This meta-analysis examined the effectiveness of supplemental Tier-2 mathematics interventions for students with mathematics difficulties (MD). We reviewed 39 experimental and quasi-experimental studies that included 40 independent samples, with 61 treatment groups. Utilizing robust variance estimation (RVE), results revealed a treatment effect of 0.41. Mixed-effects meta-regression analyses revealed that Tier-2 interventions were moderated by intervention model type, group size, and type of measure. We present recommendations for future research and implementation of mathematics practices.
Get full access to this article
View all access options for this article.
References
1.
BakerS.GerstenR.LeeD. S. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. Elementary School Journal, 103, 51–73.
2.
*BarbieriC. A.RodriguesJ.DysonN.JordanN. C. (2019). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology. Advance online publication. https://doi.org/10.1037/edu0000384
3.
*BarnesM. A.KleinA.SwankP.StarkeyP.McCandlissB.FlynnK.ZuckerT.HuangC.FallA.RobertsG. (2016). Effects of tutorial interventions in mathematics and attention for low-performing preschool children. Journal of Research on Educational Effectiveness, 9, 577–606. https://doi.org/10.1080/19345747.2016.1191575
4.
BoonenA. J. H.Van der SchootM.Van WeselF.De VriesM. H.JollesJ. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38, 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001
5.
*BryantD. P.BryantB. R.RobertsG.VaughnS.PfannenstielK. H.PorterfieldJ.GerstenR. (2011). Early numeracy intervention program for first-grade students with mathematics difficulties. Exceptional Children, 78, 7–23. https://doi.org/10.1177/001440291107800101
6.
BurnsM. K.CoddingR. S.BoiceC. H.LukitoG. (2010). Meta-analysis of acquisition and fluency math interventions with instructional and frustration level skills: Evidence for a skill-by-treatment interaction. School Psychology Review, 39, 69–83.
7.
*CaryM. G. S.ClarkeB.DoablerC. T.SmolkowskiK.FienH.BakerS. K. (2017). A practitioner implementation of a Tier 2 first-grade mathematics intervention. Learning Disabilities Quarterly, 40, 211–224. https://doi.org/10.1177/0731948717714715
8.
ChardD.HarnB. (2008). Project CIRCUITS: Center for Improving Reading Competence Using Intensive Treatments Schoolwide. In GreenwoodC.KratochwillT.ClementsM. (Eds.), Schoolwide prevention models: Lessons learned in elementary schools (pp. 70–83). Guilford.
9.
CheungA.SlavinR. (2016). How methodological features affect effect sizes in education. Educational Researcher, 45, 283–292. http://doi.org/10.3102/0013189X16656615
10.
ChoduraS.KuhnJ. T.HollingH. (2015). Interventions for children with mathematical difficulties: A meta-analysis. Zeitschirft Für Psychologie, 223, 129–144. http://doi.org/10.1027/2151-2604/a000211 https://doi-org.ezp1.lib.umn.edu/10.1027/2151-2604/a000211
11.
*ClarkeB.DoablerC. T.CaryM. S.KostyD.BakerS.FienH.SmolkowskiK. (2014). Preliminary evaluation of a Tier 2 mathematics intervention. School Psychology Review, 43, 160–177.
12.
*ClarkeB.DoablerC. T.KostyD.Kurtz NelsonE.SmolkowskiK.FienH.TurturaJ. (2017). Testing the efficacy of a kindergarten mathematics intervention by small group size. AERA Open, 3(2). https://doi.org/10.1177/2332858417706899
13.
*ClarkeB.DoablerC. T.SmolkowskiK.BakerS. K.FienH.Strand CaryM. (2016). Examining the efficacy of a Tier 2 kindergarten mathematics intervention. Journal of Learning Disabilities, 49, 152–165. https://doi.org/10.1177/0022219414538514
14.
*ClarkeB.DoablerC.SmolkowskiK.Kurtz NelsonE.FienH.BakerS. K.KostyD. (2016). Testing the immediate and long-term efficacy of a tier 2 kindergarten mathematics intervention. Journal of Research on Educational Effectiveness, 9(4), 607–634. https://doi.org/10.1080/19345747.2015.1116034
15.
CooperH.HedgesL. V.ValentineJ. C. (2009). The handbook of research synthesis and meta-analysis (2nd ed.). Russell Sage Foundation.
16.
