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  1.  20
    Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology.Ricardo Karam - 2015 - Science & Education 24 (5-6):561-590.
    Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don’t just use math, we make meaning with it in (...)
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  2.  10
    The Creative Power of Formal Analogies in Physics: The Case of Albert Einstein.Ricardo Karam - 2015 - Science & Education 24 (5-6):529-541.
    In order to show how formal analogies between different physical systems play an important conceptual work in physics, this paper analyzes the evolution of Einstein’s thoughts on the structure of radiation from the point of view of the formal analogies he used as “lenses” to “see” through the “black box” of Planck’s blackbody radiation law. A comparison is also made with his 1925 paper on the quantum gas where he used the same formal methods. Changes of formal points of view (...)
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  3.  14
    Physics Teaching: Mathematics as an Epistemological Tool.Ricardo Karam - 2015 - Science & Education 24 (5-6):645-660.
    We study the interconnection between Physics and Mathematics in concrete instances, departing from the usual expression for the Coulomb electric field, produced by a point-like charge. It is scrutinized by means of six epistemology-intensive questions and radical answers are proposed, intended to widen one’s understanding of the subject. Our interventions act along two complementary directions. One of them regards ontology, since questions induce one to look closely at the electric charge, from different perspectives, promoting reflections about its nature and reinforcing (...)
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  4.  10
    Quod Erat Demonstrandum: Understanding and Explaining Equations in Physics Teacher Education.Ricardo Karam - 2015 - Science & Education 24 (5-6):661-698.
    In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their (...)
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  5.  9
    Mathematics as an Instigator of Scientific Revolutions.Ricardo Karam - 2015 - Science & Education 24 (5-6):495-513.
    In a famous 1960 paper, Wigner discussed “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I suggest that the effectiveness of mathematics in producing successful new theories and surprising discoveries is even more unreasonable than Wigner claimed. In this paper, I present several historical case studies to support the claim that mathematics is often responsible for instigating scientific revolutions. However, that does not mean that mathematics is always the key to the universe, and other cases where mathematization was not (...)
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  6.  9
    Reality–Theoretical Models–Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School.Ricardo Karam - 2015 - Science & Education 24 (5-6):615-644.
    This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the relations made during physics lessons between the three entities Reality, Theoretical models and Mathematics are of the outmost importance. A framework has been developed to sustain analyses of the (...)
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  7.  8
    Mathematics and Physics: The Idea of a Pre-Established Harmony.Ricardo Karam - 2015 - Science & Education 24 (5-6):515-527.
    For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms popular in Victorian Britain, were not unknown in the nineteenth century, but it was only in the environment of fin-de-siècle Germany that the idea of a pre-established (...)
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  8.  5
    Introduction of the Thematic Issue on the Interplay of Physics and Mathematics.Ricardo Karam - 2015 - Science & Education 24 (5-6):487-494.
  9.  5
    Negotiating the Boundaries Between Mathematics and Physics.Ricardo Karam - 2015 - Science & Education 24 (5-6):725-748.
    This paper examines physics and mathematics textbooks published in France at the end of the 1950s and at the beginning of the 1960s for children aged 11–15 years old. It argues that at this “middle school” level, textbooks contributed to shape cultural representations of both disciplines and their mutual boundaries through their contents and their material aspect. Further, this paper argues that far from presenting clearly delimited subjects, late 1950s textbooks offered possible connections between mathematics and physics. It highlights that (...)
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  10.  17
    Obtaining Laws Through Quantifying Experiments: Justifications of Pre-Service Physics Teachers in the Case of Electric Current, Voltage and Resistance.Ricardo Karam - 2015 - Science & Education 24 (5-6):699-723.
    The language of physics is mathematics, and physics ideas, laws and models describing phenomena are usually represented in mathematical form. Therefore, an understanding of how to navigate between phenomena and the models representing them in mathematical form is important for a physics teacher so that the teacher can make physics understandable to students. Here, the focus is on the “experimental mathematization,” how laws are established through quantifying experiments. A sequence from qualitative experiments to mathematical formulations through quantifying experiments on electric (...)
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  11.  17
    Obstacles to Mathematization in Physics: The Case of the Differential.Ricardo Karam - 2015 - Science & Education 24 (5-6):591-613.
    The process of the mathematization of physical situations through differential calculus requires an understanding of the justification for and the meaning of the differential in the context of physics. In this work, four different conceptions about the differential in physics are identified and assessed according to their utility for the mathematization process. We also present an empirical study to probe the conceptions about the differential that are used by students in physics, as well students’ perceptions of how they are expected (...)
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  12.  14
    Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics.Ricardo Karam - 2015 - Science & Education 24 (5-6):543-559.
    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (...)
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