halvened [sic] through it(...) Voltage Divides Evenly is in all cases much closer to a sharing conception, without using the word, only varying in levels of specificity. This is expressed explicitly in a statement, again to Item 31230: Time Speaker Transcript 11:01 7-1: Equally divided that would be three volts there and 3volts there. And, formulated more implicitly, once again to Item 31231: Time Speaker Transcript 09:42 6-1: {Look at the following circuit. How high is the voltage?} 6voltage. There’s 4corners each labelled 1234. 09:52 Tom: Ahuh. (pause) What are you thinking here? 10:10 6-1: I’m thinking about like dividing the amount of volts by 4. A conception not found in the literature, but similar to the inverse resistance conception, is resistor as power source. Five learners (3pre-, 2 post-instruction) held this conception and demonstrated it a total of twelve times. This pre-instruction learner makes explicit reference to the idea with regards to resistors in answer to Item 15232: Time Speaker Transcript 03:11 1-1: (...) If we decrease the resistance of R2I think the, the lightbulb will shine no differently, because R1will already be powering it. 229 Shown in App. A on page 238. 230 Shown in App. A on page 238. 231 Shown in App. A on page 238. 232 Shown in App. A on page 234. 96 talking circuits There are also two forms of the argument that there is no voltage over the switch, but there is else where (2occurrences) or that an open circuit means no voltage anywhere (4occurrences). Two learners see the open point as removing an essential feature of a circuit, as in the following two examples, both as answers to Item 32 part 2253: Time Speaker Transcript 06:19 2-2: {Um, open the switch between 1and 2. How high is the voltage?} Between, it’s like, zero (voice raises) for all of them because... 06:30 Tom: Okay. 06:30 2-2: ... cos there’s no circuit. Time Speaker Transcript 06:55 2-4: I think it’s zero for all of them because, like it’s not a circuit. These two post-instruction learners seem to see “closed-ness” 254 as a property of a circuit, and dismiss the circuit on those grounds, without reasoning with regards to current at all. This could act as impetus for the inclusion of more closed circuits in lower secondary, to expand the scope of the definition of circuit, beyond closed circuits, even beyond reasoning to show the primacy of potential difference, as argued later in Section 4.3.1. Learners in seven interviews make reference to “speed”, “fast” or “slow”. This may be used with Sequential Reasoning, usually in the context that when the electricity † is at speed from the battery, it can power things well and that resistors make it slow down, such as analogies with electrons as runners. However, it can also be used in a physical way, similar to a drift velocity. This is seen in learners both in the comprehensive schools and in the selective school, with five out of the seven are pre-instruction. If this is used during non-physical reasoning, in a total for three interviews across five occurrences, this is coded as Current Speed as Important, shown in this extract: 253 Shown in App. A on page 243. 254 In contrast to a circuit with an open switch. verifying testing materials 97 Time Speaker Transcript 02:36 3-4: (...) {What happens to the current through the light bulb?} Um, I think it’s going to be, ooh, the current is going to be, er, smaller than 0.4, I think, because if the resistance increases it’s going to slow the current down. This does not appear in the earlier literature review, as it is not mentioned repeatedly or even in the text of any of the articles cited. Only Gott [1984, p. 37] in a table of results groups “using up” and “slowing down” together, which are used by a total of 15% of 300 pupils aged fifteen. I characterise these as two different conceptions, because they show reasoning with two different central ideas, usage and speed. Switch as Electricity † Toggle is a cluster of codes that sees the switch as able to act at distance in a non-physical way, all occurring in answers to Item 7 255 . In one case this is described as “the light bulb would stop shining, because the switch is open so wouldn’t be able to travel through that section [...] of the wire” 256 , despite this being on another branch. Similarly, one learner describes the switch as “restricting the flow of energy” 257 and states “(...)when you turn on the switch? It would allow more energy to pass through” 258 . One learner is even more explicit in the fact that this affects the whole circuit, “the whole circuit will be well, the currents gonna stop at one point when the switch is open” 259 . These give the impression of a switch working as it may appear to in household lighting, that the light can be turned on and off from afar, with seemingly no connecting wires or on a household appliance where a switch may even toggle between modes. 255 Shown in App. A on page 235. 256 Interviewee 5-1at 04:57. 257 Interviewee 8-3at 03:41. 258 Interviewee 8-3at 03:48. 259 Interviewee 7-3at 08:46. 98 talking circuits Argument from Power occurs twice 260 in pre-instruction learners and is seen as an analogue to the argument from current, as some semi-material that moves through the circuit. The name for this semi-material may change as before the learner has the vocabulary to reason with current, they use the everyday word power. Clashing Currents, with current coming from both sides of the battery, is shown by three learners 261 . Interestingly, all of the uses contain the word “if” and only appear once in their answers as if this conception is not very compelling or they are trying to generate new possibilities to explain the situation. The Argument from Utility is used 5times by three learners, and is as described on page 44. The quotes sound much more natural in English than the translated French quote from Johsua [1982]. For example, in this excerpt from a response to Item 3262: Time Speaker Transcript 02:21 2-3: {The resistor R in the circuit shown on the left has a smaller resistance. We swap the resistor with a resistor 2, um, with a higher resistance shown on the right. What happens to the circuit?} It gets (pause) 02:56 Tom So what are you thinking? 02:59 2-3: Um, probably (pause) probably gets smaller but not to zero. 03:18 Tom Right, yeah. Great stuff. Why don’t you reckon it goes to zero? 03:23 2-3: Because if it went to zero, then there’d be no current and it wouldn’t make the circuit work. One learner reasons in one question with an all-or-nothing approach to the relation between current and resistance, coded as Current vs Resistance. The following extended example shows the only use of the code, as well as the only use of the code in an answer to Item 23 263 , Ammeter as Energy Giver in the Giver-Taker Schema as discussed earlier: 260 Interviewee 7-2at 08:43 and Interviewee 6-1at 14:31. 261 Interviewee 6-1at 10:23, Interviewee 7-4at 05:46 and Interviewee 8-5at 02:19. 262 Shown in App. A on page 239. 263 Shown in App. A on page 242. verifying testing materials 99 Time Speaker Transcript 15:24 7-2: {A socket is built from a battery, a resistor and an ammeter. The ammeter, the ammeter shows us the current. What happened to the current on the ammeter when we add a second identical resistor?} (pause) So, okay, so just to simplify stuff... 16:01 Tom: Ahuh. 16:01 7-2: ...the majority of me thinks that resistance it’s what, you know, makes the light bulb go dimmer. 16:08 Tom: Right. 16:08 7-2: And an ammeter is what make the light bulb go brighter. (...) 16:55 7-2: Okay, on circuit what current? So yeah, this is the battery. 16:59 Tom: Ahuh. 17:02 7-2: So these, these both, both of these could be like, the giver of like, the energy. 17:09 Tom: Yeah. 17:10 7-2: Okay. I’m like, like, I feel like, I’m like, I feel like since simply they talk about the light bulb getting dimmer... 17:19 Tom: Ahuh. 17:19 7-2: ...in here. And then they talk about the quantity of the ammeter which will support my answer, which supports my answer the think that it’s the ammeter what makes the light bulb glows. 17:29 Tom: Okay. 17:30 7-2: Resistance. On top of my explanation on 3.1. that resistance makes the lightbulb dimmer. (...) 17:49 7-2: Okay, so (pause) Mmmm, well, this is, well, let’s do the ratio. 18:05 Tom: Ahuh. 18:06 7-2: R2. A1. 18:08 Tom: Yeah. 18:10 7-2: You can see this is outnumbered. 18:11 Tom: Right. 18:12 7-2: And I’d say, the majority of me thinks that resistance makes the light bulb dimmer. Yeah. And the ammeter makes the light bulb lighter. 18:19 Tom: Ahuh. 18:19 7-2: Then it’s like a weighing scale. 18:21 Tom: Yeah. 18:22 7-2: Not very good drawing but so 2Rs will be heavier. 18:28 Tom: Yeah. 18:29 7-2: Yeah. 18:30 Tom: See what you mean. 18:31 7-2: So I feel like it’s gonna it’s gonna get smaller. 18:38 Tom: Ahuh. Great, thank you. 18:48 7-2: It could actually read no current flows as well. 18:50 Tom: Okay. 18:52 7-2: ’cos it’s outnumbered to the resistance. 100 talking circuits Firstly, viewing the ammeter as providing something rather than measuring something is understandable, as it is the only component that makes current visible. Secondly, we can also see the conception that there is a kind of metaphorical balancing act that is played between the resistance and the current and whichever wins then decides the outcome, similar to the idea of ‘the world is full of competing influences for which the greater “gets its way,”’ 264 . In contrast to the physical, linear effect of resistance on current, Current vs Resistance works like a binary switch. Global Reasoning indicates that the way a circuit is connected is unimportant. Central to reasoning in one occurrence, the learner stated “because it’s [a light bulb is] still connected to a battery” 265 , despite a switch being flipped, the current would remain the same. One learner argues to Item 24 266 that more lightbulbs mean more brightness and ignores the composition of the circuit when asked about the brightness of lightbulbs contained within, stating: Time Speaker Transcript 09:48 6-4: Yeah, I would say, um, lightbulb L1and L2’cos if have L3it will make, like less bright. If I’ve doubled the brightness then it might give me like more brightness. The conception that Voltage is Punctual rather than comparative is hard to show with these questions as it is always asked between two points, rather than being implicit. One learner, however, seems to interpret this as meaning voltage takes the same value everywhere between the two points asked, stating that the “voltage may change through two to three”267. 