DennisM. S.SharpE.ChovanesJ.ThomasA.BurnsR. M.CusterB.ParkJ. (2016). A meta-analysis of empirical research on teaching students with mathematics learning difficulties. Learning Disabilities Research & Practice, 31, 156–168. http://doi.org/10.1111/ldrp.12107
17.
DentonC. A.FletcherJ. M.SimosP. C.PapanicolaouA. C.AnthonyJ. L. (2007). An implementation of a tiered intervention model: Reading outcomes and neural correlates. In HaagerD.KlingnerJ.VaughnS. (Eds.), Evidence-based reading practices for response to intervention (pp. 107–137). Brookes.
18.
*DoablerC. T.ClarkeB.KostyD. B.Kurtz-NelsonE.FienH.SmolkowskiK.BakerS. K. (2016). Testing the efficacy of a Tier 2 mathematics intervention. Exceptional Children, 83(1), 92–110. https://doi.org/10.1177/0014402916660084
19.
*DoablerC. T.ClarkeB.KostyD.SmolkowskiK.Kurtz-NelsonE.FienH.BakerS. K. (2019). Building number sense among English learners: A multisite randomized controlled trial of a Tier 2 kindergarten mathematics intervention. Early Childhood Research Quarterly, 47, 432–444. https://doi.org/10.1016/j.ecresq.2018.08.004
20.
*DoablerC. T.ClarkeB.KostyD.TurturaJ. E.FirestoneA. R.SmolkowskiK.JungjohannK.BraffordT. L.NelsonN. J.SutherlandM.FienH.MaddoxS. A. (2019). Efficacy of a first-grade mathematics intervention on measurement and data analysis. Exceptional Children, 86(1), 77–94. https://doi.org/10.1177/0014402919857993
21.
DosseyJ.McCroneS.HalvorsenK. (2016). Mathematics education in the United States 2016: A capsule summary book written for the thirteenth International Congress on Mathematical Education (ICME-13). National Council of Teachers of Mathematics.
22.
*DysonN.JordanN.BeliakoffA.Hassinger-DasB. (2015). A kindergarten number-sense intervention with contrasting practice conditions for low-achieving children. Journal for Research in Mathematics Education, 46(3), 331. https://doi.org/10.5951/jresematheduc.46.3.0331
23.
*DysonN. I.JordanN. C.RodriguesJ.BarbieriC.RinneL. (2020). A fraction sense intervention for sixth graders with or at risk for mathematics difficulties. Remedial and Special Education, 41, 244–254. https://doi.org/10.1177/0741932518807139
24.
ElbaumB.VaughnS.HughesM. T.MoodyS.W. (2000). How effective are one-to-one tutoring programs in reading for elementary students at risk for reading failure?Journal of Educational Psychology, 92, 605–619. doi:10.1037/0022-0663.92.4.605
25.
FieldA.MilesJ.FieldZ. (2012). Discovering statistics using R. Sage.
26.
*FuchsL. S.ComptonD.FuchsD.PaulsenK.BryanJ. D.HamlettC. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3), 493–513. https://doi.org/10.1037/0022-0663.97.3.493
27.
FuchsL. S.FuchsD. (2006). A framework for building capacity for responsiveness to intervention. School Psychology Review, 35, 621–626.
28.
*FuchsL. S.FuchsD.CraddockC.HollenbeckK. N.HamlettC. L.SchatschneiderC. (2008). Effects of small group tutoring with and without validated classroom instruction on at-risk students’ math problem solving: Are two tiers of prevention better than one?Journal of Educational Psychology, 100, 491–509. https://doi.org/10.1037/0022-0663.100.3.491
29.
*FuchsL. S.FuchsD.HamlettC. L.AppletonA. C. (2002). Explicitly teaching for transfer: Effects on the mathematical problem-solving performance of students with mathematics disabilities. Learning Disabilities Research & Practice, 17, 90–106. https://doi.org/10.1111/1540-5826.00036
30.
*FuchsL. S.GearyD. C.ComptonD. L.FuchsD.SchatschneiderC.HamlettC. L.DeSelmsJ.SeethalerP. M.WilsonJ.CraddockC. F.BryantJ. D.LutherK.ChangasP. (2013). Effects of first-grade number knowledge tutoring with contrasting forms of practice. Journal of Educational Psychology, 105(1), 58–77. https://doi.org/10.1037/a0030127
31.
*FuchsL. S.PowellS. R.SeethalerP. M.CirinoP. T.FletcherJ. M.FuchsD.HamlettC. L. (2010). The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties. Learning and Individual Differences, 20(2), 89–100. https://doi.org/10.1016/j.lindif.2009.09.003
32.
