Page 9: References & Additional Resources
To cite this module, please use the following:
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Bouck, E. C., Satsangi, R., & Park, J. (2017). The concept-representational-abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 1–18.
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Dougherty, B., Pedrotty Bryant, D., Bryant, B. R., & Shin, M. (2017). Helping students with mathematics difficulties understand ratios and proportions. TEACHING Exceptional Children, 49(2), 96–105.
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Fuchs, L. S., Malone, A. S., Schumacher, R. F., Namkung, J., & Wang, A. (2016). Fraction intervention for students with mathematics difficulties: Lessons learned from five randomized controlled trials. Journal of Learning Disabilities, 1–9.
Fuchs, L. S., Zumeta, R. O., Schumacher, R. F., Powell, S. R., Seethaler, P. M., Hamlett, C. L., & Fuchs, D. (2010). The effects of schema-broadening instruction on second graders’ word-problem performance and their ability to represent word problems with algebraic equations: A randomized control study. The Elementary School Journal, 110(4), 440–463.
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Hughes, E. M., Powell, S. R., Lembke, E., & Riley-Tillman, T. C. (2016). Taking the guesswork out of locating evidence-based mathematics practices for diverse learners. Learning Disabilities Research & Practice, 31(3), 130–141.
Pfannenstiel, K. H., Pedrotty Byrant, D., Bryant, B. R., & Porterfield, J. A. (2015). Cognitive strategy instruction for teaching word problems to primary-level struggling learners. Intervention in School and Clinic, 50(5), 291–296.
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Jitendra, A. K., Dupuis, D. N., Rodriguez, M. C., Zaslofsky, A. F., Slater, S., Cozine-Corroy, K., & Church, C. (2013). A randomized controlled trial of the impact of schema-based instruction on mathematical outcomes for third-grade students with mathematics difficulties. The Elementary School Journal, 114(2), 252–276.
Jitendra, A. K., Dupuis, D. N., Star, J. R., & Rodriquez, M. C. (2016). The effects of schema-based instruction on the proportional thinking of students with mathematics difficulties with and without reading difficulties. Journal of Learning Disabilities, 49(4), 354–367.
Jitendra, A. K., Griffin, C. C., Deatline-Buchman, A., Sczesniak, E. (2007). Mathematical word problem solving in third-grade classrooms. Journal of Educational Research, 100, 283–302.
Jitendra, A. K., Griffin, C. C., McGoey, K., Gardill, M. C., Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. The Journal of Educational Research, 91(6), 345–355.
Jitendra, A. K., Nelson, G., Pulles, S. M., Kiss, A. J., & Houseworth, J. (2016). Is mathematical representation of problems an evidence-based strategy for students with mathematics difficulties? Exceptional Children, 83(1), 8–25.
Jitendra, A. K., Petersen-Brown, S., Lein, A. E., Zaslofsky, A. F., Kunkel, A. K., Jung, P. G., & Egan, A. M. (2015). Teaching mathematical word problem solving: The quality of evidence for strategy instruction priming the problem structure. Journal of Learning Disabilities, 48(1), 51–72.
Jitendra, A. K., Star, J. R., Dupuis, D. N., & Rodriguez, M. C. (2013). Effectiveness of schema-based instruction for improving seventh-grade students’ proportional reasoning: A randomized experiment. Journal of Research on Educational Effectiveness, 6(2), 114–136.
Jitendra, A. K., Star, J. R., Rodriguez, M., Lindell, M., & Someki, F. (2011). Improving students’ proportional thinking using schema-based instruction. Learning and Instruction, 21, 731–745.
Jitendra, A. K., Star, J. R., Starosta, K., Leh, J. M., Sood, S., Caskie, G., & Mack, T. R. (2009). Improving seventh grade students’ learning of ratio and proportion: The role of schema-based instruction. Contemporary Educational Psychology, 34(3), 250–264.
Kastberg, D., Chan, J. Y., & Murray, G. (2016). Performance of U.S. 15-year-old students in science, reading, and mathematics literacy in an international context: First look at PISA 2015. U.S. Department of Education. Washington, DC: National Center for Education Statistics. Retrieved from https://nces.ed.gov/pubs2017/2017048.pdf
Kemp, K. A., Eaton, M. A., & Poole, S. (2009). RTI & math: The classroom connection. Port Chester, NY: Dude Publishing.
