Domain-General and Domain-Specific Antecedents of Pre-Algebraic Knowledge: Focusing on English-Language Learners With Word-Problem Difficulty

Abstract

This study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra’s initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 U.S. students at the beginning of Grade 3, end of Grade 3, and middle of Grade 4. The latent growth curve analyses revealed only word-problem solving emerged as a predictor of pre-algebraic growth across ELLs and non-ELLs. English-language learners’ stronger computational skills, along with their cognitive flexibility, potentially enabled them to effectively leverage working memory and nonverbal reasoning in acquiring pre-algebraic knowledge.

Keywords

English-language learners mathematics difficulty pre-algebraic knowledge word-problem solving

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References

Bollen

K. A.

Curran

P. J.

(2006). Latent curve models. A structural equation perspective. Wiley.

Campbell

A. E.

Davis

G. E.

Adams

V. M.

(2007). Cognitive demands and second-language learners: A framework for analyzing mathematics instructional contexts. Mathematical Thinking and Learning, 9(1), 3–30. https://doi.org/10.1080/10986060709336603

Cattell

R. B.

(1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54(1), 1–22. https://doi.org/10.1037/h0046743

Chan

(2015). Linguistic challenges in the mathematical register for EFL learners: Linguistic and multimodal strategies to help learners tackle mathematics word problems. International Journal of Bilingual Education and Bilingualism, 18(3), 306–318. https://doi.org/10.1080/13670050.2014.988114

De Smedt

. (2022). Individual differences in mathematical cognition: A Bert’s eye view. Current Opinion in Behavioral Sciences, 46, 101175. https://doi.org/10.1016/j.cobeha.2022.101175

Duncan

T. E.

Duncan

S. C.

(2004). An introduction to latent growth curve modeling. Behavior Therapy, 35(2), 333–363. https://doi.org/10.1016/S0005-7894(04)80042-X

Education Commission of the States. (2012). 50-state mathematics requirements for the standard high school diploma. https://www.ecs.org/clearinghouse/01/01/28/10128.pdf

Fong

A. B.

Jaquet

Finkelstein

(2014). Who repeats algebra I, and how does initial performance relate to improvement when the course is repeated? (REL 2015–059). Regional Educational Laboratory West, National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. http://ies.ed.gov/ncee/edlabs

Froiland

J. M.

Davison

M. L.

(2016). The longitudinal influences of peers, parents, motivation, and mathematics course-taking on high school math achievement. Learning and Individual Differences, 50(6), 252–259. https://doi.org/10.1016/j.lindif.2016.07.012

10.

Fuchs

L. S.

Compton

D. L.

Fuchs

Powell

S. R.

Schumacher

R. F.

Hamlett

C. L.

Vernier

Namkung

J. M.

Vukovic

R. K.

(2012). Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge. Developmental Psychology, 48(5), 1315–1326. https://doi.org/10.1037/a0027475

11.

Fuchs

L. S.

Gilbert

J. K.

Powell

S. R.

Cirino

P. T.

Fuchs

Hamlett

C. L.

Seethaler

P. M.

Tolar

T. D.

(2016). The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge. Developmental Psychology, 52(12), 2085–2098. https://doi.org/10.1037/dev0000227

12.

Fuchs

L. S.

Hamlett

C. L.

Powell

S. R.

(2003). Math fact fluency. Vanderbilt University.

13.

Geary

D. C.

Boykin

A. W.

Embretson

Reyna

Siegler

Berch

D. B.

Graban

(2008). The final report of the National Mathematics Advisory Panel [Report of the task group on learning processes]. U.S. Department of Education.

14.

Geary

D. C.

Hoard

M. K.

Nugent

Bailey

D. 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.

Geary

D. C.

Nicholas

Sun

(2017). Developmental change in the influence of domain-general abilities and domain-specific knowledge on mathematics achievement: An eight-year longitudinal study. Journal of Educational Psychology, 109(5), 680–693. https://doi.org/10.1037/edu0000159

16.

Gilmore

Keeble

Richardson

Cragg

(2017). The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement. Journal of Numerical Cognition, 3(2), 400–416. https://doi.org/10.5964/jnc.v3i2.51

17.

Goodrich

J. M.

Namkung

J. M.

(2019). Correlates of reading comprehension and word-problem solving skills of Spanish-speaking dual language learners. Early Childhood Research Quarterly, 48(3), 256–266. https://doi.org/10.1016/j.ecresq.2019.04.006

18.

L.-T.

Bentler

P. M.

(1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118

19.

Jacobs

V. R.

Franke

M. L.

Carpenter

T. P.

Levi

Battey

(2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288. https://doi.org/10.2307/30034868

20.

Jordan

N. C.

Hanich

L. B.

(2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33(6), 567–578. https://doi.org/10.1177%2F002221940003300605

21.

Kempert

Saalbach

Hardy

(2011). Cognitive benefits and costs of bilingualism in elementary school students: The case of mathematical word problems. Journal of Educational Psychology, 103(3), 547–561. https://doi.org/10.1037/a0023619

22.

Kieran

(1992). The learning and teaching of school algebra. In Grouws

D. A.

(Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). National Council of Teachers of Mathematics.

23.

Kline

R. B.

(2015). Principles and practice of structural equation modeling (4th ed.). Guilford Publications.

24.

