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What does it mean to understand a physics equation?: A study of undergraduate answers In three countriesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)Conference paper, Oral presentation with published abstract (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Dublin: ESERA, 2017.
##### Keywords [en]

Equations, Physics, Higher education
##### National Category

Other Physics Topics Didactics
##### Research subject

Physics with specialization in Physics Education
##### Identifiers

URN: urn:nbn:se:uu:diva-335282OAI: oai:DiVA.org:uu-335282DiVA, id: diva2:1162096
##### Conference

12th Conference of the European Science Education Research Association (ESERA 2017) DCU Dublin 21-25 Aug 2017
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true}); Available from: 2017-12-03 Created: 2017-12-03 Last updated: 2017-12-14Bibliographically approved

What does it mean to understand a physics Equation? A study of Undergraduate answers In Three countries.

*John Airey ^{1,2} Josefine Grundström Lindqvist^{1} Rebecca Kung^{3 }*

^{1}Department of Physics, Uppsala University, Sweden

^{2}Department of Mathematics and Science Education, Stockholm University, Sweden

^{3}Independent researcher, Grosse Ile, MI, USA.

*In this paper we are interested in how undergraduate students in the US, Australia and Sweden experience the physics equations they meet in their education. We asked over 350 students the same simple question: How do you know when you understand a physics equation? Students wrote free-text answers to this question and these were transcribed and coded. The analysis resulted in eight themes (significance, origin, describe, predict, parts, relationships, calculate and explain). Each of these themes represents a different disciplinary aspect of student understanding of physics equations. We argue that together the different aspects we find represent a more holistic view of physics equations that we would like all our students to experience. Based on this work we wondered how best to highlight this more holistic view of equations. This prompted us to write a set of questions that reflect the original data with respect to the eight themes. We suggest that when students are working with problem solving they may ask themselves these questions in order to check their holistic understanding of what the physics equations they are using represent. In continuing work we are asking the same question to a cohort of physics lecturers. We are also trialling the themes and related questions that we generated in teaching situations. Here we are interested in whether students perceive the questions as helpful in their learning. *

*Keywords*: International Studies in Education, Physics, Higher Education

Background

As a discipline, physics is concerned with describing the world by constructing models, the end product of this modelling process often being an equation. Despite their importance in the representation of physics knowledge, physics equations have received surprisingly little attention in the literature. The work that has been done has tended to focus on the use of equations in problem solving (see Hsu, Brewe, Foster, & Harper, 2004 for an overview and Hegde & Meera, 2012 for a more recent example). One significant study is that of Sherin (2001) who examined students ability to construct equations.* *The majority of work suggests that many students in calculus-based physics courses focus their attention exclusively on selecting an equation and substituting in known values—so called “plug and chug” (see Tuminaro 2004). This behaviour—what Redish (1994) has termed the “Dead Leaves” approach to physics equations—has been framed as a major hurdle to students’ ability to see the bigger picture of physics. However, very little work has examined what students think it means to understand a physics equation, the only work we could locate was that of Domert et al, 2007 and Hechter, 2010. Building on these two sources this study examines student understanding of physics equations in three countries. Our research questions are:

- How do students in three countries say they know that they have understood a physics equation?
- What different disciplinary aspects of equations can be seen in an analysis of the complete set of answers to research question 1?
- How might a more holistic view of the understanding of equations be communicated to students?

Method

This qualitative study uses a research design based on minimum input and maximised output. We asked students in the US (n=83), Australia (n=168) and Sweden (n=105) the same simple question:

**How do you know when you understand a physics equation?**

Students wrote free-text answers to this question and these were transcribed and coded. Using qualitative analysis techniques drawn from the phenomenographic tradition, the whole dataset was then treated as a “pool of meaning” (See Airey, 2012 for an example of this type of analysis).

