The Effect of Model-Based Problem Solving on the Performance of Students Who are Struggling in Mathematics

Abstract

The U.S. Nation’s Report Card reveals that lower performing students exhibited greater achievement decline than their average/high performing peers based on 2022 long-term trend mathematics assessments for age 9 students. Technology, including computer-assisted instruction, plays an important role in today’s dynamic learning environments. Currently, there is a lack of computer-assisted intervention programs that systematically teach generalized word problem-solving skills that are driven by mathematical models. Model-based problem solving (MBPS) is one of the essential emphases in the Common Core mathematical practice standards. This study investigated the effects of a web-based computer tutor, MBPS, on enhancing word problem-solving performance of elementary students who are struggling in mathematics. The MBPS tutor incorporates best practices that are identified by the Institute of Educational Sciences’ (IES) latest practice guide, including providing systematic instruction, visual and verbal supports, and teaching of precise mathematical language. Findings indicate that the MBPS tutor boosted participants’ performance above and beyond the business-as-usual comparison group.

Keywords

algebra readiness conceptual understanding mathematics word problem solving model-based problem solving learning disabilities at-risk students elementary mathematics intervention programs computer-assisted instruction web-based programs

Get full access to this article

View all access options for this article.

References

Blum

Leiss

(2005). “Filling up” – The problem of independence-preserving teacher interventions in lesson with demanding modeling tasks. Proceedings of CERME 4. http://www.erme.tu-dortmund.de/~erme/CERME4/CERME4_WG13.pdf#page=13

Bouck

E. C.

Satsangi

Doughty

T. T.

Courtney

W. T.

(2014). Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder. Journal of Autism and Developmental Disabilities, 44, 180–193. https://doi.org/10.1007/s10803-013-1863-2

Caldwell

J. H.

Karp

Bay-Williams

J. M.

(2011). Essential understanding series: Developing essential understanding of addition and subtraction for teaching mathematics in prekindergarten–grade 1. National Council of Teachers of Mathematics.

Carcoba Falomir

G. A.

(2019). Diagramming and algebraic word problem solving for secondary students with learning disabilities. Intervention in School and Clinic, 54(4), 212–218. https://doi.org/10.1177/1053451218782422

Common Core State Standards Initiative. (2012). Introduction: Standards for mathematical practice. https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf

Davydov

V. V.

(1982). Psychological characteristics of the formation of mathematical operations in children. In Carpenter

T. P.

Moser

J. M.

Romberg

T. A.

(Eds.), Addition and subtraction: Cognitive perspective (pp. 225–238). Lawrence Erlbaum.

Every Student Succeeds Act. (2015) Pub. Law 114-95, 129 Stat 1801.

Friendly

(2000). Power analysis for ANOVA designs. http://davidmlane.com/hyperstat/power.html

Fuchs

L. S.

Newman-Gonchar

Schumacher

Dougherty

Bucka

Karp

K. S.

Morgan

(2021). Assisting students struggling with math: Intervention in the elementary grades (WWC 2021006). National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. http://whatworks.ed.gov/

10.

Fuchs

L. S.

Seethaler

P. M.

Powell

S. R.

Fuchs

Hamlett

C. L.

Fletcher

J. M.

(2008). Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties. Exceptional Children, 74(2), 155–173. https://doi.org/10.1177/001440290807400202

11.

Geary

D. C.

(1994). Children’s mathematical development: Research and practical applications. American Psychological Association. https://doi.org/10.1037/10163-000

12.

Hughes

E. M.

Witzel

B. S.

Riccomini

P. J.

Fries

K. M.

Kanyongo

G. Y.

(2014). A meta-analysis of algebra interventions for learners with disabilities and struggling learners. The Journal of the International Association of Special Education, 15(1), 36–47. Retrieved February 28, 2023 from https://www.learntechlib.org/p/159660/

13.

Jonassen

D. H.

(2003). Designing research-based instruction for story problems. Educational Psychology Review, 15, 267–296.

14.

Kim

S. J.

Kastberg

S. E.

Xin

Y. P.

Lei

Liu

Wei

Chen

(2022). Counting strategies of students struggling in mathematics in a computer-based learning environment. The Journal of Mathematical Behavior, 68, Article 101007.

15.

Kim

S. J.

Xin

Y. P.

(2022). A synthesis of computer-assisted mathematical word problem-solving instruction for students with learning disabilities or difficulties. Learning Disabilities: A Contemporary Journal, 20(1), 27–45. https://www.ldw-ldcj.org/images/Kim__Xin_2022.pdf

16.

