Dimensional analysis: reasoning with units of measurement as a tool for improved problem-solving competency

Abstract

The key idea of dimensional analysis is to see units of measurement as a crucial source of information for solving mathematical problems. Yet, this powerful tool is hardly at all mentioned in mathematics education research within secondary schools. Hence, this study explores dimensional analysis in secondary school with respect to its occurrence in high-stakes tests and whether teaching it could make students use it as a tool in mathematical problem solving. A first result from inspecting released national tests is that knowledge of the idea behind dimensional analysis seems useful on a substantial proportion of the test items. A second result from inspecting students’ archived responses to test items is that a large proportion of the students do not make use of the information contained in units of measurement. A third result is that an intervention on teaching the elements of dimensional analysis made students significantly improved their results from pre-test to post-test. Accordingly, we recommend teaching the key idea in dimensional analysis from lower secondary school as a tool for mathematical problem solving.