This quasi–experimental study was designed to investigate the initial efficacy of a fraction–vocabulary intervention for Grade 4 students with mathematics difficulty (MD) and to explore its impact on relevant fraction competencies. Thirty–three students were assigned to either the intervention condition (n = 16) or a business–as–usual comparison condition (n = 17). The intervention occurred 3 sessions per week for 4 weeks, for a total of 11 sessions. Results indicated the main effect of the fraction–vocabulary intervention was significant for fraction–vocabulary posttest and one fraction competency—fraction arithmetic. That is, students with MD can successfully learn fraction vocabulary via a brief intervention, and improved fraction–vocabulary knowledge may positively affect their fraction competencies.
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.
BoothJ. L., & NewtonK. J. (2012). Fractions: Could they really be the gatekeeper's doorman?Contemporary Educational Psychology, 37(4), 247–253. https://doi.org/10.1016/j.cedpsych.2012.07.001
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers.
6.
DoablerC. T., ClarkeB., KostyD., Kurtz–NelsonE., FienH., SmolkowskiK., & BakerS. K. (2019). Examining the impact of group size on the treatment intensity of a tier 2 mathematics intervention within a systematic framework of replication. Journal of Learning Disabilities, 52(2), 168–180. https://doi.org/10.1177/2F0022219418789376
7.
ForsythS. R., & PowellS. R. (2017). Differences in the mathematics–vocabulary knowledge of fifth–grade students with and without learning difficulties. Learning Disabilities Research & Practice, 32(4), 231–245. https://doi.org/10.1111/ldrp.12144
8.
FrayerD., FrederickW., & KlausmeierH. (1969). A schema for testing the level of cognitive mastery. Wisconsin Center for Education Research.
9.
FuchsL. S., MaloneA. S., SchumacherR. F., NamkungJ., & WangA. (2017). Fraction intervention for students with mathematics difficulties: Lessons learned from five randomized controlled trials. Journal of Learning Disabilities, 50(6), 631–639. https://doi.org/10.1177/2F0022219416677249
10.
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
11.
HaladynaT. M., & RodriguezM. C. (2013). Developing and validating test items. Routledge.
12.
Hassinger–DasB., JordanN. C., & DysonN. (2015). Reading stories to learn math: Mathematics vocabulary instruction for children with early numeracy difficulties. The Elementary School Journal, 116(2), 242–264. https://doi.org/10.1086/683986
13.
JitendraA. K., EdwardsL. L., SacksG., & JacobsonL. A. (2004). What research says about vocabulary instruction for students with learning disabilities. Exceptional Children, 70(3), 299–322. https://doi.org/10.1177/2F001440290407000303
14.
KnightV. F., SpoonerF., BrowderD. M., SmithB. R., & WoodC. L. (2013). Using systematic instruction and graphic organizers to teach science concepts to students with autism spectrum disorders and intellectual disability. Focus on Autism and Other Developmental Disabilities, 28(2), 115–126. https://doi.org/10.1177/1088357612475301
LinX. (2022a). Fraction arithmetic. Available from X. Lin, Avenida da Universidade, Taipa, Macau.
17.
LinX. (2022b).Fraction word–problem solving. Available from X. Lin, Avenida da Universidade, Taipa, Macau.
18.
LinX., & PengP., & LuoH. J. (2021). The deficit profile of elementary students with computational difficulties versus word problem–solving difficulties. Learning Disability Quarterly, 44(2), 110–122. https://doi.org/10.1177/0731948719865499
19.
LinX., PengP., & ZengJ. G. (2021). Understanding the relation between mathematics vocabulary and mathematics performance: A meta–analysis. The Elementary School Journal, 121(3), 504–540. https://doi.org/10.1086/712504
20.
LinX., & PowellS. (2022). Fraction vocabulary. Available from X. Lin, Avenida da Universidade, Taipa, Macau.
