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Prior studies have explored the potential of erroneous examples in helping students learn more effectively by correcting errors in solutions to decimal problems. One recent study found that while students experience more confusion and frustration (confrustion) when working with erroneous examples, they demonstrate better retention of decimal concepts. In this study, we investigated whether this finding could be replicated in a digital learning game. In the erroneous examples (ErrEx) version of the game, students saw a character play the games and make mistakes, and then they corrected the characters’ errors. In the problem solving (PS) version, students played the games by themselves. We found that confrustion was significantly, negatively correlated with performance in both pretest (r = -.62, p < .001) and posttest (r = -.68, p < .001) and so was gaming the system (pretest r = -.58, p < .001, posttest r = -.66, p < .001). Posthoc (Tukey) tests indicated that students who did not see any erroneous examples (PS-only) experienced significantly lower levels of confrustion (p < .001) and gaming (p < .001). While we did not find significant differences in post-test performance across conditions, our findings show that students working with erroneous examples experience consistently higher levels of confrustion in both game and non-game contexts. 

Recent student knowledge modeling algorithms such as Deep Knowledge Tracing (DKT) and Dynamic Key-Value Memory Networks (DKVMN) have been shown to produce accurate predictions of problem correctness within the same learning system. However, these algorithms do not attempt to directly infer student knowledge. In this paper we present an extension to these algorithms to also infer knowledge. We apply this extension to DKT and DKVMN, resulting in knowledge estimates that correlate better with a posttest than knowledge estimates from Bayesian Knowledge Tracing (BKT), an algorithm designed to infer knowledge, and another classic algorithm, Performance Factors Analysis (PFA). We also apply our extension to correctness predictions from BKT and PFA, finding that knowledge estimates produced with it correlate better with the posttest than BKT and PFA’s standard knowledge estimates. These findings are significant since the primary aim of education is to prepare students for later experiences outside of the immediate learning activity.