Restricted accessResearch articleFirst published online 2021-10
Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures
Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study (n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding (g = 0.66–0.78), number line estimation (g = 0.80–1.08), fractions procedures (g = 1.07), and explanation tasks (g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.
BarbieriC. A.RodriguesJ.DysonN.JordanN. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628–648. https://doi.org/10.1037/edu0000384
3.
BenjaminiY.HochbergY. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society–Series B (Methodological), 57(1), 289–300. http://www.jstor.org/stable/2346101
4.
BoothJ. L.NewtonK. J.Twiss-GarrityL. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110–118. https://doi.org/10.1016/j.jecp.2013.09.001
5.
BottgeB. A.MaX.GassawayL.TolandM. D.ButlerM.ChoS. J. (2014). Effects of blended instructional models on math performance. Exceptional Children, 80(4), 423–437. https://doi.org/10.1177/0014402914527240
ClarkeB.DoablerC. T.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
8.
CoyneM. D.CookB. G.TherrienW. J. (2016). Recommendations for replication research in special education: A framework of systematic, conceptual replications. Remedial and Special Education, 37(4), 244–253. https://doi.org/10.1177/0741932516648463
9.
DoughertyB.BryantD. P.BryantB. R.DarroughR. L.PfannenstielK. H. (2015). Developing concepts and generalizations to build algebraic thinking: The reversibility, flexibility, and generalization approach. Intervention in School and Clinic, 50(5), 273–281. https://doi.org/10.1177/1053451214560892
10.
FuchsL. S.MaloneA. S.PreacherK. J.FuchsD.WangA. Y.PachmayrR. (2019). Effects of fourth- and fifth-grade Super Solvers intervention on fraction magnitude understanding and calculation skill: A research report. Vanderbilt University.
11.
FuchsL. S.MaloneA. S.SchumacherR. F.NamkungJ.HamlettC. L.JordanN. C.SieglerR. S.GerstenR.ChangasP. (2016). Supported self-explaining during fraction intervention. Journal of Educational Psychology, 108(4), 493–508. https://doi.org/10.1037/edu0000073
12.
FuchsL. S.SchumacherR. F.LongJ.NamkungJ.HamlettC. L.CirinoP. T.JordanN. C.SieglerR.GerstenR.ChangasP. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683–700. https://doi.org/10.1037/a0032446
13.
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(2), 499–514. https://doi.org/10.1037/a0034341
14.
GearyD. C.HoardM. K.NugentL.BaileyD. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206–223. https://doi.org/10.1037/a0025398
15.
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(3), 1202–1242. https://doi.org/10.3102/0034654309334431
16.
GerstenR.RolfhusE.ClarkeB.DeckerL. E.WilkinsC.DiminoJ. (2015). Intervention for first graders with limited number knowledge: Large-scale replication of a randomized controlled trial. American Educational Research Journal, 52(3), 516–546. https://doi.org/10.3102/0002831214565787
17.
HamdanN.GundersonE. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53(3), 587–596. https://doi.org/10.1037/dev0000252
18.
HamlettC. L.SchumacherR. S.FuchsL. S. (2011). 2011 0–2 Number Line adapted from Siegler et al. (2011). Available from L. S. Fuchs, Vanderbilt University, Nashville, TN.
19.
HayesA. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408–420. https://doi.org/10.1080/03637750903310360
Individuals With Disabilities Education Act, 20 U.S.C. §§ 1400 et seq. (2004).
22.
Instructional Research Group. (2014). Test for Understanding of Fractions, Fourth Grade (TUF-4).
23.
Instructional Research Group. (2015). Test for Understanding of Fractions, Fifth Grade (TUF-5).
24.
JayanthiM.GerstenR.TaylorM. J.SmolkowskiK.DiminoJ. (2017). Impact of the Developing Mathematical Ideas professional development program on Grade 4 students’ and teachers’ understanding of fractions (REL 2017–256). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southeast. http://ies.ed.gov/ncee/edlabs
25.
JitendraA. K.DupuisD. N.StarJ. R.RodriguezM. 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. https://doi.org/10.1177/0022219414554228
26.
