Teaching Newton's second law in final year science classes: Exploring practical bridging-in-action

 Corresponding author: Ahodegnon Zéphyrin Magloire DOGNON Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0. Teaching Newton's second law in final year science classes: Exploring practical bridging-in-action Ahodegnon Zéphyrin Magloire DOGNON 1, *, Danhin Aimé Comlan KANFFON 1, Sègbégnon Eugène OKE 1 and Cyriaque Coovi SESSOU AHODEKON 2 1 Discipline Didactics Laboratory, University of Abomey-Calavi 2 National Institute of Youth, Physical Education and Sports, University of Abomey-Calavi. World Journal of Advanced Research and Reviews, 2025, 28(02), 186-203 Publication history: Received on 15 September 2025; revised on 24 October 2025; accepted on 28 October 2025 Article DOI: https://doi.org/10.30574/wjarr.2025.28.2.3612 Abstract When teaching a subject, all of the teacher's work must be part of a learning process for the student, i.e., bringing knowledge closer to the student so that they can effectively assimilate it and truly enter into the culture of the discipline. Therefore, in physics, the development of student activity materials, right up to their implementation in the classroom, must take into account a number of criteria, including the functioning of the discipline, in order to successfully bridge the gap between the subject matter and the learners. An analysis of the activity materials used by three teachers to teach Newton's second law in the final year of high school science shows that the work instructions (tasks or types of tasks) and the systems put in place do not allow students to move between the real and theoretical worlds using appropriate models. The work produced on the board only reinforced this observation, and the discourse concocted by these three teachers does not allow for the establishment of efficient interconceptual (or inter-concept) relationships that could promote a good understanding of the law. Keywords: Newton's Second Law; Bridging-In-Action; Interconceptual Relationships; Discourse Analysis 1. Introduction 1.1. Research problematization 1.1.1. Theoretical and conceptual framework Inclusion of this research in the dual didactic and ergonomic approach In this paper, we examine certain aspects of the construction and assessment activity materials developed by teachers, as well as their discourse during classroom practice. The teacher's work, before and during the activities, is aimed at helping students better understand the law, which is the subject of learning, so that they can apply it when solving problems that require its implementation, from both a qualitative and quantitative perspective. Based on the assumption that "everything that is decided a priori feeds into the cognitive component, and the corresponding choices in terms of implementation are part of the mediative component " (Robert, 2007), we can say that this study is anchored in the cognitive and mediative components, two of the five components from which teaching practices are studied and reconstructed according to the theory of the dual didactic and ergonomic approach (Robert and Rogalski, 2002, 2005, 2008). In this approach, the materials used for construction and assessment activities, as well as the teacher's discourse, can be considered as aids provided to the student in order to bring them closer to the knowledge they are learning. World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 187 However, for these aids to be effective, they must be located within the student's zone of proximal development so that they can be easily grasped and used as a springboard to access knowledge. 1.1.2. The concept of bridging In his developmental theory of children with learning difficulties, Vygotsky (1934/1997) developed the concept of the “zone of proximal development,” which is an area where students have certain resources and, with help, can perform the task assigned to them. It is in this zone, located between the zone of autonomy, i.e., where the student can perform the task without help, and the zone of disruption, i.e., where, even with a lot of help, the student may with difficulty complete the task. It is in this zone that all forms of assistance provided to the student by either the teacher or their peers during a teaching/learning situation should take place. It should be noted that, in relation to the zone of proximal development, the acts of teaching and learning evolve in opposite directions. These developments in this zone of these two acts are easily justified when we realize that the teacher's work during the teaching act consists of transforming knowledge and gradually moving it from the zone of disruption to the zone of proximal development, while the student, during the learning act, is led to move out of their zone of autonomy with their supposed knowledge “already there” to discover and acquire knowledge in the zone of proximal development. Since the zone of proximal development is a zone of interaction, within which the student can consolidate or modify their representations of a concept, fact, or object, we believe that this notion can also be applied to adolescents, always in the school context where teaching/learning continues to contribute to