IV: SCIENCE AS A LANGUAGE

1 SCIENCE IN THE CLASSROOM, FOR EARLY CHILDHOOD AND PRIMARY EDUCATION TEACHERS IV: SCIENCE AS A LANGUAGE María José Gómez Díaz El CSIC en la Escuela, Vicepresidencia Adjunta de Cultura Científica y Ciencia Ciudadana Consejo Superior de Investigaciones Científicas (CSIC) María Pilar López Sancho Instituto de Ciencia de Materiales de Madrid (ICMM) Consejo Superior de Investigaciones Científicas (CSIC) José M. López Sancho Instituto de Física Fundamental Consejo Superior de Investigaciones Científicas (CSIC) [email protected] ABSTRACT This article proposes that science education in childhood can be conceived as the acquisition of a second language: the language of science. As noted in previous works, this language assumes the functions of Kantian categories of space, time, and causality, which allow both the representation of the world in the mind and the description of that representation. Within this framework, scientific knowledge can be understood as a symbolic system in which each signifier carries a double meaning: the semantic value, which identifies the observable, and the mathematical object that describes its behavior and transformations. These mathematical objects may be scalars, vectors, tensors, functions, or even more abstract structures such as transformation groups, since many physical laws are determined by symmetries that are precisely expressed through these groups. From this perspective, teaching science means teaching its own language—an evolved form of symbolic representation with its own grammar, the very instrument of scientific thought. As with natural languages, learning begins with simple associations between a word and an object and gradually progresses toward more complex structures, through experiments, the conceptualization of magnitudes, and mental simulations. Keywords: Science learning; Mathematical language; Mentalese; Universal grammar; Piaget; Galileo; Cognitive development. 2 1. INTRODUCTION Taking into account what has been presented in previous articles of this series, we now have the intellectual background necessary to propose an approach to teaching science in the early stages of education. Teaching consists of guiding students in the construction of a mental representation of the external world that, although simplified, incorporates the essential elements for it to function analogously to the real world. Einstein (1936) expressed this idea by stating that science is the recreation in the mind of a replica of that part of the world accessible to our senses, through intellectual structures invented by human beings. Within this framework, the analysis and organization of information that reaches the mind through the senses are carried out through mentalese (Fodor, J. A., 1975), the language of thought. If, in accordance with Galileo’s definition, we understand science as the representation in the mind of that part of the world that can be expressed through mathematical language, then scientific knowledge is built through a special language in which each signifier is associated, in addition to a concept, with a mathematical object—such as real numbers, complex numbers, or tensors—that defines and determines its behavior. Thus, teaching science is equivalent to teaching a language with its own characteristics. And, like any language, its learning must begin progressively and from early childhood, taking advantage of the critical stages of cognitive development. This process involves carrying out classroom experiments, conceptualizing magnitudes, and practicing mental simulations, conceived as exercises that facilitate the acquisition of this specialized language, which can be regarded as a true second language. 2. THE SPECIFIC LANGUAGE OF SCIENCE Once an agreement has been established on the meanings of knowledge, thought, intelligence, and learning (see previous articles in this series), we turn to Saussure (1916) to complement this theoretical framework, showing how verbal language makes it possible to connect the mental representations of different individuals. According to his theory of the linguistic sign, each person associates a signifier (the sound of a word) with a signified (the concept that has been internally constructed), housed within a neural network of the brain. When two people hear the same signifier—for example, yellow—each activates in their mind the corresponding concept, even if their sensory experiences of that color are not identical. In this way, language acts as a bridge between subjective representations, enabling the communication of ideas. However, since Galileo, the language of science has required an expansion of this system of signs (Galileo, 1623/1957). Let us recall the idea that the book of nature is written in mathematical characters, an idea that fostered the development of physics as the paradigm of rigorous science, meeting the most demanding criteria of truth. But, as a counterpart, scientific knowledge became restricted to the world of magnitudes, that is, to those quantifiable aspects of reality that can be measured and expressed mathematically through equations between measures, between numbers. 