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  1. Stereotypes about men being better than women at mathematics appear to influence female students’ interest and performance in mathematics. Given the potential motivational benefits of digital learning games, it is possible that games could help to reduce math anxiety, increase self-efficacy, and lead to better learning outcomes for female students. We are exploring this possibility in our work with Decimal Point, a digital learning game that scaffolds practice with decimal operations for 5th and 6th grade students. In several studies with various versions of the game, involving over 800 students across multiple years, we have consistently uncovered a learning advantage for female students with the game. In our most recent investigation of this gender effect, we decided to experiment with a central feature of the game: its use of prompted self-explanation to support student learning. Prior research has suggested that female students might benefit more from self-explanation than male students. In the new study, involving 214 middle school students, we compared three versions of self-explanation in the game – menu-based, scaffolded, and focused – each presenting students with a different type of prompted self-explanation after they solved problems in the game. We found that the focused approach led to more learning across all students than the menu-based approach, a result reported in an earlier paper. In the additional results reported in this paper, we again uncovered the gender effect – female students learned more from the game than male students, regardless of the version of self-explanation – and also found a trend in which female students made fewer self-explanation errors, suggesting they may have been more deliberate and thoughtful in their self-explanations. This self-explanation finding is a possible key to further investigation into how and why we see the gender effect in Decimal Point. 
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  2. Mindfulness has been shown in prior studies to be an effective device to help students develop self-regulatory skills, including executive functions. However, these effects have been rarely tested at scale in technology-assisted learning systems such as digital learning games. In this work, we investigate the effects of mindfulness in the context of playing and learning with Decimal Point, a digital learning game for mathematics. We conducted a study with 5th and 6th grade students in which three conditions were compared - the game with short mindfulness meditations integrated, the game with similar-length, age-appropriate stories integrated, and the game in its original form. From the study results, we found no differences in time spent on the game, error rates while playing, or learning outcomes across the three conditions. Embedding mindfulness prompts within the game did not enhance learning or change students’ gameplay behaviors, which suggests that we may not have successfully induced a state of mindfulness or that mindfulness is not beneficial for learning within digital learning games. We discuss the challenges of incorporating individual mindfulness meditations in elementary and middle school classrooms. 
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  3. Prompted self-explanation, in which learners are induced to explain how they have solved problems, is a powerful instructional technique. Self-explanation can be prompted within learning technology by asking learners to construct their own self-explanations or select explanations from a menu. The menu-based approach has led to the best learning outcomes in the relatively few cases it has been studied in the context of digital learning games, contrary to some self-explanation theory. In a classroom study of 214 5th and 6th graders, in which the students played a digital learning game, we compared three forms of prompted self-explanation: menu-based, scaffolded, and focused (i.e., open-ended text entry, but with a focused prompt). Students in the focused condition learned more than students in the menu-based condition at delayed posttest, with no other learning differences between the conditions. This suggests that focused self-explanations may be especially beneficial for retention and deeper knowledge. 
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  4. There is an established gender gap in middle school math education, where female students report higher anxiety and lower engagement, which negatively impact their performance and even long-term career choices. This work investigates the role of digital learning games in addressing this issue by studying Decimal Point, a math game that teaches decimal numbers and operations to 5th and 6th graders. Through data from four published studies of Decimal Point, involving 624 students in total, the authors identified a consistent gender difference that was replicated across all studies – male students tended to do better at pretest, while female students tended to learn more from the game. In addition, female students were more careful in answering self-explanation questions, which significantly mediated the relationship between gender and learning gains in two out of four studies. These findings show that learning games can be an effective tool for bridging the gender gap in middle school math education, which in turn contributes to the development of more personalized and inclusive learning platforms. 
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  5. 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. 
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  6. Confrustion, a mix of confusion and frustration sometimes experienced while grappling with instructional materials, is not necessarily detrimental to learning. Prior research has shown that studying erroneous examples can increase students’ experiences of confrustion, while at the same time helping them learn and overcome their misconceptions. In the study reported in this paper, we examined students’ knowledge and misconceptions about decimal numbers before and after they interacted with an intelligent tutoring system presenting either erroneous examples targeting misconceptions (erroneous example condition) or practice problems targeting the same misconceptions (problem-solving condition). While students in both conditions significantly improved their performance from pretest to posttest, students in the problem-solving condition improved significantly more and experienced significantly less confrustion. When controlling for confrustion levels, there were no differences in performance. This study is interesting in that, unlike prior studies, the higher confrustion that resulted from studying erroneous examples was not associated with better learning outcomes; instead, it was associated with poorer learning. We propose several possible explanations for this different outcome and hypothesize that revisions to the explanation prompts to make them more expert-like may have also made them – and the erroneous examples that they targeted – less understandable and less effective. Whether prompted self-explanation options should be modeled after the shorter, less precise language students tend to use or the longer, more precise language of experts is an open question, and an important one both for understanding the mechanisms of self-explanation and for designing self-explanation options deployed in instructional materials. 
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  7. null (Ed.)
    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. 
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