their development. We refer to any form of assistance or attempt to assist aimed at moving out of the zone of disruption and/or bringing knowledge (a notion, concept, law, etc.) that is being learned by the student closer, explicitly or not, to their zone of proximal development as “rapprochement-en-acte” (act of rapprochement). This bridging allows the student, with some effort, to encounter knowledge (discover and appropriate it) in this zone. During the teaching/learning of a subject in physics, this bridging is possible when the teacher actually moves the student between the empirical and theoretical worlds through appropriate modeling and interpretation. The difference between the concept of proximity-in-action developed by Robert and Vandebrouck (2014) and that of rapprochement-in-action is that the former focuses on "...proximities between what is intended and what students do " (Robert and Vandebrouck, 2014), while the latter includes the help of the teacher and other students in order to bring the student closer to the knowledge at stake. In a classroom setting, the entire teaching/learning process must therefore take place within the students' zone of proximal development. It is true that this is a zone whose boundaries are difficult to define because they are not explicitly accessible. This raises the issue of mastery of the teaching profession, and therefore places heavy demands on the teacher's expertise. 2. Literature review Newton's laws occupy an important place in the physics curriculum for senior science students in Benin. The explanation or interpretation of the motion of a solid or a particle whose speed does not approach that of light in a vacuum () is based on Newton's second law, also known as the center of inertia theorem (constant mass). In this paper, we will use both terms “law” and “theorem.” This is justified, on the one hand, by the fact that Newton's proposition is "the mathematical expression of a repeatable correlation, constant behavior, or statistical frequency observed among a set of facts. It is deduced from a number of observations and generalizes them, retaining their stable character" (Sagaut, 2008). It is therefore a scientific law. On the other hand, it is based on logical elements and is scientifically proven by other propositions that are already considered to be true. This is what also gives it the status of a theorem. We generally find that when solving physics problems requiring the application of this theorem, students have considerable difficulty using it efficiently. Since this law combines dynamic and kinematic concepts (force, mass, acceleration), research has identified multiple difficulties students have in using these concepts, as well as their reasoning when applying this law. World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 188 Thus, even in their final year of high school, students still have difficulty making a comprehensive assessment of the external forces applied to a body, as well as representing them appropriately (Viennot, 1989; Brasquet, 1999; Ménigaux, 1986). To remedy this situation, Dumas-Carré and Goffard (1997) suggest that the concept of force be approached through a study of interactions, using an appropriate technique. For Brasquet (1999), this proposal can help students avoid confusion between the balance of applied forces (Newton's second law) and the study of interactions (Newton's third law). When students are asked about the role of friction, they say that it always opposes motion, even though some types of friction are propulsive (Besson et al., 2007). The way in which the concept of mass is often approached with students does not allow them to later realize that the mass in Newton's second law opposes the setting in motion or change of motion of a body, since it is an inertial mass (Givry, 2003; Rosca, 2005). These are concepts that, in part, obscure Newtonian concepts for learners. Reif and Allen (1992) and Shaffer (1993) also noted difficulties experienced by students and even some experts with qualitative questions relating to the nature of the acceleration vector and its schematization in given situations. The center of inertia theorem gives rise to a purely vectorial relationship. This raises the question of the use of vectors in a physics context. On this point, Knight (1995) and Flores et al. (2004) found that both pupils and students experience considerable difficulty. All these observations were made when learners were presented with problem-solving situations requiring the application of the aforementioned law. In these situations, Viennot (1978) noted that learners' reasoning was not solely due to the effects of the formalism taught. Continuing her investigations, she found that the intuitive system acts as a barrier to academic knowledge. By studying textbooks through their developments and recommendations, Viennot (1982) highlights a reinforcement or teaching of intuitive reasoning devoid of physical meaning by certain textbooks. It should be noted that students' difficulties with Newton's second law are both qualitative and quantitative. From the point of view of the statement of the law, Nguessan (2016) noted that learners did not master the dominant syntactic structure or its conditions of applicability. 