Modelling Mathematical Reasoning in Physics Education

Abstract

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008

“…Mulhall and Gunstone (2008) have pointed out that physics teachers pay little attention to the place of mathematics in physics, and Reddish (2006) claimed that physics teachers should take a greater responsibility and teach students how to apply mathematics in physics. Moreover, Uhden et al (2011) claimed that "the knowledge about a supportive use of mathematics in physics education is still fragmentary" (p. 2) within research in physics education.…”

“…Physics and mathematics are strongly interrelated, and this relationship becomes more apparent as students advance in school. Mathematics is more than just a tool for working with physics problems; the discourse of physics is mathematical in nature (Uhden, Karam, Pietrocola, & Pospiech, 2011).…”

“…Conceptual understanding deserves a great deal of attention in physics education; physics is often regarded as a particularly difficult school subject (see e.g., Angell, Guttersrud, Henriksen, & Isnes, 2004;Carlone, 2003;Duit, Niedderer, & Schecker, 2007;Osborne, 2001). However, the nature of the students' difficulties also involves the use of mathematics (Meltzer, 2002;Redish, 2006;Uhden et al, 2011).…”

General relativity in upper secondary school: Design and evaluation of an online learning environment using the model of educational reconstruction

“…This was a recurrent critique in the interviews that relates to the frustration that students experience when approaching GR only qualitatively. This finding shows that students are aware of the close relationship between mathematics and physics [71]. However, the challenge in GR is that we do not have easy calculations at hand and that students have to rely almost exclusively on nonmathematical explanations: FG-student: (…) it is difficult to understand like.…”

Development of an explanatory framework for the solution of electricity problems

“…Sommige studies dui op wiskunde as onontbeerlik in die leer van fisika (Ayene, Damtie & Kriek 2010), terwyl ander wiskunde as 'n hindernis uitbeeld (Koichu 2010). Sommige (Uhden et al 2012) redeneer egter steeds dat kennis oor die ondersteunende gebruik van wiskunde in studente se leer van fisika gefragmenteerd is.…”