A Rasch modeling approach for measuring young children’s informal mathematics in Peru

Martín Malaspina; Benito Arias

doi:10.29333/ejmste/12303

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Martín Malaspina ¹ ^* , Benito Arias ²

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¹ Pontificia Universidad Católica del Perú, Lima, PERU² Universidad de Valladolid, Valladolid, SPAIN^* Corresponding Author

Abstract

One of the strongest predictors of future academic achievement is the early and informal math skills children begin their school studies. Because of this, it is essential to have proper tools for measuring the development of mathematical thinking at an early age to be able to intervene in a timelier, more effective way. The purpose of this research is to calibrate the items of informal mathematics from the test of early mathematics ability–third edition (TEMA-3) by applying the Rasch model. A total of 148 Peruvian preschool children (ranging in age from five to six years) participated in the study. The results show good psychometric properties of the informal mathematics dimension of the instrument, which indicates a good fit of the student sample, the items to the proposed model and a tendency toward unbiased items. We further determined that the items analyzed exhibit a consistent internal structure at the theoretical level.

Keywords

early childhood education
informal mathematics
mathematics assessment
psychometrics
Rasch model
a test of early mathematics ability

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 9, September 2022, Article No: em2147

https://doi.org/10.29333/ejmste/12303

Publication date: 02 Aug 2022

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References

Acevedo, I., Castellani, F., Cota, M. J., Lotti, G., & Székely, M. (2022). El aumento de la desigualdad en América Latina: Un efecto colateral de la pandemia [The increase in inequality in Latin America: A collateral effect of pandemic]. Banco Interamericano de Desarrollo. https://doi.org/10.18235/0003967
Amarante, V., Colacce, M., & Scalese, F. (2022). Poverty and gender in Latin America: How far can income-based measures go? Journal of International Development, 34, 109-129. https://doi.org/10.1002/jid.3584
Aragón, E. L., Delgado, C. I., Aguilar, M., Araújo, A., & Navarro, J. I. (2013). Estudio de la influencia de la inteligencia y el género en la evaluación matemática temprana [Study of the influence of intelligence and gender in the assessment of early math]. European Journal of Education and Psychology, 6(1), 5-18. https://doi.org/10.30552/ejep.v6i1.90
Balakrishnan, R., Lizarazo, S., Santoro, M., Toscani, F. G., & Vargas, M. (2021). Commodity cycles, inequality, and poverty in Latin America. International Monetary Fund.
Baroody, A. J. (2004). The developmental bases for early childhood number and operations standards. In D. H. Clements, J. Sarama, A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 173-219). Lawrence Erlbaum Associates Publishers.
Baroody, A. J., & Wilkins, J. L. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48-65). National Council of Teachers of Mathematics.
Baroody, A. J., Lai, M.-l., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. In B. Spodek, & O. N. Saracho (Eds.), Handbook of research on the education of young children (pp. 187-221). Lawrence Erlbaum Associates Publishers.
Busso, M., & Messina, J. (2020). La crisis de la desigualdad: América Latina y el Caribe en la encrucijada [The crisis of inequality: Latin America and the Caribbean at the crossroads]. Banco Interamericano de Desarrollo. https://doi.org/10.18235/0002629
Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1-29. https://doi.org/10.1177/016146811311500603
Clements, D. H., Sarama, J., & Liu, X. (2008). Development of a measure of early mathematics achievement using the Rasch model: The research-based early math assessment. Educational Psychology, 28(4), 457-482. https://doi.org/10.1080/01443410701777272
Clements, D. H., Sarama, J., & Wolfe, C. B. (2011). TEAM–Tools for early assessment in mathematics. McGraw-Hill Education.
Clements, D. H., Sarama, J., Day-Hess, C., Germeroth, C., Ganzar, J., Pugia, A., & Barker, J. (2017). Comprehensive review of assessments of early childhood mathematics competencies[Unpublished manuscript].
Connolly, A. J. (1998). Manual for the KeyMath revised/NU: A diagnostic inventory of essential mathematics. American Guidance Service
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. https://doi.org/10.1037/0012-1649.43.6.1428
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Lawrence Erlbaum Associates Publishers.
Fritz, A., Geraldi, V., & Räsänen, P. (2019). Introduction. In A. Fritz, V. Geraldi, & P. Räsänen (Eds.), International handbook of mathematical learning difficulties (pp. 1-8). Springer. https://doi.org/10.1007/978-3-319-97148-3_1
Gelman, R., & Gallistel, C. R. (1986). The child’s understanding of number. Harvard University Press. https://doi.org/10.4159/9780674037533
Ginsburg, H. P., & Baroody, A. J. (2003). Test of early mathematics ability. PRO-ED.
Ginsburg, H. P., & Baroody, A. J. (2007). TEMA-3: Test de competencia matemática básica [TEMA-3: Test of basic mathematics competence]. TEA Ediciones.
Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social Policy Report, 22(1), 3-22. https://doi.org/10.1002/j.2379-3988.2008.tb00054.x
Hresko, W. P., Peak, P. K., Herron, S. R., & Bridges, D. L. (2000). Young children’s achievement test. PRO-ED.
Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153-175. https://doi.org/10.1111/j.1467-8624.2006.00862.x
Kendall, M. G., & Gibbons, J. D. (1990). Rank correlation methods. Griffin.
Klein, A., & Starkey, P. (2006). Child math assessment. University of California, Berkeley.
Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19(6), 513-526. https://doi.org/10.1016/j.learninstruc.2008.10.002
