How math happens at home: A Rasch-based validation of the home mathematics environment scale in early childhood

Authors

  • Adi Cahya Nugraha Universitas Muhammadiyah Prof. DR. HAMKA
  • Ira Rachmadani Universitas Muhammadiyah Prof. DR. HAMKA
  • Mardiana Universitas Muhammadiyah Prof. DR. HAMKA
  • Nur Alifa Deviar Refiyanti Universitas Muhammadiyah Prof. DR. HAMKA
  • Joko Soebagyo Universitas Muhammadiyah Prof. DR. HAMKA

DOI:

https://doi.org/10.29408/jel.v11i3.30220

Keywords:

home mathematics environment, preschool home mathematics questionnaire, Rasch model analysis

Abstract

Preschool education is important for developing children’s social and cognitive skills, with early mathematical ability being a strong predictor of future success. This study evaluated the psychometric properties of the Preschool Home Mathematics Questionnaire (PHMQ) using Rasch Model Analysis. A total of 95 parents and guardians of preschool-aged children participated in the study. A total of 37 Likert-scale items were analysed. The results showed excellent person reliability (0.93) and item reliability (0.96), indicating strong consistency and well-targeted item difficulty. Of the 37 items, 32 were valid according to the Rasch fit criteria, while five items (Q13, Q15, Q22, Q24, and Q26) showed misfit based on the Outfit mean square (MNSQ), Z-standard (ZSTD), and PTMEA-CORR. The Likert scale functioned well with ordered thresholds and smooth transitions between categories. The unidimensionality test confirmed that the PHMQ measures a single construct, with 44.1% of the variance explained and only 12.8% unexplained in the first contrast. While the PHMQ shows good validity and reliability, this study focused only on basic Rasch validation. Future research should explore differential item functioning (DIF), item bias, and long-term stability to further improve this instrument and support its use in different settings.

References

Al Ali, R. M. A., & Shehab, R. T. (2020). Psychometric properties of social perception of mathematics:‎‎ Rasch model analysis. International Education Studies, 13(12), 102–110. https://doi.org/10.5539/ies.v13n12p102

Andrich, D. (1988). Rasch Models for Measuremen. SAGE Publications.

Blevins-Knabe, B., & Musun-Miller, L. (1996). Number use at home by children and their parents and its relationship to early mathematical performance. Early Development and Parenting, 5(1), 35–45. https://doi.org/10.1002/(SICI)1099-0917(199603)5:1<35::AID-EDP113>3.0.CO;2-0

Bond, T. (2015). Applying the Rasch model. Routledge. https://doi.org/10.4324/9781315814698

Bonifacci, P., Compiani, D., Affranti, A., & Peri, B. (2021). Home literacy and numeracy interact and mediate the relationship between socio-economic status and early linguistic and numeracy skills in preschoolers. Frontiers in Psychology, 12(September), 1–16. https://doi.org/10.3389/fpsyg.2021.662265

Boone, W. J., Staver, J. R., & Yale, M. S. (2014). Rasch analysis in the human sciences. Springer Netherlands. https://doi.org/10.1007/978-94-007-6857-4

Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry and Allied Disciplines, 46(1), 3–18. https://doi.org/10.1111/j.1469-7610.2004.00374.x

Cahoon, A., Cassidy, T., Purpura, D. J., & Simms, V. (2021). Developing a rigorous measure of the pre-school home mathematics environment. Journal of Numerical Cognition, 7(2), 172–194. https://doi.org/10.5964/jnc.6373

Camilli, G., Vargas, S., Ryan, S., & Barnett, W. S. (2010). Meta-analysis of the effects of early education interventions on cognitive and social development. Teachers College Record: The Voice of Scholarship in Education, 112(3), 579–620. https://doi.org/10.1177/016146811011200303

Colledani, D., González Pizzio, A. P., Devita, M., & Anselmi, P. (2025). Investigating the Functioning of Rating Scales With Rasch Models. Assessment, 32(3), 434–446. https://doi.org/10.1177/10731911241245792

Cook, R. M., & Wind, S. A. (2024). Item response theory: A modern measurement approach to reliability and precision for counseling researchers. Measurement and Evaluation in Counseling and Development, 57(2), 116–135. https://doi.org/10.1080/07481756.2023.2301284

DeFlorio, L., & Beliakoff, A. (2015). Socioeconomic status and preschoolers’ mathematical knowledge: The contribution of home activities and parent beliefs. Early Education and Development, 26(3), 319–341. https://doi.org/10.1080/10409289.2015.968239

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

Evans, T. M., Kochalka, J., Ngoon, T. J., Wu, S. S., Qin, S., Battista, C., & Menon, V. (2015). Brain structural integrity and intrinsic functional connectivity forecast 6 year longitudinal growth in children’s numerical abilities. Journal of Neuroscience, 35(33), 11743–11750. https://doi.org/10.1523/JNEUROSCI.0216-15.2015

Fischer, L., Rohm, T., Carstensen, C. H., & Gnambs, T. (2021). Linking of Rasch-scaled tests: Consequences of limited item pools and model misfit. Frontiers in Psychology, 12, 1–10. https://doi.org/10.3389/fpsyg.2021.633896

Fisher, W. P. (2007). Rating scale instrument quality criteria. Rasch Measurement Transactions, 21, 1095.

