The “Math as Prerequisite” Illusion: Historical Considerations and Implications for Physics Teaching

Karam, Ricardo; Uhden, Olaf; Höttecke, Dietmar

doi:10.1007/978-3-030-04627-9_2

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…Ever since modern science was born, mathematics and physics have been strongly intertwined, so that the role of mathematics in physics can best be described as structural [3][4][5]. Despite that, in most universities mathematics is seen just as a prerequisite for physics [6]. With only a few exceptions [7][8][9], calculus and physics are typically treated as separate subjects taught by faculty belonging to different departments, and physics instructors expect calculus courses to provide the students with the mathematical tools they need in physics.…”

Section: Introductionmentioning

confidence: 99%

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Carli

Lippiello

Perona³

et al. 2020

Phys. Rev. Phys. Educ. Res.

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In this article, we discuss the development and the administration of a multiple-choice test, which we named Test of Calculus and Vectors in Mathematics and Physics (TCV-MP), aimed at comparing students' ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics. The comparison between the two contexts was achieved by using parallel (isomorphic) questions in mathematics and physics. The final version of the test contains 34 items (17 in a purely mathematical context and 17 in the context of physics) involving different representations (graphs, words, numbers, and formal expressions) of the concepts covered by the test. The test was administered in Spring 2018 to 1252 first-year students enrolled in 23 different degree programs of the School of Science and the School of Engineering of the University of Padua. We assessed the validity, reliability, and discriminatory power of the test both as a whole and at the single-item level, obtaining values within the desired ranges. The analysis of students' answers to individual items and the comparison between parallel mathematics and physics items provides insights into the factors that affect students' ability to use derivatives, integrals, and vectors in the context of introductory physics. We believe that the instrument we have developed can be useful not only for research purposes, but also for instructors and for students.

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Section: Introductionmentioning

confidence: 99%

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Carli

Lippiello

Perona³

et al. 2020

Phys. Rev. Phys. Educ. Res.

View full text Add to dashboard Cite

show abstract

“…One of the main steps for students to take in most physics problems is the description of the physical situation using the appropriate and necessary mathematical formalism, as well as the manipulation of the proposed equation [15,[27][28][29][30][31]. According to researchers, mathematics is a necessary tool not only for understanding the physical phenomenon, but also for its satisfactory explanation.…”

Section: Student Difficulties In Problem-solving Strategiesmentioning

confidence: 99%

Common errors in mechanical physics among high school graduates in Brazil

Marcom¹,

Villar²,

Kleinke³

2021

Phys. Educ.

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Research on problem-solving strategies has been conducted since the 1940s. Experts and novices use different strategies in problem solving; the main difference is in the familiarity with which they face new problems. For multiple-choice problems, an analysis of distractors can provide possible clues about the resolution processes developed by examination candidates and reveal some learning difficulties. Thus, this study analysed data from the Brazilian National High School Examination (ENEM) because it holds great importance at the national level and mobilizes millions of candidates due to its advantages, such as admission to high social demand courses in public universities in Brazil. Our main objective was to identify some of the difficulties high school graduates face in mechanical physics. Thus, we analysed the rate of alternatives for a sample of six million students, finding that practically all the mechanics items indicated that there was no priority model in the item resolution process. Considering this finding, we concluded that the mechanics items at ENEM could be deemed difficult to solve, also indicating a greater variety of errors that students comment on. To analyse these possible mistakes made by students, we applied the analysis on distractors, which represent the reasoning hypotheses that students make when solving an item incorrectly. The analysis revealed the existence of a large set of errors in the knowledge of these students, such as mathematical immediacy (40%), symbolic forms (22%), non-scientific conception (22%), intuitive reasoning (9%), and analysis of the wrong images provided by the item (9%).

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“…Functions as means of learning in physics are not emphasized, and formulas are presented as multivariable expressions, e.g. F = ma, which can be converted to a one-variable covariational relationship by considering F (a) = ma or F (m) = ma, as also suggested by Karam et al (2019). Both functions are linear.…”

Section: How Was Covariational Reasoning Imposed On Formulas?mentioning

confidence: 99%

Unpacking structural domain of mathematics to aid inquiry in physics: a pilot study

Sokolowski

2020

Phys. Educ.

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Analysing graphs, formulating covariational relationships, and hypothesizing systems’ behaviour have emerged as frequent objectives of contemporary research in physics education. As such, these studies aim to help students achieve these objectives. While a consensus has been reached on the cognitive benefits of emphasizing the structural domain of mathematical apparatus in physics instruction, the question remains open on how to accomplish this task in school practice. This study contributes to this discussion. It attempts to determine how high-school physics students perceive formulas as a means to understand covariational relationships of natural phenomena. It also explores the hypothesis that including more structural domains of mathematics makes physics content more attractive for students. A sample of 25 advanced high-school physics students was taught kinematics, dynamics, and energy sections considering functional representations of some laws and principles traditionally covered in those sections. At the concluding phase, these students were invited to contrast formulas and their covariational embodiments as a means of providing conceptual understanding. The analysis revealed that students considered formulas as algebraic tools to attain a specific value to a particular application or carry out algebraic algorithms to solve a physics problem. They found formulas converted to covariational relationships a better fit for the learning of general phenomenon behaviour and extracting new information, especially from a graphical representation of these relationships. These findings generated the conclusion that the structural domain of mathematics can aid physics understanding by alternatively presenting formulas as mathematical entities that are transferrable to functions. It was further concluded that such parallelism would benefit not only the depth of inquiry in physics but also a general students’ STEM disposition.

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The “Math as Prerequisite” Illusion: Historical Considerations and Implications for Physics Teaching

Cited by 8 publications

References 5 publications

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Common errors in mechanical physics among high school graduates in Brazil

Unpacking structural domain of mathematics to aid inquiry in physics: a pilot study

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