Epistemic Views of the Relationship Between Physics and Mathematics: Its Influence on the Approach of Undergraduate Students to Problem Solving

Ataíde, Ana Raquel Pereira de; Greca, Ileana María

doi:10.1007/s11191-012-9492-2

Cited by 32 publications

(21 citation statements)

References 25 publications

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“…First, mathematics and physics have always been deeply linked, although not always in the same way. As described by de Ataide and Greca [1] the role of mathematics in physics historically evolved in three stages: from a way to describe analogies between physical objects in the real world and structures in an ideal world, to a mere language or a convenient tool to describe reality, and, finally, to a primary driver of new physical knowledge. This evolution came quite naturally with the ever-growing complexity of physical knowledge and the need for a consistent framework and unified theories to describe, to explain, to predict, and to understand physical reality.…”

Section: A Physics and Mathematicsmentioning

confidence: 99%

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Design and validation of a test for representational fluency of 9th grade students in physics and mathematics: The case of linear functions

Ceuppens

Deprez

Dehaene

et al. 2018

Phys. Rev. Phys. Educ. Res.

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This study reports on the development, validation, and administration of a 48-item multiple-choice test to assess students' representational fluency of linear functions in a physics context (1D kinematics) and a mathematics context. The test includes three external representations: graphs, tables, and formulas, which result in six possible representational transitions between them. Moreover, four linear function types are included: negative y intercept and positive slope, zero y intercept and positive slope, positive y intercept and negative slope, and positive y intercept and positive slope. The test is administered to 385 students aged 14-15 in the 9th grade from 13 schools in Flanders (Belgium) and-after validation-is analyzed by means of generalized estimating equations (GEE). The results show a significant main effect for all design factors and a significant interaction effect between representational transition and function type, as well as additional interaction effects with the gender of the respondents. Furthermore, representational transitions which include a formula prove to be significantly more difficult; in particular for the directly proportional function type, the transition to a formula stands out from the analysis. Mean accuracies in physics are significantly lower compared to mathematics. Function types with negative values for either y intercept or slope also result in significantly lower mean accuracies indicating the difficulty students have with negative numbers in linear functions. A distractor analysis of the incorrect answers chosen by the students reveals three distinct dominant errors: concept switching, sign switching, and switching of the directly proportional function type and the function type with positive y intercept and positive slope.

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Section: A Physics and Mathematicsmentioning

confidence: 99%

“…In this section we present the results from the validation [39]. 1 We provide a per-item overview of relevant validation quantities in Table I. In this table the items are sorted by representational transition and by function type to facilitate easy interpretation.…”

Section: A Validationmentioning

confidence: 99%

Design and validation of a test for representational fluency of 9th grade students in physics and mathematics: The case of linear functions

Ceuppens

Deprez

Dehaene

et al. 2018

Phys. Rev. Phys. Educ. Res.

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“…In particular, several studies in recent years demonstrate that students struggle to connect mathematics and physics [3][4][5]. In particular, students struggle with many mathematical aspects of thermodynamics [6][7][8] and with partial derivatives in particular [9][10][11][12]. With few exceptions [13], research on student understanding of derivatives focuses on conceptual understanding of ordinary derivatives, particularly on rate of change and graphical understanding [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Partial derivative games in thermodynamics: A cognitive task analysis

Kustusch

Roundy

Dray

et al. 2014

Phys. Rev. ST Phys. Educ. Res.

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Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task analysis for understanding expert performance and show how the epistemic games framework can be used as a tool for this type of analysis, with thermodynamics as an example. Second, through this analysis, we identify several issues related to thermodynamics that are relevant to future research into student understanding and learning of the mathematics of thermodynamics.

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“…Understanding the role of experiment is challenging for students in several ways. [1][2][3][4][5][6][7][8] Students have been shown to struggle with the operational definitions of pressure, temperature, and volume, and commonly fail to recognize the covariation among these three variables. 4 In upperdivision courses we add in entropy-a particularly challenging quantity-as a fourth canonical variable.…”

Section: Introductionmentioning

confidence: 99%

Name the experiment! Interpreting thermodynamic derivatives as thought experiments

Roundy

Kustusch

Manogue

2014

American Journal of Physics

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We introduce a series of activities to help students understand the partial derivatives that arise in thermodynamics. Students construct thought experiments that would allow them to measure given partial derivatives. These activities are constructed with a number of learning goals in mind, beginning with helping students to learn to think of thermodynamic quantities in terms of how one can measure or change them. A second learning goal is for students to understand the importance of the quantities held fixed in either a partial derivative or an experiment. Students additionally are given an experimental perspective-particularly when this activity is combined with real laboratory experiments-on the meaning of either fixing or changing entropy. In this paper, we introduce the activities and explain their learning goals. We also include examples of student work from classroom video and follow-up interviews. V

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Epistemic Views of the Relationship Between Physics and Mathematics: Its Influence on the Approach of Undergraduate Students to Problem Solving

Cited by 32 publications

References 25 publications

Design and validation of a test for representational fluency of 9th grade students in physics and mathematics: The case of linear functions

Design and validation of a test for representational fluency of 9th grade students in physics and mathematics: The case of linear functions

Partial derivative games in thermodynamics: A cognitive task analysis

Name the experiment! Interpreting thermodynamic derivatives as thought experiments

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