Purpose: An important part of mathematics programs in elementary schools are word problems. In many current theories on the development of children's mathematical problem-solving, a fundamental component is working memory. Children with math disabilities have limitations in working memory and to date, there have not been any intervention studies that have tried to develop strategies to compensate for working memory demands as they relate to problem solving in children with math disabilities.

The purpose of this study is to develop and test a series of interventions that include supplemental classroom materials and instructional strategies for children with math disabilities. The interventions are designed to compensate for working memory limitations in order to improve performance on math word problems.

Project Activities: Approximately 400 students (240 with a math disability, 160 without a math disability) in thirty-five 3rd to 5th grade classrooms will participate. Children with a math disability will be defined as children who score between the 25th and 90th percentile on a nonverbal intelligence measure and below the 10th percentile on a basic calculation and rapid number naming subtest. In Study 1, the effects of two intensive strategy conditions that manipulate the presentation order of problem-solving components (e.g., identify goals, relevant numbers) with an instruction as usual condition on solution accuracy will be compared. Study 2 compares the effects of two strategies — writing out key components of math word problems and summarizing word problems — on solution accuracy. Study 3 assesses the transfer effects of strategy training. Finally, in Study 4, the modified intervention materials based on the results of studies 1–3 will be assessed. The primary dependent measures across all studies are problem solving accuracy, comprehension, math calculation and memory.

Products: The expected outcomes from this study include the development of a supplemental intervention to compensate for working memory limitations for children with math disabilities, published reports, and presentations.

Setting: Participating students will be from elementary schools in California.

Population: Approximately 400 students (240 with a math disability, 160 without a math disability) in thirty-five 3rd to 5th grade classrooms will participate. Children with a math disability will be defined as children who score between the 25th and 90th percentile on a nonverbal intelligence measure and below the 10th percentile on a basic calculation and rapid number naming test. For the comparison group, a minimum of two children from each classroom in which the children with math disabilities are drawn who are average achievers in math (SAT10 or CAT6 > 50th percentile) will be also tested at pretest and post-test.

Intervention: In Study 1, a problem solving intervention will be developed in which the presentation of the components of the problem will be manipulated to determine the optimal order of instruction to promote solution accuracy. Students will either focus on initially identifying goals and operations or numbers and irrelevant information. In Study 2, a writing intervention will be developed in which students will be instructed on how to re-write word problems to identify the key components and summarize the problem in order to improve solution accuracy. For both Study 1 and 2, the intervention will be implemented in small groups, three days a week, over a period of eight weeks. For study 3, the researchers will examine whether training students with math disability to use a rehearsal strategy improves word problem solving performance. Training will be for one session and implemented individually. In the final study (study 4), the intervention components from study 1 and 2 that yielded the largest effects will be selected and combined with or without a working memory warm-up activity (Study 3). The interventions will be implemented for 26 sessions.

Research Design and Methods: Studies 1, 2, and 4 propose to use a within-classroom randomized design, with children randomly assigned within a classroom to one of three conditions. Each of these studies have two treatment conditions and one control condition (business as usual) embedded within classrooms. In Study 3, a random-assignment evaluation in which students will be assigned either to the working memory strategy instruction condition or to the control condition will be used.

Control Condition: Students in the control group will be tested from each classroom in which the students with a math disability are drawn. For studies 1, 2 and 4, the control group will receive the typical instruction in the classroom for word problems. In study 3, students in the control group will receive similar instructions as the students in the treatment condition but are not provided working memory strategy training instruction.

Key Measures: The researchers will assess a number of skills related to accuracy, solution planning, knowledge of problem solving components, mental computation of problems, and cognition. These experimenter-developed assessments include measures of accuracy and fluency in solving word problems, types of strategies used to solve problems, math problem solving as a function of variations in the semantic structure of a word problem, student's ability to correctly identify goals, student's ability to correctly identify the operation and algorithm, and working memory span tasks.