Gashaj, V., Thaqi, Q., Mast, F. W., & Roebers, C. M. (2023). Foundations for future math achievement: Early numeracy, home learning environment, and the absence of math anxiety. Trends in Neuroscience and Education, 33, 1–9. https://doi.org/10.1016/j.tine.2023.100217

Gilligan-Lee, K. A., Fink, E., Jerrom, L., Davies, M. P., Dempsey, C., Hughes, C., & Farran, E. K. (2023). Building numeracy skills: Associations between DUPLO® block construction and numeracy in early childhood. Journal of Intelligence, 11(8), 1–18. https://doi.org/10.3390/jintelligence11080161

Girard, C., Bastelica, T., Léone, J., Epinat-Duclos, J., Longo, L., & Prado, J. (2021). The relation between home numeracy practices and a variety of math skills in elementary school children. PLoS ONE, 16(9 September), 1–25. https://doi.org/10.1371/journal.pone.0255400

Hahn, R. A., & Barnett, W. S. (2023). Early childhood education: Health, equity, and economics. Annual Review of Public Health, 44, 75–92. https://doi.org/10.1146/annurev-publhealth-071321-032337

Johansson, M. (2025). Detecting item misfit in Rasch models. Educational Methods and Psychometrics, 3(2025), 1–58. https://doi.org/10.61186/emp.2025.5

Kurniati, A., Yuniati, S., & Rahmi, D. (2022). Media puzzle angka: Pengenalan angka pada anak tahap praoperasional (Teori Piaget) [Number puzzle media: Introduction to numbers for children in the preoperational stage (Piaget's theory)]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 6(3), 2846–2856.

Kvesic, L., Brkic, S., & Imre, A. (2020). Mathematical abilities of preschool children. World Journal of Educational Research, 7(1), 167–186. https://doi.org/10.22158/wjer.v7n1p167

Lefevre, J. A., Kwarchuk, S. L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science, 41(2), 55–66. https://doi.org/10.1037/a0014532

Linacre, J. M. (2002). Optimizing rating scale category effectiveness. Journal of Applied Measurement, 3(1), 85–106.

Ling, M.-T., Pang, V., & Ompok, C. C. (2018). Measuring change in early mathematics ability of children who learn using games: Stacked analysis in Rasch measurement. In Pacific Rim Objective Measurement Symposium (PROMS) 2016 Conference Proceedings (pp. 215–226). Springer Singapore. https://doi.org/10.1007/978-981-10-8138-5_17

Lopez-Pedersen, A., Mononen, R., Aunio, P., Scherer, R., & Melby-Lervåg, M. (2023). Improving numeracy skills in first graders with low performance in early numeracy: A randomized controlled trial. Remedial and Special Education, 44(2), 126–136. https://doi.org/10.1177/07419325221102537

Lu, L., Vasilyeva, M., & Laski, E. V. (2025). Home math environment as a mediator of socioeconomic differences in early math skills: A study of Chinese families from disparate backgrounds. Developmental Psychology, 61(3), 417–431. https://doi.org/10.1037/dev0001918

Mallinckrodt, B., Miles, J. R., & Recabarren, D. A. (2016). Using focus groups and Rasch item response theory to improve instrument development. The Counseling Psychologist, 44(2), 146–194. https://doi.org/10.1177/0011000015596437

Mantilla, A., & Edwards, S. (2019). Digital technology use by and with young children: A systematic review for the Statement on Young Children and Digital Technologies. Australasian Journal of Early Childhood, 44(2), 182–195. https://doi.org/10.1177/1836939119832744

Massof, R. (2004). Likert and Guttman scaling of visual function rating scale questionnaires. Ophthalmic Epidemiology, 11(5), 381–399. https://doi.org/10.1080/09286580490888771

McCamey, R. (2014). A primer on the one-parameter Rasch model. American Journal of Economics and Business Administration, 6(4), 159–163. https://doi.org/10.3844/ajebasp.2014.159.163

