Measuring Early Childhood Mathematical Cognition: Validating and Equating Two Forms of the Research-Based Early Mathematics Assessment

Abstract

Psychometric work with young children faces the particular challenge that children’s attention spans are relatively short, and therefore, shorter assessments are required while retaining comprehensive coverage. This article reports on three empirical studies that encompass the development and validation of the research-based early mathematics assessment-short form (REMA-SF), an instrument that measures the early mathematical competency of children from 3 to 8 years of age. The developed measure captures both children’s mathematical performance and the strategies children use to solve math problems. Results indicated that the REMA-SF can produce valid scores for measuring children’s math skills in early childhood, and the validity of the measure can be well-generalized to an external (or independent) sample. Additionally, we also equated the REMA scores between the long and short forms of the assessment: anchor items common across the forms were selected and refined in the equating process.

Keywords

early mathematics construct validity cross-observer validity test equating

Get full access to this article

View all access options for this article.

References

Andrich

(2004). Controversy and the Rasch model: A characteristic of incompatible paradigms? . In Smith

E. V.

Smith

R. M.

(Eds.), Introduction to Rasch measurement (pp. 143-166). JAM Press.

Biddlecomb

Carr

(2011). A longitudinal study of the development of mathematics strategies and underlying counting schemes. International Journal of Science and Mathematics Education, 9, 1-24. https://doi-org.du.idm.oclc.org/10.1007/s10763-010-9202-y

Bond

T. G.

Fox

C. M.

(2015). Applying the Rasch model: Fundamental measurement in the human sciences (3rd ed.). Taylor & Francis. https://doi.org/10.1111/j.1745-3984.2003.tb01103.x

Bracken

B. A.

(1984–1998). Bracken basic concept scale-revised. The Psychological Corporation, Harcourt Brace and Company.

Carpenter

T. P.

Franke

M. L.

Jacobs

V. R.

Fennema

Empson

S. B.

(1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3-20. https://doi.org/10.2307/749715

Clements

D. H.

Dumas

D. G.

Dong

Banse

H. W.

Sarama

Day-Hess

C. A.

(2020). Strategy diversity in early mathematics classrooms. Contemporary Educational Psychology, 60, 101834, https://doi.org/10.1016/j.cedpsych.2019.101834

Clements

D. H.

Sarama

(2011). Early childhood mathematics intervention. Science, 333(6045), 968-970. https://doi.org/10.1126/science.1204537

Clements

D. H.

Sarama

(2021). Learning and teaching early math: The learning trajectories approach (3rd ed.). Routledge. https://www.routledge.com/Learning-and-Teaching-Early-Math-The-Learning-Trajectories-Approach/Clements-Sarama/p/book/9780367521974.

Clements

D. H.

Sarama

Layzer

Unlu

Fesler

(2020). Effects on mathematics and executive function of a mathematics and play intervention versus mathematics alone. Journal for Research in Mathematics Education, 51(3), 301-333. https://doi.org/10.5951/jresemtheduc-2019-0069

10.

Clements

D. H.

Sarama

J. H.

Liu

X. H.

(2008). Development of a measure of early mathematics achievement using the Rasch model: The Research‐Based Early Maths Assessment. Educational Psychology, 28(4), 457-482. https://doi.org/10.1080/01443410701777272

11.

Clements

D. H.

Sarama

Wolfe

C. B.

Day-Hess

C. A.

(2017). REMA-SF ‐‐Research-based Early Mathematics Assessment Short Form. Denver, CO: Kennedy Institute, University of Denver.

12.

Clements

D. H.

Sarama

Day-Hess

C. A.

(2021). Review of assessments of early childhood mathematics competencies. Submitted for publication.

13.

Clements

D. H.

Sarama

Spitler

M. E.

Lange

A. A.

Wolfe

C. B.

(2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166. https://doi.org/10.5951/jresematheduc.42.2.0127

14.

Clements

D. H.

Sarama

Wolfe

C. B.

Spitler

M. E.

(2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. American Educational Research Journal, 50(4), 812-850. https://doi.org/10.3102/0002831212469270

15.

Dong

Dumas

D. G.

(2020). Are personality measures valid for different populations? A systematic review of measurement invariance across cultures, gender, and age. Personality and Individual Differences, 160, 1-23. https://doi.org/10.1016/j.paid.2020.109956

16.