3 Extending this theory to the scientific sign, for example to the weight of a body, we observe that each signifier acquires a double meaning: a semantic one (the force with which the Earth attracts it), linked to the real world, and an operational one (it is a vector), which defines its nature as a mathematical object, existing only in our mind but determining its nature and the laws it obeys. This conceptual reorganization requires an educational process in which students learn to translate concepts from ordinary language into entities with mathematically defined behavior. This dual structure is extremely important and very interesting from the point of view of the philosophy of knowledge. If we want to distribute 100 euros (from the real world) among 20 people (also from the real world), we first bring the two numbers, 100 and 20, into our mind. There, we manipulate these numbers according to the mathematical rules of division, disregarding what those numbers represent, and obtain as a result the number 5. We conclude the process by bringing that number back into the real world and restoring its meaning as the amount of euros given to each of the beneficiaries. Let us analyze the process. The problem arises in the real world. The relevant magnitudes are determined, also in the real world: the amount to be distributed and the number of people among whom it is distributed. These magnitudes are then assigned their corresponding mathematical objects (real numbers in this case), which are treated according to their mathematical nature, stripped of their real-world meaning. Once the corresponding mathematical operations are carried out (in the world of ideas, Plato would say), we bring the result back to the real world, where they recover their identity (euros and people), thereby solving the problem. And all this is done using the scientific language (with two meanings) as the programming language of the brain. This process is common to all human activity, not only scientific but also mental. An architect designs in his mind the building he wants to construct. He does so by imagining it composed of straight lines, circles, rectangles, etc., all of them perfect geometric ideas. Once the problems involved in constructing a building have been resolved in his mind, he returns to the real world where he reproduces his idea with real materials, although the straight lines and circles will not, by any means, have the beauty and perfection they had in his mind. Beyond Galileo But fortunately, science does not remain confined to the world of magnitudes. For centuries, mathematics was understood mainly as the science of magnitudes. It was used to measure lengths, areas, or volumes in geometry, calculate times and velocities in physics, or solve numerical operations in arithmetic and algebra. That is, it was above all an instrument for working with quantities. However, in the 19th century, the French mathematician Évariste Galois (along with contemporaries such as Cauchy and Abel) introduced a radical idea: what is essential in mathematics is not so much the measurement or value of a magnitude, but the way in which mathematical objects relate to and transform into one another. From this idea was born the concept of mathematical 4 structure, which we find in examples such as symmetry groups, permutations, or set theory. This change was a genuine revolution because it expanded the field of application of mathematics. And, strictly following Galileo’s criterion of calling science that which can be expressed in mathematical language, the expansion of mathematics pulled the sciences along with it, increasing their field of application in unimaginable ways. From then on, mathematics was no longer only used to measure and calculate, but also to describe patterns and structures present in all sciences. In physics, for example, fundamental laws are formulated in terms of symmetries; in chemistry, group theory helps explain the shape of molecules; and in computer science, modern cryptography is based on algebraic structures. Thanks to this step, mathematics went from being a language limited to the quantitative to becoming a universal tool, capable of explaining how very different natural and technological phenomena are organized and function. All these considerations lead us to propose that, since language—in the sense proposed by Chomsky, Fodor, and Saussure—contains the very essence of the process of mentally representing the world, its union with mathematical language transforms it into a tool capable of organizing reality so that it can be represented in the mind, as well as describing it through a symbolic system that constitutes science. The language of science is science itself. Therefore, teaching science can be understood as teaching a second language capable of handling reality using Platonic ideas—such as vectors, wave functions, symmetries, rotations, groups, rings, algebras, etc.—which, despite being only ideas, determine the behavior of the real world. 3. TEACHING SCIENCE AS A LANGUAGE The considerations outlined above have led us, as stated, to identify scientific language with science itself and, consequently, to approach teaching science as if it were a second language: the language of science. With regard to content planning, nothing seems more natural than to follow the history of science, which is necessarily constructivist in itself, aligning paradigm shifts with the significant changes in students’ cognitive development—changes that are well known to teachers at these educational stages. 