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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. 

This project is a second-round development iteration of the MathFlowLens Dashboard, a data visualization tool for teachers that helps them identify their students’ strategic thinking and problem solving pathways. Development is guided by a co-design process where teachers were consulted multiple times to provide feedback and usability data that are analyzed and turned into features that meet those needs. Focus groups with middle school mathematics teachers gave insight into the round-one prototype of the dashboard, the data from which was used to synthesize needs into features that address them. This project’s development saw the inclusion of a new data visualization component that allows teachers to see each individual student’s journey through a problem – as well as several other modifications and accessibility features. As an iterative product, future work should include additional focus groups with teachers and studies to evaluate the effectiveness of the tool. 

Algebra is essential for delving into advanced mathematical topics and STEM courses (Chen, 2013), requiring students to apply various problem-solving strategies to solve algebraic problems (Common Core, 2010). Yet, many students struggle with learning basic algebraic concepts (National Mathematics Advisory Panel (NMAP), 2008). Over the years, both researchers and developers have created a diverse set of educational technology tools and systems to support algebraic learning, especially in facilitating the acquisition of problem- solving strategies and procedural pathways. However, there are very few studies that examine the variable strategies, decisions, and procedural pathways during mathematical problem- solving that may provide further insight into a student’s algebraic knowledge and thinking. Such research has the potential to bolster algebraic knowledge and create a more adaptive and personalized learning environment. This multi-study project explores the effects of various problem-solving strategies on students’ future mathematics performance within the gamified algebraic learning platform From Here to There! (FH2T). Together, these four studies focus on classifying, visualizing, and predicting the procedural pathways students adopted, transitioning from a start state to a goal state in solving algebraic problems. By dissecting the nature of these pathways—optimal, sub-optimal, incomplete, and dead-end—we sought to develop tools and algorithms that could infer strategic thinking that correlated with post-test outcomes. A striking observation across studies was that students who frequently engaged in what we term ‘regular dead-ending behavior’, were more likely to demonstrate higher post-test performance, and conceptual and procedural knowledge. This finding underscores the potential of exploratory learner behavior within a low-stakes gamified framework in bolstering algebraic comprehension. The implications of these findings are twofold: they accentuate the significance of tailoring gamified platforms to student behaviors and highlight the potential benefits of fostering an environment that promotes exploration without retribution. Moreover, these insights hint at the notion that fostering exploratory behavior could be instrumental in cultivating mathematical flexibility. Additionally, the developed tools and findings from the studies, paired with other commonly used student performance metrics and visualizations are used to create a collaborative dashboard–with teachers, for teachers. 

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.