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With the support of digital learning platforms, synchronous and collaborative learning has become a prominent learning paradigm in mathematics education. Computer-Supported Collaborative Learning (CSCL) has emerged as a valuable tool for enhancing mathematical discourse, problem solving, and ultimately learning outcomes. This paper presents an innovative examination of Graspable Math (GM), a dynamic mathematic notation and learning online platform, to enable synchronous, collaborative learning between pairs of students. Through analyzing students' online log data, we adopt a data-driven method to better understand the intricate dynamics of collaborative learning in mathematics as it happens. Specifically, we apply frequency distributions, cluster analysis to present students' dynamic interaction patterns and identify distinctive profiles of collaboration. Our findings reveal several collaboration profiles that emerge through these analyses. This research not only bridges the gap in current CSCL tools for mathematics, but also provides empirical insights into the effective design and implementation of such tools. The insights gained from this research offer implications for the design of digital learning tools that support effective and engaging collaborative learning experiences. 

Abstract Tunability of interfacial effects between two-dimensional (2D) crystals is crucial not only for understanding the intrinsic properties of each system, but also for designing electronic devices based on ultra-thin heterostructures. A prerequisite of such heterostructure engineering is the availability of 2D crystals with different degrees of interfacial interactions. In this work, we report a controlled epitaxial growth of monolayer TaSe₂with different structural phases, 1Hand 1 T, on a bilayer graphene (BLG) substrate using molecular beam epitaxy, and its impact on the electronic properties of the heterostructures using angle-resolved photoemission spectroscopy. 1H-TaSe₂exhibits significant charge transfer and band hybridization at the interface, whereas 1 T-TaSe₂shows weak interactions with the substrate. The distinct interfacial interactions are attributed to the dual effects from the differences of the work functions as well as the relative interlayer distance between TaSe₂films and BLG substrate. The method demonstrated here provides a viable route towards interface engineering in a variety of transition-metal dichalcogenides that can be applied to future nano-devices with designed electronic properties. 

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.