3.1. TEACHING SCIENCE AS A SECOND LANGUAGE According to specialists, there are two fundamental processes for learning a second language (L2): acquisition and learning. Acquisition occurs naturally and unconsciously when a child is immersed in an environment where the language is spoken, as happens in bilingual families or in migratory contexts (Krashen, 1982). Learning, by contrast, takes place when the child has already mastered a mother tongue and faces the L2 as another language to be consciously incorporated, mediated, and supported by the L1. 5 As for the teaching of science, no cases of acquisition by immersion have been documented, since it is unlikely that a child would grow up in a household environment dominated by scientific discourse. This contrasts with disciplines such as music—as in the case of Mozart—or the visual arts, where early and everyday exposure can indeed favor acquisition (Bruner, 1960; Gardner, 1983). However, if the teaching of an L2 (or of science as L2) begins between the ages of 3 and 7—the so-called “golden window” for language learning—it is possible to achieve native or near-native mastery, provided that exposure is sufficient. Between ages 7 and 12, although brain plasticity decreases, children can still attain high communicative competence and grammatical structure. From this perspective, we propose that science instruction should begin at the preschool stage, adapting to the logical-cognitive capacities of the students (López Sancho & Gómez Díaz, 2016). And, as with language learning, scientific exposure should not be limited to what the child already understands. As Vygotsky notes, children select their zone of proximal development from among the information they receive, choosing the stimuli that are meaningful to them in order to progress in their learning. In fact, when it comes to spoken language, no one would think of saying: Do not talk to the baby; she doesn’t understand because she doesn’t yet know how to speak. Everyone knows that one learns to speak by listening and speaking. Similarly, one learns to think scientifically by doing and seeing science in action, even before fully understanding it. By considering science as a symbolic system, we can clearly identify its basic components: concepts, magnitudes, structures, laws, models, and paradigms, which we have already discussed. Thus, when planning a teaching unit, we can identify its specific ontology, that is, the framework in which learning will take place, defined by the concepts that will be present. This identification allows for the design of didactic sequences in which students progressively discover—and at the same time enact—the processes of observation, experimentation, law formulation, and theory building, assimilating them as part of the scientific language with which to describe and structure experience. 3.2. THE CASE OF ARCHIMEDES’ PRINCIPLE For greater clarity, we will describe the method using the pedagogical resource of casebased teaching, applying it to Archimedes’ principle in relation to water. The principle (in reality an experimental law as well as the result of a thought experiment) constitutes an excellent example of scientific inquiry in school and provides great satisfaction to students when they come to understand the process of scientific discovery for themselves. As Bruner (1960) notes, the act of discovery awakens curiosity and generates intrinsic pleasure by revealing the cause-and-effect relationships hidden in nature. 6 Unfortunately, Archimedes’ principle often proves quite opaque to children when presented in its verbal, descriptive form, leading to situations where they can recite the statement from memory yet understand almost none of its words. The CSIC en la Escuela program proposes addressing the teaching of science by first giving meaning to the words—that is, to the ontology. This is equivalent to the construction, by the students, of the necessary concepts for meaningful learning, achieved through direct manipulation of real objects. From these concepts, students are guided toward the construction of progressively more abstract mental representations of reality, which are therefore more powerful in discovering and replicating the behavior of reality (López Sancho & Gómez Díaz, 2016; Novak, 1998; Piaget, 1970). 3.3. DETERMINING THE ONTOLOGY OF THE PROBLEM Let us now imagine a group of children who are not yet familiar with Archimedes’ principle. To prepare the lesson, the teacher must first study the formal verbal definition: When a body is immersed in water, the water exerts on the immersed body an upward vertical force (called buoyant force), whose value is equal to the weight of the volume of water displaced by the immersed body. As mentioned, we begin by identifying the ontology of the process: Physical entities (expressed as nouns) Body: material object with mass and volume. Water: a substance familiar to the students. Volume of displaced water: corresponds to the volume of the submerged body, since when introduced into the fluid it displaces an amount of water exactly equal to its own volume. To illustrate this, we may use a figurine to recreate the well-known story of Archimedes immersing himself completely (head included) in a bathtub filled to the brim, spilling an amount of water equal to his own volume. Vector: a mathematical object represented by an arrow, having magnitude (the length of the arrow), direction, and sense. Vectors are added according to the parallelogram rule, resulting in a vector whose effects are equivalent to those of the original vectors. Recall the case in which one donkey plus one donkey equals one and a half donkeys. Force: a concept or abstraction of something that produces a change in the state of rest or motion of bodies and which has the mathematical nature of a vector. Weight: the force exerted by gravity on a mass. Being a force, it also has the mathematical nature of a vector. 