Description:

Co-Principal Investigator: Fuchs, Douglas

Purpose: The research team tested the efficacy of a fully developed intervention intended for elementary school students who need to support with their mathematics problem solving (MPS) skills. The field’s major approach to intervention for students with or at risk for mathematics difficulty (MD) is structured skills instruction, which is designed to compensate for student limitations in the cognitive resources associated with academic performance. Despite the efficacy of this approach, approximately 30 percent of students with MD do not respond adequately to such intervention in mathematics problem solving (MPS). To address the needs of a broader range of students, the framework for intervention must be expanded beyond structured skills instruction. An alternative approach is to strengthen the cognitive resources associated with MPS by targeting working memory. This study contrasted alternative approaches to MPS intervention, including a previously validated MPS intervention, the same MPS intervention with embedded working memory training (the innovative condition of major interest), and general working memory training with contiguous math practice (an innovative condition of secondary interest).

Project Activities: Each year, a new cohort of second-grade students who had difficulties with MPS were randomly assigned to one of four conditions: (1) the validated MPS intervention (Pirate Math), (2) Pirate Math with embedded working memory training, (3) general working memory training (Cogmed) with contiguous math practice, and (4) a business-as-usual control group. Each of the three active intervention conditions involved 45 half-hour sessions conducted one-to-one over 15 weeks. Working memory, word problem solving, and arithmetic were assessed before and 1 to3 weeks after intervention. Word problem solving and arithmetic were assessed again 4 to 6 weeks later. The research team also collected fidelity of implementation data in each of the three intervention conditions.

• General working memory training with contiguous brief math practice improves MPS and arithmetic performance.
• Working memory training is not a substitute for a validated MPS intervention when the goal is to strengthen MPS, because MPS outcomes in both of the validated MPS (Pirate Math) intervention conditions were superior to general working memory training with math practice.
• Pirate Math improves working memory, but effects on working memory were stronger with general working memory training that included math practice.
• Although Pirate Math with brief embedded working memory training improved MPS, it did not strengthen working memory and did not provide added value over Pirate Math without embedded working memory training. Such combined intervention may need to occur with greater working memory training intensity.
• Working memory plays a causal role in MPS but not in arithmetic, at least for second grade students and in terms of how MPS and arithmetic were operationalized in this study.

Structured Abstract

Setting: Participating elementary schools were located in a large, urban/suburban district in Tennessee.

Sample: The final sample comprised 240 second-grade students with or at risk for mathematics difficulty, defined by start-of-second-grade performance below the 30th percentile on a math problem-solving screener, below the 60th percentile on two working memory span tasks, and above a standard score of 9th percentile on at least 1of the 2 subtests comprising Wechsler Abbreviated Scale of Intelligence (WASI) subtests. In the control group, the general working memory training condition with math practice group, the validated structured MPS intervention with embedded working memory training, and the validated structured MPS intervention group, respectively, there were 56, 48, 45, and 42 percent males. Race and ethnicity were as follows: 25, 35, 28, and 17 percent African American, 19, 13, 7, and 17 percent White non-Hispanic, 47, 49, 58, and 53 White Hispanic, and 9, 3, 7, and 13 percent other. The respective percentages receiving English services were 49, 51, 58, and 57; special education services, 5, 2, 10, and 17; and subsidized school lunch 58, 57, 55, and 53. A follow-along group of classmates not at risk for MD was included to quantify pretest and posttest performance gaps by condition for the 240 participants with or at risk for MD.

Intervention: This efficacy study included three intervention conditions, with the innovative embedded working memory intervention of primary interest. The final segments of math practice in all three conditions involved the same arithmetic and word-problem items each session. (1) In Pirate Math without working memory training, students were taught to understand the common underlying structure of problem types, recognize problems as belonging to those problem types, represent the structure of each problem type with a problem-type (meta) number sentence, and use the meta number sentence to solve the problem. The intervention was taught in units, with cumulative review throughout. (2) The embedded working memory intervention combined Pirate Math with brief working memory training by replacing Pirate Math games that provide practice on key skills with parallel working memory games. (3)General working memory plus contiguous math practice intervention was Cogmed, a computerized visuospatial and verbal working memory training program, with eight games that require children to track and replicate a sequence of events from memory. In this condition, children received math practice feedback on the accuracy of answers but without structured math instruction.

Research Design and Methods: This randomized control trial had three levels of naturally occurring nesting: students nested within classrooms nested within schools. Data collection occurred in five annual cohorts. The four conditions were (1) control, (2) general working memory training (Cogmed) condition with brief math practice, (3) validated MPS intervention (Pirate Math) with brief embedded working memory training, and (4) validated MPS intervention (Pirate Math). Participating students were screened into the study and identified as with or without MPS difficulty. Students completed a pretest battery of working memory, MPS, and assessments. Each of the 3 active intervention conditions involved 45 half-hour sessions conducted one-to-one over 15 weeks. working memory, MPS, and arithmetic were assessed before and 1 to 3 weeks after intervention. MPS and arithmetic were assessed again 4 to 6 weeks later. Fidelity of implementation in each of the three intervention conditions was measured via a random sample of audiotaped sessions, coded in terms of adherence with key lesson activities throughout intervention.

Control Condition: In the business-as-usual control condition, students received standard classroom instruction and school interventions (as determined by school personnel).

Key Measures: Primary measures for screening were Story Problems, Automated Working Memory Assessment (AWMA) Listening Recall, and AWMA Counting Recall, and WASI. Primary working memory and math outcomes were AWMA Odd-One Out, Listening Recall from the Working Memory Test Battery-Children (WMTB-C), WMTBC Counting Recall; Word-Problems Working Memory, Second-Grade Word Problems, and Arithmetic.

Data Analytic Strategy: Conditional main effects of intervention conditions, controlling for pretest performance, were assessed using five total fitted models. Posttest working memory was treated as a latent variable, with multilevel structural equation modeling testing main effects of intervention condition. The other four models each treated one math outcome (posttest arithmetic, delayed-posttest arithmetic, posttest word problem solving, delayed-posttest word problem solving) separately as a manifest variable, regressed on pretest performance. Multilevel mediation models assessed indirect effects via working memory for significant intervention contrasts on delayed-posttest word problem solving and arithmetic, controlling for pretest performance.

Products and Publications

ERIC Citations: Find available citations in ERIC for this award here

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Journal Articles

Fuchs, L.S., Fuchs, D., Seethaler, P.M., & Barnes, M.A. (2020). Addressing the role of working memory in mathematical word-problem solving when designing intervention for struggling learners. ZDM Mathematics Education, 52, 87–96. First published online July 5, 2019. doi: 10.1007/s11858-019-01070-8

Fuchs, L. S., Fuchs, D., Sterba, S. K., Barnes, M.A., Seethaler, P. M., & Changas, P. (2022). Building word-problem solving skill and working memory capacity: a randomized control trial comparing three intervention approaches. Journal of Educational Psychology, 114(7), 1633–1653.

Publicly Available Data

Fuchs, L. S., Fuchs, D., Sterba, S. K., Barnes, M. A., Seethaler, P. M., & Changas, P. (2023). Follow-Along Classmates Working Memory, Math, and Demographics at Pre Post. LDbase. https://doi.org/10.33009/ldbase.1678287555.e308

Fuchs, L. S., Fuchs, D., Sterba, S. K., Barnes, M. A., Seethaler, P. M., & Changas, P. (2023). Working Memory Training and Math Students with MD at Pre Post Delayed Post. LDbase. https://doi.org/10.33009/ldbase.1678287942.1ef4