Development of a Fraction Vocabulary Measure

Abstract

Developing mathematics proficiency requires an understanding of mathematics vocabulary. Although previous research has developed several measures of mathematics vocabulary at different grade levels, no study focused solely on fraction vocabularies. We developed and tested a measure of fraction vocabulary for students in Grade 4 to determine the internal consistency and difficulty level of such a measure. Analysis indicated the measure demonstrated high internal consistency. Students, on average, answered less than one-third of fraction vocabularies correctly. We also detected performance differences between students with and without mathematics difficulty and dual-language learners and their peers.

Keywords

fractions mathematics vocabulary

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References

Anselmi

Colledani

Robusto

(2019). A comparison of classical and modern measures of internal consistency. Frontiers in Psychology, 10, Article 2714. https://doi.org/10.3389/fpsyg.2019.02714

Baumann

J. F.

Graves

M. F.

(2010). What is academic vocabulary? Journal of Adolescent & Adult Literacy, 54(1), 4–13. https://doi.org/10.1598/JAAL.54.1.1

Bond

T. G.

Fox

C. M.

(2007). Applying the Rasch model: Fundamental measurements in the human sciences (2nd ed.). Lawrence Erlbaum.

Bruner

J. S.

(1966). Toward a theory of instruction. Harvard University Press.

Burnett

Irons

(2014). ORIGO stepping stones Texas. ORIGO Education.

Charles

R. I.

Murphy

S. J.

Caldwell

J. H.

Sammons

K. B.

Copley

Schielack

J. F.

. . .Wray

J. A.

(2014). Texas EnVisionMATH 2.0. Pearson Education.

Dixon

J. K.

Larson

M. R.

Burger

E. B.

Sandoval-Martinez

M. E.

(2014). Texas go math! Student edition. Houghton Mifflin Harcourt.

Dunston

P. J.

Tyminski

A. M.

(2013). What’s the big deal about vocabulary? Mathematics Teaching in the Middle School, 19(1), 38–45. https://doi.org/10.5951/mathteacmiddscho.19.1.0038

Forsyth

S. R.

Powell

S. 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

10.

Fuchs

L. S.

DeSelms

Deason

J. L.

(2012). Word problem-specific language assessment. Vanderbilt University.

11.

Fuchs

L. S.

Fuchs

Stuebing

Fletcher

J. M.

Hamlett

C. L.

Lambert

(2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Educational Psychology, 100(1), 30–47. https://doi.org/10.1037/0022-0663.100.1.30

12.

Gay

A. S.

(2008). Helping teachers connect vocabulary and conceptual understanding. The Mathematics Teacher, 102(3), 218–223. https://doi.org/10.5951/MT.102.3.0218

13.

Haladyna

T. M.

Rodriguez

M. C.

(2013). Developing and validating test items. Routledge.

14.

Hassinger-Das

Jordan

N. C.

Dyson

(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

15.

Hughes

E. M.

Powell

S. R.

Lee

J. Y.

(2020). Development and psychometric report of a middle-school mathematics vocabulary measure. Assessment for Effective Intervention, 45(3), 226–234. https://doi.org/10.1177/1534508418820116

16.

Irribarra

D. T.

Freund

Irribarra

M. D. T.

(2022). Package ‘WrightMap.’ Retrieved from: https://cran.r-project.org/web/packages/WrightMap/WrightMap.pdf

17.

Kellar

W. R.

(1939). The relative contribution of certain factors to individual differences in algebraic problem solving ability. The Journal of Experimental Education, 8(1), 26–35. https://doi.org/10.1080/00220973.1939.11010144

18.

Liang

J. H.

Heckman

P. E.

Abedi

(2018). Prior year’s predictors of eighth-grade algebra achievement. Journal of Advanced Academics, 29(3), 249–269. https://doi.org/10.1177/1932202X18770172

19.

Lin

Peng

Luo

H. 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

20.

Lin

Peng

Zeng

J. 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

21.

