COGNITIVE STRUCTURE ANALYSIS: ASSESSING STUDENTS’ KNOWLEDGE OF PRECALCULUS

Abstract

Assessment has been a key part of education, playing the role of determining how much students have learned. Traditionally, assessments have focused on whether students give the correct answer to problems, implying that the number of correctly answered test items is a valid measure of how much students know. Unfortunately, the focus on correct answers has also resulted in neglecting the potential ability of assessments to provide diagnostic feedback to educators as to what concepts students have mastered and where the gaps in their knowledge are, thus potentially informing the day-to-day teaching process. The present paper describes an assessment technique called Cognitive Structure Analysis that is derived from John Leddo’s integrated knowledge structure framework (Leddo et al., 1990) that combines several prominent knowledge representation frameworks in cognitive psychology. In a previous study (Leddo et al., 2022), CSA-based assessments of Algebra 1 knowledge correlated .966 with student problem-solving performance. The present study replicates the Leddo et al. (2022) findings on the subject of precalculus. Using a Google Form, students were queried on four types of knowledge considered the basis of mastery of precalculus concepts: factual, procedural, strategic, and rationale. From students’ responses to these queries, measures of each type of knowledge and a combined knowledge score were created. Students were also given problems to solve. Correlations between each knowledge component score and problem-solving performance were high and the correlation between overall CSA-assessed knowledge and problem-solving performance was .80. Results suggest that CSA