264 diSessa [2018, p. 69] 265 Interviewee 8-1at 02:33. 266 Shown in App. A on page 236. 267 Interviewee 1-1at 11:58. verifying testing materials 101 The final summative code present is Personification and Analogy, which is shown in Interviewee 7-2’s answer to Item 28. As I have already discussed, this learner shows complex and varied reasoning and draws on two analogies to try and describe the brightness of two lightbulbs in a series circuits. The first of which is that of runners in a race 268 and when this seems no longer satisfactory they use “electrical race cars” 269 . The conclusion they draw is “they’d be both the same, whatever happens to R is gonna happen to both of them” 270 , i.e. that a change in conditions (a changing resistance) would affect both light bulbs equally. This concludes the overview of the undiagnosed codes present summatively in answers. It is widely reflective of the literature discussed previously. However, some conceptions are illustrated in a way particular to the English language. Ideas are presented with addenda and in increased depth when compared with previous studies discussed in Section 2.3, at least those in the English Language. When compared with previous work there has been: changes in linguistic context, learner age and research recency, that will result in changes of conceptions based on prior knowledge. There are a few exceptional cases highlighted throughout this section, notably the remarkably common Resistor as Power-Source conception, not found in the literature. Some of these conceptions are used to develop new answer options in Section 3.2.11. Although the goal was to establish convergent validity for the testing and spoken outcomes, this also serves as a summary for those alternative conceptions present in the population interviewed. 3.2.6Coded Interview Results vs Question Codings As a measure of establishing convergent validity for the two outcomes: conception as measured by test and spoken conception. Convergent validity is “the degree to which the operationalization is similar to (converges on) other operationalizations to which it should be theoretically 268 Interviewee 7-2at 10:15. 269 Interviewee 7-2at 10:31. 270 Interviewee 7-2at 10:31. 102 talking circuits similar” 271 . In order to establish correlation between these two nominal variables, I use Cohen’s Kappa ( κCohen ). In order to produce the contingency tables shown in Tables 3.5and 3.6, a set of cases defined by Urban-Woldron and Hopf [2012] are used. Answer combinations for these are Shown in App. A.3. For the question answers, if the question is unanswered or answered ambiguously (i.e. multiple boxes crossed) this is coded as None . If the answer combination is found, it is coded as True , else False . Similarly, with the interview answers, if there was an answer missing or answered too vague or no response provided in the answers necessary for the answer combination, this was coded None . If a conception to be diagnosed was shown in any of the answers necessary for the answer combination, it was marked True and else False . These corresponding cases were then used to make contingency tables. Cohen’s Kappa for physical conceptions κCohen, PC =0.58 ( 82% Agreement), alternative conceptions κCohen, AC =0.51 ( 78% Agreement) and all conceptions κCohen, All =0.55 ( 80% Agreement) are then calculated for the True and False (i.e. Found vs Not Found) values, all fall within the bounds of a “moderate” Kappa Statistic as described in Landis and Koch [1977]. These are all likely underestimates, due to the fact that, if a learner finds an answer convincing and simply ticks that answer after reading it aloud, this is not counted. Considering this factor, and that some level of disagreement between spoken and written answers is expected, these statistics seem indicative of the test being able to reliably diagnose the learners’ conceptions it claims to measure. The high concurrences of “No AC” and “Not Answered” in both physical and alternative conceptions result from: a high incidence of vague (11%) or non-reasoned (13%) answers and the fact only the limited alternative conceptions for which the Urban-Woldron and Hopf [2012] tests codes, included in Section 3.2.3, can be included. Together this is taken to establish at least moderate concurrent validity answering TA-RQ1positively, improvements are made in following sections. 271 Trochim et al. [2016, p. 132] verifying testing materials 103 Spoken Responses PC Found PC Not Found No AC Question Answers PC Found 57 27 30 PC Not Found 21 167 60 Not Answered 0 2 442 Table 3.5:A Cross-tabulation of Physical Conceptions (PC) from Answers and Spoken Responses. Spoken Responses AC Found AC Not Found No AC Question Answers AC Found 55 27 18 AC Not Found 24 125 82 Not Answered 9 60 499 Table 3.6:A Cross-tabulation of Alternative Conceptions (AC) from the Urban-Woldron and Hopf [2012] Test found in Answers and Spoken Responses. 3.2.7Linguistic Mismatches In the following excerpt, the learner exhibits Sequential Reasoning, but if we were to translate it to similarly colloquial statements in German, “power” would be replaced by “Strom” and the learner would appear to exhibit a Current Use conception. Hence, perhaps the lower occurrence of Current Use conceptions in the spoken answers in English compared with the written answer patterns, where there may be an undifferentiated electricity † use conception that need not be expressed with the word current. An example answering Item 15272: Time Speaker Transcript 02:10 6-1: {In the circuit below 2resistors and a light bulb are connected to a battery. If we keep R[sic] the same, but decrease resistance of R2, what happens to the brightness of the light bulb?} (pause) I’d say the lightbulb would shine brighter. 02:35 Tom: Right, great. Thank you. Why, why do you reckon that? 02:39 6-1: If you decrease resistance, I’d say more power would get through? 02:43 Tom: Yes. 02:43 6-1: Lighting it up more. 272 Shown in App. A on page 234. 104 talking circuits The code for Sequential Reasoning (42 counts) is the second most common after that for the Physical Conceptions (79 counts) and much more common than all of the Usage conceptions combined (17 counts). This might call into question whether we are actually measuring the conception with the answer pairings. Figure 3.3shows the coincidences between the items that have answer pairings that diagnose Sequential Reasoning and Usage Conceptions and the codes on students’ spoken responses. The Figure shows strong connections between Sequential Reasoning and a large number of items, among them the items that diagnose it. Usage Conceptions are strongly connected to only the items that code for them. The other group connected strongly to them are the Sharing conceptions, particularly Item 21 that contains the word share in one of its answer options. Including Sequential Reasoning as Usage only changes one diagnosis, marginally improving correlation between answer patterns, shown in blue in Table 3.7. Again, including Sharing conceptions in the diagnosis of Current Usage and comparing with answer behaviour shows very little impact on the diagnoses questions, changing only one diagnosis, marginally reducing the correlation of answer patterns - see red arrows in Table 3.7. Overall the “ask the same question” approach 273 to questionnaire adaptation seems to have worked here, reflected in both written and spoken answers, but we can see a mismatch between the ideas as discussed by Germanand English-speaking learners. Spoken Responses CU Found CU Unfound No AC Question Answers CU Found 41 ←− 5 5 CU Unfound 31 ←− 22 8 No Answer 03 ←− 7 70 Table 3.7:Current Usage (CU) Conception from Answers and Spoken Responses. Arrows show the change in co-occurrences if sequential reasoning or sharing are taken to mean usage, blue and red respectively. 273 Harkness [2003] verifying testing materials 105 Sequential Reasoning Item 21 Item 22 Item 28 Current Usage Item 311 Item 24 Item 312Item 16Item 7 Item 14 Current Sharing Item 322 Item 23 Voltage Sharing Current-Distance Current-Energy Confusion Current Speed as Important Current is TakenCurrent is Required Current-Power SR In Interview & No Answer Pairing Usage Conceptions Plausibly Related Ideas Sharing Current as Passive Imprecise Language Item 10 Item 25 Item 27 Item 29 SR Answer Pairings Usage Answer Pairing Item 4 Sharing Undifferentiated Quantities Lacking Voltage-Current DistinctionArgument from Power Partial Current Usage Total Current Usage Item 26 Item 2 Item 15Item 13 Figure 3.3:Coincidence map of Sequential Reasoning Codes, Usage Conception Codes and the Questions intended to diagnose them. Yellow tags are for items, purple tags are deductive categories and blue tags do not appear in the literature review. Line thickness indicates number of co-occurrences ranging from 1-8. 112 talking circuits       E5(B #11!'&!11!/#"/!:'#!"1#%#"3(*13(*11!/!/!/!'/!'1-#" D""/0 !!%&!11!/#"+#+'# &'* E =/"*!#""-0   E =/"*!#""-B0   EB =/"*!#"B"-D0   "!/*'"!!&(1#'1/"*!#"B"-D * ED =/"*!#""-0   E =/"*!#""-B0   E =/"*!#"B"-D0   &'()&*+(,)+-**,,",.) ),/)+/&)&, # ,,0,& Figure 3.5:Item 31 including an example of how to fill in a numerical answer. With these changes made, all barriers and unintended distractor features are removed. 