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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 misconcep- tions 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 aca- demic 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 ef- fectiveness of CWAFs in two scenarios: next-problem-correctness within-skill and next-problem-correctness within-assignment, re- gardless of the skill. We find that receiving CWAF leads to a signifi- cant 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 Com- mon Wrong Answers (CWAs) and how the use of crowdsourced CWAFs can enhance student learning through remediation. 

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. 

Prior work analyzing tutoring sessions provided evidence that highly effective tutors, through their interaction with students and their experience, can perceptively recognize incorrect processes or “bugs” when students incorrectly answer problems. Researchers have studied these tutoring interactions examining instructional approaches to address incorrect processes and observed that the format of the feedback can influence learning outcomes. In this work, we recognize the incorrect answers caused by these buggy processes as Common Wrong Answers (CWAs). We examine the ability of teachers and instructional designers to identify CWAs proactively. As teachers and instructional designers deeply understand the common approaches and mistakes students make when solving mathematical problems, we examine the feasibility of proactively identifying CWAs and generating Common Wrong Answer Feedback (CWAFs) as a formative feedback intervention for addressing student learning needs. As such, we analyze CWAFs in three sets of analyses. We first report on the accuracy of the CWAs predicted by the teachers and instructional designers on the problems across two activities.We then measure the effectiveness of the CWAFs using an intent-to-treat analysis. Finally, we explore the existence of personalization effects of the CWAFs for the students working on the two mathematics activities. 

Prior work analyzing tutoring sessions provided evidence that highly effective tutors, through their interaction with students and their experience, can perceptively recognize incorrect processes or “bugs” when students incorrectly answer problems. Researchers have studied these tutoring interactions examining instructional approaches to address incorrect processes and observed that the format of the feedback can influence learning outcomes. In this work, we recognize the incorrect answers caused by these buggy processes as Common Wrong Answers (CWAs). We examine the ability of teachers and instructional designers to identify CWAs proactively. As teachers and instructional designers deeply understand the common approaches and mistakes students make when solving mathematical problems, we examine the feasibility of proactively identifying CWAs and generating Common Wrong Answer Feedback (CWAFs) as a formative feedback intervention for addressing student learning needs. As such, we analyze CWAFs in three sets of analyses. We first report on the accuracy of the CWAs predicted by the teachers and instructional designers on the problems across two activities. We then measure the effectiveness of the CWAFs using an intent-to-treat analysis. Finally, we explore the existence of personalization effects of the CWAFs for the students working on the two mathematics activities.