Kingsdorf, S., & Krawec, J. (2016). A broad look at the literature on math word problem-solving interventions for third graders. Cogent Education, 3. Retrieved from http://www.tandfonline.com/doi/full/10.1080/2331186X.2015.1135770
Kingsdorf, S., & Krawec, J. (2014). Error analysis of mathematical word problem solving across students with and without learning disabilities. Learning Disabilities Research & Practice, 29(2), 66–74.
Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115.
Lembke, E. & Stecker, P. (2007). Curriculum-based measurement in mathematics: An evidence-based formative assessment procedure. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
McLeskey, J., Barringer, M-D., Billingsley, B., Brownell, M., Jackson, D., Kennedy, M., Lewis, T., Maheady, L., Rodriguez, J., Scheeler, M. C., Winn, J., & Ziegler, D. (2017, January). High-leverage practices in special education. Arlington, VA: Council for Exceptional Children & CEEDAR Center.
Middle School Matters Institute. (2017). Word problem structures: Student reference cards. Retrieved from https://greatmiddleschools.org/download-view/word-problem-student-cards/
Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research & Practice, 22(1), 75–83.
Montague, M., Enders, C., & Dietz, S. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly, 34(4), 262–272.
Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106(2), 469–481.
Morales, R. V., Shute, V. J., & Pellegrino, J. W. (1985). Developmental differences in understanding and solving simple mathematics word problems. Cognition and Instruction, 2(1), 41–57.
National Assessment of Educational Progress. (2017). The Nation’s Report Card: Mathematics. National Achievement Level Results: 4th Grade. Retrieved from https://www.nationsreportcard.gov/math_2017/#/nation/achievement?grade=4
National Assessment of Educational Progress. (2017). The Nation’s Report Card: Mathematics. National Achievement Level Results: 8th Grade. Retrieved from https://www.nationsreportcard.gov/math_2017/#/nation/achievement?grade=8
National Center for Education Progress. (2015). The Nation’s Report Card: Mathematics. National Achievement Level Results: 12th Grade. Retrieved from https://www.nationsreportcard.gov/reading_math_g12_2015/#mathematics
National Center for Education Statistics. (2015). Selected findings from TIMSS 2015 U.S. performance in mathematics at grades 4 and 8. Retrieved from https://nces.ed.gov/timss/timss2015/findings.asp
National Center on Intensive Intervention. (2016). Principles for designing intervention in mathematics. Washington, DC: Office of Special Education, U.S. Department of Education. Retrieved from http://www.intensiveintervention.org/sites/default/files/Princip_Effect_Math_508.pdf
National Mathematics Advisory Panel. Foundations for success: The final report of the National Mathematics Advisory Panel. U. S. Department of Education: Washington, DC, 2008.
Orosco, M. J. (2014). Word problem strategy for Latino English language learners at risk for math disabilities. Learning Disability Quarterly, 37(1), 45–53.
Peltier, C., & Vannest, K. J. (2017). Using the concrete representational abstract (CRA) instructional framework for mathematics with students with emotional and behavioral disorders. Preventing School Failure: Alternative Education for Children and Youth. Retrieved from http://www.tandfonline.com/doi/abs/10.1080/1045988X.2017.1354809
Powell, S. (2017, October). Evidence-based practices related to problem solving. PowerPoint presentation. Retrieved from http://www.sarahpowellphd.com/presentations.html
Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26(2), 94–108.
Provasnik, S., Malley, L., Stephens, M., Landeros, K., Perkins, R., & Tang, J. H. (2016). Highlights from TIMSS and TIMSS Advanced 2015: Mathematics and science achievement of U.S. students in grades 4 and 8 and in advanced courses at the end of high school in an international context. Washington, DC: U.S. Department of Education, National Center for Education Statistics. Retrieved from https://nces.ed.gov/pubs2017/2017002.pdf
Reys, B. J., & Reys, R. E. (2006). The development and publication of elementary mathematics textbooks: Let the buyer beware! Phi Delta Kappan, 87(5), 377–383.
Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529–544.