JitendraA. K.HarwellM. R.DupuisD. N.KarlS. R. (2017). A randomized trial of the effects of schema-based instruction on proportional problem-solving for students with mathematics problem-solving difficulties. Journal of Learning Disabilities, 50(3), 322–336. https://doi.org/10.1177/0022219416629646
27.
JordanN. C.HansenN.FuchsL. S.SieglerR. S.GerstenR.MicklosD. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001
28.
LahmeB.McLemanC.NakamayeM.UmlandK. (2019). The number line: Unifying the evolving definition of number in K–12 mathematics. Notices of the American Mathematical Society, 66(9), 1465–1470. https://www.ams.org/journals/notices/201909/rnoti-p1465.pdf
29.
MaloneA. S.FuchsL. S.SterbaS. K.FuchsD.Foreman-MurrayL. (2019). Does an integrated focus on fractions and decimals improve at-risk students’ rational number magnitude performance?Contemporary Educational Psychology, 59. https://doi.org/10.1016/j.cedpsych.2019.101782
30.
MaxwellS. E.ColeD. A.MitchellM. A. (2011). Bias in cross-sectional analyses of longitudinal mediation: Partial and complete mediation under an autoregressive model. Multivariate Behavioral Research, 46(5), 816–841. https://doi.org/10.1080/00273171.2011.606716
NamkungJ. M.FuchsL. S. (2016). Cognitive predictors of calculations and number line estimation with whole numbers and fractions among at-risk students. Journal of Educational Psychology, 108(2), 214–228. https://doi.org/10.1037/edu0000055
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.
PowellS. R.FuchsL. S. (2015). Intensive intervention in mathematics. Learning Disabilities Research & Practice, 30(4), 182–192. https://doi.org/10.1111/ldrp.12087
37.
ResnickI.JordanN. C.HansenN.RajanV.RodriguesJ.SieglerR. S.FuchsL. S. (2016). Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade. Developmental Psychology, 52(5), 746–757. https://doi.org/10.1037/dev0000102
SchumacherR. F.JayanthiM.GerstenR.DiminoJ.SpalloneS.HaymondK. (2018). Using the number line to promote understanding of fractions for struggling fifth graders: A formative pilot study. Learning Disabilities Research & Practice, 33(4), 192–206. https://doi.org/10.1111/ldrp.12169
40.
SchumacherR. F.MaloneA. S. (2017). Error patterns with fraction calculations at fourth grade as a function of students’ mathematics achievement status. Elementary School Journal, 118(1), 105–127. https://doi.org/10.1086/692914
41.
ShaughnessyM.BoerstT.BallD. L. (2015). Simulating teaching: New possibilities for assessing teaching practice. In BartellT. G.BiedaK. N.PutnamR. T.BradfieldK.DominguezH. (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 924–927). Michigan State University.
42.
SieglerR. S.DuncanG. J.Davis-KeanP. E.DuckworthK.ClaessensA.EngelM.SusperreguyM. I.ChenM. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697. https://doi.org/10.1177/0956797612440101
43.
SieglerR. S.ThompsonC. A.SchneiderM. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001
44.
SimJ.WrightC. C. (2005). The kappa statistic in reliability studies: Use, interpretation, and sample size requirements. Physical Therapy, 85(3), 257–268. https://doi.org/10.1093/ptj/85.3.257
45.
TianJ.SieglerR. S. (2017). Fractions learning in children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 614–620. https://doi.org/10.1177/0022219416662032
46.
U.S. Department of Education, Institute of Education Sciences, & What Works Clearinghouse. (2020). What Works Clearinghouse: Standards handbook (Version 4.1). https://ies.ed.gov/ncee/wwc/Handbooks
47.
WilkinsonG. S.RobertsonG. J. (2006). WRAT4: Wide Range Achievement Test. NCS Pearson.
48.
WillettJ. B. (1988). Questions and answers in the measurement of change. Review of Research in Education, 15, 345–422. https://doi.org/10.2307/1167368
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