3.2.11 Questions and Diagnoses Added In order to maintain comparability with previous German-language results, I wanted to change as little on the test as possible. Ideally, only adding second tiers to questions that did not originally have them, also minimising additions to reduce any extra time and energy needed to fill out the test. This was achieved adding additional tiers to 7items and adding two answer options to an existing second tier, no changes were made to the first tiers of any Items. The simplest group of which to explain are the addition of a second tier to the three questions regarding parallel circuits, consisting of the answer options shown in Figure 3.6. The bottom-left answer represents the Physical Conception. The top-right offers a series-like answer, without having to solely apply to a series circuit. The top-left answer represents the discussed conception Mathematically Parallel and the bottom right verifying testing materials 113 Parallel as Opposite, discussed in Section 3.2.8. The answer options are identical and in the same layout in all of the three items.       5(  #!  2#+'#"-B 2#+'# 2#+'# 2#+'#"- 2#+'#"-B  #!"&!!'"/ !#!! *111#1#" @/"3"--A !'1-"!!'+ (+'" ('!!' !#! #!(' #"-#&&""+ !&+#+'#"- ( !1!( #!(' !**!#+ !#"+#+'# 5(  5"#+#+'#/!#!"-1#'1 +!""+-!  !$ 1#'1#" # 1#'1#" "!-#&&"1 1#'1-! "!#"#1 5(B  5"+#+'#/#1#'1"-/!#!/# #"+GH@C(A"-GH @C(A+'"5GD@(*A !#/**-&!#!/#BGH@C(A   +'"#"!/ (11"D @(*A +'"# (&! +'"#"!/ 1"D @(*A  #!"&!!'"/ 1#!#(! +'" )!#"+(" +'"#1!// 2'"+"+1# '1&!(!#- 1#'1%('+ +'"#"- >!((!+'"'- '*#"1#'1 &'()&*+(,)+-**'",.) ),/)+/&)&, # '0,& Figure 3.6:Item 9with additional second tier post Interview Study. Resistors as Power-Source is chosen to be added as a measured concept due to it being the most often occurring unmeasured conception that is not either an argument pattern (sharing, geometry or halving) or a more general difficulty (electricity † cluster term). This conception is tested with both resistors and lightbulbs. In Item 2, shown in Figure 3.7, the word current is used instead of power as the question asks about current specifically in order that more testwise students do not see it as the odd answer out, using the word power. We would expect this to be acceptable as learners using this conception also exhibit the electricity † cluster term. Item 13 follows a similar pattern, but resistor R2is swapped instead. In Item 24, shown in Figure 3.8, we are free to use the word ‘power’ in the distractor, without looking like the odd answer out. The phrasing is deliberately chosen to sound colloquial, to reflect the social language of the alternative conception, as shown by the learners. The Giving-Taking-Requiring idea is tricky to develop answer patterns for due to its proximity in meaning to Current Use. For this reason, it 114 talking circuits       <!11' >!(/' ' 5(  +#+'#/#1#'1"-/!#!/##"+G H@C(A"-GH@C(A+'"5GD@(*A #/**-&!#!/#BGH@C(A  +'"#(11"D@(*A +'"#(&! +'"#1"D@(*A  #!"&!!'"/ 1 #!# (!+'" )!#"+ (" +'"#1!/ / 2'"+" +1# '1&!(! #- 1#'1 %('+ +'"# "- >!((! +'" '-'*#" 1#'1 &'()&*+(,)+-**&",.) ),/)+/&)&, # &0,& Figure 3.7:Item 2with additional second tier post Interview Study.   F F   5(B  +#+'##'#1&!(#!"-"((((!/'+'"@*#+'!"#A " 5# 5( 5(11'"!4! <!+'"&1!/   /!#!"-(! +'""!" 5#(! +'"(#"( +'"#-! !#!!##1- +""!*' ('++'"&! !'!#! #"!!" "!'!+'" !'!#! 5(D  ) " ! %&' #'11!/# #'11!/# #'1B1!/# #'1"-1!/# #'1"-B1!/#  #!"&!!'"/ "-*!/+! "-B(-#"+ /&!( (!+'"" ! #!+#+'#-"-"-B (!1!( B11+'"&!(  +'"#-/" "- 5(  5"+#+'#!#/!#!"-1#'1+!""+-! #$!" 1#'1#"# 1#'1#""!-#&&"1 1#'1-!"!#"#1 &'()&*+(,)+-**-",.) ),/)+/&)&, # -0,& Figure 3.8:Item 24 with additional second tier post Interview Study. was tested both in situations where it is in direct opposition to the idea of Current Use (e.g. Item 2, Figure 3.7), as well as where the Current Use idea would not change the answer (e.g. Item 16, Figure 3.9). The answers all use the word “need” and, again, necessitate the use of current so as not to be perceived as different by testwise learners. The answer options to Item 16 must also be sufficiently vague to not enable learners to scaffold their answer to the numerical part of the question. verifying testing materials 115       B5(D B #+#!#"*#+'!"##"!+!I "- "-B <!"!&#!*111!"! "-B D5( D 5"+#+'#!"#/!#!"-1#'1+!""+-! #$!" 1#'1#"# 1#'1#""!-#&&"1 1#'1-!"!#"#1 5( 1#'1#"*#+'11( !1+'"#@(*A  #"#!#% ,3(*1!/#"!/!#"@(*A0  2'"5G    2'"5G   B 2'"5BG   D #!"&!!'"/ 111#'1"- ((!'"!& +'"&!(  5B#+1!! (!+'" +'"*1# "1+ "+#"+#+'# !1 -#&&"+# (!11 '1!# +'"!'( &'()&*+(,)+-**(",.) ),/)+/&)&, # (0,& Figure 3.9:Item 16 with additional second tier post Interview Study. In testing for the Current-Distance conception, it was judged important to test in a variety of situations: parallel (Item 16, Figure 3.9), series (Item 22, Figure 3.10) and short circuits (Item 24, Figure 3.8). Additionally, including an answer which demonstrates both the idea that current reduces with distance and the same rule in obverse i.e. points at the same distance (from the battery) have the same current flowing through them, as in Item 22. Item 22 was chosen as it is the only item where current is assessed at equidistant points from the battery, where there is not the possible confusion due to use of ammeters. Two answers were added to the second tier, shown highlighted in blue in Figure 3.10. Current could not be organically added to the answer so, in order to make that answer less conspicuous to testwise learners, another answer option was added referring to points A and B, reflecting the Clashing Currents conception. There is also a possible, already existing, answer combination for this conception in Item 21. A full list of cases for diagnosing conceptions with additions is given in Appendix A.3and assessed in Section 3.3. 116 talking circuits   E E   5(  #&'   ! 2#+'# 2#+'# 2#+'#B 2#+'#"- 2#+'#"-D  #!"&!!'"/ !#!! *111#1#" @/"3"--A !'1-"!!'+ (+'" ('!!' !#! #!(' #"-#&&""+ !&+#+'#"- ( !1!( #!(' !**!#+ !#"+#+'# E5( E 1#'1#"+#+'#!"##1!/#"  ( +'"## "= +'"## =" +'"# ("-= E #!"&!!'"/ +'"# (#"#+#+'# "-= (-#"+&!(  2'"+"! "-=&!(! #-!& 1#'1''* !(!&+'" 1#'1' '*11!&+'" F5( F !!%+#+'#1!/  =!1#'11!/1!/#" =!1#'11!/1!/#" =!1#'11!//#(#" 1!/-!"! 1!/-!"! F  ''*11+'" #"!(!+'"1&&! ''*!(!&+'" >!#1+'"1&&! +'"#(#" /!1+#+'# +'"#-/" !1#'1"1 #+1!!>! #(!+'" &'()&*+(,)+-**2",.) ),/)+/&)&, # 20,& Figure 3.10:Item 22 with additions to the second tier post Interview Study, new options highlighted in blue. In a subsequent iteration (post interventional study) and in an ongoing project, Denkey Concepts, adapting this questionnaire into Japanese. Three items examining learners’ understanding of open and closed circuits were added. This is a key learning outcome in the primary curriculum in England 285 , Wales 286 and Japan 287 . This makes questions on this topic essential for examining the understanding of pre-instruction learners at early secondary and may contribute to alleviating some of the floor effects of the test with expectedly easier questions. 285 Department for Education [2013] 286 Addysg Cymru [2020] 287 Monbu-kagaku-sh¯ o [2017] verifying testing materials 117 3.3Statistical Methods for Questionnaire Analysis In addition to the cognitive laboratory interviews for ensuring test quality, I also present the following quantitative data analysis regarding the use of the testing materials for future research. A range of methods are used to address particular aspects of reliability and suitability. Of special interest is the difficulty of the test, both in reflecting the content taught and with regards to the suitability of the method of seeking spoken elaboration in testing for difficulty. As, when learners are encouraged to self-elaborate, this has been shown to improve outcomes 288 , but this is a meta-cognitive skill that not all learners (particular at ages 12-13) will have developed to do internally. Hence, in-situ test score difficulty will be higher than during cognitive laboratory interviews. 3.3.1Examining Sub-Scales with Factor Analysis Following Engelhardt [1997], I perform a factor analysis to identify “select groups of items that all appear to measure the same idea” 289 . Engelhardt [1997] gives very little information on how her factor analysis was completed, except for that it was analysed with the “Little Jiffy” criterion, i.e. factors are kept if their eigenvalue is over 1. School 1School 2School 3Total EG1 146 (6)136 (5)44 (2)326 (13) EG2 125 (6)122 (6) Total 444 (19) Table 3.9:Number of Participants included in Factor Analysis, total number shown per school, per experimental group (EG). Number shown in brackets shows number of classes. Here, I take the post test results 290 from all schools in both intervention groups, numbers of learners and classes are shown in Table 3.9. Student answers to the redeveloped test are marked in two different ways. 288 Chi et al. [1994b] 289 Huffman and Heller [1995, p. 137] 290 In line with Huffman and Heller [1995]. 118 talking circuits Firstly, using the new rubric. This means any additional tiers to the questions are included in the marking scheme for assigning if the question is marked correctly. For example, Item 16-d is added as an additional tier in the redeveloped test. In contrast, tests marked with the old rubric will mark Item 16 correct regardless of the answer to the final part in Item 16291. For Item 22292, where new answer options are added, questions are marked as NA if they contain a new answer option, and hence, not counted when making the tetrachoric table for the factor analysis. The new rubric is only marked as correct if all the parts (both original and redeveloped) are correct. As we expect there to be correlation between the factors (showing some underlying understanding of the topic as a whole), an oblique (non-orthogonal) method is used here, oblimin , and a maximum likelihood optimisation. 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 Component Number Factor Eigenvalue New Old Figure 3.11:Screeplots showing post-test results the adapted test, but marked using the old and new marking criteria. The black horizontal line at y=1 represents the “Little Jiffy” criterion. 