Rittle-Johnson, B., & Star, J. (2010). Evidence-based practices for supporting understanding and skill in mathematics. Proceedings of the Carnegie Learning Webinar.
Spear-Swerling, L. T. (2006, March). The use of manipulatives in mathematics instruction. Retrieved from http://www.ldonline.org/spearswerling/The_Use_of_Manipulatives_in_Mathematics_Instruction
Stevens, E. A., & Powell, S. R. (2016). Focus on inclusive education: Unpacking word problems for diverse learners: A guide to using schemas. Childhood Education, 92(1), 86–91.
Strickland, T. K. (2016). Using the CRA-I strategy to develop conceptual and procedural knowledge of quadratic expressions. TEACHING Exceptional Children, 49(2), 115–125.
Strickland, T. K., & Maccini, P. (2012). The effects of concrete-representational-abstract integration strategy on the ability of students with learning disabilities to multiply linear expressions within area problems. Remedial and Special Education, 34(3), 142–153.
Strickland, T. K., & Maccini, P. ( 2013). Exploration of quadratic expressions through multiple representations for students with mathematics disabilities. Learning Disabilities, 19(2), 61–71.
Tindal, G. (2013). Curriculum-based measurement: A brief history of nearly everything from the 1970s to the present. ISRN Education. Retrieved from https://www.hindawi.com/journals/isrn/2013/958530/
Understanding Language. (2013). Guidelines for design of mathematics instruction and materials for ELLs. Retrieved from http://ell.stanford.edu/sites/default/files/math_learnmore_files/3.Guidelines for Math Instructional Materials Development 08-14-13 copy.pdf
U.S. Department of Education. (n.d.) Exemplary mathematics programs. Retrieved from http://www.k12academics.com/education-reform/us-department-education-exemplary-mathematics-programs
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
van Garderen, D., Scheuermann, A., & Jackson, C. (2012). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145–160.
van Garderen, D., Scheuermann, A., Poch, A. (2014). Challenges students with learning disabilities experience when using diagrams as a visualization tool to solve mathematics word problems. ZDM: International Journal on Mathematics Education, 46, 135–149. doi:10.1007/s11858-013-0519-1
What Works Clearinghouse, & National Center for Educational Evaluation. (2012). Improving mathematics problem solving in grades 4 through 8. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/mps_pg_052212.pdf
Zorfass, J., Han, A., & PowerUp WHAT WORKS. (n.d.). Using visual representations in mathematics. Retrieved from http://www.ldonline.org/article/61885/
Bouck, E. C., Satsangi, R., & Park, J. (2017). The concrete-representational-abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39(4), 211–228. DOI: 10.1177/0741932517721712
In this article, the authors attempt to establish the Concrete-Representational-Abstract (CRA) approach as a legitimate evidence-based practice for improving mathematics performance among students with learning challenges. While first reflecting on the often-conflicting or unclear methods for determine whether a given practice is, in fact, evidence-based, the authors apply a rigorous data-driven evaluative approach to conclude that CRA meets their criteria in this context. Notes on further studies and applications are also included.
Doabler, C. T., Carey, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. TEACHING Exceptional Children, 44(4), 48–57.
This article reviews promising research into the effectiveness of core mathematics instruction among students with learning disabilities. Covered here are step-by-step guidelines for enhancing core instruction, examples of visual representations, and a model dialogue of a kindergarten teacher introducing mathematics concepts, among much more.
Doabler, C. T., & Fien, H. (2013). Explicit mathematics instruction: What teachers can do for teaching students with mathematics difficulties. Intervention in School and Clinic, 48(5), 276–285.
This article stressing the critical importance of explicit mathematics instruction—especially for students with mathematics disabilities or struggling learners—includes a research overview of the explicit instruction, as well as teacher models, tips for guided practice, model wording for more effectively and clearly introducing mathematics topics, and more.
Jitendra, A. K., Nelson, G., Pulles, S. M., Kiss, A. J., & Houseworth, J. (2016). Is mathematics representation of problems an evidence-based strategy for students with mathematics difficulties? Exceptional Children, 83(1), 8–25.