Dong

Fan

Cheung

F. M.

(2020). Development of a short form of the CPAI-A (Form B) with Rasch analyses. Journal of Applied Measurement, 21(4), 515-532.

17.

Dorans

N. J.

Moses

T. P.

Eignor

D. R.

(2010). Principles and practices of test score equating (ETS Research Rep. No. RR-10-29). ETS.

18.

Duncan

G. J.

Magnuson

(2011). The nature and impact of early achievement skills, attention skills, and behavior problems. In Duncan

G. J.

Murnane

(Eds.), Whither opportunity? Rising inequality and the uncertain life chances of low-income children (pp. 47-70). Sage.

19.

Fuson

K. C.

Smith

S. T.

Cicero

A. M. L.

(1997). Supporting latino first grader’s ten-structured thinking in urban classrooms. Journal for Research in Mathematics Education, 28(6), 738-760. https://doi.org/10.2307/749640

20.

Holland

P. W.

Dorans

N. J.

(2006). Linking and equating. In Brennan

R. L.

(Ed.), Educational Measurement (4th ed., pp. 187-220). Praeger.

21.

Linacre

J. M.

(2002). What do infit and outfit, mean-square and standardized mean? Rasch Measurement Transactions, 16(2), 878.

22.

Linacre

J. M.

(2016). Winsteps Rasch measurement computer program user’s guide. Winsteps.com. http://www.winsteps.com/.

23.

Linacre

J. M.

(2021). Winsteps® Rasch measurement computer program. Winsteps.com.

24.

Livingston

S. A.

(2004). Equating test scores (without IRT). ETS. https://www.ets.org/Media/Research/pdf/LIVINGSTON.pdf.

25.

McCrae

R. R.

Costa

P. T.

, (2007). Brief versions of the NEO-PI-3. Journal of Individual Differences, 28(3), 116-128. https://doi.org/10.1027/1614-0001.28.3.116

26.

OECD . (2014). Strong performers and successful reformers in education - Lessons from PISA 2012 for the United States. OECD Publishing. https://doi.org/10.1787/9789264207585-en

27.

Sarama

Clements

D. H.

(2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. https://doi.org/10.4324/9780203883785.

28.

Sarama

Clements

D. H.

Wolfe

C. B.

Spitler

M. E.

(2012). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. Journal of Research on Educational Effectiveness, 5(2), 105-135. https://doi.org/10.1080119345747.2011,627980.

29.

Shepard

L. A.

(1994). The challenges of assessing young children appropriately. The Phi Delta Kappan, 76(3), 206-212. https://www.jstor.org/stable/20405297

30.

Siegler

R. S.

(1993). Adaptive and non-adaptive characteristics of low income children’s strategy use. In Penner

L. A.

Batsche

G. M.

Knoff

H. M.

Nelson

D. L.

(Eds.), Contributions of psychology to science and mathematics education (pp. 341-366). American Psychological Association.

31.

Smith

R. M.

(2004). Fit analysis in latent trait measurement models. In Smith

E. V.

Smith

R. M.

(Eds.), Introduction to Rasch measurement (pp. 73-92). JAM Press.

32.

Smith

G. T.

McCarthy

D. M.

Anderson

K. G.

(2000). On the sins of short-form development. Psychological Assessment, 12(1), 102-111. https://doi.org/10.1037/1040-3590.12.1.102

33.

Tipton

Olsen

R. B.

(2018). A review of statistical methods for generalizing from evaluations of educational interventions. Educational Researcher, 47(8), 516-524. https://doi.org/10.3102/0013189x18781522.

34.

Watts

T. W.

Duncan

G. J.

Siegler

R. S.

Davis-Kean

P. E.

(2014). What’s past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43(7), 352-360. https://doi.org/10.3102/0013189X14553660.

35.

Wilson

(2005). Constructing measures: An item response modeling approach. Erlbaum.

36.

Woodcock

R. W.

McGrew

K. S.

Mather

(2001). Woodcock-johnson III tests of achievement (3rd ed.). Riverside.

37.

Wright

B. D.

Linacre

J. M.

(1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8, 370-371.

38.

Wright

B. D.

Masters

G. N.

(1982). Rating scale analysis. MESA Press.

39.

C. H.

Osborn-Popp

S. E.

(2005). Test equating by common items and common subjects: Concepts and applications. Practical Assessment, Research, and Evaluation, 10(1), Article 4. https://doi.org/10.7275/68dy-z131

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.

0.00 MB

0.13 MB