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

Abstract

As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal) on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.

Teachers’ Core Beliefs about Improving Students’ Transfer of Algebraic Skills from Mathematics into Physics in Senior Pre-university Education

“…Moreover, the individual studies above are in line with large scale international studies in which there is a clear decline in students' achievements in physics related to insufficient mathematical competence in a number of different countries (e.g. Mullis et al, 2016;Nilsen et al, 2013).…”

“…Teachers have the experience that students encounter difficulties when applying mathematics in physics class (Ivanjek et al, 2016;Karam, 2014;Nilsen, Angell & Grønmo, 2013;Quinn, 2013). Such transfer problems can be intractable and concern students of all ages, including those in pre-university education (Awodun, Omotade & Adeniyi, 2013;Basson, 2002;Molefe, 2006;Roorda, 2012).…”

The importance of discourse and attitude in learning astronomy. A mixed methods approach to illuminate the results of the TIMSS 2011 survey.

“…Furthermore, most students preferred science tasks with no mathematics competencies involved, and 8 th grade astronomy requires no mathematics. This is supported by previous research, as students often struggle with applying mathematics in physics (Lie, Angell, & Rohatgi, 2010;Nilsen et al, 2013;Redish, 2006), and by Girl 1 from School A, who made reference to the problem of applying mathematics competencies to another subject (Rebello, Cui, Bennett, Zollman, & Ozimek, 2007).…”

“…One major reason why students struggle with physics in Norway is related to difficulties with mathematics (Nilsen, Angell, & Grønmo, 2013). Since no mathematics competencies are required for 8 th grade astronomy in Norway, we hypothesized that this may lead to high self-efficacy in astronomy.…”

The dependence on mathematical theory in TIMSS, PISA and TIMSS Advanced test items and its relation to student achievement

“…As an example, since the Norwegian value minus the Russian value in Table 8 is around 8%, we may conclude that Norwegian students are significantly more "negative" to relevance of mathematical theorems in physics items than Russian students. The relation between TIMSS Advanced physics achievement and other measures of mathematics competence in Norway and Sweden has previously been addressed in (Lie et al 2012;Nilsen et al 2013). Now, let us turn to TIMSS Advanced 2015 mathematics.…”