Role Of Mathematics In Physics Research Articles

A structuralist view for interpreting the role of mathematics in physics

A structuralist view for interpreting the role of mathematics in physics

Pre-service physics teachers’ developing views on the role of mathematics in the teaching and learning of physics

This qualitative, questionnaire and interview-based study explores how pre-service physics teachers think about the role that mathematics plays in the teaching and learning of physics at university and school level and whether these views change during their pre-service teacher education. Many of the pre-service teachers were aware of the complex relationship between these two subjects at university level, noting that success in mathematics can often mask a lack of conceptual understanding in physics and that there can be a disconnect between the physics and mathematical aspects of undergraduate courses. At school level, many stressed the importance of a focus on conceptual understanding and that technical competence in mathematics lessons does not always transfer to physics lessons. Almost all the pre-service physics teachers changed their views during the year, often in response to their classroom experiences. As they became more attuned to the difficulties students faced with respect to the mathematical challenges involved in learning physics, many took a more pragmatic position that balanced the role of mathematics in physics with acceptance that they must respond to student needs. We suggest that these changing views can be framed in terms of two re-orientations. A disciplinary re-orientation where the role that mathematics plays in order to be successful in physics is reassessed, and a pedagogical re-orientation that attends to pragmatic, teaching considerations. We recommend that direct attention to the role of mathematics in school physics should be an integral part of pre-service physics teacher education in order to encourage these re-orientations.

Curriculum Emphases, Mathematics and Teaching Practices: Swedish Upper-Secondary Physics Teachers\u2019 Views

This article addresses physics teachers’ views about physics teaching in upper-secondary school. Their views have been investigated nationwide through a web-based questionnaire. The questionnaire has been developed based on several published instruments and is part of an ongoing project on the role of mathematics in physics teaching at upper-secondary school. The selected part of the results from the analysis of the questionnaire reported on here cross-correlate physics teachers’ views about aims of physics teaching with their view of physics classroom activities, and perceived hindrances in the teaching of physics. Three hundred seventy-nine teachers responded to the questionnaire (45% response rate). The result indicates that teachers with a high agreement with a Fundamental Physics curriculum emphasis regarded mathematics as a problem for physics teaching, whereas teachers with high agreement with the curriculum emphases Physics, Technology and Society or Knowledge Development in Physics did not do so. This means that teachers with a main focus on fundamental theories and concepts believe that mathematics is a problem to a higher extent than teachers with main focus on the role of physics in society and applied aspects or physics knowledge development do. Consequences for teaching and further research are discussed.

The role of mathematics in physics: Building knowledge and describing the empirical world

This paper considers why mathematics is used in physics. It traces the use of mathematics in physics through primary school, junior high school and senior high school in NSW, Australia, considering its role from the point of view of Systemic Functional Linguistics and Legitimation Code Theory. To understand the development of mathematics, two genres that play differing roles in the discipline of physics are introduced: ‘derivation’ and ‘quantification’. Through an analysis using the concepts of semantic density and semantic gravity from Legitimation Code Theory, these genres are shown to aid physics in developing new knowledge and linking its theory to the empirical world. This paper contributes to the growing body of research considering forms of knowledge in academic disciplines and the role of non-linguistic semiotic resources in organizing this knowledge.

The role of mathematics in physics: Building knowledge and describing the empirical world

This paper considers why mathematics is used in physics. It traces the use of mathe-matics in physics through primary school, junior high school and senior high school in NSW, Australia, considering its role from the point of view of Systemic Functional Linguistics and Legitimation Code Theory. To understand the development of mathematics, two genres that play differing roles in the discipline of physics are introduced: ‘derivation’ and ‘quantifica-tion’. Through an analysis using the concepts of semantic density and semantic gravity from Legitimation Code Theory, these genres are shown to aid physics in developing new knowl-edge and linking its theory to the empirical world. This paper contributes to the growing body of research considering forms of knowledge in academic disciplines and the role of non-lin-guistic semiotic resources in organizing this knowledge.