2.1. Research question and hypothesis All these difficulties and modes of reasoning observed in students in the research cannot be attributed solely to the students or teachers, as Lefèvre and Allevy (1998) found in their research that there is always a gap between the model taught and the model actually learned by students. To this end, we asked ourselves the question: how does the teacher go about bringing students in science classes closer to Newton's second law? Our aim here is to characterize the choices teachers make to help students construct Newton's second law, i.e., to examine the choices teachers make in mobilizing the concepts involved and the interconceptual relationships established that enable students to effectively appropriate the law and its application in given situations. We postulate that the activity materials developed and the teacher's discourse are designed to give meaning to Newton's second law. With this in mind, we will analyze the activity materials used to construct and assess knowledge related to this subject, as well as the discourse used by the teacher during class. 3. Méthods 3.1. Sample and corpus composition In this study, which is part of a thesis, we focused on certain aspects of physics teachers' classroom practices. We worked with three teachers of the subject in classroom settings. To ensure that they had all received the necessary academic and professional training to enable them to perform their job efficiently, all three teachers were certified. The students' activity materials were collected and their work on the board was photographed for analysis. Similarly, the lessons of the three teachers were filmed to examine the oral organization of each of them during the teaching/learning sessions on Newton's second law. The first teacher, whom we have named T1, taught the law in a 1 hour 32 minute session, while the second, named T2, did so in two sessions lasting a total of 3 hours 9 minutes. The third teacher, named T3, devoted two sessions with a total duration of 2 hours and 43 minutes to the topic. The teachers' speeches and exchanges with the students were transcribed in full. World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 189 3.2. Data processing and analysis In order to bring a subject closer to students, its teaching/learning must follow, more or less, the same logic as the discipline to which it belongs. Physics operates between the empirical world (the world of objects and events) and the theoretical world (the world of laws, theories, paradigms, theorems, etc.) through models (Gaidioz et al., 2004; Gaidioz and Tiberghien, 2003; Borromeo, 2006). The antithetical polysemy of the concept of a model (Béziau, 2011) has prompted scientists and philosophers of science to reflect on it. Among the definitions proposed, one in particular catches our attention: “a structure is a model of a formal theory if all the axioms of that theory are validated for that theory” (Badiou, 2007, p. 107). Taking this definition into account, we see that the model cannot be housed solely in one of the two worlds (the real world or the theoretical world) nor can it be completely separated from both, because the model can be abstract or real. To characterize the variability of the model between the two worlds, Béziau and Kritz (2000) developed the concepts of “model of” and “model for.” These two concepts have allowed us to understand that a representation (diagram, model, drawing, etc.) derived from reality is a model of that reality, while the latter is a model for the representation. In this sense, there are not only models belonging to the real world or very close to it, which we can describe as physical models (Rey, 2010) or model-realities (Béziau, 2011), but also models in the theoretical world that are described as mathematical models (Borromeo, 2006). The following diagram presents the teaching/learning of a knowledge object related to the functioning of the discipline. Figure 1 Scheme for teaching/learning a subject related to the functioning of physics • SR: actual situation • PM: physical model • RM: reality model • MM: mathematical model • MR: mathematical result The analysis of construction and assessment activity materials will be based on this diagram. This will enable us to see whether the teaching of Newton's second law by each of these teachers is consistent with the logic of how the discipline works, as any connection with a subject that students are learning must fit into this perspective. As for the oral organization of each teacher, we extracted their discourse from the whole transcribed during their ordinary classroom practice. The teacher's discourse is often improvised. However, we postulate that this discourse is always concocted in such a way as to bring the knowledge at stake closer to the students so that they can appropriate it and invest it effectively in World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 190 other situations, for problem solving. This generally requires accommodations on the part of the students. In this sense, the mobilization and articulation of different concepts by the teacher in his or her discourse is not random. They are well-directed