Lariviere

D. O.

Powell

S. R.

Akther

S. S.

(2024). A synthesis of prealgebraic reasoning interventions for students with mathematics difficulty in Grades 6 through 8. Learning Disabilities Research & Practice, 39(1), 4–17. https://doi.org/10.1177/09388982231222179

25.

Lee

S. F.

Bull

M. L.

R. H. M.

(2011). Are patterns important? An investigation of the relationships between proficiencies in patterns, computation, executive functioning, and algebraic word problems. Journal of Educational Psychology, 103(2), 269–281. https://doi.org/10.1037/a0023068

26.

Lin

(2021). Investigating the unique predictors of word-problem solving using meta-analytic structural equation modeling. Educational Psychology Review, 33(3), 1097–1124. https://doi.org/10.1007/s10648-020-09554-w

27.

Lin

Peng

Luo

(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%2F0731948719865499

28.

Lin

Peng

Zeng

(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

29.

Lin

Powell

S. R.

(2022). The roles of initial mathematics, reading, and cognitive skills in subsequent mathematics performance: A meta-analytic structural equation modeling approach. Review of Educational Research, 92(2), 288–325. https://doi.org/10.3102%2F00346543211054576

30.

Little

R. J.

(1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83(404), 1198–1202. https://doi.org/10.1080/01621459.1988.10478722

31.

MacCallum

R. C.

Browne

M. W.

Sugawara

H. M.

(1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. https://doi.org/10.1037/1082-989X.1.2.130

32.

Matthews

Rittle-Johnson

(2009). In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology, 104(1), 1–21. https://doi.org/10.1016/j.jecp.2008.08.004

33.

Miyake

Shah

(Eds.). (1999). Models of working memory: Mechanisms of active maintenance and executive control. Cambridge University Press.

34.

Muthén

L. K.

Muthén

B. O.

(2007). Mplus user’s guide (5th ed.). Author. (Original work published 1998)

35.

National Center for Education Statistics. (2019). The nation’s report card. National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.

36.

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Author.

37.

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

38.

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf

39.

Noonan

(2017). STEM jobs: 2017 update. Office of the Chief Economist, Economics and Statistics Administration. U.S. Department of Commerce.

40.

Orosco

M. J.

(2014). Word problem strategy for Latino English language learners at risk for math disabilities. Learning Disability Quarterly, 37(1), 45–53. https://doi.org/10.1177/2F0731948713504206

41.

Peng

Lin

Ünal

Z. E.

Lee

Namkung

Chow

Sales

(2020). Examining the mutual relations between language and mathematics: A meta-analysis. Psychological Bulletin, 146(7), 595–634. https://doi.org/10.1037/bul0000231

42.

Piaget

(1976). Piaget’s theory. In Inhelder

Chipman

H. H.

Zwingmann

(Eds.), Piaget and his school (pp. 11–23). Springer.

43.

Pickering

S. J.

Gathercole

S. E.

(2001). Working memory test battery for children. Psychological Corporation.

44.

Pillay

Wilss

Boulton-Lewis

(1998). Sequential development of algebra knowledge: A cognitive analysis. Mathematics Education Research Journal, 10(2), 87–102. https://doi.org/10.1007/BF03217344

45.

Powell

S. R.

(2007). Open equations. Speedway.

46.

Powell

S. R.

Berry

K. A.

(2015). Texas word problems. Speedway.

47.

Powell

S. R.

Berry

K. A.

Fall

A.-M.

Roberts

Fuchs

L. S.

Barnes

M. A.

(2021). Alternative paths to improved word-problem performance: An advantage for embedding pre-algebraic reasoning instruction within word-problem intervention. Journal of Educational Psychology, 113(5), 898–910. https://doi.org/10.1037/edu0000513

48.

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 and Writing Quarterly: Overcoming Learning Difficulties, 36(2), 124–141. https://doi.org/10.1080/10573569.2019.1677538

49.

Powell

S. R.

Stevens

E. A.

Berry

K. A.

(2019). Effects of a word-problem intervention on word-problem language features for third-grade students with mathematics difficulty. Learning Disabilities: A Multidisciplinary Journal, 24(2), 1–14. https://doi.org/10.18666/LDMJ-2019-V24-I2-9835

50.

Rosseel

(2012). Lavaan: An R package for structural equation modeling and more. Version 0.5–12 (BETA). Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02

51.

Susac

Bubic

Vrbanc

Planinic

(2014). Development of abstract mathematical reasoning: The case of algebra. Frontiers in Human Neuroscience, 8, Article 679. https://doi.org/10.3389/fnhum.2014.00679

52.

Wechsler

Hsiao-pin

(2011). WASI-II: Wechsler abbreviated scale of intelligence (2nd ed.). Pearson.

53.

What Works Clearinghouse. (2017). What works clearinghouse: Procedures and standards handbook (Version 4.0). Author. https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Standards-Handbook-v4-1-508.pdf

54.

Wilkinson

G. S.

(2008). Wide range achievement test (Rev. 4). Pearson.

55.

Wong

T. T.-Y.

C. S.-H.

(2017). Component processes in arithmetic word-problem solving and their correlates. Journal of Educational Psychology, 109(4), 520–531. https://doi.org/10.1037/edu0000149

56.

Xin

Y. P.

Zhang

(2009). Exploring a conceptual model-based approach to teaching situated word problems. The Journal of Educational Research, 102(6), 427–442. https://doi.org/10.3200/JOER.102.6.427-442

57.

Zhu

(1999). WASI manual. The Psychological Corporation.

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