Impacts of low enrolment in Secondary Schools physics to attainment of Kenyan Vision 2030: A case study of Nandi North Sub County

The objectives of Kenyan secondary school physics curriculum is to build a firm foundation for further education and training as well as technological and industrial development. Physics curriculum emphasizes the experimental approach which should prepare the learner to teaching and learning scientific concepts and ideas in the modern technology. Hence by the end of the course, the learners should be able to use scientific knowledge to enhance development of industries and propel country to achieve vision 2030. Despite the importance of physics, the performance and enrolment of students in Physics has not been impressive. The study seeks to establish factors that contribute to low enrolment of physics in Kenyan secondary schools. This study will specifically looked into students’ attitudes towards physics subject, the difficult that physics teachers have in handling physics topics and the relationship between KCPE performance in science and physics performance. The study adopted descriptive survey design. The study was conducted in Nandi North sub County and the target population was teachers and students in 35 secondary schools in the area of study. The study employed the use of stratified and simple random sampling to select the respondents. Questionnaire and document analysis was used in data collection. It was established that students have a formed opinion on the nature of the subject, majorly on difficulty level and having mathematical manipulations which scares them off. Teachers find most of the topics in physics easy to handle, however, some topics like electromagnetic induction, Electronics and Waves tend to be challenging. Document analysis of KCPE results revealed that learner’s background in primary science was weak. There are far fewer high school students enrolled in physics and realizing the required grades, thus the Kenyan vision 2030 remains just a mirage. It was recommended among others that teachers teaching Physics and Mathematics should work in consultation with each other so as to help the students in appreciating the role of Mathematics in Physics .The findings have implications for designing interventions and identifying pedagogical techniques that link primary science and secondary school physics.

Temporal naturalism

Two people may claim both to be naturalists, but have divergent conceptions of basic elements of the natural world which lead them to mean different things when they talk about laws of nature, or states, or the role of mathematics in physics. These disagreements do not much affect the ordinary practice of science which is about small subsystems of the universe, described or explained against a background, idealized to be fixed. But these issues become crucial when we consider including the whole universe within our system, for then there is no fixed background to reference observables to. I argue here that the key issue responsible for divergent versions of naturalism and divergent approaches to cosmology is the conception of time. One version, which I call temporal naturalism, holds that time, in the sense of the succession of present moments, is real, and that laws of nature evolve in that time. This is contrasted with timeless naturalism, which holds that laws are immutable and the present moment and its passage are illusions. I argue that temporal naturalism is empirically more adequate than the alternatives, because it offers testable explanations for puzzles its rivals cannot address, and is likely a better basis for solving major puzzles that presently face cosmology and physics.This essay also addresses the problem of qualia and experience within naturalism and argues that only temporal naturalism can make a place for qualia as intrinsic qualities of matter.

Quod erat demonstrandum: Understanding and Explaining Equations in Physics Teacher Education

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 master’s degree in two European universities. The course had two main goals: (1) To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and (2) To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived.

On the Role of Mathematics in Physics

I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a physical system, it will sometimes produce solutions that are unphysical—i.e. describe a physical system that simply cannot exist in the real world. It is argued that this poses a problem for the epistemic position of realism in physics: a mathematical theory that professes to give a correct description of physical reality should not contain such unrealistic objects. Some concrete examples are examined, and their implications for physics are discussed from a relativist epistemic perspective. I argue that the appearance of the unphysical entities and solutions also has significance for the teaching of physics. It is recommended that the students be exposed from the start to a relativist ontology, as advocated by the theory of radical constructivism; here the unphysical objects do not pose an epistemic problem.

On the Role of Mathematics in Physics: A Constructivist Epistemic Perspective

The association between the observable physical world and the mathematical models used in theoretical physics to describe this world is examined. Such models will frequently exhibit solutions that are unexpected, in the sense that they describe physical situations which are different from that which the physicist may initially have had in mind when the model is employed. It will then often be the case that such an unexpected solution actually represents a physically realisable situation. However, this solution may also, in some cases, describe a system that is unphysical—i.e. a system that, according to our physical intuition, simply cannot exist. It is argued that this latter fact poses a problem for the epistemic position of realism in physics: a mathematical theory that professes to give a correct description of physical reality should not give rise to such unrealistic solutions. Some concrete examples are examined, and their implications are discussed from the relativist epistemic perspective that is implicit in the theory of radical constructivism. It is suggested that the occurrence of these unphysical solutions also has significance for the teaching of physics. In conclusion, it is advocated that the students be exposed, from the start of their physics education (mainly in secondary school), to the relativist ontology that is advocated by radical constructivism; here the appearance of unphysical solutions does not pose an epistemic problem.

