Considering that young children spend a great deal of time outside of school, there is a need to increase the expertise of adults when it comes to engaging young children with numerical activities. This study presents the Cognitive Affective Mathematics Adult Education framework used to design such a course for interested adults. Focusing on promoting young children’s competency for comparing sets, we illustrate how the framework was used to design the course and how the framework was used to analyze the impact of the course on the relevant expertise of the participating adults. The findings indicated that the adults had gained knowledge in the various strategies one can use to compare sets, had become aware of the importance of evaluating those strategies, and had acquired the ability to take the children’s ages and abilities into account when tailoring activities that engage them with set comparisons.
Anderson, A., & Anderson, J. (2018). Math-in-context: The types of math preschoolers ‘do’ at home. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 183–202). Springer, Cham.
Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Barkai, R., Levenson, E., Tsamir, P., & Tirosh, D. (2022). Adults’ awareness of number-related ideas raised by young children. Research in Mathematics Education. https://doi.org/10.1080/14794802.2021.2010238
Baroody, A. J. (1984). Children’s difficulties in subtraction: Some causes and questions. Journal for Research in Mathematics Education, 15(3), 203–213. https://doi.org/10.2307/748349
Baroody, A. J. (2004). The developmental bases for early childhood number and operations standards. In D.H. Clements, & J. Sarama (Eds.), Engaging Young Children in Mathematics Standards for Early Childhood Mathematics Education (pp. 173–220). Taylor and Francis.
Cannon, J., & Ginsburg, H.P. (2008). “Doing the math”: Maternal beliefs about early mathematics versus language learning. Early Education and Development, 19(2), 238–260. https://doi.org/10.1080/10409280801963913
Clarke, B., Cheeseman, J., & Clarke, D. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78–103. https://doi.org/10.1007/BF03217430
Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Harvard University Press.
Ginsburg, H.P. (2016). Helping early childhood educators to understand and assess young children’s mathematical minds. ZDM Mathematics Education, 48(7), 941–946. https://link.springer.com/article/10.1007/s11858-016-0807-7
Greenes, C., Ginsburg, H.P., & Balfanz, R. (2004). Big math for little kids. Early Childhood Research Quarterly, 19(1), 159–166. https://doi.org/10.1016/j.ecresq.2004.01.010
Greenfield, D.B., & Scott, M. S. (1986). Young children’s preference for complementary pairs: Evidence against a shift to a taxonomic preference. Developmental Psychology, 22(1), 19–21. https://doi.org/10.1037/0012-1618.104.22.168
Gunderson, E.A., & Levine, S.C. (2011). Some types of parent number talk count more than others: Relations between parents’ input and children’s cardinal-number knowledge. Developmental Science, 14(5), 1021–1032. https://doi.org/10.1111/j.1467-7687.2011.01050.x
Israel National Mathematics Preschool Curriculum (INMPC). (2010). Retrieved March 18, 2020 from https://edu.gov.il/minhalpedagogy/preschool/subject/math/Pages/math-curriculum.aspx
Levenson, E., Barkai, R., Tirosh, D., & Tsamir, P. (2021). Studying adults’ beliefs related to engaging children with number concepts. In M. Inprasitha, N. Changsri, & N. Boonsena (Eds.), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 205–215). PME. https://pme44.kku.ac.th/home/uploads/volumn/pme44 vol3.pdf
Levenson, E. S., Barkai, R., Tirosh, D., & Tsamir, P. (2022). Exploring adults’ awareness of and suggestions for early childhood numerical activities. Educational Studies in Mathematics, 109, 5–21. https://doi.org/10.1007/s10649-021-10063-y
Levine, S.C., Suriyakham, L.W., Rowe, M. L., Huttenlocher, J., & Gunderson, E.A. (2010). What counts in the development of young children’s number knowledge? Developmental Psychology, 46(5), 1309–1319. https://doi.org/10.1037/a0019671
Marti, M., Merz, E. C., Repka, K.R., Landers, C., Noble, K. G., & Duch, H. (2018). Parent involvement in the getting ready for school intervention is associated with changes in school readiness skills. Frontiers in Psychology, 9, 759. https://doi.org/10.3389/fpsyg.2018.00759
Mason, J. (2011). Noticing: Roots and branches. In M.G. Sherin, V.R. Jacobs, & R.A. Phillipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35–50). Routledge.
