How Common are Common Wrong Answers? Crowdsourcing Remediation at Scale

Abstract

Solving mathematical problems is cognitively complex, involving strategy formulation, solution development, and the application of learned concepts. However, gaps in students' knowledge or weakly grasped concepts can lead to errors. Teachers play a crucial role in predicting and addressing these difficulties, which directly influence learning outcomes. However, preemptively identifying misconceptions leading to errors can be challenging. This study leverages historical data to assist teachers in recognizing common errors and addressing gaps in knowledge through feedback. We present a longitudinal analysis of incorrect answers from the 2015-2020 academic years on two curricula, Illustrative Math and EngageNY, for grades 6, 7, and 8. We find consistent errors across 5 years despite varying student and teacher populations. Based on these Common Wrong Answers (CWAs), we designed a crowdsourcing platform for teachers to provide Common Wrong Answer Feedback (CWAF). This paper reports on an in vivo randomized study testing the effectiveness of CWAFs in two scenarios: next-problem-correctness within-skill and next-problem-correctness within-assignment, regardless of the skill. We find that receiving CWAF leads to a significant increase in correctness for consecutive problems within-skill. However, the effect was not significant for all consecutive problems within-assignment, irrespective of the associated skill. This paper investigates the potential of scalable approaches in identifying Common Wrong Answers (CWAs) and how the use of crowdsourced CWAFs can enhance student learning through remediation.