because, in principle, they should enable the student to make sense of the knowledge at stake. These concepts, mobilized by the teacher through his or her discourse in order to give meaning to the law and promote effective learning on the part of the students, are in fact lexies, i.e., meaningful functional units. Teaching practices are complex and require modeling in order to characterize them. In this study, we also pay particular attention to the teacher's discourse when teaching Newton's second law, and its lexicometric analysis (de Hosson et al., 2018) leads us to modeling. We create these models by developing concept maps (Manrique et al., 2016) of each teacher's filmed discourse. The concept map allows us to understand the meaningful functional units of the teacher's discourse and how they relate to each other in order to bring the law, the subject of teaching, closer to the students. This concept map also allows us to approach the teacher's methodological profile through the mobilization of the concepts directly at stake in the law, how they give meaning to them in the network, and also how they move students through the different elements of the real and theoretical worlds through models. Certain applications of old and new knowledge (Robert, 2007) can also be seen, to the extent of the data we were able to collect and our means of investigation, through the articulation of interconceptual relationships manipulated by the teacher during the teaching/learning session on the law in question. The concept map allows us to grasp all of these connections in action. 4. Results, interpretation and discussion 4.1. Interpretation and discussion of the activity materials proposed to the pupils by teachers P1 and P3. Teachers P1 and P3 proposed the same activity materials to their pupils, even though they did not work in the same schools. However, they both work in the commune of Comé. When asked why they were so uniform, they all told us that they meet up from time to time to work on the sheets together. World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 191 Table 1 Compilation of cognitive activities proposed to learners by teachers P1 and P3 Consignes Work to be done content Potential cognitive activities involved Situation in relation to the discipline's operating cycle 4.4B1 Using the fundamental relation of dynamics, establish the centre of inertia theorem. Write the logical-mathematical (∑𝐹 𝑒𝑥𝑡 =𝑑𝑝  𝑑𝑡 ) expression of the fundamental relation of translational dynamics from its statement. Introduce into this expression that of the momentum vector (𝑝 = 𝑚𝑣) and then, mass being a constant, derive the velocity vector 𝑣 with respect to time to obtain the acceleration vector 𝑎 in order to find the logical-mathematical (∑𝐹 𝑒𝑥𝑡 =𝑚𝑎) relation of the centre of inertia theorem. Modelling a law by its logicalmathematical relationship. Passing from one logicalmathematical relationship to another: using mathematical skills. Mathematical model (MM) 4.4B2 Write the vector relation expressing the relative equilibrium of a solid in a nongalilean reference frame. Write down the logical-mathematical relationship expressing the relative equilibrium of a solid in a non-galilean frame of reference, based on a translation of d'Alembert's theorem and the explicit expression of the corrective force. Modelling a law using a logicalmathematical relationship: using mathematical skills. Mathematical Model (MM) 4.4B3 Show that the motion of the solid S is rectilinear and uniformly accelerated. List the prerequisites for applying the centre of inertia theorem. List the external mechanical actions exerted on List the external mechanical actions exerted on the material system whose motion is being studied and represent them by force vectors. Write the contextualised logical-mathematical relationship of the centre of inertia theorem applied to the semi-modelled system presented. Solve the vector equation obtained to derive the algebraic value a. index x of the acceleration along the track modelled by the righthand segment left [𝐴𝐵] Associate the "straight" aspect of the track with that of 𝑎𝑥>0 to give the explicit nature of the motion of the solid. - Mathematical modelling: modelling mechanical actions using the concept of force, then modelling the latter using the concept of vector. - Contextualisation of the logicalmathematical relationship of the centre of inertia theorem. - Use of mathematical skills to solve the vector equation. Physical Model – Mathematical Model – mathematical result (PMMM-MR) 4.4.4 Deduce the characteristics of the velocity vector 𝑣𝐵 󰇍 󰇍 󰇍 󰇍  at B and the duration t of the path AB. Identify the point of application, the direction and the sense of the velocity vector 𝑣𝐵 then, Either write the contextualised logicomathematical relation of the kinetic energy theorem and solve the algebraic equation obtained to derive the value of the norm 𝑣𝐵; Or write the relation independent of time between points A and B to derive the value of the norm 𝑣𝐵 . Write the hourly equation of motion of the solid on the inclined plane and set 𝑥 = 𝐴𝐵 for 𝑡 =𝑡𝐴𝐵 to derive the value of the latter. - Contextualisation of the logical-mathematical relationship of the kinetic energy theorem. - Use of