291 Refer back to Figure 3.9for details. 292 Refer back to Figure 3.10 for details. verifying testing materials 119 The screeplots for these two methods are shown in Figure 3.11. For the new rubric coded data, there is a clear “elbow” 293 at Component Number =3 . This also nearly corresponds to the cut off for the “Little Jiffy” criterion (component 4has an eigenvalue of 0.868 ). The data from the old rubric is, however, less clear cut. There appears to be two points where the gradient markedly changes, one at Component Number =2 and one at Component Number =4 . As results become significantly more difficult to interpret at Component Number =4 , introducing a factor consisting of only two items, which accounts for only an additional 4% of the variance, it is ignored. Factor weightings for each question with each rubric where then calculated, all of those larger than 0.4294 , are shown in Table 3.10. Both sets of factors give results that can be interpreted similarly. In both cases factor F1seems related to the questions that ask the relationship between current and resistance (corresponding to an a priori topic “I/R” in the table). Factor 2asks about other properties of current, specifically current conservation (corresponding to an a priori topic “I” in the table) and involve exclusively lightbulbs rather than resistors. Factor 3relates to voltage (corresponding to an a priori topic “V” in the table and branching (including parallel) circuits, this is shown by the column “Branching”). The weighting split of I16 is of particular interest, as it is both on the topic of current conservation and a branching circuit, the dual loading is, in fact, desirable. I6and I27 both contain possibly unfamiliar apparatus, motors and a variable resistor respectively. This may contribute to their poor correlation to other items, again as Factors 1and 2split along lines of what the circuits contain, lightbulbs only (Factor 2) or resistors (Factor 1). I7is only one tiered, containing a branching circuit of only light bulbs and the only question on current to contain a switch. This makes it difficult to categorise and comparatively easy to guess, perhaps, why it is not found consistently in one factor. 293 Where the “scree” begins and the “mountain” stops, hence the name screeplot. 294 Hair et al. [2010] state that there is a judgement call to be made on the cutoff to be used for factor loadings. In this case, all loadings between 0.3 and 0.4 are shown in the table for completeness. The largest loadings for low loading questions are also shown. 120 talking circuits That the above threshold factor weightings are found more consistently within these a priori categories for the new rubric, evidence the fact that additional tiers will ensure that questions probe a given topic and prevent guess work. Further to this, the other noted differences across the factors evidence the importance of which components seem to be in the questions and the fact that branching circuits are interpreted by learners differently. 3.3.2Test Internal Consistency Following Pe¸sman and Eryılmaz [2010], among others, Cronbach’s α is used as a measure of internal consistency for the test. Similarly to Section 3.3.1, n=444 post-tests are used from across 19 classes, each with 26 items. The overall Cronbach’s alpha of the new test is αFull, New =0.745 , described as acceptable, i.e. 0.7 ≤α<0.8295 . As marking with the old rubric produces NaN values in Item 22 and ignoring them would bias the Cronbach’s alpha, due to the fact that it is calculated via the variance of each item and variance is dependant on n . For this reason in order to compare the answers from the two marking rubrics, Item 22 is simply excluded. Performing this calculation gives, α!I22, New =0.735296 and α!I22, Old =0.716 , the new marking rubric giving a marginal increase in internal consistency. Using the cocron package 297 , these are determined to be significantly different ( p=0.003 ), i.e. the internal consistency of the new marking rubric is significantly higher than that of the old. Gardner [1995] emphasises the importance that Cronbach’s alpha should only be used when a scale is used to measure one construct. Here, it could be argued, that a single construct could be a single factor, or that “understanding of simple electric circuits” counts as a single construct. There are examples shown in Taber [2018b] that show practice in Science Education Research of reporting Cronbach’s alpha for more disparately connected knowledge areas than those included here. Hence, for com295 Nunnally and Bernstein [1994] 296 !I22 means excluding item 22. 297 Diedenhofen and Musch [2016] verifying testing materials 121 Old New Branch Topic F1F2F3Change F1F2F3 I2I/R 0.717 T0.709 I3I/R 0.500 0.621 I4I0.581 0.546 I6I/R (0.244) (0.184) I7Y I (0.185) (-0.184) (0.126) I9Y P -0.486 T0.437 I10 I/R 0.549 0.467 I13 I/R 0.794 T0.745 I14 Y P 0.576 0.514 I15 I/R 0.559 0.683 I16 Y I 0.669 T (-0.300)0.541 0.463 I20 Y P 0.574 T (0.353) I21 I0.497 0.543 I22 I0.798 O0.710 I23 I/R (0.386)0.510 I24 Y I (0.358) T 0.605 I25 I/R 0.657 0.744 I26 I/R 0.419 0.547 I27 I/R 0.421 0.518 0.565 (0.381) I28 I0.623 0.690 I29 I/R 0.421 0.552 I30 Y P (0.381) T (0.242) I311 V0.498 0.614 I312 V0.970 0.916 I321 V0.686 0.829 I322 V0.462 0.445 Table 3.10:Factor Weightings for Exploratory Factor Analysis for old and new rubrics. Branching shows questions containing branching circuits. Changed shows additions of Tiers (T) or Options (O). All weightings over 0.4 are shown, weightings above 0.3 as well as the highest weightings of below threshold questions are also shown in brackets. 128 talking circuits −2 0 2 4 −2−101234 Beta for Sub-Group: Less Than Median Raw Scores Beta for Sub-Group: Greater or Equal to Median Raw Scores 7 14 15 25 9 27 30 20 24 4 6 Figure 3.14:Goodness of Fit Plot for the Old Rubric. −2 0 2 4 6 −2 0 1 2 3 4 27 Beta for Sub-Group: Greater or Equal to Median Raw Scores Beta for Sub-Group: Less Than Median Raw Scores −1 7 14 2 13 20 9 4 6 28 Figure 3.15:Goodness of Fit Plot for the New Rubric. For perfect alignment of item parameters between high and low scorers, items should lie along the diagonal, i.e. item parameters are the same in each sub-group. Each ellipse represents and item parameters and the errors for each group. Red circles show items whose error bars to not cross the diagonal. High contrast labels show items that do not meet a criteria in the Item Fit Statistics. Low contrast labels show acceptable Item Fit Statistics, but do not cross the diagonal. verifying testing materials 129 Both rubrics result in Andersen Likelihood-Ratio tests statistics that indicate significant differences in item parameters for high and low ability groups. This can be seen visually in Figures 3.14 and 3.15. These Figures display the item parameters and their respective errors for learners that score more than (or equal to) the median on the x-axis and less than the median on the y-axis. Essentially, this analysis splits learners into two groups with high and low concept knowledge on electric circuits. If there were to be perfect agreement between the item parameters, they would lie along the diagonal. The high contrast labels for both show the items with poor Item Fit Statistics, low contrast labels show items where the error does not overlap the diagonal, but they have acceptable Item Fit Statistics. It is apparent from Figures 3.14 and 3.15 that there is a strong overlap of the groups. In other words there is strong overlap between items with poor Item Fit Statistics and those that show strong variation between groups, either that violate the crossing condition or are very close to doing so. I take this as the final piece of evidence that the test is not suitable for Rasch scaling. However, whether it is desirable is another question. From development of the test, one may have assumed that the test would be Rasch scalable, i.e. that a unidimensional “concept understanding” measurement scale can be established 303 and this may be the case if we are truly able to measure concept knowledge,. However, once a particular topic had been comprehended with sufficient span, it should be able to be applied across items. Simply put, two learners with the same “concept understanding” and sufficient span would perform equally well across the set of questions. However, in a test that is specifically developed on the basis of alternative conceptions, two learners with identical person parameters could feasibly find it easier or more challenging to answer groupings of given questions that align with different alternative conceptions. Hence, violating the invariance condition necessary for Rasch analysis. Ivanjek et al. [2021]’s test, also framed around alternative conceptions, returns excellent item fit statistics despite this. This could imply that a spread of difficulty, better matching the learners, could overcome this hurdle and that a weak 303 Planinic et al. [2019] 130 talking circuits co-correlation between items testing for given alternative conceptions make these possible sub-scales tolerable to the Rasch scaling process. Researchers wishing to use the test presented here further, may wish to implement it with older or higher ability learners. Or, if using it with lower secondary, add easier questions to improve the usability of the data that this test provides. On the basis of the marginal changes and the failure of both rubrics to meet necessary criteria, it is impossible to evaluate the differences between each of the rubrics on the basis of Rasch results. 