7 Causal or situational relations (expressed as verbs and prepositions) Vertical: a concept that should not be taken as universally understood. Submerged: the state of a body within water, either partially or totally immersed. Equilibrium: condition in which the forces applied to a body cancel out, so that the body, in this case, does not move. To bring these concepts into shared understanding—deconstructing misconceptions and constructing new knowledge where lacking—we prepare a container of appropriate size filled with water and a variety of objects: some that float, some that sink, and some that remain suspended midway. We may use natural items, such as fruits, and artificial ones such as plastic bottles (empty or filled with water), marbles, stones, caps, etc. What matters is that children can experiment with them, observe, compare, and, above all, acquire the concepts that form the ontology, necessary to understand the phenomenon of buoyancy. Next, in view of the container, we ask pertinent questions: What does it mean to float, to have buoyancy, to have weight? These concepts must be constructed from the actions and sensations of submerging floating objects or pulling them upward in the water—the basis of the well-known naïve formulation of Archimedes’ principle that “things weigh less in water.” Through this activity, the foundations are laid for building the shared scenario of the phenomenon (body, water, force, weight, buoyancy, etc.), necessary to collectively travel the path leading to scientific knowledge. We conclude this section by emphasizing that it is essential for the students and the teacher to share the same mental framework, with its ontology—the concepts involved in the phenomenon under study—and its epistemological dimension—the observations to be made and how they are to be made. With these concepts, some tied to real objects and others to mathematical entities, each student constructs in their imagination a personal space in which to represent the process that leads to Archimedes’ principle. The teacher’s art lies in ensuring that all these personal frameworks converge into a single shared one. It is in this mysterious, almost magical, common mental space— imagined and shared—that true teaching takes place. Only then can students’ mental representations connect with the teacher’s, establishing a common space of thought: the place where, strictly speaking, the extraordinary process of learning occurs. 4. OBSERVATION IS NOT THE SAME AS EXPERIMENTATION At the conclusion of our exploration, we clarify that observation is not the same as experimentation. In science, it is not enough to superficially observe what happens; an experiment is, in fact, the way in which scientists interrogate nature about what they 8 wish to know. Therefore, it must be carefully designed so as to corner nature (R. Gomer, 1979), so to speak, leaving it no choice but to respond clearly to the question we pose. 4.1. A QUALITATIVE EXPERIMENT FOR YOUNG CHILDREN To clearly distinguish between the effects of weight and buoyancy in this context, we propose the following experiment: we construct a kind of submersible hot-air balloon, formed by a small air-inflated balloon, attached with thick thread and adhesive tape to a transparent plastic cup serving as a basket. Several of these devices will be made with balloons of different sizes, allowing us to study the possible effect of volume on the system’s behavior in water. For pedagogical purposes, and to facilitate an initial understanding of the phenomenon, the following idealized model is adopted—as is the case with all scientific models. The total buoyant force is attributed to the effect of the balloon, disregarding the volume of the cup and the marbles; similarly, the entire weight is assigned to the set of marbles, ignoring the weight of the balloon and the air it contains. This simplification allows us to interpret the system as a model of opposing vertical forces (entirely real), each represented by a vector (a mathematical object): the buoyant force upward, applied at the center of the balloon, and the weight downward, applied at the center of the cup. Both forces will be represented by arrows whose lengths are proportional to their magnitudes, making it clearly visible which of the two predominates. We then place the balloon attached to the cup on the surface of the water, carefully submerging the assembly so that the cup is filled with water and completely immersed. We release it and begin to add small marbles one by one, counting their number if the students’ age allows. 