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

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.

Is TIMSS Advanced an appropriate instrument for evaluating mathematical performance at the advanced level of Norwegian upper secondary school? An analysis of curriculum documents and assessment items

Given that the results of international large-scale achievement studies attract a lot of attention and may affect educational policies, the primary aim of the present study is to discuss the appropriateness of the mathematics tests developed for the two cycles of TIMSS Advanced for evaluating the mathematical performance of Norwegian upper secondary school students. This will here be done by employing a methodology for alignment studies developed by Porter (2002), which entails analyzing and describing the mathematical content of the Norwegian curriculum documents and the TIMSS Advanced assessment items, and calculating the agreement between these. The analyses show a moderate alignment between the different iterations of TIMSS Advanced and the curriculum followed by the participating students, implying that the emphasis in the Norwegian mathematics curriculum differs somewhat from that of the TIMSS Advanced tests. These analyses do not warrant the conclusion that the TIMSS Advanced tests were inappropriate instruments for assessing the mathematical performance of Norwegian students. They do, however, imply that the differences in emphasis between the different iterations of TIMSS Advanced and the curriculum followed by the participating students should be taken into account in order to make valid interpretations of the results of this large-scale survey. Finally, as alignment is evaluated by contrasting alignment indices calculated for different combinations of the intended and assessed curriculum, additional research is needed if one is to make more firm judgments. One additional contribution of the present study is demonstrating a powerful methodology for conducting this kind of research.

TIMSS Advanced 2008: Fall i fysikk-kompetanse i Norge og Sverige

TIMSS Advanced 2008 is an international comparative study, and deals with examining student achievement in mathematics and physics in the final year at upper secondary school. The theme of this article is to look at how Norwegian and Swedish students performed in physics in 2008 compared to the study conducted in 1995. The results from the TIMSS Advanced study provide an unambiguous picture. There is a significant decline in the performance in physics since the previous study in 1995 for both Norwegian and Swedish students. One important reason is related to the generally low level of results in science and mathematics at all levels in schools as shown by the downward trend for students in lower grades. The decline in physics performance can thus be explained by the fact that students with significantly weaker skills than before in mathematics and science come into upper secondary school. Lack of knowledge of basic arithmetic and algebra seems to be a contributing factor for this downwards trend in physics at upper secondary school level.