Assessing and Remediating Knowledge Improves Problem-solving Performance in Middle School Math Compared to Remediating Problemsolving Steps

A widespread practice in education is to give students problems to solve, ask them to show their work and, when they make mistakes, show them the correct way to solve the problem to arrive at the right answer. This approach is consistent with the precepts of Classical Test Theory, which operationalizes learning in terms of the number of correct answers given to problems. The present paper challenges this approach by comparing it to an alternative that assesses what subject matter knowledge students have using a methodology called Cognitive Structure Analysis (CSA) and remediating any knowledge gaps. This study follows a previous study (Leddo and Ahmad, 2024) that showed that when high schoolers had their mathematics knowledge assessed and remediated using CSA, they performed 10 percentage points better on a post-test than those whose problem-solving steps were assessed and remediated. The present study extends this to middle school math. Middle schoolers were initially either given problems to solve and feedback in the form of being shown correct step-by-step solutions to the problems or had their concept knowledge assessed using CSA and then provided feedback to remediate any knowledge deficiencies they had. All students were then given a 20-question problem-solving post-test. Results showed that those whose CSA-assessed knowledge was remediated scored 13 percentage points higher on the post-test than those whose step-by-step procedures were remediated. Moreover, those students who had their step-by-step procedures remediated showed no improvement in problem solving performance from pre-test to post-test. Results suggest that assessing and remediating concept knowledge may provide a quick, cheap, and easy way to improve academic performance compared to the traditional assessment and remediation approach of emphasizing correct solutions to problems.