9 It is important to observe that as the number of marbles increases—and with it the magnitude of the weight vector—the volume of the submerged part of the balloon also increases. This effect should be represented graphically by showing the lengthening of the buoyant force vector as the submerged portion increases. In any equilibrium situation (without external intervention), both vectors—weight and buoyancy—will always have the same length, since the balloon does not move. As more marbles are added, a point will be reached at which the system remains submerged, floating between two levels of water, in a more or less stable state of equilibrium. Adding one more marble will cause the system to sink to the bottom; removing one marble will cause it to rise toward the surface. If the marbles are too heavy to achieve this equilibrium, lighter objects such as 5or 10-cent euro coins or even paper clips may be used instead. At this stage, the advantage of having constructed devices with balloons of different sizes becomes clear. By comparing the size of the different balloons with the number of marbles each can keep floating midway, we can easily reach the conclusion that the larger the volume of the balloon, the greater the weight—or number of marbles—it can hold in equilibrium. We may thus deduce that buoyant force depends on the volume of the balloon. And since buoyancy is equal to the weight it manages to keep suspended (the number of marbles), we can state that the larger the volume of the balloon, the greater the weight it can support while floating. When a body, in this case the balloon, is submerged in water, the water exerts on the submerged body an upward vertical force (called buoyant force) whose value depends on the volume of water displaced by the submerged body (the balloon). To conclude, we wish to highlight once again that two clearly different types of entities were involved in the experiment: on the one hand, observable physical objects from the real world—such as the balloon, the water, the marbles, the cup, or the string—and, on the other, mathematical objects that exist only in our imagination – or in Plato’s world of ideas, as he himself would say, such as forces and vectors represented by arrows. And yet, it is precisely these mathematical objects that allow us to describe, explain, and predict the behavior of real bodies! Thanks to them, we can model natural phenomena, anticipate their effects, and grasp the deeper logic that governs the physical world. 16 Finally, the understanding of the new paradigm can be reinforced with linear polarization experiments, which can be easily carried out using accessible materials. In this way, students progressively assimilate the wave model without the need for mathematical formalism, while developing increasing metacognitive awareness of how scientific knowledge is constructed. Thus, teaching becomes not merely the transmission of content, but a guided reconstruction of the paradigm shifts that structure the history of scientific thought— shifts that can be reflected upon in order to examine the limits of validity and applicability of each theory. At the beginning of the 20th century, the discovery of the photoelectric effect by Hertz—the emission of electrons by certain metals when illuminated, which we have sometimes demonstrated in our courses—revealed a behavior that could not be explained by the wave model of light, introducing a new disequilibrium into normal science based on the wave theory of light. In 1905, Einstein proposed that light is composed of quanta, or discrete packets of energy, which we now call photons. This new model did not revive the old corpuscular idea, but rather introduced a paradigm entirely different from Newton’s. Whereas Newtonian corpuscles were classical material particles, with mass and well-defined trajectories, Einstein’s photons are quantum entities, massless, behaving like particles only at the moment of interaction, and whose energy depends on the frequency of light, not its intensity. The photon does not contradict the wave model but complements it within a new dual vision: light is neither particle nor wave, but something that behaves as a wave or as a particle depending on the question asked of it, depending on the experiment. This perspective on the nature of things—whose ultimate answer lies beyond our reach— marked a paradigm shift and opened the way to modern physics. 6. GENDER AND INCLUSION IN LANGUAGE Language is not only a means of communication but also a symbolic system that organizes experience and shapes the perception of reality. From the perspective of the Sapir–Whorf hypothesis, linguistic structure is not neutral: while it reflects the social world, it also molds it and constrains the possibilities of thought and action. Within this framework, the analysis of sexist language becomes highly relevant, since its persistence reproduces gender inequalities, limits the visibility of certain groups, and perpetuates hierarchical conceptions in social, professional, and cultural domains. 6.1. LANGUAGE AND THE ONTOGENY OF WORLD REPRESENTATION Changes in language cannot be understood as mere terminological substitutions but as genuine paradigmatic transformations. Just as in the scientific revolutions described by 17 Thomas Kuhn (1962), the introduction of new terms and concepts triggers a reorganization of the interpretative framework of reality. Similarly, in Piaget’s model of cognitive development (1936/1977), these processes resemble dynamics of disequilibrium and accommodation, in which preexisting schemes are questioned and reorganized. In the case of inclusion and gender, transforming the social reality represented by language necessarily requires transforming the conceptual structures that language itself embodies. Childhood represents a privileged stage for introducing such transformations. At this age, language acquisition—and with it, the conceptual universe it conveys—is especially permeable. Introducing inclusive language early in life makes it possible