Lenes, R., Størksen, I., McClelland, M. M., & Idsøe, T. (2022). The role of mother’s education and child gender for children’s vocabulary and math skills in the transition from early childhood education and care to first grade in Norway. European Early Childhood Education Research Journal, 30(3), 403-422. https://doi.org/10.1080/1350293X.2022.2055101
León, J., & Collahua, Y. (2016). El efecto del nivel socioeconómico en el rendimiento de los estudiantes peruanos: Un balance de los últimos 15 años [The effect of the socioeconomic level on the performance of Peruvian students: A balance of the last 15 years]. In GRADE. Investigación para el desarrollo en el Perú: Once balances [Research for development in Peru: Eleven balances] (pp. 109-162). GRADE.
Linacre J. M. (2014). Winsteps Rasch measurement [Computer software]. Winsteps.
Linacre, J. M. (2002). What do infit and outfit, mean‐square and standardized mean? Rasch Measurement Transactions, 16, 878.
Linacre, J. M. (2019). A userʹs guide to WINSTEPS [Computer manual]. Winsteps. https://www.winsteps.com/manuals.htm
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
NCTM. (2003). Principios y estándares para la educación matemática [Principles and standards for mathematical education]. Sociedad Andaluza de Educación Matemática Thales [Andalusian Mathematical Education Society Thales].
NCTM. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. National Council of Teachers of Mathematics.
Newcomer, P. L. (2001). Diagnostic achievement battery. PRO-ED.
Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Childhood Research Quarterly, 36, 550-560. https://doi.org/10.1016/j.ecresq.2016.02.003
NRC. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. The National Academies Press. https://doi.org/10.17226/12519
Nuñez, M. C. & Pascual, M. I. (2011). Habilidades matemáticas básicas en alumnos de 3º de Infantil: Detección temprana de dificultades de aprendizaje y orientaciones para la intervención [Basic mathematical skills in students of 3rd Infant: early detection of learning difficulties and orientations for intervention]. Revista Diálogo Educacional [Educational Dialogue Magazine], 11(32), 83-105. https://doi.org/10.7213/rde.v11i32.4087
OECD. (2015). The ABC of gender equality in education: Aptitude, behaviour, confidence. PISA, OECD. https://doi.org/10.1787/9789264229945-en
Purpura, D. J., Baroody, A. J., & Lonigan, C. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge. Journal of Educational Psychology, 105(2), 453-464. https://doi.org/10.1037/a0031753
Purpura, D. J., & Lonigan, C. J. (2013). Informal numeracy skills: The structure and relations among numbering, relations, and arithmetic operations in preschool. American Educational Research Journal, 50(1), 178-209. https://doi.org/10.3102/0002831212465332
Purpura, D. J., & Lonigan, C. J. (2015). Early numeracy assessment: The development of the preschool early numeracy scales. Early Education and Development, 26(2), 286-313. https://doi.org/10.1080/10409289.2015.991084
Rapin, I. (2016). Dyscalculia and the calculating brain. Pediatric Neurology, 61, 11-20. https://doi.org/10.1016/j.pediatrneurol.2016.02.007
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Danish Institute for Educational Research.
Romano, E., Babchishin, L., Pagani, L. S., & Kohen, D. (2010). School readiness and later achievement: Replication and extension using a nationwide Canadian survey. Developmental Psychology, 46(5), 995-1007. https://doi.org/10.1037/a0018880
Ryoo, J. H., Molfese, V. J., Brown, E. T., Karp, K. S., Welch, G. W., & Bovaird, J. A. (2015). Examining factor structures on the test of early mathematics ability–3: A longitudinal approach. Learning and Individual Differences, 41, 21-29. https://doi.org/10.1016/j.lindif.2015.06.003
Ryoo, J. H., Molfese, V. J., Heaton, R., Zhou, X., Brown, E. T., Prokasky, A., & Davis, E. (2014). Early mathematics skills from prekindergarten to first grade: Score changes and ability group differences in Kentucky, Nebraska, and Shanghai samples. Journal of Advanced Academics, 25(3), 162-188. https://doi.org/10.1177/1932202X14538975
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. https://doi.org/10.4324/9780203883785
Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99-120. https://doi.org/10.1016/j.ecresq.2004.01.002
Susperreguy, M. I., & Davis-Kean, P. E. (2016). Maternal math talk in the home and math skills in preschool children. Early Education and Development, 27(6), 841-857. https://doi.org/10.1080/10409289.2016.1148480
Susperreguy, M. I., Douglas, H., Xu, C., Molina-Rojas, N., & LeFevre, J. A. (2020). Expanding the home numeracy model to Chilean children: Relations among parental expectations, attitudes, activities, and children’s mathematical outcomes. Early Childhood Research Quarterly, 50, 16-28. https://doi.org/10.1016/j.ecresq.2018.06.010
UNESCO Institute for Statistics. (2017). More than one-half of children and adolescents are not learning worldwide. UNESCO Institute for Statistics.
UNESCO. (2018). Achieving gender equality in education: Don’t forget the boys [Policy paper]. UNESCO. https://en.unesco.org/gem-report/node/2426
Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89(2), 539-555.https://doi.org/10.1111/cdev.12713
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, 352-360. https://doi.org/10.3102/0013189X14553660
Woodcock, R., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson tests of achievement. Riverside Publishing.
Wright, B. D., & Stone, M. H. (1979). Best test design: Rasch measurement. MESA Press.
Yao, S. Y., Muñez, D., Bull, R., Lee, K., Khng, K. H., & Poon, K. (2017). Rasch modeling of the test of early mathematics ability–Third edition with a sample of K1 children in Singapore. Journal of Psychoeducational Assessment, 35(6), 615-627. https://doi.org/10.1177/0734282916651021

