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Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students’ perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers’ propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students’ precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students’ performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students’ performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving. 

There have been numerous efforts documenting the effects of open science in existing papers; however, these efforts typically only consider the author's analyses and supplemental materials from the papers. While understanding the current rate of open science adoption is important, it is also vital that we explore the factors that may encourage such adoption. One such factor may be publishing organizations setting open science requirements for submitted articles: encouraging researchers to adopt more rigorous reporting and research practices. For example, within the education technology discipline, theACM Conference on Learning @ Scale (L@S) has been promoting open science practices since 2018 through a Call For Papers statement. The purpose of this study was to replicate previous papers within the proceedings of L@S and compare the degree of open science adoption and robust reproducibility practices to other conferences in education technology without a statement on open science. Specifically, we examined 93 papers and documented the open science practices used. We then attempted to reproduce the results with invitation from authors to bolster the chance of success. Finally, we compared the overall adoption rates to those from other conferences in education technology. Although the overall responses to the survey were low, our cursory review suggests that researchers at L@S might be more familiar with open science practices compared to the researchers who published in the International Conference on Artificial Intelligence in Education (AIED) and the International Conference on Educational Data Mining (EDM): 13 of 28 AIED and EDM responses were unfamiliar with preregistrations and 7 unfamiliar with preprints, while only 2 of 7 L@S responses were unfamiliar with preregistrations and 0 with preprints. The overall adoption of open science practices at L@S was much lower with only 1% of papers providing open data, 5% providing open materials, and no papers had a preregistration. All openly accessible work can be found in an Open Science Framework project. 

Prior work analyzing tutoring sessions provided evidence that highly effective tutors, through their interaction with students and their experience, can perceptively recognize incorrect processes or “bugs” when students incorrectly answer problems. Researchers have studied these tutoring interactions examining instructional approaches to address incorrect processes and observed that the format of the feedback can influence learning outcomes. In this work, we recognize the incorrect answers caused by these buggy processes as Common Wrong Answers (CWAs). We examine the ability of teachers and instructional designers to identify CWAs proactively. As teachers and instructional designers deeply understand the common approaches and mistakes students make when solving mathematical problems, we examine the feasibility of proactively identifying CWAs and generating Common Wrong Answer Feedback (CWAFs) as a formative feedback intervention for addressing student learning needs. As such, we analyze CWAFs in three sets of analyses. We first report on the accuracy of the CWAs predicted by the teachers and instructional designers on the problems across two activities. We then measure the effectiveness of the CWAFs using an intent-to-treat analysis. Finally, we explore the existence of personalization effects of the CWAFs for the students working on the two mathematics activities.