Melhuish, E. C. (2011). Preschool matters. Science, 333(6040), 299–300. https://doi.org/10.1126/science.1209459

Missall, K., Hojnoski, R. L., Caskie, G. I. L., & Repasky, P. (2015). Home numeracy environments of preschoolers: Examining relations among mathematical activities, parent mathematical beliefs, and early mathematical skills. Early Education and Development, 26(3), 356–376. https://doi.org/10.1080/10409289.2015.968243

Mofreh, S. A. M., Ghafar, M. N. A., Omar, A. H. H., Mosaku, M., & Ma’ruf, A. (2014). Psychometric properties on lecturers’ beliefs on teaching function: Rasch model analysis. International Education Studies, 7(11), 47–55. https://doi.org/10.5539/ies.v7n11p47

Nadlifah, & Latif, M. A. (2024). Creative freedom and holistic growth: Implementation of the STEAM approach in Islamic early childhood education. Golden Age: Jurnal Ilmiah Tumbuh Kembang Anak Usia Dini, 9(4), 689–702. https://doi.org/10.14421/jga.2024.94-09

Nemoto, T., & Beglar, D. (2014). Developing Likert-scale questionnaires campus reference data. JALT2013 Conference Proceedings.

Niklas, F., & Schneider, W. (2014). Casting the die before the die is cast: the importance of the home numeracy environment for preschool children. European Journal of Psychology of Education, 29(3), 327–345. https://doi.org/10.1007/s10212-013-0201-6

Noa, K., & Pennucci, A. (2014). Early childhood education for low-income students: A review of the evidence and benefit-cost analysis. Washington State Institute for Public Policy.

Nugraha, A. C., & Muntazhimah, M. (2024). Analisis konten penelitian kemampuan numerasi awal pada anak usia dini: Tinjauan metodologi penelitian [Content analysis of research on early numeracy skills in young children: A review of research methodology]. Jurnal Obsesi: Jurnal Pendidikan Anak Usia Dini, 8(5), 1174–1184. https://doi.org/10.31004/obsesi.v8i5.6027

Othman, N., & Zaini, M. A. Y. M. (2019). Reliability testing on instrument development measuring the attitude and perception towards academic and personality: Application of the Rasch model. International Journal of Academic Research in Business and Social Sciences, 9(1), 191–209. https://doi.org/10.6007/IJARBSS/v9-i1/5388

Pan, Y., Hu, B. Y., Hunt, J., Wu, Z., Chen, Y., & He, M. (2023). Chinese preschool children’s home numeracy experiences and their mathematical abilities. Journal of Early Childhood Research, 21(1), 31–45. https://doi.org/10.1177/1476718X221125583

Papic, M. M., & Papic, C. (2025). Is confidence in mathematics pedagogy enough? Exploring early childhood teachers’ mathematics beliefs and confidence. Early Childhood Education Journal. https://doi.org/10.1007/s10643-024-01840-4

Pesu, L., Viljaranta, J., & Aunola, K. (2016). The role of parents’ and teachers’ beliefs in children’s self-concept development. Journal of Applied Developmental Psychology, 44, 63–71. https://doi.org/10.1016/j.appdev.2016.03.001

Petronzi, D., Schalkwyk, G., & Petronzi, R. (2023). A pilot math anxiety storybook approach to normalize math talk in children and to support emotion regulation. Journal of Research in Childhood Education, 00(00), 1–19. https://doi.org/10.1080/02568543.2023.2214591

Phillips, D. A. (2017). Commentary: Beyond more of the same – sustaining the benefits of preschool education – reflections on Bierman et al. (2016). Journal of Child Psychology and Psychiatry and Allied Disciplines, 58(2), 138–139. https://doi.org/10.1111/jcpp.12674

Piussi, R., Thomeé, R., Samuelsson, K., & Hamrin Senorski, E. (2025). Measurement properties of the Swedish version of the Knee self‐efficacy scale: A Rasch analysis. Journal of Experimental Orthopaedics, 12(2). https://doi.org/10.1002/jeo2.70306

Prusinski, E., Mahler, P. P., Collins, M., & Couch, H. (2023). Strengthening early childhood education and care in a “Childcare Desert.” Early Childhood Education Journal, 51(7), 1317–1333. https://doi.org/10.1007/s10643-022-01375-6

Purnomo, Y. W., Ainun, T. R., Nina, P. La, Utami, K., Wijayanti, R., & Ismail, S. N. (2022). Mother as a teacher at home: Challenges and opportunities for parental involvement in online mathematics learning for elementary school students. New Educational Review, 69, 130–140. https://doi.org/10.15804/tner.2022.69.3.10

