The Effect of Mathematics Difficulty Intervention Programs on Mathematics Performance: A Second-Order Meta-Analysis

Abstract

Determining and evaluating the effects of mathematics difficulty intervention programs designed for students with MD are important for guiding teachers, researchers, and policy-makers. In this context, this research examines the influence of MD intervention programs on students' mathematical performance. Between 2009 and 2022, a total of 13 meta-analytical studies have been conducted. The research is currently exploring the consequences of intervention efforts on students diagnosed with MD for this objective. The analysis of this effect size value employs a second-order meta-analytical approach. Upon concluding the analysis process, it has been determined that the effect of MD intervention programs on students' mathematical performance is of moderate magnitude (ES = 0.70). Further, it is found that the location that MD intervention programs comprise, publication period, and features of participants are variables that cause meaningful differences in students’ mathematics performance. According to the study results, types of the program and school level are variables that do not cause any meaningful difference. However, the program of EI intervention has an important effect on the mathematics performances of individuals with MD. Obtained results and directions for forthcoming studies are discussed in the scope of this study.

Keywords

• Intervention program
• Mathematics difficulty
• Mathematics performance
• Meta-analysis

References

1. American Psychiatric Association [APA]. (2013). Diagnostic and statical manual of mental disorders: DSM-5. Washington, D.C: American Psychiatric Association.
2. Aunio, P., Korhonen, J., Ragpot, L., Törmänen, M., & Henning, E. (2021). An early numeracy intervention for first-graders at risk for mathematical learning difficulties. Early Childhood Research Quarterly, 55, 252-262. https://doi.org/10.1016/j.ecresq.2020.12.002
3. Benavides-Varela, S., Zandonella Callegher, C., Fagiolini, B., Leo, I., Altoè, G., & Lucangeli, D. (2020). Effectiveness of digital-based interventions for children with mathematical learning difficulties: A meta-analysis. Computers & Education, 157, 103953. https://doi.org/10.1016/j.compedu.-2020.103953
4. Bender, W. N. (2016). Learning disabilities: Characteristics, identification, and teaching strategies (6th ed). Pearson/Allyn and Bacon.
5. Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2011). Introduction to meta-analysis. West Sussex:John Wiley & Sons.
6. Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332(6033), 1049-1053.
7. Chodura, S., Kuhn, J.-T., & Holling, H. (2015). Interventions for children with mathematical difficulties: A meta-analysis. Zeitschrift Für Psychologie, 223(2), 129-144. https://doi.org/10.1027/2151-2604/a000211
8. Cook, B. G., Buysse, V., Klingner, J., Landrum, T. J., McWilliam, R. A., Tankersley, M., & Test, D. W. (2015). CEC’s standards for classifying the evidence base of practices in special education. Remedial and Special Education, 36(4), 220–234. https://doi.org/10.1177/0741932514557271