to construct more egalitarian worldviews and to interrupt the intergenerational transmission of sexist stereotypes. In professional and academic contexts, the use of expressions such as mankind, chairman, or housewife reflects and reinforces the traditional association between authority, competence, and masculinity, as opposed to caregiving and domestic roles traditionally assigned to femininity. Likewise, the distinction between actor and actress, or the perception of some professions as “male” (engineer, doctor) and others as “female” (nurse, secretary), shapes vocational aspirations and limits opportunities for personal and professional development. The gradual shift toward neutral forms—humankind, chairperson, firefighter, police officer, server—constitutes a linguistic mechanism that helps to mitigate the reproduction of stereotypes. This process is far from trivial: it has a direct impact on social cognition by modifying the reference frameworks that guide the attribution of roles and competences. Empirical evidence shows that sexist language contributes to structural phenomena such as the “glass ceiling,” understood as the invisible barrier that prevents women from reaching positions of power and prestige. Attributing women’s achievements to luck or external circumstances, rather than to their competence and effort, reveals a gender bias that undermines the social recognition of female ability. As Bourdieu (1991) argues, language functions as an instrument of symbolic power that legitimizes or delegitimizes social realities, and in this case, serves to reproduce inequalities in the distribution of resources, prestige, and opportunities. 6.2. SOCIAL INERTIA TO CHANGE The analysis of sexist language confirms that linguistic change is inseparable from social change. Transformations toward inclusive terminology must be understood as genuine processes of conceptual revolution, comparable to scientific paradigm shifts and to the cognitive restructuring that occurs during childhood development. The implementation of inclusive language in early education, as well as in professional and social contexts, not only corrects a linguistic asymmetry but also contributes to the construction of more egalitarian societies. Consequently, the study of sexist language cannot be reduced to a semantic issue; it constitutes a central field of inquiry for 18 understanding the symbolic mechanisms that sustain gender inequality and for designing strategies of cultural transformation. The modification of connotative biases does not occur automatically. On the contrary, it requires processes of re-signification that often involve social tensions comparable to those described by Kuhn (1962) in his analysis of scientific revolutions. Just as scientific paradigms resist change until a cumulative crisis of anomalies arises, social meanings frequently react with hostility to change, despite empirical evidence or criticism. Only through conflictive processes of cultural transformation is it possible to replace a dominant semantic network with an alternative one, as occurs in shifts of perspective on gender, class, or race. This analogy with Kuhnian paradigm shifts underscores the epistemological dimension of the struggle for meaning: it is not merely about naming differently, but about perceiving reality through new lenses. Language, thus conceived, does not simply mirror reality but actively participates in its reconfiguration. 6.3. SCIENCE CANNOT BE SEXIST Science, as a form of knowledge grounded in observation and experimentation, aspires to objectivity. Yet it is not immune to the social, political, and cultural contexts in which it is produced. Within the Western scientific tradition—with roots in the Aristotelian corpus—an androcentric bias has been perpetuated for centuries, systematically excluding women from the spaces of knowledge creation and transmission, both as subjects and as objects of inquiry. From the outset, women were denied access to schools, academies, and universities. They were not allowed to learn Latin, the lingua franca of science and culture, which excluded them from scientific discourse. Even the great thinkers who challenged established doctrines failed to recognize this structural injustice. The Enlightenment, the French Revolution, and the U.S. Constitution, despite their ideals of equality, ignored women’s rights. Some courageous voices, such as Mary Wollstonecraft (A Vindication of the Rights of Woman, 1792) and Olympe de Gouges (Déclaration des droits de la femme et de la citoyenne, 1791), denounced this exclusion, but they were silenced or, at best, ignored. It was not until the 19th century that some universities began admitting women, and suffragist movements paved the way toward greater social and political participation. During the 20th century, feminist thought sought to identify and reconstruct the role of women as active agents in the history of science, adopting different theoretical approaches, most of them neglected by official academia. In the 1970s, the first critical voices emerged, analyzing the construction of knowledge from a gender perspective. Sandra Harding (1991), Evelyn Fox Keller (1985), and Londa Schiebinger (1989, 1991), among others, considered gender as an analytical category that influences the ways in which knowledge is produced, communicated, and applied. Several authors demonstrated the necessity of addressing the history of knowledge through a