Missall, K., Hojnoski, R. L., Caskie, G. I., & 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
Reardon, S.F., & Portilla, X.A. (2016). Recent trends in income, racial, and ethnic school readiness gaps at kindergarten entry. Aera Open, 2(3), 1–18. https://doi.org/10.1177/2332858416657343
Sarama, J., & Clements, D. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. https://doi.org/10.4324/9780203883785
Sherin, M. G., & Van Es, E.A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37. https://doi.org/10.1177%2F0022487108328155
Skwarchuk, S. L. (2009). How do parents support preschoolers’ numeracy learning experiences at home? Early Childhood Education Journal, 37(3), 189–197. https://doi.org/10.1007/s10643-009-0340-1
Sonnenschein, S., Metzger, S.R., Dowling, R., Gay, B., & Simons, C. L. (2016). Extending an effective classroom-based math board game intervention to preschoolers’ homes. Journal of Applied Research on Children: Informing Policy for Children at Risk, 7(2), Article 1. Available at https://digitalcommons.library.tmc.edu/childrenatrisk/vol7/iss2/1
Sonnenschein, S., Stites, M., & Dowling, R. (2021). Learning at home: What preschool children’s parents do and what they want to learn from their children’s teachers. Journal of Early Childhood Research, 19(3), 309–322. https://doi.org/10.1177/1476718X20971321
Starkey, P., & Klein, A. (2000). Fostering parental support for children’s mathematical development: An intervention with Head Start families. Early Education and Development, 11(5), 659–680. https://doi.org/s15566935eed1105 7
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.2307/1175860
Sullivan, P., & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In Making sense of mathematics teacher education (pp. 147–163). Springer, Dordrecht.
Tirosh, D., Tsamir, P., Levenson, E., & Tabach, M. (2011). From preschool teachers’ professional development to children’s knowledge: comparing sets. Journal of Mathematics Teacher Education, 14(2), 113–131. https://doi.org/10.1007/s10857-011-9172-1
Tirosh, D., Tsamir, P., Levenson, E., & Barkai, R. (2017). Working with parents to promote preschool children’s numeracy: Teachers’ attitudes and beliefs. In S. Phillipson, P. Sullivan, & A. Gervasoni (Eds.), Engaging families as the first mathematics educators of children (pp. 181–198). Springer. https://doi.org/10.1007/978-981-10-2553-2_11
Tirosh, D., Tsamir, P., Levenson, E. S., & Barkai, R. (2020). Setting the table with toddlers: a playful context for engaging in one-to-one correspondence. ZDM Mathematics Education, 52, 717–728. https://doi.org/10.1007/s11858-019-01126-9
Tsamir, P. (1999). The transition from comparison of finite to the comparison of infinite sets: Teaching prospective teachers. Educational Studies in Mathematics, 38, 209–234. https://doi.org/10.1007/978-94-017-1584-3_10
Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81–95. https://doi.org/10.1007/s10649-008-9133-5
Tsamir, P., Tirosh, D., & Levenson, E. (2010). Exploring the relationship between justification and monitoring among kindergarten children. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (CERME 6) (pp. 1891–1901). Institut National de Recherche Pédagogique and ERME. https://hal.archives-ouvertes.fr/hal-02182374/file/cerme6 proceedings.pdf
Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2014). Employing the CAMTE framework: Focusing on preschool teachers’ knowledge and self-efficacy related to students’ conceptions. In C. Benz, B. Brandt, U. Kortenkamp, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early Mathematics Learning – Selected Papers from the POEM 2012 Conference (pp. 291–306). Springer. https://doi.org/10.1007/s10857-013-9260-5
Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM Mathematics Education, 47(4), 639–651. https://doi.org/10.1007/s11858-015-0668-5
Tsamir, P., Tirosh, D., Levenson, E., & Barkai, R. (2018). Engaging young children with mathematical activities involving different representations: Triangles, patterns, and counting objects. Center for Educational Policy Studies Journal, 8(2), 9–30. https://doi.org/10.26529/cepsj.271
van Es, E.A., & Sherin, M. G. (2021). Expanding on prior conceptualizations of teacher noticing. ZDM Mathematics Education, 53(1), 17–27. https://doi.org/10.1007/s11858-020-01211-4
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
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://psycnet.apa.org/doi/10.1080/03004430.2011.609617