Decoding Fact Fluency and Strategy Flexibility in Solving One-Step Algebra Problems: An Individual Differences Analysis
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| Title: | Decoding Fact Fluency and Strategy Flexibility in Solving One-Step Algebra Problems: An Individual Differences Analysis |
|---|---|
| Language: | English |
| Authors: | Bye, Jeffrey K., Harsch, Rina M., Varma, Sashank |
| Source: | Journal of Numerical Cognition. 2022 8(2):281-294. |
| Availability: | Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: support@psychopen.eu; Web site: https://jnc.psychopen.eu |
| Peer Reviewed: | Y |
| Page Count: | 14 |
| Publication Date: | 2022 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Higher Education Postsecondary Education |
| Descriptors: | Algebra, Problem Solving, Mathematics Instruction, Arithmetic, Task Analysis, Thinking Skills, Undergraduate Students, Reaction Time, Cognitive Processes, Individual Differences, Decision Making, Prediction, Correlation, Mathematics Achievement, Mathematical Concepts, Concept Formation, College Entrance Examinations |
| Assessment and Survey Identifiers: | ACT Assessment, SAT (College Admission Test) |
| ISSN: | 2363-8761 |
| Abstract: | Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study investigated the strategies people choose when solving these problems, and whether some people are more flexible in their choices than others. U.S. undergraduates (n = 59) solved missing-operand problems and made speeded verifications of arithmetic sentences corresponding to the direct- and inverse-matched facts. To 'decode' their strategy as direct or inverse, each participant's response times (RTs) for missing-operand problems were regressed on their RTs for the corresponding direct and inverse facts. Our findings replicated the problem size effect for the arithmetic verification task and extended this effect to missing-operand (i.e., one-step) algebra problems, suggesting that the two tasks draw on common representations and processes in the addition (but not subtraction) context. We found individual differences in strategy choice and flexibility such that participants varied both in terms of fluency for retrieving the direct fact and sensitivity to the potential benefit of switching to the inverse fact, which was validated by self-report. We did not find a predicted relation between strategy flexibility and standardized mathematical achievement. These findings inform our understanding of the cognitive processes involved in strategy flexibility in algebra and establish an RT-decoding paradigm for future examination of individual differences in students' learning of early algebra concepts. |
| Abstractor: | As Provided |
| Notes: | https://osf.io/gxypt |
| Entry Date: | 2022 |
| Accession Number: | EJ1354977 |
| Database: | ERIC |
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