Analysis and Results

In our analysis we initially looked for differences across countries, however it quickly became apparent that there was a range of answers that repeated across countries. This led us to treat the data as a single set. This first analysis resulted in 15 preliminary categories. These categories were later broken up and reconstructed to form eight themes: Significance, Origin, Describe, Predict, Parts, Relationships, Calculate and Explain. We suggest that each of these eight themes represents a different disciplinary aspect of the expressed student understanding of physics equations. We argue that together the different aspects we find represent a more holistic view of physics equations that we would like all our students to experience. Based on this work we wondered how best to highlight this more holistic view of equations. This prompted us to write a set of questions that reflect the original data with respect to the eight themes:

**1 ****Significance: Why, when, where**

Do you know why the equation is needed?

Do you know where the equation can and cannot be used? (boundary conditions/areas of physics).

Do you understand what the equation means for its area of physics?

What status does this equation have in physics? (fundamental law, empirical approximation, mathematical conversion, etc.).

**2 ****Origin**

Do you know the historical roots of the equation?

Can you derive the equation?

**3 ****Describe/visualize**

Can you use the equation to describe a real-life situation?

Can you describe an experiment that the equation models?

Can you visualize the equation by drawing diagrams, graphs etc.

**4 ****Predict**

Can you use the equation to predict?

**5 ****Parts **

Can you describe the physical meaning of each of the components of the equation?

How does a change in one component affect other components in the equation?

Can you manipulate/rearrange the equation?

**6 ****Other equations**

Can you relate this equation to other equations you know?

Can you construct the equation from other equations that you know?

**7 ****Calculate**

Can you use the equation to solve a physics problem?

Can you use the equation to solve a physics problem in a different context than the one in which it was presented?

When you use the equation to calculate an answer do you know:

- How your answer relates to the original variables?
- The physical meaning of this answer?
- Whether your answer is reasonable?

**8 ****Explain**

Can you explain the equation to someone else?

Discussion and conclusion

The motivation for this study came from an experience the first author had a number of years ago. In an interview situation, students were asked in passing about whether they understood a certain equation. They replied “yes” and that the equation was “trivial”. However when questioned about what one of the terms in the equation meant and the students did not know! The students clearly meant that the equation was trivial from a mathematical point of view—they knew they could easily use the equation to “calculate stuff” so they said that they understood it. In Redish’s (1994) terms they were using the “Dead Leaves” approach to physics equations.

We believe the questions we have generated in this study have the potential to help physics students who *think* they understand a physics equation to check whether there might be other aspects that they may not yet have considered.

Our questions are based on student-generated data. Potentially physics lecturers could experience physics equations in even more complex ways. In continuing work we are therefore asking the same question to a cohort of physics lecturers. We are also trialling the themes and related questions that we generated in various teaching situations. Here we are interested in whether students perceive the questions as helpful in their learning.

Acknowledgements

Support from the Swedish Research Council, VR project no. 2016-04113, is gratefully acknowledged.

REFERENCES

Airey, J. (2012). “I don’t teach language.” The linguistic attitudes of physics lecturers in Sweden. *AILA Review, 25*(2012), 64–79.

Domert, D., Airey, J., Linder, C., & Kung, R. (2007). An exploration of university physics students' epistemological mindsets towards the understanding of physics equations. NorDiNa,Nordic Studies in Science Education(3), 15-28.

Hechter, R. P. (2010). What does it understand the equation' really mean? Physics Education, 45(132).

Hegde, B. & Meera, B. N. (2012). How do they solve it? An insight into the learner's approach to the mechanism of physics problem solving. Phys. Rev. ST Phys. Educ. Res. 8, 010109

Hsu, L., Brewe, E., Foster, T. M., & Harper, K. A. (2004). Resource Letter RPS-1: Research in problem solving. American Journal of Physics, 72(9), 1147-1156.

Redish, E. (1994). The implications of cognitive studies for teaching physics. American Journal of Physics, 62(6), 796-803.

Sherin, B. L. (2001). How students understand physics equations. Cognitive Instruction, 19, 479-541.

Tuminaro, J. (2004). A Cognitive framework for analyzing and describing introductory students' use of mathematics in physics. PhD Thesis. University of Maryland, Physics Department.

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