Myers

J. A.

Witzel

B. S.

Powell

S. R.

Pigott

Xin

Y. P.

Hughes

E. M.

(2022). A meta-analysis of mathematics word-problem solving interventions for elementary students who evidence mathematics difficulties. Review of Educational Research, 92(5), 695–742. https://doi.org/10.3102/00346543211070049

17.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.

18.

National School Choice Week Team. (2022). Pandemic pods are here, are you in? https://schoolchoiceweek.com/learning-pods/

19.

Pearson. (2004). Stanford achievement test (10th ed., SAT-10).

20.

Polotskaia

Savard

(2018). Using the relational paradigm: Effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education, 20(1), 70–90. https://doi.org/10.1080/14794802.2018.1442740

21.

Steffe

L. P.

von Glasersfeld

Richards

Cobb

(1983). Children’s counting types: Philosophy, theory, and application. Praeger.

22.

Thompson

P. W.

(1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25, 165–208. https://doi.org/10.1007/BF01273861

23.

U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress. (2022). Mathematica assessment.

24.

What Works Clearinghouse. (2020). What works clearinghouse standards handbook (Version 4.1). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/handbooks

25.

Witzel

B. S.

Myers

J. A.

Xin

Y. P.

(2022). Conceptually intensifying word problem solving for students with math difficulties. Intervention in School and Clinic, 58(1), 9–14. https://doi.org/10.1177/10534512211047580

26.

Woodward

Monroe

Baxter

(2001). Enhancing student achievement on performance assessment in mathematics. Learning Disability Quarterly, 24(1), 33–46. https://doi.org/10.2307/1511294

27.

Xin

Y. P.

(2007). Word-problem-solving tasks presented in textbooks and their relation to student performance: A cross-curriculum comparison case study. The Journal of Educational Research, 100, 347–359. https://doi.org/10.3200/JOER.100.6.347-360

28.

Xin

Y. P.

(2012). Conceptual model-based problem solving: Teach students with learning difficulties to solve math problems. Sense. https://doi.org/10.1007/978-94-6209-104-7_1

29.

Xin

Y. P.

(2015). Research related to modeling and problem solving: Conceptual model-based problem solving: Emphasizing pre algebraic conceptualization of mathematical relations. In Silver

E. A.

Kenney

P. A.

(Eds.), More lessons learned from research: Useful and useable research related to core mathematical practices (pp. 235–246). National Council of Teachers of Mathematics (NCTM).

30.

Xin

Y. P.

(2016). Conceptual model-based problem solving. In Fermer

Kilpatrick

Pehkonen

(Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 231–254). Springer.

31.

Xin

Y. P.

(2019). The effect of a conceptual model-based approach on “additive” word problem solving of elementary students who are struggling in mathematics. ZDM: Mathematics Education, 51(1), 139–150. https://doi.org/10.1007/s11858-018-1002-9

32.

Xin

Y. P.

Jitendra

Deatline-Buchman

(2005). Effects of mathematical word problem-solving instruction on middle school students with learning problems. The Journal of Special Education, 39, 181–192. https://doi.org/10.1177/00224669050390030501

33.

Xin

Y. P.

Kastberg

Chen

(2015). Conceptual model-based problem solving: A response to intervention program for students with learning difficulties in mathematics (COMPS-RtI). National Science Foundation (NSF) funded project.

34.

Xin

Y. P.

Park

Tzur

(2020). The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities. The Journal of Mathematical Behavior, 58, Article 100762. https://doi.org/10.1016/j.jmathb.2020.100762

35.

Xin

Y. P.

Tzur Si

Hord

Liu

Park

J. Y.

(2017). An intelligent tutor-assisted math problem-solving intervention program for students with learning difficulties. Learning Disability Quarterly, 40(1), 16. https://doi.org/10.1177/07319487166487400

36.

Xin

Y. P.

Wang

Sanders

(2018). Conceptual Model-based Mathematics Intelligent Tutors (COMMIT). NSF I-Corps Funded Project.

37.

Xin

Y. P.

Wiles

Lin

(2008). Teaching conceptual model-based word-problem story grammar to enhance mathematics problem solving. The Journal of Special Education, 42, 163–178. https://doi.org/10.1177/0022466907312895

38.

Xin

Y. P.

Zhang

Park

J. Y.

Tom

Whipple

(2011). A comparison of two mathematics problem-solving strategies: Facilitate algebra-readiness. The Journal of Educational Research, 104, 381–395. https://doi.org/10.1080/00220671.2010.487080

39.

Zhang

Xin

Y. P.

(2012). A follow-up meta-analysis of word problem solving interventions for students with learning problems. The Journal of Educational Research, 105(5), 303–318. https://doi.org/10.1080/00220671.2011.627397