Lin

Powell

(2023). Initial efficacy of a fraction vocabulary intervention for students experiencing mathematics difficulty in grade 4. Learning Disabilities Research & Practice. Advance online publication. https://doi.org/10.1111/ldrp.12321

22.

Miles

D. D.

(1999). Algebra vocabulary: Domain-specific language as predictor of algebra skills (Publication No. 9221551) [Doctoral dissertation, University of Connecticut]. ProQuest Dissertations and Theses Global.

23.

Moschkovich

J. N.

(2015). Scaffolding student participation in mathematical practices. ZDM: Mathematics Education, 47(7), 1067–1078. https://doi.org/10.1007/s11858-015-0730-3

24.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards mathematics. Author.

25.

Nelson

Kiss

A. 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

26.

Nelson

Powell

S. 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

27.

Pearson Inc. (2004). Stanford Achievement Test, Tenth Edition (SAT-10).

28.

Peng

Lin

(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

29.

Petersen-Brown

Lundberg

A. R.

Ray

J. E.

Dela Paz

I. N.

Riss

C. L.

Panahon

C. 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

30.

Powell

S. R.

Berry

K. A.

(2021). Grade 4 word-problem screener.

31.

Powell

S. R.

Berry

K. A.

Tran

L. M.

(2020). Performance differences on a measure of mathematics vocabulary for English learners and non-English learners with and without mathematics difficulty. Reading & Writing Quarterly, 36(2), 124–141. https://doi.org/10.1080/10573569.2019.1677538

32.

Powell

S. R.

Bos

S. E.

Lin

(2021). The assessment of mathematics vocabulary in the elementary and middle school grades. In Fritz-Stratmann

Gürsoy

Herzog

(Eds.), Diversity dimensions in mathematics and language learning (pp. 313–330). De Grutyer. https://doi.org/10.1515/9783110661941-016

33.

Powell

S. R.

Driver

M. 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

34.

Powell

S. R.

Driver

M. K.

Roberts

Fall

A.-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

35.

Powell

S. R.

Nelson

(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

36.

Purpura

D. J.

Logan

J. A. R.

(2015). The nonlinear relations of the approximate number system and mathematical language to early mathematics development. Developmental Psychology, 51(12), 1717–1724. https://doi.org/10.1037/dev0000055

37.

Purpura

D. J.

Napoli

A. R.

Wehrspann

E. A.

Gold

Z. 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

38.

Purpura

D. J.

Schmitt

S. A.

Napoli

A. R.

Dobbs-Oates

King

Y. A.

Hornburg

C. B.

Westerberg

Borriello

G. A.

Bryant

L. M.

Anaya

L. Y.

Kung

Litkowski

Lin

Rolan

(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

39.

Robitzsch

Kiefer

(2020). TAM: Test analysis modules (R package version 3.5-19). Retrieved from: https://CRAN.R-project.org/package=TAM

40.

Rubenstein

R. N.

Thompson

D. R.

(2002). Understanding and supporting children’s mathematical vocabulary development. Teaching Children Mathematics, 9(2), 107–113.

41.

Runnels

(2012). Using the Rasch model to validate a multiple choice English achievement test. International Journal of Language Studies, 6(4), 141–153.

42.

Schleppegrell

M. 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

43.

Schumacher

R. F.

Jayanthi

Gersten

Dimino

Spallone

Haymond

K. 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

44.

Siegler

R. S.

Duncan

G. J.

Davis-Kean

P. E.

Duckworth

Claessens

Engel

Susperreguy

M. I.

Chen

(2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697. https://doi.org/10.1177/0956797612440101

45.

Siegler

R. S.

Pyke

A. A.

(2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994–2004. https://doi.org/10.1037/a0031200

46.

Siegler

R. S.

Thompson

C. A.

Schneider

(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

47.

Willse

J. T.

Shu

(2018). CTT: Classical test theory functions. In R package version 2.3.3. Retrieved from: https://CRAN.R-project.org/package=CTT

48.

Adams

(2007). Applying the Rasch model to psycho-social measurement: A practical approach. Educational Measurement Solutions.

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