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Background: Prior work has shown that middle school students struggle with algebra and that game‐based educational technologies, such as DragonBox and From Here to There!, are effective at improving students' algebraic performance. However, it remains unclear which aspects of algebraic knowledge shift as a result of playing these games and what game design features support algebraic learning. Objective: Using the data from a randomized controlled trial conducted in the 2020–2021 academic year, we (a) examined students' relative performance on assessment items measuring conceptual knowledge, procedural knowledge and procedural flexibility in algebraic equation solving, and (b) identified changes in these aspects of algebraic knowledge after playing DragonBox or From Here to There!. Methods: Eight hundred eighty‐seven seventh‐graders were randomly assigned to playing DragonBox or From Here to There! for nine 30‐min sessions throughout the school year. Students also completed a pretest, midtest and posttest measuring their algebraic knowledge. Results and Conclusion: First, prior to the intervention, students scored the highest on procedural knowledge and lowest on conceptual knowledge. Second, students significantly improved and maintained learning gains on conceptual knowledge throughout the intervention. Their performance on procedural knowledge and procedural flexibility items increased at midtest but decreased at posttest. Third, the pattern of results was consistent for students in the DragonBox and From Here to There! conditions, suggesting that both games may support students' conceptual understanding of algebra. The findings have implications for research and practice on supporting algebraic learning through game‐based technologies during and beyond educational disruptions. Lay Description: What is already known about this topic: Middle school students struggle with aspects of algebra.DragonBox and From Here to There! are two game‐based technologies designed to support students' algebraic learning.Both games implement point rewards and dynamic interactions; they differ in the uses of algebraic notation and problem structures. What this paper adds: Both games improved seventh‐graders' conceptual knowledge of algebraic equivalence.Students also improved on procedural knowledge and procedural flexibility, but the gains did not last to the end of the intervention. Implications for practice and/or policy: The games and their shared features may provide an engaging way to support students' conceptual understanding of algebra. [ABSTRACT FROM AUTHOR]

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e., static vs. sequential line‐by‐line vs. dynamic format that demonstrates the problem‐solving process) impact learning. We conducted an online experiment in which 230 algebra students completed a pretest, studied worked examples in one of six presentation conditions, and completed a posttest. We found that overall, students improved from pretest to posttest after viewing the worked examples; we did not find significant differences on posttest performance between worked example presentations. These results have implications for the design of worked examples in online tutoring systems as well as for cognitive load theory and perceptual learning theory in the design of worked examples. [ABSTRACT FROM AUTHOR]

Emergent technologies present platforms for educational researchers to conduct randomized controlled trials (RCTs) and collect rich data to study students’ performance, behavior, learning processes, and outcomes in authentic learning environments. As educational research increasingly uses methods and data collection from such platforms, it is necessary to consider the most appropriate ways to analyze this data to draw causal inferences from RCTs. Here, we examine whether and how analysis results are impacted by accounting for multilevel variance in samples from RCTs with student-level randomization within one platform. We propose and demonstrate a method that leverages auxiliary non-experimental “remnant” data collected within a learning platform to inform analysis decisions. Specifically, we compare five commonly-applied analysis methods to estimate treatment effects while accounting for, or ignoring, class-level factors and observed measures of confidence and accuracy to identify best practices under real-world conditions. We find that methods that account for groups as either fixed effects or random effects consistently outperform those that ignore group-level factors, even though randomization was applied at the student level. However, we found no meaningful differences between the use of fixed or random effects as a means to account for groups. We conclude that analyses of online experiments should account for the naturally-nested structure of students within classes, despite the notion that student-level randomization may alleviate group-level differences. Further, we demonstrate how to use remnant data to identify appropriate methods for analyzing experiments. These findings provide practical guidelines for researchers conducting RCTs in similar educational technologies to make more informed decisions when approaching analyses. [ABSTRACT FROM AUTHOR]

Given the recent call to strengthen collaboration between researchers and relevant practitioners, we consider participatory design as a way to advance Cognitive Science. Building on examples from the Learning Sciences and Human−Computer Interaction, we (a) explore what, why, who, when, and where researchers can collaborate with community members in Cognitive Science research; (b) examine the ways in which participatory‐design research can benefit the field; and (c) share ideas to incorporate participatory design into existing basic and applied research programs. Through this article, we hope to spark deeper discussions on how cognitive scientists can collaborate with community members to benefit both research and practice. [ABSTRACT FROM AUTHOR]

• We test how knowledge and symbols (numbers or variables) impact problem solving. • Math knowledge positively predicts students' strategy efficiency on simple problems. • High-knowledge students are more efficient on complex variable vs numerical problems. • Low-knowledge students are less efficient on complex variable vs numerical problems. • Symbols may impact students' use of systemic structures in problem solving. To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and − 3 in 3 + 5 – 3). We examined how symbols—specifically variables versus numbers—and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use of systemic structures within an online algebra game where students could dynamically transform expressions. We found that on simple problems, symbols did not impact students' strategy efficiency, although students with higher vs lower algebraic knowledge were more efficient at solving these problems. On complex problems, students with higher algebraic knowledge were more efficient at solving variable vs numerical problems, whereas students with lower algebraic knowledge were less efficient at solving variable vs numerical problems. The visualizations and examination of first steps further revealed that whether students leveraged systemic structures during their problem-solving varied across problems. The findings have implications for research on cognitive processes of symbols and practices on teaching mathematics. [ABSTRACT FROM AUTHOR]