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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.
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Assessment Designs that Elicit Multimodal Strategies: What We Can Learn about Early Childhood CT by Design
Performance assessments can provide meaningful insights into young children's knowledge; however, documenting assessment responses as incorrect or correct limits our understanding of students’ abilities. One method of improving our ability to measure student understanding is by documenting the strategies students use to engage with assessment tasks. In this study, we describe how purposeful assessment design can provide insight into students’ thinking by qualitatively examining how students solve performance assessment items using multimodal strategies.
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- Award ID(s):
- 1842116
- PAR ID:
- 10351300
- Date Published:
- Journal Name:
- International Conference of the Learning Sciences
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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