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Learning to derive subgoals reduces the gap between experts and students and prepares students for future problem solving. This paper explores a training strategy using backward worked examples (BWE) and backward problem solving (BPS) within an intelligent logic tutor to support backward strategy learning, with analysis of student experience, performance, and proof construction. Results show that students trained with both BWE and BPS outperform those receiving none or only BWE, demonstrating more efficient subgoal derivation. 

Humans adopt various problem-solving strategies depending on their mastery level, problem type, and complexity. Many of these problem-solving strategies have been integrated within intelligent problem-solvers to solve structured and complex problems efficiently. One such strategy is the means-ends analysis which involves comparing the goal and the givens of a problem and iteratively setting up subgoal(s) at each step until the subgoal(s) are straightforward to derive from the givens. However, little is known about the impact of explicitly teaching novices such a strategy for structured problem-solving with tutors. In this study, we teach novices a subgoal-directed problem-solving strategy inspired by means-ends analysis using a problem-based training intervention within an intelligent logic-proof tutor. As we analyzed students’ performance and problem-solving approaches after training, we observed that the students who learned the strategy used it more when solving new problems, constructed optimal logic proofs, and outperformed those who did not learn the strategy. 

Problem decomposition into sub-problems or subgoals and recomposition of the solutions to the subgoals into one complete solution is a common strategy to reduce difficulties in structured problem solving. In this study, we use a datadriven graph-mining-based method to decompose historical student solutions of logic-proof problems into Chunks. We design a new problem type where we present these chunks in a Parsons Problem fashion and asked students to reconstruct the complete solution from the chunks. We incorporated these problems within an intelligent logic tutor and called them Chunky Parsons Problems (CPP). These problems demonstrate the process of problem decomposition to students and require them to pay attention to the decomposed solution while they reconstruct the complete solution. The aim of introducing CPP was to improve students’ problem-solving skills and performance by improving their decomposition-recomposition skills without significantly increasing training difficulty. Our analysis showed that CPPs could be as easy as Worked Examples (WE). And, students who received CPP with simple explanations attached to the chunks had marginally higher scores than those who received CPPs without explanation or did not receive them. Also, the normalized learning gain of these students shifted more towards the positive side than other students. Finally, as we looked into their proof-construction traces in posttest problems, we observed them to form identifiable chunks aligned with those found in historical solutions with higher efficiency.