Project: Embedding Working Memory Training within Math Problem Solving

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Information for the broader "Embedding Working Memory Training within Math Problem Solving" project is described below. This project page will eventually contain full data/codebooks related to this broader grant and its aims, but in the meantime will gradually make the data available via linking out to published articles produced from this overarching project, as well as making available the data associated with each of these individual studies/manuscripts.

Purpose: The research team will test the efficacy of a fully-developed intervention intended for elementary school students at risk for poor math problem solving outcomes, which embeds working memory (WM) training into a previously validated math problem solving intervention (Pirate Math). WM is the resource-limited capacity that allocates attention and plans and sequences and maintains information in short term memory while processing the same or other information. The efficacy study will test the embedded WM training intervention against Pirate Math only, general WM training (with separate math problem solving practice), and business-as-usual instruction. Even though previous efficacy studies have demonstrated strong effects of Pirate Math for improving math outcomes for students at risk for poor math problem solving outcomes, a substantial proportion of these studies' samples failed to show improvements. An alternative approach to intervention that seems potentially promising for these students involves training to strengthen the cognitive or linguistic resources associated with learning. The embedded WM training intervention is intended to both strengthen WM while increasing math problem solving skills and provide linkages between WM training activities and math problem solving.

Project Activities: The research team will conduct a randomized control trial to test the efficacy of the embedded WM intervention against two intervention contrast conditions and a control condition. The embedded WM intervention combines WM training with math problem solving training and is intended to improve math outcomes for students at risk for poor math problem solving outcomes. Data collection will occur in four cohorts, one during each project year.

Products: The products of this project will be evidence of the efficacy of the embedded WM intervention for second grade students at risk for poor math problem solving outcomes, and peer-reviewed publications.

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

Sample: The sample will include approximately 300 second grade, at-risk students and about 270 second grade, low-risk students. "At risk" will be defined as performing below the 30th percentile on a math problem solving screener, below the 65th percentile on a composite of two WM span tasks, and above 80 on both Wechsler Abbreviated Scale of Intelligence (WASI) subtests at the start of second grade.

Intervention: This efficacy study includes three different intervention conditions, with the embedded WM intervention being the primary intervention of interest. In Pirate Math without WM training, students are taught by tutors 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 meta-equation, and use the meta-equation to solve the problem. The intervention is taught as units, with cumulative reviews incorporated throughout. The embedded WM intervention combines Pirate Math with WM training by replacing the Sorting Game with Memory Games appropriate for the unit being studied. Finally, the general WM plus math problem solving practice intervention is CogMed, a WM training program that includes eight types of general WM activities not connected to academic content, plus 15 minutes of math problem solving practice during each session. CogMed is administered on a computer, though a tutor leads the training, tracks results, and provides support. The tutor will provide math problem solving practice, including independent problem solving with corrective feedback.

Research Design and Methods: The research team will conduct a randomized control trial with three levels of naturally-occurring nesting: students nested within classrooms nested within schools. Data collection will occur in four cohorts, one during each project year. The efficacy study includes four conditions: embedded WM, two intervention contrast conditions, and a control condition. Each year, participating students are given a series of screenings, and those identified as at-risk for poor math problem solving outcomes are randomly assigned at the individual level to condition and pre-tests are administered. For all three intervention conditions, a tutor will deliver the intervention for 20 weeks, 3 times per week, and 30 minutes per session to a single student at a time in a quiet location outside the classroom. Tutors will participate in a 2-day workshop and weekly training meetings to ensure high levels of implementation. At-risk students will be given a set of pre-tests, will complete the intervention sessions, and then will take a series of post-tests and delayed (administered in the fall of the following year) post-tests. Students not identified as at-risk will be given the pre-tests, post-tests, and delayed post-tests at the same time as the at-risk students. Researchers will measure fidelity of implementation through audiotapes, observations, and checklists of key lesson activities.

Control Condition: In the business-as-usual control condition, students will receive standard classroom instruction and school interventions (if naturally occurring).

Key Measures: Primary measures for screening for at-risk status will include the Pennies Test and the KeyMath-Revised Problem Solving, which both measure students' ability to solve and comprehend word problems respectively, as well as the Abbreviated Scale of Intelligence (WASI), which measures general cognitive ability. Primary outcome measures will include the Vanderbilt Story Problems test and the Iowa Test of Basic Skills- Data Interpretation and Problem Solving, which both measure students' math problem solving skills. Students will also be assessed on WM specific to math problem solving through a researcher designed assessment. Researchers will assess WM span with the Automated Working Memory Assessment. The research team will measure other cognitive/linguistic variables using the Wide Range Achievement Test (WRAT)-4-Arithmetic, the WRAT-Reading, WASI Vocabulary and WASI Matrix Reasoning, and the Strengths/Weaknesses of ADHD-Symptoms & Normal-Behavior.

Project Active From
September 2015 to August 2021
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Developmental Design
Educational Environment
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