9. Cooper, H., & Koenka, A. C. (2012). The overview of reviews: Unique challenges and opportunities when research syntheses are the principal elements of new integrative scholarship. American Psychologist, 67, 446-462. https://doi.org/10.1037/a0027119
10. Cortiella, C., & Burnette, J. (2008). Challenging changing: How schools and districts are improving the performance of special education students. New York, NY: National Center for Learning Disabilities.
11. Dennis, M. S., 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. https://doi.org/10.1111/ldrp.12107
12. Fritz, A., Haase, V. G., & Rasanen, P. (2019). International handbook of mathematical learning difficulties: From the laboratory to the classroom. Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-319-97148-3
13. Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343-1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x
14. Gersten, R., Baker, S., Pugach, M., Scanlon, D., & Chard, D. (2001). Contemporary research on special education teaching. Handbook of Research on Teaching, 4, 695-722.
15. Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P. & Flojo, J. (2009). Mathematics instruction for students with learning disabilities; A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242. https://doi.org/10.3102/0034654309334431
16. Hew, K. F., Bai, S., Huang, W., Dawson, P., Du, J., Huang, G., Jia, C., & Thankrit, K. (2021). On the use of flipped classroom across various disciplines: Insights from a second-order meta-analysis. Australasian Journal of Educational Technology, 37(2), 132-151. https://doi.org/10.14742/-ajet.6475
17. Higgins, J.,P.,T., Green, S, (2011). Cochrane handbook for systematic reviews of interventions. The Cochrane Collaboration.
18. Huedo-Medina, T. B., Sánchez-Meca, J., Marin-Martinez, F., & Botella, J. (2006). Assessing heterogeneity in meta-analysis: Q statistic or I² index?. Psychological methods, 11(2), 193-206. https://doi.org/10.1037/1082-989X.11.2.193
19. Iseman, J. S., & Naglieri, J. A. (2011). A cognitive strategy instruction to improve math calculation for children with ADHD and LD: A randomized controlled study. Journal of Learning Disabilities, 44(2), 184-195.
20. Jin, Z. C., Zhou, X. H., & He, J. (2015). Statistical methods for dealing with publication bias in meta‐analysis. Statistics in Medicine, 34(2), 343-360. https://doi.org/10.1002/sim.6342
21. Jitendra, A. K., Alghamdi, A., Edmunds, R., McKevett, N. M., Mouanoutoua, J., & Roesslein, R. (2020). The effects of Tier 2 mathematics interventions for students with mathematics difficulties: A meta-analysis. Exceptional Children, 87(3), 307-325. https://doi.org/10.1177/00144029209-69187
22. Jitendra, A. K., Lein, A. E., Im, S., Alghamdi, A. A., Hefte, S. B., & Mouanoutoua, J. (2018). Mathematical interventions for secondary students with learning disabilities and mathematics difficulties: A meta-analysis. Exceptional Children, 84(2), 177-196. https://doi.org/10.1177/0014402917737467
23. Kaufmann, L., & von Aster, M. (2012). The diagnosis and management of dyscalculia. Deutsches Ärzteblatt International, 109(45), 767-778. https://doi.org/10.3238%2Farztebl.2012.0767
24. Kelly, K. (2020). Identifying, assessing and supporting learners with dyscalculia (1st edition). SAGE Publications Ltd.
25. Kung, J., Chiappelli, F., Cajulis, O. O., Avezova, R., Kossan, G., Chew, L., & Maida, C. A. (2010). From systematic reviews to clinical recommendations for evidence-based health care: Validation of revised assessment of multiple systematic reviews (R-AMSTAR) for grading of clinical relevance. The Open Dentistry Journal, 4, 84-91. https://doi.org/10.2174/18742106010-04010084
26. Lein, A. E., Jitendra, A. K., & Harwell, M. R. (2020). Effectiveness of mathematical word problem solving interventions for students with learning disabilities and/or mathematics difficulties: A meta-analysis. Journal of Educational Psychology, 112(7), 1388-1408. https://doi.org/10.1037-/edu0000453
27. Marfo, P., & Okyere, G. A. (2019). The accuracy of effect-size estimates under normals and contaminated normals in meta-analysis. Heliyon, 5(6), e01838. https://doi.org/10.1016/j.heli-yon.2019.e01838
28. Mathur, M. B., & VanderWeele, T. J. (2021). Estimating publication bias in meta-analyses of peer‐reviewed studies: A meta-meta-analysis across disciplines and journal tiers. Research Synthesis Methods, 12(2), 176-191. https://doi.org/10.1002/jrsm.1464
29. Mazzocco, M. M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29–47). Paul H. Brookes Publishing Co.
30. Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371-387. https://doi.org/10.1016/j.jecp.2013.01.005
31. Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage Publication.
32. 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. https://doi.org/10.1037/a0035176
33. Morsanyi, K., van Bers, B. M. C. W., McCormack, T., & McGourty, J. (2018). The prevalence of specific learning disorder in mathematics and comorbidity with other developmental disorders in primary school-age children. British Journal of Psychology, 109(4), 917-940. https://doi.org/10.1111/bjop.12322
34. Möller, K., Fischer, U., Cress, U., & Nuerk, H.-C. (2012). Diagnostics and intervention in developmental dyscalculia: Current issues and novel perspectives. In Z. Breznitz, O. Rubinsten, V. J. Molfese, & D. L. Molfese (Eds.), Reading, writing, mathematics and the developing brain: Listening to many voices (pp. 233–294). New York, NY: Springer.
35. Myers, J. A., Brownell, M. T., Griffin, C. C., Hughes, E. M., Witzel, B. S., Gage, N. A., Peyton, D., Acosta, K., & Wang, J. (2021). Mathematics interventions for adolescents with mathematics difficulties: A meta-analysis. Learning Disabilities Research & Practice, 36(2), 145-166. https://doi.org/10.1111/ldrp.12244