How to cite this article

APA

Malaspina, M., & Arias, B. (2022). A Rasch modeling approach for measuring young children’s informal mathematics in Peru. Eurasia Journal of Mathematics, Science and Technology Education, 18(9), em2147. https://doi.org/10.29333/ejmste/12303

Vancouver

Malaspina M, Arias B. A Rasch modeling approach for measuring young children’s informal mathematics in Peru. EURASIA J Math Sci Tech Ed. 2022;18(9):em2147. https://doi.org/10.29333/ejmste/12303

AMA

Malaspina M, Arias B. A Rasch modeling approach for measuring young children’s informal mathematics in Peru. EURASIA J Math Sci Tech Ed. 2022;18(9), em2147. https://doi.org/10.29333/ejmste/12303

Chicago

Malaspina, Martín, and Benito Arias. "A Rasch modeling approach for measuring young children’s informal mathematics in Peru". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 9 (2022): em2147. https://doi.org/10.29333/ejmste/12303

Harvard

Malaspina, M., and Arias, B. (2022). A Rasch modeling approach for measuring young children’s informal mathematics in Peru. Eurasia Journal of Mathematics, Science and Technology Education, 18(9), em2147. https://doi.org/10.29333/ejmste/12303

MLA

Malaspina, Martín et al. "A Rasch modeling approach for measuring young children’s informal mathematics in Peru". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 9, 2022, em2147. https://doi.org/10.29333/ejmste/12303