*FuchsL. S.PowellS. R.SeethalerP. M.CirinoP. T.FletcherJ. M.FuchsD.HamlettC. L.ZumetaR. O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101, 561–576. https://doi.org/10.1037/a0014701
33.
FuchsL. S.SchumacherR. F.SterbaS. K.LongJ.NamkungJ.MaloneA.HamlettC. L.JordanN. C.GerstenR.SieglerR. S.ChangasP. (2014).Does working memory moderate the effects of fraction intervention?An aptitude–treatment interaction. Journal of Educational Psychology, 106, 499–514. https://doi.org/10.1037/a0034341
34.
*FuchsL. S.SeethalerP. M.PowellS. R.FuchsD.HamlettC. L.FletcherJ. M. (2008). Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties. Exceptional Children, 74, 155–173. https://doi.org/10.1177/001440290807400202
35.
GerstenR.BeckmannS.ClarkeB.FoegenA.MarshL.StarJ. R.WitzelB. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009-4060). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. http://ies.ed.gov/ncee/wwc/publications
36.
GerstenR.ChardD. J.JayanthiM.BakerS. K.MorphyP.FlojoJ. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. https://doi.org/10.3102/0034654309334431
37.
*GerstenR.RolfhusE.ClarkeB.DeckerL. E.WilkinsC.DiminoJ. (2015). Intervention for first graders with limited number knowledge. American Educational Research Journal, 52(3), 516–546. https://doi.org/10.3102/0002831214565787
38.
GordonR. S. J. (1983). An operational classification of disease prevention. Public Health Reports, 98, 107–109.
39.
GrahamS.LiuX.BartlettB.NgC.HarrisK. R.AitkenA.BarkelA.KavanaughC.TalukdarJ. (2018). Reading for writing: A meta- analysis of the impact of reading interventions on writing. Review of Educational Research, 88, 243–284. https://doi.org/10.3102/0034654317746927
40.
*Hassinger-DasB.JordanN. C.DysonN. (2015). Reading stories to learn math: mathematics vocabulary instruction for children with early numeracy difficulties. Elementary School Journal, 116(2), 242–264. https://doi.org/10.1086/683986
41.
HedgesL. V.TiptonE.JohnsonM. C. (2010). Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods, 1, 39–65. https://doi.org/10.1002/jrsm.5
42.
HughesE. M.WitzelB. S.RiccominiP. J.FriesK. M.KanyongoG. Y. (2014). A meta-analysis of algebra interventions for learners with disabilities and struggling learners. Journal of the International Association of Special Education, 15, 36–47.
43.
HwangJ.RiccominiP. J. (2016). Enhancing mathematical problem solving for secondary students with or at risk of learning disabilities: A literature review. Learning Disabilities Research & Practice, 31, 169–181. https://doi.org/10.1111/ldrp.12105
44.
*JitendraA. K.DupuisD. N.RodriguezM. C.ZaslofskyA. F.SlaterS.Cozine-CorroyK.ChurchC. (2013). A randomized controlled trial of the impact of schema-based instruction on mathematical outcomes for third-grade students with mathematics difficulties. Elementary School Journal, 114, 252–276. https://doi.org/10.1086/673199
45.
JitendraA. K.LeinA. E.ImS. H.AlghamdiA. A.HefteS. B.MouanoutouaJ. (2018). Mathematical interventions for secondary students with learning disabilities and mathematics difficulties: A meta-analysis. Exceptional Children, 84, 177–196. https://doi.org/10.1177/0014402917737467
46.
JitendraA. K.NelsonG.PullesS. M.KissA. J.HouseworthJ. (2016). Is mathematical representation of problems an evidence-based strategy for students with mathematics difficulties. Exceptional Children, 83(1), 8–25. https://doi.org/10.1177/0014402915625062
47.
JitendraA. K.Petersen-BrownS.LeinA.ZaslofskyA.KunkelA.JungP.-G.EganA. (2015). Teaching mathematical word problem solving: The quality of evidence for strategy instruction priming the problem structure. Journal of Learning Disabilities, 48, 51–72. https://doi.org/10.1177/0022219413487408
48.
*JitendraA. K.RodriguezM.KaniveR.HuangJ. P.ChurchC.CorroyK. A.ZaslofskyA. (2013). Impact of small-group tutoring interventions on the mathematical problem solving and achievement of third-grade students with mathematics difficulties. Learning Disability Quarterly, 36(1), 21–35. https://doi.org/10.1177/0731948712457561
49.