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

Reid, K. (2016). Counting on it: Early numeracy development and the preschool child. Australian Council for Educational Research, 2, 1–16. https://research.acer.edu.au/learning_processes/19%0Awww.acer.edu.au

Saracho, O. N., & Spodek, B. (2010). Parents and children engaging in storybook reading. Early Child Development and Care, 180(10), 1379–1389. https://doi.org/10.1080/03004430903135605

Seitz, M., & Weinert, S. (2022). Numeracy skills in young children as predictors of mathematical competence. British Journal of Developmental Psychology, 40(2), 224–241. https://doi.org/10.1111/bjdp.12408

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

Sumintono, B., & Widhiarso, W. (2014). Aplikasi model Rasch untuk penelitian ilmu-ilmu sosial (edisi revisi) [Application of the Rasch model to social science research (revised edition)]. Trim Komunikata Publishing House.

Suryani, Y. E. (2018). Aplikasi Rasch model dalam mengevaluasi intelligenz structure test (IST). Psikohumaniora: Jurnal Penelitian Psikologi, 3(1), 73. https://doi.org/10.21580/pjpp.v3i1.2052

Tabatabaee-Yazdi, M., Motallebzadeh, K., Ashraf, H., & Baghaei, P. (2018). Development and validation of a teacher success questionnaire using the Rasch model. International Journal of Instruction, 11(2), 129–144. https://doi.org/10.12973/iji.2018.11210a

Tennant, A., & Küçükdeveci, A. A. (2023). Application of the Rasch measurement model in rehabilitation research and practice: early developments, current practice, and future challenges. Frontiers in Rehabilitation Sciences, 4. https://doi.org/10.3389/fresc.2023.1208670

Tennant, A., & Pallant, J. (2006). Unidimensionality Matters. Rasch Measurement Transactions, 20, 1048–1051.

Toll, S. W. M., & Van Luit, J. E. H. (2014). Explaining numeracy development in weak performing kindergartners. Journal of Experimental Child Psychology, 124(1), 97–111. https://doi.org/10.1016/j.jecp.2014.02.001

Van Rooijen, M., Verhoeven, L., & Steenbergen, B. (2011). Early numeracy in cerebral palsy: Review and future research. Developmental Medicine and Child Neurology, 53(3), 202–209. https://doi.org/10.1111/j.1469-8749.2010.03834.x

Van Zile-Tamsen, C. (2017). Using Rasch analysis to inform rating scale development. Research in Higher Education, 58(8), 922–933. https://doi.org/10.1007/s11162-017-9448-0

Vandermaas-Peeler, M., Ferretti, L., & Loving, S. (2012). Playing the ladybug game: Parent guidance of young children’s numeracy activities. Early Child Development and Care, 182(10), 1289–1307. https://doi.org/10.1080/03004430.2011.609617

Vandermaas‐Peeler, M., Nelson, J., Bumpass, C., & Sassine, B. (2009). Numeracy‐related exchanges in joint storybook reading and play. International Journal of Early Years Education, 17(1), 67–84. https://doi.org/10.1080/09669760802699910

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (86th ed.). Harvard University Press.

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

Wolf, S., & McCoy, D. C. (2019). Household Socioeconomic Status and Parental Investments: Direct and Indirect Relations With School Readiness in Ghana. Child Development, 90(1), 260–278. https://doi.org/10.1111/cdev.12899

Yamashita, T. (2022). Analyzing Likert scale surveys with Rasch models. Research Methods in Applied Linguistics, 1(3), 100022. https://doi.org/10.1016/j.rmal.2022.100022

Yoshikawa, H., Weiland, C., & Brooks-Gunn, J. (2016). When does preschool matter? Future of Children, 26(2), 21–36. https://doi.org/10.1353/foc.2016.0010

Yuniria, A. R., Atikah, C., & Asmawati, L. (2025). Interactive educational games: Boosting numeracy skills in 4-5 year-olds through multimedia. AL-ISHLAH: Jurnal Pendidikan, 17(1). https://doi.org/10.35445/alishlah.v17i1.5503

Zhang, B., & Konstantopoulos, S. (2025). Short- and long-term effects of approaches to learning on reading and mathematics achievement in childhood: a fixed effects approach. Educational Research and Evaluation, 1–32. https://doi.org/10.1080/13803611.2024.2441785

Downloads

Published

31-07-2025

How to Cite

Nugraha, A. C., Rachmadani, I., Mardiana, Refiyanti, N. A. D., & Soebagyo, J. (2025). How math happens at home: A Rasch-based validation of the home mathematics environment scale in early childhood. Jurnal Elemen, 11(3), 720–740. https://doi.org/10.29408/jel.v11i3.30220

Issue

Section

Articles

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.