3.3.4Using Confirmatory Factor Analysis to Assess Misconceptions Following Urban-Woldron and Hopf [2012], the test that my translation originally stems from, a confirmatory factor analysis (CFA) for each of the coded for alternative conceptions was carried out. This was done using the lavaan package 304 . The model parameters are given in Table 3.14. Of note here is that it is only possible to give goodness of fit parameters for models with four or more items coding for an latent variable. This is because there are no degrees of freedom remaining in a configuration lower than that and it essentially becomes a “three equations with three unknowns” problem, so no optimisation is necessary. It can, however, be the case that no solutions exists, as with the case of no conversion in the case of the “geometrically parallel confusion” and the “current impelled by resistances” latent variables. 304 Rosseel et al. [2024] verifying testing materials 131 Alternative Conception Abbr. Item nConv. SRMR CFI RMSEA [90% CI] Current Use CU 4 702 ✓0.020 0.918 0.030 [0.000,0.087] A Battery is a Constant Current Source ABaCCS 4 754 ✓0.013 1.000 0.000 [0.000,0.065] Current is Independent of Resistance CIIR 4 780 ✓0.109 0.629 0.368 [0.327,0.411] Inverse Resistance IR 3 782 ✓- - - Higher Resistance means Higher Current HTRHC 3 787 ✓- - - Local Argumentation LA 3 629 ✓- - - Sequential Argumentation SA 4 765 ✓0.020 0.901 0.028 [0.000,0.082] General Problems with Parallel Circuits GPRPC 4 750 ✓0.011 1.000 0.000 [0.000,0.064] Parallel Opposite Confusion POC 3 754 ✓- - - Geometrically Parallel Confusion GPC 3 743 - - - Resistors give Current RGC 3 764 ✓- - - Current Impelled by Resistances CIR 3 684 - - - Current and Proximity CP 3 677 ✓- - - Table 3.14:Table showing confirmatory factor analysis for all of the coded for misconceptions. “Conv.” gives whether the model converges. SRMR is “Standardized Root Mean Squared Residual”, CFI is “Comparative Fit Index”. RMSEA is “Root Mean Square Error of Approximation”. 132 talking circuits For the latent variables that can be modelled, all show acceptable fit parameters, except one, “current is independent of resistance”. Acceptable fit parameters are defined by Hu and Bentler [1999] as SRMR (Standardized Root Mean Squared Residual) <0.08 , CFI (Comparative Fit Index) >0.95 , RMSEA (Root Mean Square Error of Approximation) <0.06 , also stating that older publications recommend CFI >0.90 . As the RMSEA and SRMR conditions are tested by Hu and Bentler [1999] and provide robust rejection conditions alone, I feel comfortable in accepting slightly lower CFIs. In addition to model fits, CFA gives loadings. These give a measure similar to correlation of the latent trait and the measured item encoding. There are lots of available “rules of thumb” for evaluating sizes of these loadings, but the most widely used seems to be from Stevens [2009] at Loading >0.4 . Using this, all models will be considered and discussed. Note that models with poor fit or that did not converge, are not shown. Each diagram shows the factor loading for the given answer combination used to diagnose each alternative conception from Table A.1. verifying testing materials 133 0.30 0.24 0.30 −0.19 0.91 0.94 0.91 0.96 1.00 CU1 CU2 CU3 CU4 CU 0.24 0.35 0.44 0.16 0.94 0.88 0.81 0.97 1.00 ABCCS1 ABCCS2 ABCCS3 ABCCS4 ABaCCS Figure 3.16:Confirmatory factor analysis loadings for Current Use (CU) and A Battery is a Constant Current Source (ABaCCS) alternative conceptions. All factor loadings for current use codings are deemed to be weak, with CU4loading negatively (see Figure 3.16). In the answer options acting as distractors from CU1,CU2and CU3the option reads “The current is the same in the whole circuit”, whereas as a distractor from CU4the option reads “The current is the same in a series circuit”. As this is something often learnt rote during classes, this may act as a too strong a distractor to make the encoding of current use reliable. If the CFA is rerun with this item removed, the factors of the other items do not improve. One of the factor loadings for A Battery is a Constant Current Source is above the threshold value and the rest show weak positive loading (see Figure 3.16). The weakest loading occurs on a question that uses motors instead of resistances (as the rest do) This would understandably change the triggering of given misconceptions, weakening the loading. 134 talking circuits 0.24 0.47 0.33 0.94 0.78 0.89 1.00 IR1 IR2 IR3 IR 0.20 0.39 0.44 0.96 0.85 0.80 1.00 HTRHC1 HTRHC2 HTRHC3 HTRHC Figure 3.17:Confirmatory factor analysis loadings for Inverse Resistance (IR) and Higher Resistance means Higher Current Use (HTRHC) alternative conceptions. Inverse Resistance and Higher Resistance means Higher Current Use load positively onto all of the answer combinations (see Figure 3.17) and the interpretation of both is very similar, as the idea of the latter is the former concept, plus current use. The second (or why) answer in the combinations for IR1,IR2and IR3are the same as in HTRHC1,HTRHC3 and HTRHC2, respectively, partially explaining the similarities in their loadings. The higher loadings occur for Items 6and 23, corresponding to IR2and IR3and HTRHC3and HTRHC2, where a component is being added instead of swapped out. This is a misconception triggering factor that could be considered in future research. verifying testing materials 135 0.18 −0.08 0.48 0.97 0.99 0.77 1.00 LA1 LA2 LA3 LA −0.05 0.19 0.23 0.44 1.00 0.96 0.95 0.81 1.00 SA1 SA2 SA3 SA4 SA Figure 3.18:Confirmatory factor analysis loadings for Local Argumentation (LA) and Sequential Argumentation (SA) alternative conceptions. The scale of Local Argumentation is dominated by a loading onto the third encoding with weak and even negative loadings on the other factors (see Figure 3.18). Considering that LA2and LA3are single answer encodings that have a considerably higher type I (false-positive) error rate, would mean that I would recommend that the scale be entirely redeveloped on the basis of LA1.LA1works on the basis of numerical answer inputs for Item 16 and hence would be considerably more reliable to develop a scale around. The answer combinations for Sequential Argumentation are quite complex in order to account for learners holding the conception that current can flow in either direction - this, however, makes it more difficult to interpret the loadings, shown in Figure 3.18. Despite this, it is worth noting that the higher loadings are on encodings SA3and SA4, two answer combinations internal to a single item, compared to SA1and SA2, which rely on answers across multiple items and hence multiple contexts. 136 talking circuits 0.67 0.51 0.24 0.49 0.55 0.74 0.94 0.76 1.00 GPRPC1 GPRPC2 GPRPC3 GPRPC4 GPRPC 0.69 0.57 0.70 0.52 0.68 0.52 1.00 POC1 POC2 POC3 POC Figure 3.19:Confirmatory factor analysis loadings for General Problems with Parallel Circuits (GPRPC) and Parallel Opposite Confusion (POC) alternative conceptions. All factor loadings for General Problems with Parallel Circuits, apart from GPRPC3, load strongly onto a single variable (see Figure 3.19). However, this coding defined by Urban-Woldron and Hopf [2012], is essentially just the inverse of getting the answer correct, so does not really constitute a true alternative conception, making it difficult to interpret. Parallel Opposite Confusion constitutes the only latent variable loaded on highly by all answer combinations in its encoding (see Figure 3.19). The required answer combinations consist of a plausibly chosen set of circuits where the components are “opposite”, and the justification “The resistors must be opposite each other in the circuit”, for circuits containing resistors or light bulbs. This shows the high level of consistency of the surface level heuristic use when searching for parallel circuits and gives an indication for this being a consistently held alternative conception, measurable by this scale across the population. This also suggests that the teaching of identification of parallel circuits may need to be taught explicitly as this heuristic is ingrained across contexts. Resistors Give Current is loaded on strongly by the first two codes and only weakly positively by the third (see Figure 3.20). The RGC1&2both verifying testing materials 137 0.43 0.84 0.13 0.81 0.30 0.98 1.00 RGC1 RGC2 RGC3 RGC 0.41 0.11 0.07 0.83 0.99 0.99 1.00 CP1 CP2 CP3 CP Figure 3.20:Confirmatory factor analysis loadings for Resistors Give Current (RGC) and Current and Proximity (CP) alternative conceptions. use resistors in the questions, where as RGC3uses light bulbs. For this reason, I would recommend redevelopment of the scale exclusively on the basis of questions involving resistors. Current and Proximity, sometimes Current-Distance, is dominated by the loading on CP1(see Figure 3.20). As stated Section 3.2.11 the conception was tested for across a variety of situations: parallel (Item 16), series (Item 22) and in short circuits (Item 24). This variation of the physical context may have led to this lack of coherence, inline with Engelhardt and Beichner [2004] and Ivanjek et al. [2021]. 240 talking circuits A.1.2Question Pack 2 DRAFT DRAFT F25609U0P1PL0V0 28.04.2021, Page 1/6 evasys Electricity Thinking Aloud - Question Pack 2 Goethe-Universität, Frankfurt am Main Thomas Weatherby Department of Physics Education Question Pack 2 Mark as shown: Please use a ball-point pen or a thin felt tip. This form will be processed automatically. Correction: Please follow the examples shown on the left hand side to help optimize the reading results. 1. Item 10 1.1 In this circuit there are two resistors and a light bulb connected to a battery. If we keep R2 the same but decrease the resistance of R1, what happens to the brightness of the light bulb? The light bulb shines brighter. The light bulb shines no differently. The light bulb gets dimmer. 2. Item 13 2.1 In a circuit with a light bulb and two resistors with resistances R1 = 10 Ω and R2 = 10 Ω, there is a current I = 0.4 A. The resistor R2 is swapped for a resistor with R3 = 20 Ω. What happens to the current through the light bulb? The current is now smaller than 0.4 A. The current is the same as before. The current is now larger than 0.4 A. testing materials 241 DRAFT DRAFT F25609U0P2PL0V0 28.04.2021, Page 2/6 evasys Electricity Thinking Aloud - Question Pack 2 3. Item 29 3.1 In the circuit below two resistors and a light bulb are connected to a battery. If we keep R2 the same but increase the resistance of R1, what happens to the brightness of the light bulb? The light bulb shines brighter. The light bulb shines no differently. The light bulb gets dimmer. 