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            This study examined the relations among strategic planning, execution, and strategy efficiency during problem-solving in a digital algebra learning game with 7th-grade students. We used pre-solving pause time as a proxy indicator of strategic planning, and the productivity of the initial strategy as a measure of effective strategy execution. Additionally, we explored how these variables correlated with students’ posttest scores assessing algebraic knowledge. Mediation analyses at both the problem and student levels indicated that longer pre-solving pause times were associated with greater strategy efficiency. When considering both the direct and indirect effects of pre-solving pause time on strategy efficiency, the results revealed a partial positive mediation through the productivity of the initial strategy. Lastly, the results of a path analysis showed that strategy efficiency significantly predicted algebraic knowledge with a positive effect. These findings suggest that longer pause times are associated with more efficient problem solving as they increase the likelihood of a productive initial step, highlighting a positive mediating role of execution in the relation between planning and strategy efficiency in algebraic problem solving.more » « lessFree, publicly-accessible full text available August 23, 2026
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