COGNITIVE STRUCTURE ANALYSIS: ASSESSING ELEMENTARY SCHOOL STUDENTS IN MATH TO DETERMINE THE TYPES OF KNOWLEDGE THEY HAVE

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 (CSA) 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. Previous studies with middle and high school students revealed strong correlations between students’ factual, procedural, strategic and rationale subject matter knowledge and their problem solving performance. Given that the Leddo et al. (1990) research showed that all four types of knowledge were present in highly experienced people but that novices tended to be characterized by factual and procedural knowledge, the question arises as to whether elementary school students would show significant correlations between only factual and procedural knowledge and problem solving performance on school subject matter due to their lack of academic experience. The present study investigated this question using fifth graders studying math. 20 fifth graders were taught beginning and advanced concepts in solving distance = rate * time problems. Afterwards, they were assessed on their concept knowledge using CSA and given practical problems to solve. Results showed significant correlations between factual and procedural knowledge as assessed by CSA and problem solving performance. Correlations between strategic and rationale knowledge were not statistically significant. These results suggest that elementary school students not only have less subject matter knowledge than their older counterparts, but that the type of knowledge they have is also qualitatively different. This finding may have implications for how to teach students in order to nurture advanced thinking skills.