4. Item 26 4.1 In the circuit below both light bulbs L1 and L2 glow with the same brightness. What happens to the brightness of both light bulbs if we increase the resistance R? L1 stays the same. L2 gets dimmer. L1 gets dimmer. L2 stays the same. L1 and L2 both get brighter. L1 and L2 both get dimmer. L1 and L2 both stay the same. 5. Item 28 5.1 In the circuit below the light bulb glows and the ammeter shows a current of 0.2 A. Now we put in a second Ammeter A2 on the other side of the circuit. What current does the ammeter A2 show? More than 0.2 A. Exactly 0.2 A. Less than 0.2 A, but not 0 A. 0 A. 5.2 Give a reason for your answer. The current is the same in the whole circuit. Some of the current gets used up in the light bulb. All of the current gets used up in the light bulb. 242 talking circuits DRAFT DRAFT F25609U0P3PL0V0 28.04.2021, Page 3/6 evasys Electricity Thinking Aloud - Question Pack 2 6. Item 14 6.1 Which resistors are connected in parallel to each other? R1 and R2. R1 and R3. None of the resistors are parallel to another. R2 and R3. 7. Item 23 7.1 A circuit is built from a battery, a resistor and an ammeter. The Ammeter shows us the current. What happens to the current on the Ammeter, when we add a second identical resistor R? It gets bigger. It stays the same. It gets smaller, but not zero. No current flows. 7.2 Give a reason for your answer. Two resistors need more current than one. It is the same battery, so the current remains the same. The current is shared over both resistors, so it is halved. The battery cannot push as much current as before through both the resistors. The battery is not strong enough to get any current through both resistors. testing materials 243 DRAFT DRAFT F25609U0P4PL0V0 28.04.2021, Page 4/6 evasys Electricity Thinking Aloud - Question Pack 2 8. Item 32 The following circuit is made from two identical light bulbs and a closed switch. How high is the voltage (potential difference): 8.1 Between points 1 and 2: . V 8.2 Between points 2 and 3: . V 8.3 Between points 3 and 4: . V Now we open the switch between points 1 and 2. How high is the voltage (potential difference): 8.4 Between points 1 and 2: . V 8.5 Between points 2 and 3: . V 8.6 Between points 3 and 4: . V 9. Item 2 9.1 In a circuit with a light bulb and two resistors with resistances R1 = 10 Ω and R2 = 10 Ω there is a current I = 0.4 A. The resistor R1 is swapped for a resistor with R3 = 20 Ω. How does this change the current through the light bulb? The current is bigger than 0.4 A. The current is the same as before. The current is smaller than 0.4 A. 244 talking circuits DRAFT DRAFT F25609U0P5PL0V0 28.04.2021, Page 5/6 evasys Electricity Thinking Aloud - Question Pack 2 10. Item 21 10.1 Look at the circuit on the right. How bright do the light bulbs glow? Both light bulbs glow. L1 glows brighter than L2. Both light bulbs glow. L2 glows brighter than L1. Both light bulbs glow with the same brightness. L1 glows. L2 does not. L2 glows. L1 does not. 10.2 Give a reason for your answer. L1 uses up all the current. There is no more current left for L2. L1 uses up some of the current. So, there is less current left for L2. The current is the same in the whole circuit. The current is shared between both light bulbs evenly. L2 is closer to the battery. So, it gets more current. 11. Item 6 11.1 A circuit is made from a battery and a motor. The motor is running (shown on the left). Then we add a second motor (shown on the right). What happens to current in the circuit? It gets bigger. It stays the same. It gets smaller, but not to zero. No current flows. 11.2 Give a reason for your answer. The battery is not strong enough to get any current through both motors. It is the same battery, so the current stays the same. The battery cannot push as much current as before through both the motors. Two motors need more current than one. The current is shared over both motors, so it is halved. testing materials 245 DRAFT DRAFT F25609U0P6PL0V0 28.04.2021, Page 6/6 evasys Electricity Thinking Aloud - Question Pack 2 12. Item 30 12.1 In which of the circuits are R1 and R2 connected in parallel to the battery? Circuits 1, 2 and 3 Circuit 2 Circuit 1 Circuits 1 and 2 Circuits 2 and 3 246 talking circuits A.1.3Question Pack 3 DRAFT DRAFT F25610U0P1PL0V0 28.04.2021, Page 1/6 evasys Electricity Thinking Aloud - Question Pack 3 Goethe-Universität, Frankfurt am Main Thomas Weatherby Department of Physics Education Question Pack 3 Mark as shown: Please use a ball-point pen or a thin felt tip. This form will be processed automatically. Correction: Please follow the examples shown on the left hand side to help optimize the reading results. 1. Item 25 1.1 In the circuit to the right two resistors and a light bulb are connected to a battery. If we keep R1 the same and increase the resistance of R2, what happens to the brightness of the light bulb? The light bulb shines brighter. The light bulb shines no differently. The light bulb gets dimmer. 2. Item 2 2.1 In a circuit with a light bulb and two resistors with resistances R1 = 10 Ω and R2 = 10 Ω there is a current I = 0.4 A. The resistor R1 is swapped for a resistor with R3 = 20 Ω. How does this change the current through the light bulb? The current is bigger than 0.4 A. The current is the same as before. The current is smaller than 0.4 A. testing materials 247 DRAFT DRAFT F25610U0P2PL0V0 28.04.2021, Page 2/6 evasys Electricity Thinking Aloud - Question Pack 3 3. Item 3 3.1 The resistor R1 in a circuit (shown on the left) has a small resistance. We swap that resistor with a resistor R2 with a higher resistance (shown on the right). What happens to the current in the circuit? It gets bigger. It gets smaller, but not to zero. It stays the same. No current flows. 3.2 Give a reason for your answer. The battery is not strong enough to get any current through the bigger resistance. The battery cannot push as much current as before through the bigger resistance. The bigger resistance needs more current than a smaller resistance. It is the same battery, so the current remains the same. 4. Item 21 4.1 Look at the circuit on the right. How bright do the light bulbs glow? Both light bulbs glow. L1 glows brighter than L2. Both light bulbs glow. L2 glows brighter than L1. Both light bulbs glow with the same brightness. L1 glows. L2 does not. L2 glows. L1 does not. 4.2 Give a reason for your answer. L1 uses up all the current. There is no more current left for L2. L1 uses up some of the current. So, there is less current left for L2. The current is the same in the whole circuit. The current is shared between both light bulbs evenly. L2 is closer to the battery. So, it gets more current. 248 talking circuits DRAFT DRAFT F25610U0P3PL0V0 28.04.2021, Page 3/6 evasys Electricity Thinking Aloud - Question Pack 3 5. Item 20 5.1 In which circuits (on the right) are the lightbulbs L1 and L2 connected in parallel to the battery? Circuit 1 Circuit 2 Circuit 3 Circuits 1 and 2 Circuits 1, 2 and 4 6. Item 6 6.1 A circuit is made from a battery and a motor. The motor is running (shown on the left). Then we add a second motor (shown on the right). What happens to current in the circuit? It gets bigger. It stays the same. It gets smaller, but not to zero. No current flows. 6.2 Give a reason for your answer. The battery is not strong enough to get any current through both motors. It is the same battery, so the current stays the same. The battery cannot push as much current as before through both the motors. Two motors need more current than one. The current is shared over both motors, so it is halved. testing materials 249 DRAFT DRAFT F25610U0P4PL0V0 28.04.2021, Page 4/6 evasys Electricity Thinking Aloud - Question Pack 3 7. Item 30 7.1 In which of the circuits are R1 and R2 connected in parallel to the battery? Circuits 1, 2 and 3 Circuit 2 Circuit 1 Circuits 1 and 2 Circuits 2 and 3 256 talking circuits DRAFT DRAFT F26098U0P5PL0V0 21.10.2021, Page 5/12 evasys Post-Test - Weatherby 10. Item 9 10.1 In which of the circuits are R1 and R2 parallel to each other? Circuits 1, 2 and 3 Circuit 2 Circuit 1 Circuits 1 and 2 Circuits 2 and 3 10.2 Give a reason for your answer. For resistors to be parallel their lines (when extended) should not touch. The same current must go through both resistors. The resistors must be in different branches of the circuit and have the same voltage over them. The resistors must be opposite each other in the circuit. 11. Item 10 11.1 In this circuit there are two resistors and a light bulb connected to a battery. What happens to the brightness of the light bulb if R2 stays the same and we make R1 smaller? The light bulb shines brighter. The light bulb shines no differently. The light bulb does not shine as brightly. 12. Item 13 12.1 In a circuit with a light bulb and two resistors with resistances R1 = 10 Ω (Ohms) and R2 = 10 Ω (Ohms) has a current I = 0.4 A (Amps). The resistor R2 is swapped for a resistor with R3 = 20 Ω (Ohms). What happens to the current through the light bulb? The current is now smaller than 0.4 A (Amps). The current is the same as before. The current is now larger than 0.4 A (Amps). 12.2 Give a reason for your answer. A larger resistor gives more current. More resistance means the current is lower everywhere. Current can reach the light bulb from both sides. The lightbulb takes as much current as it needs. Some more current gets used up in the light bulb. F26098U2145863008P5PL1V1 21.10.2021, Page 5/12 testing materials 257 DRAFT DRAFT F26098U0P6PL0V0 21.10.2021, Page 6/12 evasys Post-Test - Weatherby 13. Item 14 13.1 Which resistors in the picture on the right are in parallel to each other? R1 and R2. R1 and R3. None of the resistors are parallel to another. R2 and R3. 