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This study examined the relations among strategic planning, execution, and strategy efficiency during problem-solving in a digital algebra learning game with 7th-grade students. We used pre-solving pause time as a proxy indicator of strategic planning, and the productivity of the initial strategy as a measure of effective strategy execution. Additionally, we explored how these variables correlated with students’ posttest scores assessing algebraic knowledge. Mediation analyses at both the problem and student levels indicated that longer pre-solving pause times were associated with greater strategy efficiency. When considering both the direct and indirect effects of pre-solving pause time on strategy efficiency, the results revealed a partial positive mediation through the productivity of the initial strategy. Lastly, the results of a path analysis showed that strategy efficiency significantly predicted algebraic knowledge with a positive effect. These findings suggest that longer pause times are associated with more efficient problem solving as they increase the likelihood of a productive initial step, highlighting a positive mediating role of execution in the relation between planning and strategy efficiency in algebraic problem solving. 

Large language models have recently been able to perform well in a wide variety of circumstances. In this work, we explore the possi- bility of large language models, specifically GPT-3, to write explanations for middle-school mathematics problems, with the goal of eventually us- ing this process to rapidly generate explanations for the mathematics problems of new curricula as they emerge, shortening the time to inte- grate new curricula into online learning platforms. To generate expla- nations, two approaches were taken. The first approach attempted to summarize the salient advice in tutoring chat logs between students and live tutors. The second approach attempted to generate explanations us- ing few-shot learning from explanations written by teachers for similar mathematics problems. After explanations were generated, a survey was used to compare their quality to that of explanations written by teachers. We test our methodology using the GPT-3 language model. Ultimately, the synthetic explanations were unable to outperform teacher written explanations. In the future more powerful large language models may be employed, and GPT-3 may still be effective as a tool to augment teachers’ process for writing explanations, rather than as a tool to replace them. The prompts, explanations, survey results, analysis code, and a dataset of tutoring chat logs are all available at BLINDED FOR REVIEW. 

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.