# LEARNERS’ BELIEFS &amp; CONCEPTIONS ABOUT THE ROLE OF MATHEMATICS IN PHYSICS

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ABSTRACT
Mathematics is an essential part of what we call physics. It plays an important role in physics research as well as in learning physics. It can be a useful tool or a barrier too high to overcome for some of our students. Only recently this aspect of learning physics has been given more attention. The study presented here makes a contribution to this field of research by providing a first view on students’ conceptions about the role of mathematics in (learning) physics. These beliefs are functioning as filters for perception and processing and therefore have an important impact on our students’ learning processes.
To know about students’ conceptions can inspire teachers to create more adequate learning environments for our students and help them to be more efficient. German learners grade 10 and 12 as well as physics teacher students in their 4th semester have been surveyed.
Quantitative methods have been applied – structural equation modeling (sem) to ensure one-dimensional measures as well as measurement invariance across groups and a general linear model approach (glm) to test for within-subjects effects (distal vs. proximal beliefs and graphical vs. algebraic representations), between-subjects effects (group, achievement, sex) and interaction effects. The results encourage further in depth research.

INTRODUCTION
Mathematics plays an important role in doing and learning physics. There are studies and publications dealing with philosophical aspects, attempts to model math use in physics and studies focusing on the learners’ perspective in terms off attitudes and conceptions towards mathematics or science (see Krey 2012 for a review).
The motivation for research on students’ prior knowledge, attitudes etc. is, that all of these intuitive theories influence the learners’ way in which things are perceived, information is processed, and new things are learnt (eg. Pehkonen & Törner, 1996; Köller et al., 2000 or for teachers’ beliefs Pajares, 1992). This instrumental reason for studying beliefs is complemented by a substantial one – namely, these beliefs are core components of what we call mathematical or scientific literacy, e.g., the relevance of nos-knowledge, which should include conceptions about the role of mathematics for scientific (e.g., physics) research and science (e.g., physics) learning.
While there are a few philosophical approaches towards exploring the role of mathematics in physics, there is a lack of empirical findings about students beliefs in this field, although there are first attempts to close this gap (eg. Bing, 2008; Krey, 2012). While a few interviews have been conducted within the scope of this study, its main focus lies on
developing an instrument with which a quantitative approach becomes possible.
Research on the nature of science as well as common sense, suggest, that it is necessary to distinguish between proximal and distal beliefs (Hogan, 2000, 52): “Distal knowledge of the nature of science refers to students’ knowledge about [...] the professional scientific community. Proximal knowledge of the nature of science refers to students’ understanding
of and perspectives on the nature of their own science knowledge-building practices and the scientific knowledge they form or encounter.“
Based on first interviews conducted with grade 10 students, I assumed that in general it would make a difference whether students are confronted with mathematical representations in graphical or algebraic form. When I use the term “graphical
representation” I am referring to a graph in a coordinate system (see Friel, Curcio, & Bright, 2001 for an overview), while “algebraic representation” refers to equations that need to be constructed and interpreted when learning physics (Sherin, 2001).
The purpose of this research project was to collect data that help to describe the learners belief system about the role of mathematics in physics. A complete description of an individual learners’ belief system was not intended. For this purpose a few fields of interest have been nominated and operationalized. These fields include the students’ self-feeling
when dealing with mathematical representations (sf), their beliefs about aesthetics of mathematical representations (aest) epistemological aspects and their beliefs concerning relatively non-controversial functions that mathematics fulfils in physics (e.g. Fischer, 2006; Frey 1967).
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