*KiuharaS. A.RouseA. G.DaiT.WitzelB. S.MorphyP.UnkerB. (2019). Constructing Written Arguments to Develop Fraction Knowledge. Journal of Educational Psychology, 1(999). https://doi.org/10.1037/edu0000391
50.
KroesbergenE. H.Van LuitJ. E. (2003). Mathematics interventions for children with special educational needs: A meta-analysis. Remedial and Special Education, 24, 97–114.
51.
LeeJ. (2012). College for all gaps between desirable and actual P–12 math achievement trajectories for college readiness. Educational Researcher, 41, 43–55. https://doi.org/10.3102/0013189X11432746
52.
LipseyM. W.PuzioK.YunC.HebertM. A.Steinka-FryK.ColeM. W.RobertsM.AnthonyK. S.BusickM. D. (2012). Translating the statistical representation of the effects of education interventions into more readily interpretable forms (NCSER 2013-3000). National Center for Special Education Research, Institute of Education Sciences, U.S. Department of Education.
53.
LipseyM. W.WilsonD. B. (2001). Practical meta-analysis. Sage.
54.
MazzoccoM. M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In BerchD. B.MazzoccoM. M. M. (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29–47). Brookes.
55.
MontagueM.DietzS. (2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75, 285–302.
56.
*MoranA. S.SwansonH. L.GerberM. M.FungW. (2014). The effects of paraphrasing interventions on problem-solving accuracy for children at risk for math disabilities. Learning Disabilities Research & Practice, 29, 97–105. https://doi.org/10.1111/ldrp.12035
57.
MorrisS. B. (2008). Estimating effect sizes from pretest posttest-control group designs. Organizational Research Methods, 11, 364–386. https://doi.org/10.1177/1094428106291059
58.
MurphyM. M.MazzoccoM. M.HanichL. B.EarlyM. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40(5), 458–478. https://doi.org/10.1177/00222194070400050901
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.
61.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standard in mathematics.
62.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. http://www.ed.gov/mathpanel
63.
NelsonG.McMasterK. L. (2019). The effects of early numeracy interventions for students in preschool and early elementary: A meta-analysis. Journal of Educational Psychology, 111(6), 1001–1022. https://doi.org/10.1037/edu0000334
64.
No Child Left Behind Act of 2001, 20 U.S.C. § 6319 (2002).
65.
PeltierC.VannestK. J. (2017). A meta-analysis of schema instruction on the problem-solving performance of elementary school students. Review of Educational Research, 87, 899–920https://doi.org/10.3102/0034654317720163
66.
PengP.WangC.NamkungJ. (2018). Understanding the cognition related to mathematics difficulties: A meta-analysis on the cognitive deficit profiles and the bottleneck theory. Review of Educational Research, 88, 434–476. https://doi.org/10.1177/0022219414521667
67.
PolaninJ. R.Tanner-SmithE. E.HennessyE. (2016). Estimating the difference between published and unpublished effect sizes: A meta-review. Review of Educational Research, 86, 207–236. https://doi.org/10.3102/0034654315582067
68.
*PowellS. R.DriverM. K. (2015). The influence of mathematics vocabulary instruction embedded within addition tutoring for first-grade students with mathematics difficulty. Learning Disability Quarterly, 38(4), 221–233. https://doi.org/10.1177/0731948714564574
69.
*PowellS. R.DriverM. K.JulianT. E. (2015). The effect of tutoring with nonstandard equations for students with mathematics difficulty. Journal of Learning Disabilities, 48(5), 523–534. https://doi.org/10.1177/0022219413512613
70.
*PowellS. R.FuchsL. S. (2010). Contribution of equal-sign instruction beyond word-problem tutoring for third-grade students with mathematics difficulty. Journal of Educational Psychology, 102, 381–394. https://doi.org/10.1037/a0018447
71.
*PowellS. R.FuchsL. S.CirinoP. T.FuchsD.ComptonD. L.ChangasP. C. (2015). Effects of a multitier support system on calculation, word problem, and prealgebraic performance among at-risk learners. Exceptional Children, 81(4), 443–470. https://doi.org/10.1177/0014402914563702
72.
R Core Team. (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing. http://www.R-project.org/
73.