Here the authors set out to answer the question posed by their article’s title, and they do so in the affirmative. Included here are notes on the presentation of mathematics problems as a strategy and a discussion of the finding that such a presentation does indeed qualify as an evidence-based practice.
Krawec, J., Huang, J., Montague, M., Kressler, B., & Melia de Alba, A. (2012). The effects of cognitive strategy instruction on knowledge of math problem-solving processes of middle school students with learning disabilities. Learning Disability Quarterly, 36(2), 80–92.
This article examines the effectiveness of “Solve It!” a “cognitive strategy intervention designed to improve the math problem solving of middle school students with learning disabilities.” The results of the research indicate that students who received instruction that included “Solve It!” did in fact use more mathematics strategies when approaching problems than their peers who did not.
Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the Common Core Standards in mathematics for students with mathematics difficulties. Learning Disabilities Research & Practice, 28(1), 38–48.
In this article, the authors detail a number of possible concerns related to teaching students with mathematics difficulties using the current Common Core Standards. They set out a rationale and process for instruction that utilizes a modified version better suited to students who struggle with the subject. On hand here also are notes on evidence-based interventions and possible direction for future inquiry and instruction.
Shih Dennis, M., Sharp, E., Chovanes, J., Thomas, A., Burns, R. M., Custer, B., & Park, J. (2016). A meta-analysis of empirical research on teaching students with mathematics learning difficulties. Learning Disabilities Research & Practice, 31(3), 156–168.
This article summarizes 14 years of research on the effect of experimental instruction on students with mathematics difficulties. The authors’ findings indicate that a variety of instructional interventions contributed to improved math performance among students, though these effects were heavily influenced by factors including the students’ ages, grade levels, and severity of mathematics difficulties.
van Gardener, D., & Scheuermann, A. (2014). Challenges students identified with a learning disability and as high-achieving experience when using diagrams as a visualization tool to solve mathematics word problems. Mathematics Education, 46, 135–149.
The use of visualization tools is widely regarded as an effective way to better help students to complete mathematics problems, but what are the challenges they present to students who struggle with mathematics or to students with disabilities? In this article, the authors examine that question, in the process identifying nine challenges frequently encountered by students with special learning needs. The implications for further research and instructional practice are assessed and discussed.
van Gardener, D., Scheuermann, A., Poch, A., & Murray, M. M. (2018). Visual representation in mathematics: Special education teachers’ knowledge and emphasis for instruction. Teacher Education and Special Education, 41(1), 7–23. https://doi.org/10.1177/0888406416665448
Though the use of visual representations in mathematics instruction is an increasingly common practice, relatively little information is available about their use in the context of special education. Research conducted by these authors suggest that these tools are used less often and in narrower circumstances among students with disabilities than is typical in general education classrooms. A breakdown of the data from a wide-scale survey is analyzed, and implications for future research and classroom practices are discussed.
Wilson, G. L. (2013). The math frame: Reaching mathematical common core heights for students who struggle. TEACHING Exceptional Children, 46(1), 36–46.
In this article, the authors examine the ways in which the Common Core Standards can be employed to improve the mathematics performance of students with disabilities. On hand here are thoughts on the challenges presented by word problems, as well as a step-by-step “math frame” (with detailed examples) for helping students to engage and solve them.
Bemidji Area Schools. (2013). Math word problem intervention strategy: Identification of common word problem structures and using schema-based strategies. Retrieved from http://www.bemidji.k12.mn.us/wp-content/uploads/2013/11/Word-Problem-ID.pdf
This online resource breaks down some of the most common varieties of mathematics word problems, offering examples of each, as well as outlining an intervention strategy for students who are struggling.
Charles A. Dana Center, the University of Texas at Austin. (n.d.). Integrating social and emotional learning and the Common Core State Standards for mathematics. Retrieved from http://www.insidemathematics.org/assets/common-core-resources/social-emotional-learning/a__integrating_sel_and_ccssm_making_the_case.pdf
The Common Core State Standards have significantly changed the way that classroom teachers approach instructional topics, and mathematics instruction is certainly no exception. This resource made available by the University of Texas at Austin’s Charles A. Dana Center, endorses the use of social and emotional learning strategies to deliver a “more comprehensive approach through a number of creative strategies that leverage students’ diverse strengths.”