14. Item 15 14.1 In the circuit on the right two resistors and a light bulb are connected to a battery. If we keep R1 the same and decrease the resistance of R2 , what happens to the brightness of the light bulb? The light bulb shines brighter. The light bulb shines no differently. The light bulb does not shine as brightly. 15. Item 16 The light bulbs in the picture are all the same. The total current is 1.2 A (Amps). How large are the currents in the branches? Write the missing currents for I1, I2 and I3. Example showing how to fill in 12.05 A (Amps): 15.1 Current I1 = . A 15.2 Current I2 = . A 15.3 Current I3 = . A 15.4 Give a reason for your answer. All lightbulbs need the same amount of current from the battery. I3 is the closest so gets the most current. The current splits evenly at each branch in the circuit. As the voltage difference is the same over all the bulbs, so is the current through them. F26098U2145863008P6PL1V1 21.10.2021, Page 6/12 258 talking circuits DRAFT DRAFT F26098U0P7PL0V0 21.10.2021, Page 7/12 evasys Post-Test - Weatherby 16. Item 20 16.1 In which circuits (on the right) are the lightbulbs L1 and L2 parallel to the battery? Circuit 1 Circuit 2 Circuit 3 Circuits 1 and 2 Circuits 1, 2 and 4 16.2 Give a reason for your answer. For resistors to be parallel their lines (when extended) should not touch. The same current must go through both resistors. The resistors must be in different branches of the circuit and have the same voltage over them. The resistors must be opposite each other in the circuit. 17. Item 22 17.1 The light bulb in the circuit on the right is glowing. Which of these statements about the currents through A and B is true? The current is bigger at A than B. The current is bigger at B than A. The current is the same at A and B. 17.2 Give a reason for your answer The current is the same in a series circuit. A and B are the same distance from the battery. Current can get to A and B from both sides of the battery The light bulb uses up some of the current. The light bulb uses up all of the current. 18. Item 21 18.1 Look at the circuit below. How bright do the light bulbs glow? Both light bulbs glow. L1 glows brighter than L2. Both light bulbs glow. L2 glows brighter than L1. Both light bulbs glow with the same brightness. L1 glows. L2 does not. L2 glows. L1 does not. 18.2 Give a reason for your answer. L1 uses up all the current. There is no more current left for L2. L1 uses up some of the current. So, there is less current left for L2. The current is the same in the whole circuit. The current is shared between both light bulbs evenly. L2 is closer to the battery. So, it gets more current. F26098U2145863008P7PL1V1 21.10.2021, Page 7/12 testing materials 259 DRAFT DRAFT F26098U0P8PL0V0 21.10.2021, Page 8/12 evasys Post-Test - Weatherby 19. Item 23 19.1 A circuit is built from a battery, a resistor and an Ammeter. The Ammeter shows us the current (picture on the right). What happens to the current on the Ammeter, when we add a second identical resistance R? It gets bigger. It stays the same. It gets smaller, but not zero. No current flows. 19.2 Give a reason for your answer. Two resistors need more current than one. It is the same battery, so the current remains the same. The current is shared over both resistors, so it is halved. The battery cannot push as much current as before through both the resistors. The battery is not strong enough to get the current through both resistors. 20. Item 24 20.1 Compare the brightness of the light bulbs L1, L2 and L3 in both circuits (see diagram). Light bulb L1 glows the brightest. Light bulb L2 glows the brightest. Light bulb L3 glows the brightest. Light bulbs L1 and L2 glow the brightest. Light bulbs L1 and L3 glow the brightest. 20.2 Give a reason for your answer. L1 and L2 power each other. L1 and L3 are the same distance away form the battery. L2 gets more current than the others. L2 is short circuited and L1 and L3 have the same voltage over them. L3 gets all the current from the battery. The current is shared between L1 and L2. 21. Item 25 21.1 In the circuit to the right two resistors and a light bulb are connected to a battery. If we keep R1 the same and increase the resistance of R2 , what happens to the brightness of the light bulb? The light bulb shines brighter. The light bulb shines no differently. The light bulb does not shine as brightly. F26098U2145863008P8PL1V1 21.10.2021, Page 8/12 260 talking circuits DRAFT DRAFT F26098U0P9PL0V0 21.10.2021, Page 9/12 evasys Post-Test - Weatherby 22. Item 26 22.1 In the circuit below, both light bulbs L1 and L2 glow with the same brightness. What happens to the brightness of both light bulbs if we increase the resistance R? L1 stays the same. L2 gets dimmer. L1 gets dimmer. L2 stays the same. L1 and L2 both get brighter. L1 and L2 both get dimmer. L1 and L2 both stay the same. 23. Item 27 The circuit on the right is built from two Ammeters and a variable resistor. Both Ammeters show us the current. Now we increase the resistance R. 23.1 What happens to the current at Ammeter A1? It gets bigger. It stays the same. It gets smaller. 23.2 What happens to the current at Ammeter A2? It gets bigger. It stays the same. It gets smaller. 23.3 Give a reason for your answers. A larger resistor needs more current than a smaller resistor. It is the same battery, so it gives the same current. A bigger resistance means a smaller current everywhere in the circuit. A bigger resistance means a smaller current after the resistance. So, the current before the resistor does not change. A bigger resistance means a smaller current after the resistance. So, the current before the resistor gets bigger. F26098U2145863008P9PL1V1 21.10.2021, Page 9/12 testing materials 261 DRAFT DRAFT F26098U0P10PL0V0 21.10.2021, Page 10/12 evasys Post-Test - Weatherby 24. Item 28 24.1 In the circuit below the light bulb glows and the Ammeter shows a current of 0.2 A (Amps). Now we put in a second Ammeter A2 on the other side of the light bulb. What current does the Ammeter A2 show? More than 0.2 A (Amps). Exactly 0.2 A (Amps). Less than 0.2 A (Amps), but not 0 A (Amps). 0 A (Amps). 24.2 Give a reason for your answer. The current is the same in the whole circuit. Some of the current gets used up in the light bulb. All of the current gets used up in the light bulb. 25. Item 29 25.1 In the circuit below two resistors and a light bulb are connected to a battery. What happens to the brightness of the light bulb if R2 stays the same and we make R1 bigger? The light bulb shines brighter. The light bulb shines no differently. The light bulb does not shine as brightly. 26. Item 30 26.1 In which of the circuits are R1 and R2 parallel to each other? Circuits 1, 2 and 3 Circuit 2 Circuit 1 Circuits 1 and 2 Circuits 2 and 3 26.2 Give a reason for your answer. For resistors to be parallel their lines (when extended) should not touch. The same current must go through both resistors. The resistors must be in different branches of the circuit and have the same voltage over them. The resistors must be opposite each other in the circuit. F26098U2145863008P10PL1V1 21.10.2021, Page 10/12 262 talking circuits DRAFT DRAFT F26098U0P11PL0V0 21.10.2021, Page 11/12 evasys Post-Test - Weatherby 27. Item 31 Fill out the following two questions like in the example. The example below shows how you would fill in 4.25 V as an answer: Look at the following circuit. How high is the voltage (potential difference): 27.1 Between points 1 and 2: . V 27.2 Between points 2 and 3: . V 27.3 Between points 3 and 4: . V We now put another of the same light bulbs between point 3 and 4. How high is the voltage in the circuit with two light bulbs: 27.4 Between points 1 and 2: . V 27.5 Between points 2 and 3: . V 27.6 Between points 3 and 4: . V F26098U2145863008P11PL1V1 21.10.2021, Page 11/12 testing materials 263 DRAFT DRAFT F26098U0P12PL0V0 21.10.2021, Page 12/12 evasys Post-Test - Weatherby 28. Item 32 The following circuit is made from two identical light bulbs and a closed switch. How high is the voltage (potential difference): 28.1 Between points 1 and 2: . V 28.2 Between points 2 and 3: . V 28.3 Between points 3 and 4: . V Now we open the switch between points 1 and 2. How high is the voltage (potential difference): 28.4 Between points 1 and 2: . V 28.5 Between points 2 and 3: . V 28.6 Between points 3 and 4: . V F26098U2145863008P12PL1V1 21.10.2021, Page 12/12 264 talking circuits A.3Table Showing Codes in New and Redeveloped Tests Case 1Case 2Case 3Case 4 Current Use I21: A1B2or A2B5I4: A1B2or A3B2I28: A3B2or A1B2I22: A1B2or A2B2 A Battery is a Constant Current Source I3: A3B4I27: A2B2C2I23: A2B2I6: A2B2 Current is Independent of Resistance I25: B2and I29: B2I10: A2and I15: A2I10: A2and I25: B2I15: A2and I29: B2 Inverse Resistance I3: A1B3I23: A1B1I6: A1B4 The Higher the Resistance, the Higher the Current I3: A2B3I6: A3B4I23: A3B1 Local Argumentation (Looking at Individual Points on the Circuit) I16:I1,2 =0.3A,I3=0.6AI7: A2I24: A3Redundant I16: B3 Sequential Argumentation (Going Through Components Step-by-Step) (I10: A2and I29: B2and I15: A1and I25: B3) or (I10: A1and I29: B3and I15: A2and I25: B2) (I2: A1and I13: A2) or (I2: A2and I13: A1)I27: A2B3C4I26: A1,2 General Problems Recognising Parallel Circuits I9: A2,3,4I20: A2I14: A1,2,3,5I30: A2,3,4 Parallel Opposite Confusion I9: A4B1I20: B1I30: A4B1 Geometrically Parallel Confusion I9: A1,2B4I20: A2B4I30: A1,4B4 Resistors give Current I2: A3B1I13: A3B1I24: A4B1 Current Impelled by Resistances I2: A2B4I13: A2B4I16:I1,2,3 =0.4Aand B1 Current and Proximity I16:I3>I1,2 and B2I22: A3B2I24: A5B3 Table A.1:Table Showing Alternative Conceptions in Answer Combinations. Below the vertical line midline marker are new answer combinations developed on the basis of chapter 3. B Vocabulary List B.1 List of Possibly Unknown Words used in “An Introduction to Electric Circuits” List of words rarer than rank 16,577 appearing in “An Introduction to Electric Circuits” and an explanation as to whether they are contained within the vocabulary list - this list can be seen in the booklet for EG2. Included in Vocab list. Root Word(s) Root Word Freq. Notes airflow Yes air, flow 376,2019 Literal compound of two common words. ammeter Yes - - Topic specific vocabulary. ampere Yes - - appliance Yes - - In the phrasal word "household appliance". attaches No attach 9565 Inflection of common verb. behaves No behave 6649 Inflection of common verb. bumping No bump 7670 Inflection of common verb. conditioners Yes, as air conditioner - - In the phrasal word "air conditioners" conduction Yes - - Topic specific vocabulary.conductive Yes - - conductors Yes - - 272 talking circuits Which of the diagrams shows the Light Bulbs lit up correctly? 