mathematical skills to solve the algebraic equation obtained and to establish and then exploit the equation of time. Mathematical Model – Mathematical Result (MM-MR) World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 192 According to the title of the activity, "What are Newton's second and third laws? Since the two laws are not used in the same way, insofar as the second law requires a balance of forces whereas the third law is more a study of interactions, such a grouping could lead to confusion as to their applicability (Viennot, 1989). The first instruction, "from the fundamental relation of dynamics, establish the theorem of the centre of inertia", means that by starting from a relation, we can directly establish a theorem (or a law). Returning to the latter, starting from its logical-mathematical relationship (Oké and al, 2019), requires an interpretation to reconstitute certain parameters that were rendered mute during the mathematical modelling (or simply the mathematisation) of the theorem. The second set of instructions, "write the vector relation expressing the relative equilibrium of a solid in a non-galilean reference frame", is a pure and simple reproduction of what is stated in the support because it does not require any adaptation of knowledge. This is what Robert (2007) calls a "simple, isolated task". In reality, this type of task does not allow students to put old and new knowledge to work for effective learning. The learning of Newton's third law, although not the subject of our work, was announced in the title of the activity and reduced to a simple reading of the statement in the support without any further development, as no instructions were given. To assimilate the knowledge taught, each pupil has to work individually to decode, memorise and adapt to the situation. Such a way of teaching a scientific law can only increase the gap between the knowledge taught and that actually learnt by the pupils (Lefèvre and Allevy, 1998). The last two instructions give rise to more or less complex tasks requiring some adaptation of knowledge. An analysis of the content of the actual work to be done in relation to each instruction shows that the teaching of Newton's second law in the science final year as proposed by these two teachers did not at all respect the appropriate methodology for the subject: the scientific approach. Since this is a scientific law designed to explain phenomena (in the real world), we believe that its teaching should start with a few observations that give rise to questions, followed by the formulation of hypotheses leading to experiments (reality or physical modelling) with the collection of data (mathematical models and/or mathematical results), which will be analysed and/or interpreted to conclude with the formulation of the law in question. It is only after this stage that we need to return to the conditions of applicability of the law and the meaning and/or role of each of the "pivotal" concepts it contains. The knowledge activity relating to Newton's second law proposed by the teachers (P1 and P3) is practically a pure and simple mathematisation. 4.2. Interpretation and discussion of P1 and P3 productions on the blackboard The first thing P1 noticed was that the title of the activity had been changed on the board during the teaching session. On his teaching sheet we read "What are Newton's second and third laws?" whereas on the blackboard the teacher wrote "What is Newton's second law? As for teacher P3, it was the number of the activity that was changed on the blackboard (4-3B instead of 4-4B on the sheet we recovered). In relation to instruction 4-4B1, Teacher P1 had the students establish the expression ∑𝐹 𝑒𝑥 = 𝑀𝑎𝐺 without any other precision (written on the board) whereas after having done the same thing (∑𝐹 𝑒𝑥𝑡 = 𝑚𝑎𝐺), with one difference in notation, P3 added that "this is Newton's second also called the theorem of the centre of inertia". As we pointed out when we analysed the activity support, this is the logical-mathematical relationship translating the centre of inertia theorem and not the theorem itself. As far as instruction 4-4B2 was concerned, since it was simply a question of writing down a vector relationship, the two teachers remained practically the same, except that P1 included the notion of driving force, but without any other details. In the development of instruction 4-4B3, at the level of the balance of the external forces applied to the solid we read: • " - the weight 𝑃 󰇍  of the solid (P1 and P3), • the normal reaction 𝑅 󰇍  𝑛 of the inclined plane (P1 and P3), • the friction force 𝑓  of the solid (P1) or the friction forces 𝑓  (P3) »." By remaining within the same scientific logic according to which a force is the modelling of a mechanical action of one body on another, the rhetoric "force of a body" is not part of a Newtonian vision (Viennot, 1989). A body on its own does World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 193 not, on the whole, possess force. In order to help students to engage in a scientific discourse on the concept of force, we think it would be better to say: • " - the force 𝑃 󰇍  modelling the attraction exerted by the Earth on the solid, • the force 𝑅 󰇍  𝑛 modelling the