36. Myers, J. A., Hughes, E. M., Witzel, B. S., Anderson, R. D., & Owens, J. (2022). A meta-analysis of mathematical interventions for increasing the word problem solving performance of upper elementary and secondary students with mathematics difficulties. Journal of Research on Educational Effectiveness, 1-35. https://doi.org/10.1080/19345747.2022.2080131
37. Myers, J. A., Wang, J., Brownell, M. T., & Gagnon, J. C. (2015). Mathematics interventions for students with learning disabilities (LD) in secondary school: A review of the literature. Learning Disabilities: A Contemporary Journal, 13(2), 207–235.
38. National Assessment of Educational Progress [NAEP]. (2019). Mathematics assessments. New York. USA.
39. Nelson, G., & Powell, S. R. (2018). Computation error analysis: Students with mathematics difficulty compared to typically achieving students. Assessment for Effective Intervention, 43(3), 144–156. https://doi.org/10.1177/1534508417745627
40. Nelson, G., Park, S., Brafford, T., Heller, N. A., Crawford, A. R., & Drake, K. R. (2022). Reporting quality in math meta-analyses for students with or at risk of disabilities. Exceptional Children, 88(2), 125-144. https://doi.org/10.1177/00144029211050851
41. Polanin, J. R., Maynard, B. R., & Dell, N. A. (2017). Overviews in education research: A systematic review and analysis. Review of Educational Research, 87(1), 172-203. https://doi.org/10.3102/-00346543166311
42. Polloway, E., Patton, J., Serna, L., & Bailey, J. (2017). Strategies for teaching learners with special needs. Enhanced Pearson eText (11th edition). Pearson.
43. 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. https://doi.org/10.1111/ldrp.12001
44. Powell, S. R., Lembke, E. S., Ketterlin-Geller, L. R., Petscher, Y., Hwang, J., Bos, S. E., Cox, T., Hirt, S., & Mason, E. N. (2021). Data-based individualization in mathematics to support middleschool teachers and their students with mathematics learning difficulty. Studies in Educational Evaluation, 69, 100897. https://doi.org/10.1016/j.stueduc.2020.100897
45. Powell, S. R., Nelson, G., & Peng, P. (2017). Mathematics trajectories from preschool to postsecondary: The predictive nature of mathematics performance. Manuscript submitted for publication.
46. Ran, H., Kasli, M., & Secada, W. G. (2021). A Meta-Analysis on computer technology intervention effects on mathematics achievement for low-performing students in K-12 classrooms. Journal of Educational Computing Research, 59(1), 119-153. https://doi.org/10.1177/0735633120952-063
47. Schmidt, F. L. and Oh, I.S. (2013) Methods for second-order meta-analysis and illustrative applications. Organizational Behavior and Human Decision Processes, 121(2): 204–218. https://doi.org/10.-1016/j.obhdp.2013.03.002
48. Shin, M., & Bryant, D. P. (2015). Fraction interventions for students struggling to learn mathematics: A research synthesis. Remedial and Special Education, 36(6), 374–387. https://doi.org/10.1177/-0741932515572910
49. Stevens, E. A., Rodgers, M. A., & Powell, S. R. (2018). Mathematics interventions for upper elementary and secondary students: A meta-analysis of research. Remedial and Special Education, 39(6), 327-340. https://doi.org/10.1177/0741932517731887
50. Stevenson, N. A., & Reed, D. K. (2017). To change the things I can: Making instruction more intensive. Intervention in School and Clinic, 53(2), 74-80. https://doi.org/10.1177/1053451217693365
51. Stock, P., Desoete, A., & Roeyers, H. (2010). Detecting children with arithmetic disabilities from kindergarten: Evidence from a 3-year longitudinal study on the role of preparatory arithmetic abilities. Journal of Learning Disabilities, 43(3), 250-268. https://doi.org/10.1177/002221-9409345011
52. Swanson, H. L., & Hoskyn, M. (1998). Experimental intervention research on students with learning disabilities: A meta-analysis of treatment outcomes. Review of educational research, 68(3), 277-321. https://doi.org/10.3102/00346543068003277
53. Swanson, H. L., Lussier, C. M., & Orosco, M. J. (2015). Cognitive strategies, working memory, and growth in word problem solving in children with math difficulties. Journal of Learning Disabilities, 48, 339–358. https://doi.org/10.1177/0022219413498771
54. Turner, H., M., I., & Bernard, R. M. (2006). Calculating and synthesizing effect sizes. Contemporary Issues in Communication Science And Disorders, 33, 42-55. https://doi.org/10.1044/cicsd _33_S_42
55. United Nations [UN]. (2018). The sustainable development goals report. New York. USA.
56. Vickers, A., Goyal, N., Harland, R., & Rees, R. (1998). Do certain countries produce only positive results? A systematic review of controlled trials. Controlled Clinical Trials, 19(2), 159-166. https://doi.org/10.1016/S0197-2456(97)00150-5
57. Wei, X., Lenz, K. B., & Blackorby, J. (2013). Math growth trajectories of students with disabilities: Disability category, gender, racial, and socioeconomic status differences from ages 7 to 17. Remedial and Special Education, 34, 154–165. https://doi.org/10.1177/0741932512448253
58. Witzel, Bradley S., & Little, Mary E. (2016). Teaching elementary mathematics to struggling learners (1st ed.). The Guilford Press.
59. World Health Organization [WHO] (2005). ICD-10. International statistical classification of diseases and related health problems, 10th revision; Chapter V: Mental and behavioural disorders (F81.2). Geneva, Switzerland: Author.
60. Wu, T., Shen, H., Sheng, Y., Zhao, F., Guo, N., Liao, L., Li, L., Li, Y., & Dong, X. (2020). Use of cognitive correction training improves learning for children with mathematics learning disability. Applied Neuropsychology: Child, 9(2), 172-178. https://doi.org/10.1080/21622965.-2018.1552866
61. Young, J. (2017). Technology-enhanced mathematics instruction: A second-order meta-analysis of 30 years of research. Educational Research Review, 22, 19-33. https://doi.org/10.1016/j.edurev.-2017.07.001
62. Zhang, D., & Xin, Y. P. (2012). A follow-up meta-analysis for word-problem-solving interventions for students with mathematics difficulties. The Journal of Educational Research, 105(5), 303-318. https://doi.org/10.1080/00220671.2011.627397