A Trace-based Framework for Analyzing and Synthesizing Educational Progressions


A key challenge in teaching a procedural skill is finding an effective progression of example problems that the learner can solve in order to internalize the procedure. In many learning domains, generation of such problems is typically done by hand and there are few tools to help automate this process. We reduce this effort by borrowing ideas from test case generation in software engineering and show how we can use execution traces as a framework for abstracting the characteristics of a given procedure and defining a partial ordering that reflects the relative difficulty of two traces. We also show how we can use this framework to analyze the completeness of expert-designed progressions and fill in holes. Furthermore, we demonstrate how our framework can automatically synthesize new problems by generating large sets of problems for elementary and middle school mathematics. We present the results of a user study with a popular algebra-learning game confirming that our partial ordering can accurately predict user evaluation of procedural difficulty.