normal reaction exerted by the inclined plane on the solid, • the resultant f  of the forces modelling the friction between the inclined plane and the solid". In relation to the first part of instruction 4.4B4, the characteristics of the velocity vector 𝑣𝐵 in B, the use by the two teachers of the time-independent relationship (in the case of uniformly varied rectilinear motion) to calculate the norm of 𝑣𝐵 can be understood insofar as they have devoted an entire activity to the theorem of kinetic energy but not yet tackled. However, taking into account the fact that this theorem has already been learned by the students in the first science class and that scientific knowledge is cumulative, they should not be forced to refrain from also using this theorem to calculate the norm of 𝑣𝐵 as P1 said in the following terms: P1 : “ We know the speed at B and we also know the distance between A and B, so we can use the time-independent relationship. It's true that using the kinetic energy theorem will give the same result, but we haven't seen the theorem yet, so it's better to use it given that the motion is uniformly varied and we know everything involved in the time-independent relationship except vB, so it's better to go that way.” With regard to the second part of the instructions, i.e. the calculation of the time 𝑡𝐴𝐵, P3 and P1 used the time equations for speed and uniformly varied rectilinear motion respectively. At this level, only P1 specified the origin of the dates and the origin of the spaces. Teacher P3 did not mention this explicitly on the blackboard, even though the use of time equations necessarily requires such details. The developments made by teachers P1 and P3 confirmed the pure mathematisation of Newton's second law during its teaching/learning in the final year of secondary school. This does not allow the students to properly grasp the law and apply it efficiently in given situations. On the whole, this is an unsuccessful attempt to bring this law closer to the students. 4.3. Interpretation and discussion of the activity materials proposed to the pupils by the teacher P2 World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 194 Table 2 Compilation of cognitive activities proposed to learners by teachers P1 and P3 Consignes Work to be done content Potential cognitive activities involved Situation in relation to the discipline's operating cycle C.1By replacing the expression for the momentum vector in the relation 𝑑𝑝  𝑑𝑡 = ∑𝐹 𝑒𝑥𝑡 , show that ∑𝐹 𝑒𝑥𝑡 =𝑚𝑎. Deduce from this the statement of the centre of inertia theorem (Newton's 2nd law). - Introduce into the logico-mathematical expression (𝑑𝑝  𝑑𝑡 =∑𝐹 𝑒𝑥𝑡) of the fundamental relation of dynamics, that 𝑝 = 𝑚𝑣. Derive the velocity vector 𝑣 with respect to time to obtain the acceleration vector 𝑎 in order to find the logico-mathematical relation ∑𝐹 𝑒𝑥𝑡 = 𝑚𝑎 of the centre of inertia theorem. - Formulation of centre of inertia theorem from ∑𝐹 𝑒𝑥𝑡 = 𝑚𝑎. - Implementation of mathematical skills (when going from 𝑣 to 𝑎. - Reconstructing the syntactic structure of the centre of inertia theorem from its logicalmathematical relationship. From a mathematical model (MM) to a mathematical result (MR) then to another mathematical model (MM) followed by interpretation. C.2Apply Newton's 2nd Law to a solid material whose centre of inertia is moving in a uniform circular motion. - Name the resultant of the forces applied to it and deduce its characteristics. - Write the expression for the acceleration vector in the case of circular motion of a material point = 𝑎𝜏𝜏+𝑎𝑛𝑛 󰇍  . Find what this expression is worth in the case of uniform circular motion (𝑎 = 𝑟𝜔2𝑛 󰇍  ). Replace this expression in the logical-mathematical relation of the centre of inertia theorem to have ∑𝐹 𝑒𝑥𝑡 =𝑚𝑟𝜔2𝑛 󰇍  - Assign a name, in this case, to the resultant ((∑𝐹 𝑒𝑥𝑡) forces applied. Then identify the characteristics of this resultant. Use of mathematical skills (when moving from the logicalmathematical relationship of the centre of inertia to its contextualised relationship). From a mathematical model (MM) to a mathematical result (RM) then to another mathematical model (MM) followed by interpretation. C.3Translate the relative equilibrium of a solid in a nongalilean reference frame using a corrective force 𝐹 𝑖 (force of inertia). Express or represent in mathematical language the state of relative equilibrium of a solid in a non-galilean reference frame, with the introduction of a corrective force 𝐹 𝑖. Mathematisation of a physical model: using physical and mathematical skills. From a reality model (RM) to a mathematical model (MM) and then to the mathematical result (MR). C.4Recall the principle of action and reaction (Newton's 3rd law). Reconstruct the principle of action and reaction (simple, isolated reconstruction). Mathematisation of a physical model: using physical and mathematical skills. From a reality model (RM) to a mathematical model (MM). World Journal of Advanced Research and Reviews, 2025, 28(02), 186-202 201 Compliance with ethical standards Disclosure of conflict of interest All four authors acknowledge that there is no conflict of interest. They all agree with what is written in this article. 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