gender perspective in order to approach reality more accurately. To 19 understand history without acknowledging the role of women is like trying to explain the functioning of a clock without considering some of the gears that make it work. Free from prejudices and cultural biases, many studies have highlighted the scientific contributions of women who were rendered invisible throughout history, denouncing the sexist assumptions of academia. For instance, Rosalind Franklin’s crucial X-ray diffraction images made possible the discovery of the DNA double helix, yet her role was long overshadowed by the fame of Watson and Crick. Similarly, Nettie Stevens identified the XY sex-determination system, but her discovery was attributed for decades to her male contemporaries. Lise Meitner, who provided the theoretical explanation for nuclear fission, was excluded from the Nobel Prize awarded to her collaborator Otto Hahn. More recently, Jocelyn Bell Burnell discovered the first radio pulsars, a breakthrough that earned the Nobel Prize in Physics in 1974—but it was awarded only to her male supervisor. These and many other cases illustrate how structural biases in academia have systematically marginalized women, despite their decisive contributions to the advancement of science. Including women’s scientific achievements in textbooks can help foster scientific vocations; but more importantly, it allows the narrative to align more closely with reality and, therefore, to be more credible. Presenting the success stories of women such as Marie Curie, awarded two Nobel Prizes in Physics and Chemistry; Rita LeviMontalcini, Nobel Prize in Medicine; or Jennifer Doudna and Emmanuelle Charpentier, Nobel Prize in Chemistry for the development of CRISPR gene-editing, provides powerful role models for girls who wish to become scientists, demonstrating that excellence and recognition are within their reach. Today, in the 21st century, we continue to face this problem from new interdisciplinary perspectives, recognizing that science is not neutral and that the full inclusion of women in research and teaching remains an unfinished task. The issue is highly complex, and it is essential to keep it in mind in education to avoid, even unintentionally, transmitting biased values that perpetuate the gender gap. 7. CONCLUSION This article has argued that science education should be conceived as the learning of a specific language, a second language that allows us to represent and understand reality differently from everyday language. As in any language, learning begins with simple fragments of experience, which can be translated into accessible words and concepts, and progresses toward more complex structures that require new meanings and symbolic tools to be expressed. The developmental process of individuals or societies throughout history can be imagined as the growth of the layers of an onion, where each new layer reveals a more detailed knowledge of reality. Each transition between layers implies a point of wonder, a form of cognitive disequilibrium—in Piaget’s terms—or a crisis, like those Kuhn described in scientific revolutions. These moments of strangeness should be 20 pedagogically leveraged as drivers of learning: they activate curiosity, foster distrust of students’ prior models, and push them to construct new explanatory frameworks. In the division we have proposed of the history of science according to its paradigms— which assign different meanings to apparently identical phenomena—light is first interpreted as a corpuscle in the Newtonian tradition, later as a wave in the theories of Huygens, Young, Fresnel, and Maxwell, and finally, in the 20th century, as a quantum entity with wave–particle duality, whose observed behavior depends on the type of experiment performed. If we could revisit this history in dialogue with the scientists of each era, we would need to use the same words with different meanings, in the same way that we use different forms of language to communicate with a three-year-old, a seven-year-old, a twelve-year-old, or a seventeen-year-old. Something similar happens with the electron: initially discovered as a particle, it was soon recognized to have wave-like properties, until the current quantum formulation, in which it is not a matter of “being” one thing or another, but of manifesting different properties depending on how it is observed. Thus, in both the historical evolution of science and in the cognitive development of individuals, paradigm shifts involve profound transformations in language and, therefore, in the categories with which we describe reality. Teaching science in this way is not about transmitting finished theories but about showing how they are built, when they apply, and why they change. The key lies in helping students understand that each theory has a field of validity, and that the value of a theory does not reside in its absolute truth, but in its usefulness within certain limits. To reach Mars, Newtonian mechanics suffices; but to build a transistor or a laser, we need quantum mechanics. To understand this is to understand the very nature of science: a language in constant evolution, modeling the world according to the questions we ask and the instruments we have to answer them. To conclude this series of articles, we would like to recall Carl Sagan’s words in an interview with Charlie Rose in May 1996, in which he delved into the critical role of science as a way of thinking and as a defense against deception and manipulation: “Science is more than a body of knowledge; it is a way of thinking. It is a way of skeptically interrogating the universe. If we are not able to ask skeptical questions, to interrogate those who tell us that something is true, to be skeptical of those in authority, then we’re up for grabs for the next charlatan—political or religious—who comes ambling along.” 