Abstract
Almost 5% of Australian students fail to reach minimum standards for numeracy as assessed on the national assessment and monitoring program, and this is of particular concern in light of evidence that poor numeracy contributes to lifelong problems such as difficulty getting and maintaining employment. Learning progressions, particularly in mathematics, have been identified as effective ways to support teachers’ understanding of skill development and connect assessment and pedagogy. The aim of the study described in this chapter was to design an assessment of early numeracy skills for students with additional learning needs that could be mapped to a learning progression. Trialled with 2597 students from 65 schools, a set of items based on teacher observation and judgement measured skills that provide a foundation for participation in numeracy learning across the school years. Analysis of the data, using a partial credit approach to item response modelling, found that the items could describe numeracy learning across a broad range of proficiency, although gaps were identified for students at the highest and lowest extremes of numeracy understanding. Analysis of differential item functioning (DIF) suggested that the items measured numeracy skills and understanding consistently for students with different sub types of additional learning need.
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References
Adams, R., & Khoo, S. T. (1996). Quest. Melbourne, Australia: Australian Council for Educational Research.
Adams, R., Wu, M., Macaskill, G., Haldane, S., & Xun Sun, X. (2015). ConQuest. Berkley, CA: Australian Council for Educational Research, University of California.
Australian Curriculum, Assessment and Reporting Authority. (2015). NAPLAN achievement in Reading, persuasive writing, language conventions and numeracy: National report for 2015. Sydney, Australia: ACARA.
Baron-Cohen, S., Leslie, A. M., & Frith, U. (1985). Does the autistic child have a ‘theory of mind’? Cognition, 21, 37–46.
Birnie, B. F. (2015). Making the case for differentiation. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 88(2), 62–65. https://doi.org/10.1080/00098655.2014.998601.
Black, P., Wilson, M., & Yao, S. Y. (2011). Road maps for learning: A guide to the navigation of learning progressions. Measurement: Interdisciplinary Research & Perspective, 9(2–3), 71–123.
Butterworth, B. (1999). The mathematical brain. London: Macmillan.
Commonwealth of Australia. (2016). Access to real learning: The impact of policy, funding and culture on students with disability, being a report of the Senate Standing Committee on Education. Canberra, Australia: Australian Government Publishing Service. Retrieved 18 January 2016 from http://www.aph.gov.au/Parliamentary_Business/Committees/Senate/Education_and_Employment/students_with_disability/Report
Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all children: Prekindergarten teachers lay the foundation for later success in mathematics when they attend to the concepts that young children can and should learn. Phi Delta Kappan, 97(3), 63–68.
Gallistel, R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Numerical Cognition, 44(1–2), 43–74.
Gelman, R., & Butterworth, B. (2005). Number and language: How are they related? Trends in Cognitive Science, 9(1), 6–10.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Heritage, M. (2008). Learning progressions: Supporting instruction and formative assessment. Washington, DC: Council of Chief State School Officers. Retrieved from www.ccsso.org/content/PDFs/FAST%20Learning%20Progressions.pdf
Hiniker, A., Rosenberg-Lee, M., & Menon, V. (2016). Distinctive role of symbolic number sense in mediating the mathematical abilities of children with autism. Journal of Autism Developmental Disorders, 46, 1268–1281. https://doi.org/10.1007/s10803-015-2666-4.
Jung, M. (2011). Number relationships in preschool. Teaching Children Mathematics, 17(9), 550–557.
Kleemans, T., Peeters, M., Segers, E., & Verhoeven, L. (2012). Child and home predictors of early numeracy skills in kindergarten. Early Childhood Research Quarterly, 27, 471–477. https://doi.org/10.1016/j.ecresq.2011.12.004.
LeFevre, J., Skwarchuk, S., 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, 55–66. https://doi.org/10.1037/a0014532.
Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
Plaisier, M. A., Bergmann Tiest, W. M., & Kappers, A. M. L. (2009). One, two, three, many – Subistising in active touch. Acta Psychologica, 131, 163–170.
Powell, S. R., & Fuchs, L. S. (2012). Early numerical competencies and students with mathematics difficulty. Focus on Exceptional Children, 44(5), 1–16.
Purpura, D. J., & Napoli, A. M. (2015). Early literacy and numeracy: Untangling the relation between specific components. Mathematical thinking and learning: An International Journal, 17, 197–218.
Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press.
Victorian Department of Education and Training (DET). (2016). ABLES. Retrieved from http://www.education.vic.gov.au/school/teachers/teachingresources/diversity/Pages/ables.aspx.
Vygotsky, L.S. (1929/1993). The collected works of L. S. Vygotsky, Volume 2: The fundamentals of defectology (Abnormal psychology and learning disabilities) (R. W. Rieber & A. S. Carton, Trans.). New York: Plenum Press.
Wilson, M. (2005). Constructing measures: An item-response modeling approach. Mahwah, NJ: Lawrence Erlbaum Associates.
Woods, K., & Griffin, P. (2013). Judgement-based performance measures of literacy for students with additional needs: Seeing students through the eyes of experienced special education teachers. Assessment in Education: Principles, Policy & Practice, 20(3), 325–348.
Wright, B. D., & Stone, M. H. (1999). Measurement essentials (2nd ed.). Wilmington, DE: Wide Range Inc..
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An earlier version of this chapter was included on the Australian Association for Research in Education’s (AARE) website as a refereed conference paper from the 2016 AARE Annual Conference.
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Strickland, J., Woods, K., Pavlovic, M. (2020). Assessing and Understanding Early Numeracy for Students with Additional Learning Needs. In: Griffin, P., Woods, K. (eds) Understanding Students with Additional Needs as Learners. Springer, Cham. https://doi.org/10.1007/978-3-030-56596-1_9
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