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Abstract Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in‐lab eye tracking and a sample of 85 undergraduates from a STEM‐focused university, we investigated how higher‐order operator position (HOO; i.e., multiplication/division operators and the presence of superfluous brackets impacted students' time to first fixation to the HOO, response time, and percent of correct responses). Students solved order‐of‐operations problems presented in six ways (3 HOO positions × presence of brackets). We found that HOO position and presence of superfluous brackets had separate and combined impacts on calculating arithmetic expressions. Superfluous brackets most influenced undergraduates' performance when higher‐order operators were located in the center of mathematical expressions. Implications for learning and future directions are discussed about observing eye movements and gaining insights into students' processes when solving arithmetic expressions. 

ABSTRACT BackgroundEducational technologies typically provide teachers with analytics regarding student proficiency, but few digital tools provide teachers with process‐based information about students' variable problem‐solving strategies as they solve problems. Utilising design thinking and co‐designing with teachers can provide insight to researchers about what educators need to make instructional decisions based on student problem‐solving data. ObjectivesThis case study presents a collaboration where researchers and teachers co‐designed MathFlowLens, a teacher‐facing dashboard that provides analytics and visualisations about students' diverse problem‐solving strategies and behaviours used when solving online math problems in the classroom. MethodsOver several sessions, teachers discussed, mocked up, and were provided with behavioural data and strategy visualisations from students' math problem‐solving that demonstrated the variability of strategic approaches. Throughout this process, the team documented, transcribed, and used these conversations and artefacts to inform the design and development of the teacher tool. Results and ConclusionsTeachers discussed and designed prototypes of data dashboards and provided the research team with ongoing feedback to inform the iteration of the tool development. 

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. 

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined 1) how different ML algorithms influenced the precision of middle-school students’ (N = 359) performance (i.e. posttest math knowledge scores) prediction and 2) what types of in-game features (i.e. student in-game behaviors, math anxiety, mathematical strategies) were associated with student math knowledge scores. The results indicated that the Random Forest algorithm showed the best performance (i.e. the accuracy of models, error measures) in predicting posttest math knowledge scores among the seven algorithms employed. Out of 37 features included in the model, the validity of the students’ first mathematical transformation was the most predictive of their posttest math knowledge scores. Implications for game learning analytics and supporting students’ algebraic learning are discussed based on the findings. 

For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional materials to direct students’ attention and facilitate accurate and efficient problem solving. This online study examines the impact of operator position and superfluous brackets on students’ performance solving arithmetic problems. A total of 528 students completed a baseline assessment of math knowledge, then were randomly assigned to one of six conditions that varied in the placement of higher-order operator and the presence or absence of superfluous brackets: [a] brackets-left (e.g., (5 * 4) + 2 + 3), [b] no brackets-left (e.g., 5 * 4 + 2 + 3), [c] brackets-center (e.g., 2 + (5 * 4) + 3), [d] no brackets-center (e.g., 2 + 5 * 4 + 3), [e] brackets-right (e.g., 2 + 3 + (5 * 4)), and [f] no brackets-right (e.g., 2 + 3 + 5 * 4). Participants simplified expressions in an online learning platform with the goal to “master” the content by answering three questions correctly in a row. Results showed that, on average, students were more accurate in problem solving when the higher-order operator was on the left side and less accurate when it was on the right compared to in the center. There was also a main effect of the presence of brackets on mastery speed. However, interaction effects showed that these main effects were driven by the center position: superfluous brackets only improved accuracy when students solved expressions with brackets with the operator in the center. This study advances research on perceptual learning in math by revealing how operator position and presence of superfluous brackets impact students’ performance. Additionally, this research provides implications for instructors who can use perceptual cues to support students during problem solving. 

This emerging technology report introduces the WearableLearning (WL) platform as a tool to exercise computational thinking and STEM learning for 5-12th grade students through mobile technology-augmented active game play and game creation. Freely available at WearableLearning.org, it allows students and teachers to play, create, debug, and manage multiplayer, active games. To date, WearableLearning has been used in schools and afterschool programs by roughly 500 students and 25 teachers to create games covering STEM curricular content. WearableLearning enables the creation of physically active and social games, while offering possibilities for research on computational thinking, embodied cognition, collaborative learning, game-based learning, and practical applications of technology in STEM classrooms.