Using a multi-dimensional approach to understanding to assess primary students' mathematical knowledge

Abstract

Mathematics assessment should involve more than just assessing students' knowledge of content. How students understand the content is important and should also be a part of the assessment process. For robust knowledge, students need a multi-dimensional understanding of content, including a focus on skills, properties, uses, and representations related to the content under study. This paper discusses the importance of assessing students' understanding across various dimensions and illustrates how their understanding can vary by dimension. Specific examples of assessment items come from the International Project on Mathematical Attainment, a longitudinal study of primary students' achievement in which the United States of America and Singapore were participants. Achievement results from these two countries illustrate how a focus on overall results, without consideration of an analysis by dimension of understanding, can mask important similarities and differences in achievement.