8.- REFERENCES • Arago, F. (1819). Mémoire sur l’action des rayons du soleil analysés par le prisme. Imprimerie Royale. • Bruner, J. S. (1960). The process of education. Harvard University Press. • Carey, S. (1985). Conceptual change in childhood. MIT Press. • Carey, S. (2009). The origin of concepts. Oxford University Press. • Carnot, S. (1824). Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. Bachelier. 21 • Cassirer, E. (1923). Substance and function & Einstein’s theory of relativity (W. C. Swabey & M. C. Swabey, Trads.). Open Court. • Chomsky, N. (1965). Aspects of the theory of syntax. MIT Press. • Chomsky, N. (1980). Rules and representations. Columbia University Press. • Dehaene, S. (2020). How we learn: Why brains learn better than any machine… for now. Viking. • Einstein, A. (1905a). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 17, 132–148. • Einstein, A. (1905b). Zur Elektrodynamik bewegter Körper. Annalen der Physik, 17, 891–921. • Einstein, A. (1907). Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. Jahrbuch der Radioaktivität und Elektronik, 4, 411– 462. • Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 49, 769–822. • Einstein, A. (1936). Physics and reality. Journal of the Franklin Institute, 221(3), 349–382. https://doi.org/10.1016/S0016-0032(36)91047-5. • Feynman, R. P., Leighton, R. B., & Sands, M. (1965). The Feynman lectures on physics (Vol. III). Addison-Wesley. • Fodor, J. A. (1975). The language of thought. Harvard University Press. • Fox Keller, E. (1985). Reflections on Gender and Science. Yale University Press. • Fresnel, A.-J. (1818). Mémoire sur la diffraction de la lumière. Imprimerie Royale. • Galileo Galilei. (1623/1957). Il Saggiatore [El ensayador] (E. García Riaza, Trad.). Espasa-Calpe. • Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. Basic Books. • Galois, É. (1846). Œuvres mathématiques d’Évariste Galois (J. Liouville, Ed.). Mallet-Bachelier. • Harding, S. (1991). Whose Science? Whose Knowledge? Thinking from Women’s Lives. Cornell University Press.Hertz, H. R. (1887). Über einen Einfluss des ultravioletten Lichtes auf die elektrische Entladung. Annalen der Physik, 31, 983–1000. • Huygens, C. (1678). Traité de la lumière. Pierre van der Aa. • Jackendoff, R. (2002). Foundations of language: Brain, meaning, grammar, evolution. Oxford University Press. • Kant, I. (1781/2006). Crítica de la razón pura (M. González, Trad.). Alfaguara. • Krashen, S. (1982). Principles and practice in second language acquisition. Pergamon. • Kuhn, T. S. (1962). The structure of scientific revolutions. University of Chicago Press. • López Sancho, J. M., & Gómez Díaz, M. J. (2016). La ciencia en la escuela: Aprender investigando. El CSIC en la Escuela. • Maxwell, J. C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society of London, 155, 459–512. • Maxwell, J. C. (1871). Theory of heat. Longmans, Green. • Novak, J. D. (1998). Learning, creating, and using knowledge: Concept maps as facilitative tools in schools and corporations. Lawrence Erlbaum. 22 • Pearl, J., & Mackenzie, D. (2018). The book of why: The new science of cause and effect. Basic Books. • Piaget, J. (1970). La ciencia de la educación y la psicología del niño. Ariel. • Piaget, J. (1975). La equilibración de las estructuras cognitivas: Problema central del desarrollo. Paidós. • Pinker, S. (1994). The language instinct. William Morrow. • Poincaré, H. (1905). La valeur de la science. Flammarion. • Quian Quiroga, R. (2012). Borges and memory: Encounters with the human brain. MIT Press. • Saussure, F. de. (1916). Cours de linguistique générale. Payot. • Thomas, M. W. (2020). Teaching science as a second language: A constructivist approach. Routledge. • Schiebinger, L. (1989). The Mind Has No Sex? Women in the Origins of Modern Science. Harvard University Press. • Schiebinger, L. (1991). The Mind Has No Sex? (Revised edition). Harvard University Press. • Vosniadou, S., & Brewer, W. F. (1992). Mental models of the Earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535–585. https://doi.org/10.1016/0010-0285(92)90018-W. • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. • Young, T. (1802). The Bakerian Lecture: On the theory of light and colours. Philosophical Transactions of the Royal Society of London, 92, 12–48. https://doi.org/10.1098/rstl.1802.0004. PARADIGMS OF LIGHT AND THEIR CORRESPONDENCE WITH PIAGET’S STAGES Paradigm of light Cognitive stage (Piaget) Didactic description Corpuscular (Newton, 1704) Preoperational thought (2– 7 years) Intuitive explanation: light consists of particles traveling in straight lines. Suitable for everyday experience and concrete thinking. Wave (Huygens, Young, Fresnel, 1678–1821) Concrete operations (7–11 years) Use of analogies (water waves) to understand phenomena such as interference and 23 diffraction. Development of logical causality. Quantum (Einstein, 1905) Formal operations (12+ years) Light behaves as a wave or as a particle depending on the experiment. Requires abstract thought and handling of conceptual dualities.