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Student modeling within intelligent tutoring systems is a task largely driven by binary models that predict student knowledge or next problem correctness (i.e., Knowledge Tracing (KT)). However, using a binary construct for student assessment often causes researchers to overlook the feedback innate to these platforms. The present study considers a novel method of tabling an algorithmically determined partial credit score and problem difficulty bin for each student's current problem to predict both binary and partial next problem correctness. This study was conducted using log files from ASSISTments, an adaptive mathematics tutor, from the 2012-2013 school year. The dataset consisted of 338,297 problem logs linked to 15,253 unique student identification numbers. Findings suggest that an efficiently tabled model considering partial credit and problem difficulty performs about as well as KT on binary predictions of next problem correctness. This method provides the groundwork for modifying KT in an attempt to optimize student modeling.

Prerequisite skill structures have been closely studied in past years leading to many data-intensive methods aimed at refining such structures. While many of these proposed methods have yielded success, defining and refining hierarchies of skill relationships are often difficult tasks. The relationship between skills in a graph could either be causal, therefore, a prerequisite relationship (skill A must be learned before skill B). The relationship may be noncausal, in which case the ordering of skills does not matter and may indicate that both skills are prerequisites of another skill. In this study, we propose a simple, effective method of determining the strength of pre-to-post-requisite skill relationships. We then compare our results with a teacher-level survey about the strength of the relationships of the observed skills and find that the survey results largely confirm our findings in the data-driven approach.

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