NamkungJ. M., FuchsL. S., & KoziloN. (2018). Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole–number skill?Learning and Individual Differences, 61(1), 151–157. https://doi.org/10.1016/j.lindif.2017.11.018
NelsonG., & KissA. J. (2021). Effects of a first–grade mathematics vocabulary intervention: A pilot study for students with mathematics difficulty. Learning Disabilities Research & Practice, 36(2), 167–178. https://doi.org/10.1111/ldrp.12242
25.
NelsonG., & PowellS. R. (2018). A systematic review of longitudinal studies of mathematics difficulty. Journal of Learning Disabilities, 51(6), 523–539. https://doi.org/10.1177/0022219417714773
26.
Pearson Inc. (2004). Stanford Achievement Test, Tenth Edition (SAT–10).
27.
PengP., & LinX. (2019). The relation between mathematics vocabulary and mathematics performance among fourth graders. Learning and Individual Differences, 69(1), 11–21. https://doi.org/10.1016/j.lindif.2018.11.006
28.
Petersen–BrownS., LundbergA. R., RayJ. E., Dela PazI. N., RissC. L., & PanahonC. J. (2019). Applying spaced practice in the schools to teach math vocabulary. Psychology in the Schools, 56(6), 977–991. https://doi.org/10.1002/pits.22248
29.
PowellS. R., & BerryK. A. (2021). Grade 4 Word–Problem Screener. Available from S. R. Powell, 1912 Speedway, D5300, Austin, TX 78712.
30.
PowellS. R., & DoablerC. (2020–2024). The role of algebraic reasoning with in additive and multiplicative multi–step problem solving for students with mathematics difficulty (R324A200176). U.S. Department of Education, National Center for Special Education Research, Institute of Education Sciences. https://ies.ed.gov/funding/grantsearch/details.asp?ID=4438
31.
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/10.1177/2F0731948714564574
32.
PowellS. R., DriverM. K., RobertsG., & FallA.–M. (2017). An analysis of the mathematics vocabulary knowledge of third– and fifth–grade students: Connections to general vocabulary and mathematics computation. Learning and Individual Differences, 57(5), 22–32. https://doi.org/10.1016/j.lindif.2017.05.011
33.
PowellS. R., & NelsonG. (2017). An investigation of the mathematics–vocabulary knowledge of first–grade students. The Elementary School Journal, 117(4), 664–686. https://doi.org/10.1086/691604
34.
PurpuraD. J., NapoliA. R., WehrspannE. A., & GoldZ. S. (2017). Causal connections between mathematical language and mathematical knowledge: A dialogic reading intervention. Journal of Research on Educational Effectiveness, 10(1), 116–137. https://doi.org/10.1080/19345747.2016.1204639
35.
PurpuraD. J., SchmittS. A., NapoliA. R., Dobbs–OatesJ., KingY. A., HornburgC. B., WesterbergL., BorrielloG. A., BryantL. M., AnayaL. Y., KungM., LitkowskiE., LinJ., & RolanE. (2021). Engaging caregivers and children in picture books: A family–implemented mathematical language intervention. Journal of Educational Psychology, 113(7), 1338–1353. https://doi.org/10.1037/edu0000662
36.
SchleppegrellM. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159. https://doi.org/10.1080/10573560601158461
37.
SchumacherR. F., JayanthiM., GerstenR., DiminoJ., SpalloneS., & HaymondK. S. (2018). Using the number line to promote understanding of fractions for struggling fifth graders: A formative pilot study. Learning Disabilities Research and Practice, 33(4), 192–206. https://doi.org/10.1111/ldrp.12169
38.
SchumacherR. F., NamkungJ. M., & FuchsL. S. (2010). 2010 Fraction Battery. L. S. Fuchs, 228 Peabody, Vanderbilt University, Nashville, TN 37203.
39.
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
40.
SieglerR. S., FazioL. K., BaileyD. H., & ZhouX. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004