Jitendra, A. & Lein, A. (2015). Alert 22: Priming the problem structure. Current Practice Alert. Division for Learning Disabilities, & the Division for Research. Retrieved from http://s3.amazonaws.com/cmi-teaching-ld/alerts/26/uploaded_files/original_DLD_Alert22_rev2.pdf?1429566239
Seeking a solution to the challenge of students with disabilities and struggling learners faced with complex word problems, this resource a trio of approaches to strategy instruction to “prime the problem structure.” These include conceptually based problem-solving models, schema-based instruction, and schema-broadening instruction.
Doing What Works. (2012). Effective problem-solving instruction, part 1: Visual representation. Doing What Works presentation transcript. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/wwc_mps_pg_vr.pdf
This breakdown of a Doing What Works slide presentation is itself a handy resource for teachers who wish to improve student mathematics performance in grades four through eight through the use of visual representations. Included here is a basic guide for strategy intervention, some common types of visual representations, and tips on how to model the use of visuals to better familiarize students with how they can be used to solve problems.
Hott, B. L., & Oettinger Montani, T. (2014). Strategies and interventions to support students with mathematics disabilities. Retrieved from https://www.council-for-learning-disabilities.org/wp-content/uploads/2014/12/Math_Disabilities_Support.pdf
Developed in conjunction with the Council for Learning Disabilities, this resource offers informative overviews of strategies designed to improve the mathematics performance of struggling students, including RIDE, FAST DRAW, the TINS Strategy, and numerous strategies for supporting vocabulary development.
Middle School Matters Institute. (2017). Word problem structures: Teacher reference cards. Retrieved from https://greatmiddleschools.org/download-view/word-problem-teacher-cards/
These teacher reference cards for various schema-based mathematics word problems cover ratios and proportions, combinations, comparisons, and change or join type problems, among others.
Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/early_math_pg_111313.pdf
This What Works Clearinghouse educator’s guide for teaching math to young students presents five key recommendations for more effective instruction as well as the research evidence upon which each of them is based. The recommendations include the use of progress monitoring, the use of developmental progressions to teach geometry and number operations, and the integration of mathematics instruction throughout the school day.
Understanding Language. (2014). Principles for mathematics instruction for ELLs. Retrieved from http://ell.stanford.edu/sites/default/files/math_learnmore_files/2.Principles for Math Instruction 8-14-13.pdf
English language learners (ELLs) face unique challenges when it comes to mathematics instruction. This resource advances key instructional principles for improving their academic performance, including a focus on mathematical reasoning rather than accuracy in language use, balancing conceptual understanding and procedural fluency, and maintaining high cognitive demands and a rigorous approach to challenging students to meet their learning goals.
Zwiers, J., Dieckmann, J., Rutherford-Quach, S., Daro, V., Skarin, R., Weiss, S., & Malamut, J. (2017). Principles for the design of mathematics curricula: Promoting language and content development. Retrieved from http://ell.stanford.edu/sites/default/files/u6232/ULSCALE_ToA_Principles_MLRs__Final_v2.0_030217.pdf
The purpose of this resource is to “provide guidance to mathematics teachers for recognizing and supporting students’ language development processes in the context of mathematical sense making.” To do so, its authors promote the use of scaffolding and language instruction to better prepare students to approach mathematical problems independently and with the tools they need to be successful.
Hosted by Stanford University’s Graduate School of Educating, the Understanding Language Website offers resources on literacy instruction across content areas, including mathematics. Visitors here will find resources on supporting ELLs in mathematics, annotated math tasks for various grade levels, instructional videos, and much more.
The online home of the Common Core State Standards Initiative (CCSS) is the perfect place to visit for anyone wishing to learn more about the Standards themselves and how those Standards are being applied in their own states. A section specifically for parents contains a useful FAQ as well as responses to some of the most common myths about the CCSS.
Evidence for ESSA
Developed by the Center for Research and Reform in Education (CRRE) at Johns Hopkins University School of Education, this unique and interactive Website simplifies the task of finding evidence-based math programs that also meet the standards established under the Every Student Succeeds Act. Visitors can easily sort results by grade level, evidence base, program features, and the students for whom the programs were specifically designed.