Mathematical models in physics: A study with prospective physics teacher

The aims of this study are “to reveal prospective physics teachers’ characterization of the relationship between mathematics and physics” and “to analyze their abilities to model physical phenomena”. For these purposes, an achievement test consisting of two parts has been administered to 24 student teachers of physics. The first part aims to reveal their opinions about the relationship between mathematics and physics and the second part aims to determine their abilities about the construction of a model. The analysis shows that the candidate physics teachers state the role of mathematics in physics in three different ways and that although they generate their own methods for modeling physical phenomena they have serious difficulties in forming a model. As a recommendation of this study, it can be said that model and modeling process should be tackled as an object and model teaching should not content with model as a tool. Key words: Mathematics, physics, modelling, student’s teachers.

Views about Physics held by Physics Teachers with Differing Approaches to Teaching Physics

Physics teachers’ approaches to teaching physics are generally considered to be linked to their views about physics. In this qualitative study, the views about physics held by a group of physics teachers whose teaching practice was traditional were explored and compared with the views held by physics teachers who used conceptual change approaches. A particular focus of the study was teachers’ views about the role of mathematics in physics. The findings suggest the traditional teachers saw physics as discovered, close approximations of reality while the conceptual change teachers’ views about physics ranged from a social constructivist perspective to more realist views. However, most teachers did not appear to have given much thought to the nature of physics or physics knowledge, nor to the role of mathematics in physics.

Mathematics and the science of analogies

Analogies have been used to great effect in the physical sciences. A brief review is given of the relevant points about the role of mathematics in physics and a simple framework in which analogies are viewed in terms of mechanism and descriptive, usually mathematical, components. The main body of the paper analyzes cases, principally in wave theory and electromagnetism, to emphasize three points: the importance of the mathematical description component in powerful analogies; the possibly destructive aspect of the mechanism component of analogies; and the underlying reasons for the choice of particular analogies.

Thinking about physics

Physical scientists are problem solvers. They are comfortable doing science: they find problems, solve them, and explain their solutions. Roger Newton believes that his fellow physicists might be too comfortable with their roles as solvers of problems. He argues that physicists should spend more time thinking about physics. If they did, he believes, they would become even more skilled at solving problems and doing science. As Newton points out in this thought-provoking book, problem solving is always influenced by the theoretical assumptions of the problem solver. Too often, though, he believes, physicists haven't subjected their assumptions to thorough scrutiny. Newton's goal is to provide a framework within which the fundamental theories of modern physics can be explored, interpreted, and understood. Surely physics is more than a collection of experimental results, assembled to satisfy the curiosity of appreciative experts, Newton writes. Physics, according to Newton, has moved beyond the describing and naming of curious phenomena, which is the goal of some other branches of science. Physicists have spent a great part of the twentieth century searching for explanations of experimental findings. Newton agrees that experimental facts are vital to the study of physics, but only because they lead to the development of a theory that can explain them. Facts, he argues, should undergird theory. Newton's explanatory sweep is both broad and deep. He covers such topics as quantum mechanics, classical mechanics, field theory, thermodynamics, the role of mathematics in physics, and the concepts of probability and causality. For Newton the fundamental entity in quantum theory is the field, from which physicists can explain the particle-like and wave-like properties that are observed in experiments. He grounds his explanations in the quantum field. Although this is not designed as a stand-alone textbook, it is essential reading for advanced undergraduate students, graduate students, professors, and researchers. This is a clear, concise, up-to-date book about the concepts and theories that underlie the study of contemporary physics. Readers will find that they will become better-informed physicists and, therefore, better thinkers and problem solvers too.

The Role of Mathematics in Physics

Previous articleNext article No AccessArticlesThe Role of Mathematics in Physics*C. S. SHARMAC. S. SHARMABirkbeck College, University of London Search for more articles by this author *This is a revised version of a paper written at the invitation of the British Society for the Philosophy of Science for their 1980 Conference held at Chelsea College, London in September 1980. The revision has benefited from comments made from the chair by Professor H. Post, from the floor by Dr D. A. Gillies, Dr J. Dorling and Dr J. Mayberry, in reply by Dr. M. L. G. Redhead and in private by Dr R. G. Wilson. The present draft has been further revised in the light of comments and suggestions made by the Editor and his three referees. While acknowledging his gratitude to everyone who has contributed to the present form of the work, the author claims sole responsibility for the obscurities and shortcomings which survive.PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The British Journal for the Philosophy of Science Volume 33, Number 3September 1982 Society: The British Society for the Philosophy of Science Views: 3Total views on this site Views: 3Total views on this site Article DOIhttps://doi.org/10.1093/bjps/33.3.275 Views: 3Total views on this site © 1982 by The Author. All rights reserved.PDF download Crossref reports no articles citing this article.

A Note on the Role of Mathematics in Physics

A Note on the Role of Mathematics in Physics