Data Analytic Strategy: Hierarchical linear modeling will be used to analyze post-test performance comparing ability groups and treatment differences. Hierarchical regression analyses will also be used to determine whether different ability groups benefit more from strategy training.

Related IES Projects: Age-related Changes in Word Problem Solving and Working Memory (R305H020055)

Products and Publications

Book chapter

Swanson, H.L. (2011). The Influence of Working Memory Growth on Reading and Math Performance in Children With Math and/or Reading Disabilities. In P. Barrouillet, and V. Gaillard (Eds.), Cognitive Development and Working Memory (pp. 203–230). London: Psychological Press.

Swanson, H.L. (2014). Working Memory, Intelligence and Learning Disabilities. In T. Papadopoulos, R.K. Parrila, and J. Kirby (Eds.), Cognition, Intelligence and Achievement: A Tribute to J.P. Das (pp. 3–12). New York: Elsevier.

Swanson, H.L. (2016). Working Memory and Strategy Instruction in Children With Learning Disabilities. In R. Schiff, and M. Joshi (Eds.), Interventions in Learning Disabilities: A Handbook on Systematic Training Programs for Individuals With Learning Disabilities (pp. 227–241). New York: Springer. doi:10.1007/978–3–319–31235–4_14

Swanson, H.L., and Alloway, T. (2011). Working Memory, Learning, and Academic Achievement. In K. Harris, T. Urban, and S. Graham (Eds.), APA Handbook of Educational Psychology, Volume 1 (pp. 327–366). Washington, DC: American Psychological Association.

Book chapter, edition specified

Swanson, H.L. (in press). Cognition and Cognitive Disabilities. In L. Corno, and E. Anderman (Eds.), Handbook of Educational Psychology (3rd ed.). Washington, DC: American Psychological Association.

Swanson, H.L., and Stomel, D.M. (2013). Learning Disabilities and Memory. In B.Y.L. Wong, and D. Butler (Eds.), Learning About Learning Disabilities (4th ed., pp. 27–57). San Diego, CA: Academic Press.

Swanson, H.L., and Zheng, X. (2013). Memory Difficulties in Children and Adults With Learning Disabilities. In H.L. Swanson, K. Harris, and S. Graham (Eds.), Handbook of Learning Disabilities (2nd ed., pp. 214–238). New York: Guilford Press.

Journal article, monograph, or newsletter

Fung, W., Orosco, M.J., and Swanson, H.L. (2014). Influence of Reading and Calculation on Children at Risk and not at Risk for Word Problem Solving: Is Math Motivation a Mediator? Learning and Individual Differences, 36: 84–91. doi:10.1016/j.lindif.2014.10.011

Jerman, O., Reynolds, C., and Swanson, H.L. (2012). Does Growth in Working Memory Span or Executive Processes Predict Growth in Reading and Math in Children With Reading Disabilities?. Learning Disability Quarterly, 35(3): 144–157.

Moran, A., Gerber, M., Swanson, H.L., and Fung, W. (2014). The Effects of Paraphrasing Interventions on Problem Solving Accuracy for Children at Risk for Math Disabilities. Learning Disabilities Research and Practice, 29(3): 97–105. doi:10.1111/ldrp.12035

Orosco, M., Swanson, H.L., O'Connor, R., and Lussier, C. (2011). The Effects of Dynamic Math on English Language Learners' Word Problem Solving. Journal of Special Education, 20(10): 1–12.

Rennie, B., Beebe-Frankenberger, M., and Swanson, H.L. (2014). A Longitudinal Study of Neuropsychological Functioning and Academic Achievement in Children With and Without Signs of Attention-Deficit/Hyperactivity Disorder. Journal of Clinical and Experimental Neuropsychology, 36(6): 621–635. doi:10.1080/13803395.2014.921284

Sisco-Taylor, D. Fung, W., and Swanson, H.L. (2015). Do Curriculum-Based Measures Predict Performance on Word-Problem-Solving Measures?. Assessment for Effective Intervention, 40(3): 131–142. doi:10.1177/1534508414556504

Swanson, H. L. (in press). Cognitive strategy interventions improve word problem solving and working memory in children with math disabilities. Frontiers in Psychology: Developmental Psychology.

