Complementary measures of conceptual understanding: a case about triangle concepts

Abstract

Mathematics curricula from many countries have emphasized conceptual understanding as more important than the mastery of isolated skills. However, researchers and educators have used different measures to access students’ conceptual understanding of mathematics. Thus, it seems necessary to further explore whether and to what extent different measurement techniques could lead to coherent findings. Therefore, this study compares the techniques that are commonly used in school settings with those proposed by researchers as effective in addressing conceptual understanding. Specifically, this study compares three techniques used to assess the quality of the conceptual understanding of triangles, conducted among a class of grade 8 students in China. The three techniques were a definition-example-nonexample test, a concept-mapping task, and a traditional paper-and-pencil test on the operations of the concepts and their relationships. The results show that these techniques provide complementary, rather than convergent, insights into students’ conceptual understanding. Their strengths and limitations in addressing students’ conceptual understanding were identified. The findings not only provide information for researchers, educators, and classroom teachers in identifying alternative techniques in assessing conceptual understanding but also a more holistic view of students’ conceptual understanding when different perspectives of this understanding are made explicit.