Mathematics teachers’ assessment of mathematical understanding

Abstract

Mathematical understanding is considered to have a multidimensional structure and an important place in mathematics teaching. The focus of the assessments in mathematics courses is on the multidimensional evaluation of mathematical understanding. However, a review of related literature shows the lack of studies on assessing mathematical understanding using multidimensional structures. For this reason, the current study attempted to develop a scale for assessing teachers' mathematical understanding. The instrument development model, an exploratory sequential mixed methods model, has been used in line with this aim during the scale’s development. The study’s qualitative data were collected through a mathematical understanding assessment form and semi-structured interviews developed by the authors. Qualitative data emerged from 17 mathematics teachers working in middle schools or high schools who were determined using the easy access sampling method. Five themes were arrived at from the content analysis with the obtained qualitative data: applying rules, transferring knowledge, generating questions and solutions, generalizing, and exploring information. The initial version of the instrument prepared in accordance with these themes was applied to a total of 501 primary school mathematics preservice teachers from nine different universities in Turkey during the 2018 spring semester. Cronbach’s alpha (α) assessment was performed for the scale’s reliability. Item-total correlations were calculated as item statistics. Exploratory and confirmatory factor analyses were applied to test the scale’s construct validity. The item loadings for the scale were seen to vary between.431 and.759 in this process; the reliability of the sub-dimensions and the scale’s fit indices were seen to be at sufficient levels. As a result of all the performed analyses, a scale form consisting of 21 items and five sub-dimension was obtained. The results from the scale development process show that the preservice teachers took into account the factor of transferring knowledge the most and the factor of producing questions and solution pathways the least.