Swanson, H. L. (2012). Cognitive profile of adolescents with math disabilities: Are the profiles different from those with reading disabilities? Child Neuropsychology, 18 (2), 125–143.

Swanson, H. L. (2016). Word Problem Solving, Working Memory and Serious Math Difficulties: Do Cognitive Strategies Really Make a Difference? Journal of Applied Research in Memory and Cognition, 5(4): 368–383. doi:10.1016/j.jarmac.2016.04.012

Swanson, H. L. and Fung, W. (2016). Working Memory Components and Problem-Solving Accuracy: Are There Multiple Pathways?. Journal of Educational Psychology, 108(8): 1153–1177. doi:10.1037/edu0000116

Swanson, H.L. (2014). Does Cognitive Strategy Training on Word Problems Compensate for Working Memory Capacity in Children With Math Difficulties?. Journal of Educational Psychology, 106(3): 831–848. doi:10.1037/a0035838

Swanson, H.L. (2011). Intellectual Growth in Children as a Function of Domain Specific and Domain General Working Memory Subgroups. Intelligence, 39(6): 481–492. doi:10.1016/j.intell.2011.10.001

Swanson, H.L. (2011). Working Memory, Attention, and Mathematical Problem Solving: A Longitudinal Study of Elementary School Children. Journal of Educational Psychology, 103(4): 821–837. doi:10.1037/a0025114

Swanson, H.L. (2015). Cognitive Strategy Interventions Improve Word Problem Solving and Working Memory in Children With Math Disabilities. Frontiers in Psychology, 69: 1–13. doi:10.3389/fpsyg.2015.01099

Swanson, H.L., Lussier, C., and Orosco, M.J. (2013). Effects of Cognitive Strategy Interventions and Cognitive Moderators on Word Problem Solving in Children at Risk for Problem Solving Difficulties. Learning Disabilities Research and Practice, 28(4): 170–183. doi:10.1111/ldrp.12019

Swanson, H.L., Lussier, C., and Orosco, M.J. (2013). Cognitive Strategies, Working Memory, and Growth in Word Problem Solving in Children With Math Difficulties. Journal of Learning Disabilities. doi:10.1177/0022219413498771

Swanson, H.L., Moran, A., Bocian, K., and Lussier, C. (2013). Generative Strategies, Working Memory, and Word Problem Solving Accuracy in Children at Risk for Math Disabilities. Learning Disability Quarterly, 36(4): 203–214. doi:10.1177/0731948712464034

Swanson, H.L., Moran, A., Lussier, C., and Fung, W. (2014). The Effect of Explicit and Direct Generative Strategy Training and Working Memory on Word Problem Solving Accuracy in Children at Risk for Math Difficulties. Learning Disability Quarterly, 37(2): 111–123. doi:10.1177/0731948713507264

Swanson, H.L., Orosco, M., and Lussier, C. (2014). The Effects of Mathematics Strategy Instruction for Children With Serious Problem-Solving Difficulties. Exceptional Children, 80: 149–168. doi:10.1177/001440291408000202

Zheng, X., Flynn, L., and Swanson, H.L. (2013). Experimental Intervention Studies on Word Problem Solving and Math Disabilities: A Selective Analysis of the Literature. Learning Disability Quarterly, 36(2): 97–111. doi:10.1177/0731948712444277

Zheng, X., Swanson, H. L., & Marcoulides, G. A. (2011). Working memory components as predictors of children's mathematical word problem solving. Journal of Experimental Child Psychology, 110 (4), 481–498. doi:http://dx.doi.org/10.1016/j.jecp.2011.06.001