Rittle-JohnsonB.JordanN. C. (2016). Synthesis of IES-funded research on mathematics: 2002–2013 (NCER 2016- 2003). National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. http://ies.ed.gov/
74.
SchulteA. C. (2016). Prevention and response to intervention: Past, present, and future. In JimersonS. R.BurnsM. K.VanDerHeydenA. M. (Eds.), Handbook of response to intervention: The science and practice of multi-tiered systems of support (2nd ed., pp. 59–71). Springer.
75.
ShinM.BryantD. P. (2015). Fraction interventions for students struggling to learn mathematics: A research synthesis. Remedial and Special Education, 36, 374–387. https://doi.org/10.1177/0741932515572910
76.
StevensE. A.RodgersM. A.PowellS. R. (2018). Mathematics interventions for upper elementary and secondary students: A meta-analysis of research. Remedial and Special Education, 39, 327–340. https://doi.org/10.1177/0741932517731887
77.
*SwansonH. L. (2014). Does cognitive strategy training on word problems compensate for working memory capacity in children with math difficulties?Journal of Educational Psychology, 106, 831–848. https://doi.org/10.1037/a0035838
78.
*SwansonH. L. (2015). Cognitive strategy interventions improve word problem solving and working memory in children with math disabilities. Frontiers in Psychology, 6(August), 1–13. https://doi.org/10.3389/fpsyg.2015.01099
79.
SwansonH. L.HoskynM. (1998). Experimental intervention research on students with learning disabilities: A meta-analysis of treatment outcomes. Review of Educational Research, 68, 277–321. https://doi.org/10.3102/00346543068003277
80.
*SwansonH. L.KongJ. E.MoranA. S.OroscoM. J. (2019). Paraphrasing interventions and problem-solving accuracy: Do generative procedures help English language learners with math difficulties?Learning Disabilities Research & Practice, 34(2), 68–84. https://doi.org/10.1111/ldrp.12194
81.
*SwansonH. L.LussierC.OroscoM. (2013). Effects of cognitive strategy interventions and cognitive moderators on word problem solving in children at risk for problem solving difficulties. Learning Disabilities Research & Practice, 28, 170–183. https://doi.org/10.1111/ldrp.12019
82.
*SwansonH. L.MoranA.LussierC.FungW. (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, 111–123. https://doi.org/10.1177/0731948713507264
83.
TiptonE. (2015). Small sample adjustments for robust variance estimation with meta-regression. Psychological Methods, 20, 375–393. https://doi.org/10.1037/met0000011
84.
TranL.SanchezT.ArellanoB.SwansonH. L. (2011). A meta-analysis of the RTI literature for children at risk for reading disabilities. Journal of Learning Disabilities, 44, 283–295. https://doi.org/10.1177/0022219410378447
85.
VaughnS.Linan-ThompsonS.KouzekananiK.BryantD. P.DicksonS.BlozisS. A. (2003). Grouping for reading instruction for students with reading difficulties. Remedial and Special Education, 24, 301–315.
86.
*WangA. Y.FuchsL. S.FuchsD.GilbertJ. K.KrowkaS.AbramsonR. (2019). Embedding self-regulation instruction within fractions intervention for third graders with mathematics difficulties. Journal of Learning Disabilities, 52, 337–348. https://doi.org/10.1177/0022219419851750
87.
WanzekJ.VaughnS.ScammaccaN.GatlinB.WalkerM.CapinP. (2016). Meta-analyses of the effects of Tier 2 type reading interventions in Grades K–3. Educational Psychology Review, 28, 551–576. https://doi.org/10.1007/s10648-015-9321-7
88.
XinY. P.JitendraA. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. TheJournal of Special Education, 32, 207–225. https://doi.org/10.1177/002246699903200402
89.
*XinY. P.JitendraA. K.Deatline-BuchmanA. (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
90.
*XinY. P.ZhangD.ParkJ. Y.TomK.WhippleA.SiL. (2011). A comparison of two mathematics problem-solving strategies: Facilitate algebra-readiness. Journal of Educational Research, 104, 381–395. https://doi.org/10.1080/00220671.2010.487080
91.
ZhangD.XinY. P. (2012). A follow-up meta-analysis for word-problem-solving interventions for students with mathematics difficulties. Journal of Educational Research, 105, 303–318. https://doi.org/10.1080/00220671.2011.627397
92.
ZhengX.FlynnL. J.SwansonH. L. (2013). Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly, 36, 97–111. https://doi.org/10.1177/0731948712444277
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