1.2. 3.4. Which of the diagrams shows the Light Bulbs lit up correctly? 1.2. 3.4. Which of the diagrams shows the Light Bulbs lit up correctly? 1.2. 3.4. questions featured in “talking circuits”273 Which diagram shows the correct currents? 1.2. 3.4. Which diagram shows the correct currents? 1.2. 3.4. Which diagram shows the correct currents? 1.2. 3.4. Lesson Ten Rob thinks that the current measured by the ammeter with a “?” is less than 6A. He thinks that more resistors use up more current. What actually happens to the current? 1. More resistors do use more current. 2. More resistors make more current. 3. Regardless of how many resistors there are, the battery always gives the same current. 4. The current does get lower, but it’s not used up. 274 talking circuits Rob thinks that the current measured by the ammeter with a “?” is less than 6A. He thinks that more resistors use up more current. How would you explain where he’s got confused? 1. More resistors make more current, but only after the Ammeter. 2. Current works like a bike chain, it pushes energy around the circuit but does not get used up. 3. Even though there are more resistors, they come after the ammeter so nothing changes. 4. The battery provides as much current as it can, so it is always the same. What does the “?” Ammeter show? More or less than 6A? 1. More than 6A. 2. The same, 6A. 3. Less than 6A. 4. We need more information about the battery. What does the “?” Ammeter show? Without using V=IR. Write a number. [Numerical Input] Which explanation best fits how you got your last answer. 1. 6Ω means the Current is 6Amps. There are 12Ω in the second circuit, which means the Ammeter shows 12A. 2. The Resistance has doubled so the Current has doubled to 12A. 3. The Resistance has doubled so the Current has halved to 3A. 4. The battery is giving 6A. Lesson Twelve Choose the false statement about Potential Difference: Write the true statements in your booklet. 1. Is a difference in potential between two places in the circuit. 2. It can only exist if a Current is flowing. 3. Causes a Current to flow. 4. Is measured by a Voltmeter in Volts. Choose the false statement about Current: Write the true statements in your booklet. 1. Current is the amount of charge per second flowing around the circuit. 2. Current is measured by an Ammeter in Amps. 3. The amount of current flowing into a junction is the same as current that flows out. 4. Current gets used up in the light bulbs as it goes through. questions featured in “talking circuits”275 Choose the false statement about Resistance: Write the true statements in your booklet. 1. Resistance tell us how much a material interferes with the flow of electrons. 2. The higher the resistance, the lower the current. 3. The higher the resistance, the higher the current. 4. The Resistance of a component can be calculated by the Potential Difference over it, divided by the current through it. Choose the correct statement about a series circuit. 1. Electric potential drops bit by bit over the light bulbs in series. 2. Electric potential is the same everywhere in a series circuit. 3. Electric potential gets used up in a series circuit. 4. The light bulbs make the electric pressure in a series circuit. Choose the correct statement about a series circuit. 1. Electric Potential is the same in the whole circuit. 2. Electric Potential drops more over the resistance closer to the battery. 3. Electric Potential drops the same over the same resistance. 4. Electric Potential always drops by the same amount over a resistor. Choose the correct statement about a series circuit. 1. Electric Potential is the same in the whole circuit. 2. Electric Potential drops more over higher resistances. 3. Electric Potential drops less over higher resistances. 4. Electric Potential always drops by the same amount over a resistor. Choose the correct statement about a series circuit. 1. Each light bulb uses a bit of the potential up. 2. The sum of the potential difference over all of the resistors is always the potential difference from the battery. 3. The potential difference is lost to the atmosphere. 4. The battery changes the potential difference it gives depending on the resistances. D Additional Figures and Tables D.1Inter-item Correlations 1 0.42 0.03 0.23 0.5 0.28 0.14 0.29 0.23 0.27 0.22 0.2 0.12 0.01 0.19 0.1 −0.02 0.16 −0.06 0.01 0.11 0.09 0.1 0.1 0.1 0.02 1 0.08 0.18 0.32 0.27 0.19 0.32 0.12 0.13 0.25 0.15 0.06 0.01 0.16 0.15 0.02 0.13 −0.03 0.02 0.01 0.09 0.08 0.03 0.11 −0.02 1 0.06 0.03 −0.01 0.13 0.08 0.12 0.04 0.04 −0.06 0.03 −0.03 −0.02 0.01 0 0.04 0 −0.01 0.07 0 −0.06 −0.02 −0.02 −0.03 1 0.22 0.31 0.09 0.25 0.11 0.14 0.14 0.08 0.07 −0.01 0.16 0.14 −0.02 0.1 0.03 0.03 −0.03 0.11 0 −0.05 −0.05 0.09 1 0.31 0.22 0.4 0.3 0.3 0.25 0.18 0.08 0.02 0.21 0.14 −0.03 0.17 0.05 0.06 0.13 0.13 0.09 0.12 0.12 0.04 1 0.19 0.31 0.21 0.25 0.23 0.06 0 −0.01 0.16 0.07 0.04 0.14 −0.06 −0.02 0 0.03 0.13 0.08 0.08 0.05 1 0.25 0.2 0.21 0.26 0.14 −0.05 −0.03 0.07 0.02 0.11 0.2 0.04 0.09 0.04 0.08 0.01 −0.02 −0.02 −0.04 1 0.29 0.24 0.37 0.09 −0.01 0 0.18 0.15 0.03 0.21 −0.04 −0.03 −0.04 0.09 0.03 0.03 0.1 0.11 1 0.26 0.29 0.14 0.01 0.01 0.13 0.12 0.01 0.15 0 −0.01 0 0 −0.01 0.03 0.03 0.02 1 0.18 0.21 0.04 0.09 0.19 0.15 −0.04 0.24 −0.04 0.01 0.07 0.09 0.05 0.12 −0.02 −0.03 1 0.11 −0.03 0 0.12 0.18 0.03 0.17 −0.04 0.05 0.04 0.05 0.11 0.1 0.1 0.15 1 0.03 0.05 0.23 0.33 0.05 0.26 0.01 0.03 0.09 0.12 0.01 0.09 0.09 0.05 1 0.03 0.03 −0.02 0.08 −0.01 0.03 −0.06 0.1 0.02 0.06 −0.03 −0.03 0.05 1 0.11 0.09 −0.01 0.1 −0.01 −0.02 −0.02 −0.02 −0.02 −0.01 −0.01 −0.01 1 0.26 0.07 0.27 −0.03 0.02 −0.03 0.03 0.05 0.06 0.06 0.07 1 −0.02 0.34 −0.08 0.03 0.02 0.11 0.11 0.12 0.04 0.04 1 −0.01 −0.02 0.08 −0.04 0 0.12 0.2 0.2 −0.02 1 −0.03 0.08 0.03 0.14 0.01 0.05 0.14 0.06 1 −0.04 −0.04 0.07 0.06 −0.01 −0.01 −0.02 1 0.08 0.11 0.06 0.27 0.13 0.06 1 0.25 0.1 0.11 −0.02 0.14 1 −0.01 0.11 −0.02 0.05 1 0.17 0.17 −0.02 1 0.5 −0.01 1 −0.01 1 −1−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Q2 Q3 Q6 Q10 Q13 Q15 Q23 Q25 Q26 Q27 Q29 Q4 Q7 Q16 Q21 Q22 Q24 Q28 Q9 Q14 Q20 Q30 Q311 Q312 Q321 Q322 Q2 Q3 Q6 Q10 Q13 Q15 Q23 Q25 Q26 Q27 Q29 Q4 Q7 Q16 Q21 Q22 Q24 Q28 Q9 Q14 Q20 Q30 Q311 Q312 Q321 Q322 Figure D.1:Inter-item Correlation of each Item for the new Rubric Bibliography Amy Adcock. 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Quantitative Untersuchungen der Zusammenh¨ ange der Neigungen zu empathisierender und systematisierender Denkweise und Interesse an Physik ISBN 978-3-8325-6021-8 42.00 EUR (open access) Vollst¨ andige ¨ Ubersicht unter: https://www.logos-verlag.de/spcl Alle erschienenen B¨ ucher k¨ onnen unter der angegebenen ISBN direkt online (http://www.logosverlag.de) oder telefonisch (030 - 42 85 10 90) beim Logos Verlag Berlin bestellt werden. Studien zum Physikund Chemielernen Herausgegeben von Martin Hopf und Mathias Ropohl Die Reihe umfasst inzwischen eine große Zahl von wissenschaftlichen Arbeiten aus vielen Arbeitsgruppen der Physikund Chemiedidaktik und zeichnet damit ein g¨ ultiges Bild der empirischen physikund chemiedidaktischen Forschung im deutschsprachigen Raum. Die Herausgeber laden daher Interessenten zu neuen Beitr¨ agen ein und bitten sie, sich im Bedarfsfall an den Logos-Verlag oder an ein Mitglied des Herausgeberteams zu wenden. Kontaktadressen: Univ.-Prof. Dr. Martin Hopf Universit¨ at Wien, ¨ Osterreichisches Kompetenzzentrum f¨ ur Didaktik der Physik, Porzellangasse 4, Stiege 2, 1090 Wien, ¨ Osterreich, Tel. +43-1-4277-60330, e-mail: [email protected] Prof. Dr. Mathias Ropohl Didaktik der Chemie, Fakult¨ at f¨ ur Chemie, Universit¨ at Duisburg-Essen, Sch¨ utzenbahn 70, 45127 Essen, Tel. 0201-183 2704, e-mail: [email protected] Logos Verlag Berlin ISBN 978-3-8325-6008-9 Learning about electric circuits demands abstract thinking, new vocabulary and using concepts that contrast with learners’ prior knowledge. Drawing on helpful ideas from everyday experiences with pressure, such as bike tyres and balloons, and evidence from cognitive science, I present an accessible approach using the electron gas model for the first time in English. Building on the design principles of digital tools and collaborative learning, I designed a tablet-based system to scaffold small-group talk to foster conceptual change: “Talking Circuits”. This prompting tool enabled real-time assessment of student-student talk, so that lengthy and expensive collaborative learning interventions could be more easily implemented. In a comparative study of 228 learners, aged 12 to 14, I compared two conditions taught using the electron gas model: one using standard classroom materials and the second adding the “Talking Circuits” application. Concept knowledge and motivation were measured in preand post-tests. Results show no significant changes in learning outcomes. The only statistically significant, albeit small, changes were reductions in perceived competence. This tentatively points to the need for longer implementation timeframes and teacher professional development. Learning electricity is demanding; conceptual change likely needs more time than typical British timetables allow.