Instructional Influences on Content Area Explanations and Representational Knowledge: Evidence for the Construct Validity of Measures of Principled Understanding

Recent calls for understanding-based mathematics instruction imply a need for alternative kinds of assessment. The purpose of this study was to determine if elementary students who received understanding-based mathematics instruction in a key domain (fractions), would outperform students who received more traditional instruction. The results showed that students who received understandings-based instruction on fraction principles performed better than students in a more traditionally instructed group on nearly all measures of principled understanding, and equally well on measures of computation. In response to understandings-based instruction, many students appeared to add new ideas about fractions to their existing knowledge, without discarding or reworking previously learned ideas. Results also showed the feasibility of assessing important aspects of mathematical understanding through students’ use of mathematical representations and language. Further, students used their representational knowledge when they wrote justifications and explanations to the assessment.