Teaching moves and preschoolers’ arithmetical accuracy

References

• Alvarado, M. (2015). The utility of written numerals for preschool children when solving additive problems/La utilidad de los numerales escritos en la resolución de problemas aditivos en niños preescolares. Estudios de Psicología, 36(1), 92–112. https://doi.org/10.1080/02109395.2014.1000026
   Web of Science ®Google Scholar
• Au, J., Jaeggi, S. M., & Buschkuehl, M. (2018). Effects of non-symbolic arithmetic training on symbolic arithmetic and the approximate number system. Acta Psychologica, 185, 1–12. https://doi.org/10.1016/j.actpsy.2018.01.005
   PubMed Web of Science ®Google Scholar
• Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14, 16–18, 46–47.
   Google Scholar
• Baratta-Lorton, M. (1976). Mathematics their way. Addison-Wesley.
   Google Scholar
• Baroody, A. J. (1987). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18(2), 141–157. https://doi.org/10.5951/jresematheduc.18.2.0141
   Web of Science ®Google Scholar
• Baroody, A. J. (1995). The role of the number-after rule in the invention of computational short cuts. Cognition and Instruction, 13(2), 189–219.
   Web of Science ®Google Scholar
• Baroody, A. J. (2017). The use of concrete experiences in early childhood mathematics instruction. Advances in Child Development and Behavior, 53, 43–94. https://doi.org/10.1016/bs.acdb.2017.03.001
   PubMed Web of Science ®Google Scholar
• Baroody, A. J., Clements, D. H., & Sarama, J. (2019). Teaching and learning mathematics in early childhood programs. In C. Brown, M. B. McMullen, & N. File (Eds.), The Wiley handbook of early childhood care and education (1st ed., pp. 329–353). Wiley Blackwell Publishing.
   Google Scholar
• Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2015). The impact of highly and minimally guided discovery instruction on promoting the learning of reasoning strategies for basic add-1 and doubles combinations. Early Childhood Research Quarterly, 30, 93–105. https://doi.org/10.1016/j.ecresq.2014.09.003
   Web of Science ®Google Scholar
• Bialystok, E., & Codd, J. (2000). Representing quantity beyond whole numbers: Some, none, and part. Canadian Journal of Experimental Psychology = Revue Canadienne de Psychologie Experimentale, 54(2), 117–128. https://doi.org/10.1037/h0087334
   PubMed Web of Science ®Google Scholar
• Brizuela, B. M. (2006). Young children’s notations for fractions. Educational Studies in Mathematics, 62(3), 281–305.
   Google Scholar
• Carpenter, T. P., & Franke, M. L. (2004). Cognitively guided instruction: Challenging the core of educational practice. In J. Glennan, K. Thomas, S. J. Bodilly, J. R. Galegher, & K. A. Kerr (Eds.), Expanding the reach of education reforms: Perspectives from leaders in the scale-up of educational interventions (pp. 41–80). RAND Corporation.
   Google Scholar
• Child Trends Databank. (2014). Early childhood program enrollment. Retrieved April 11, 2019, from Author: https://www.census.gov/data/tables/time-series/demo/school-enrollment/cps-historical-time-series.html
   Google Scholar
• Clements, D. H., Agodini, R., & Harris, B. (2013). Instructional practices and student math achievement: Correlations from a study of math curricula. Mathematica Policy Research.
   Google Scholar
• Clements, D. H., Fuson, K. C., & Sarama, J. (2019). Critiques of the common core in early math: A research-based response. Journal for Research in Mathematics Education, 50(1), 11–22. https://doi.org/10.5951/jresematheduc.50.1.0011.
   Web of Science ®Google Scholar
• Clements, D. H., & Sarama, J. (2013). Building Blocks, Volumes 1 and 2. Columbus, OH: McGraw-Hill Education.
   Google Scholar
• Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). Routledge.
   Google Scholar
• Davenport, L. R., Henry, C. S., Clements, D. H., & Sarama, J. (2019). No more math fact frenzy. Heinemann.
   Google Scholar
• Day-Hess, C. A., & Clements, D. H. (2017). The DREME network: Research and interventions in early childhood mathematics. Advances in Child Development and Behavior, 53, 1–42. https://doi.org/10.1016/bs.acdb.2017.03.002
   PubMed Web of Science ®Google Scholar
• Engel, M., Claessens, A., & Finch, M. A. (2013). Teaching students what they already know? The (mis) alignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis, 35(2), 157–178. https://doi.org/10.3102/0162373712461850
   Web of Science ®Google Scholar
• Ernest, P. (1985). The number line as a teaching aid. Educational Studies in Mathematics, 16(4), 411–424. https://doi.org/10.2307/3482448.
   Google Scholar
• Ewers-Rogers, J., & Cowan, R. (1996). Children as apprentices to number. Early Childhood Development and Care, 125(15), 15–17.
   Google Scholar
• Fryer, J., Roland, G., & Levitt, S. D. (2004). Understanding the black-white test score gap in the first two years of school. The Review of Economics and Statistics, 86(2), 447–464. https://doi.org/10.1162/003465304323031049
   Web of Science ®Google Scholar
• Fuson, K. C. (2009). Avoiding misinterpretations of Piaget and Vygotsky: Mathematical teaching without learning, learning without teaching, or helpful learning-path teaching? Cognitive Development, 24(4), 343–361. https://doi.org/10.1016/j.cogdev.2009.09.009.
   Web of Science ®Google Scholar
• Gallistel, C. R., & Gelman, R. (2005). Mathematical cognition. In K. Holyoak & R. Morrison (Eds.), Cambridge handbook of thinking and reasoning (pp. 559–588). Cambridge University Press.
   Google Scholar
• Geary, D. C. (2005). The role of cognitive theory in the study of learning disability in mathematics. Journal of Learning Disabilities, 38(4), 305–307. https://doi.org/10.1177/00222194050380040401
   PubMed Web of Science ®Google Scholar
• Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
   PubMed Web of Science ®Google Scholar
• Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Harvard University Press.
   Google Scholar
• Griffin, S. (2004). Number worlds: A research-based math- ematics program for young children. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: Standards for early mathematics education (pp. 325–342). Erlbaum.
   Google Scholar
• Guarino, C., Dieterle, S. G., Bargagliotti, A. E., & Mason, W. M. (2013). What can we learn about effective early mathematics teaching? A framework for estimating causal effects using longitudinal survey data. Journal of Research on Educational Effectiveness, 6(2), 164–198. https://doi.org/10.1080/19345747.2012.706695
   Web of Science ®Google Scholar
• Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E. (2013). Multivariate data analysis: Advanced diagnostics for multiple regression [Online supplement]. http://www.mvstats.com/Downloads/Supplements/Advanced_Regression_Diagnostics.pdf
   Google Scholar
• Hughes, M. (1981). Can preschool children add and subtract? Educational Psychology, 1(3), 207–219.
   Google Scholar
• Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Basil Blackwell.
   Google Scholar
• Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology. General, 123(3), 284–296. https://doi.org/10.1037//0096-3445.123.3.284
   PubMed Web of Science ®Google Scholar
• IBM Corp. (2019). IBM SPSS statistics for Windows, version 26.0. IBM Corp.
   Google Scholar
• Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1–2), 185–197. https://doi.org/10.1007/s11858-015-0717-0.
   Google Scholar
• Klein, A., Starkey, P., & Ramirez, A. B. (2002). Pre-K mathematics curriculum. Scott Foresman.
   Google Scholar
• Klein, J. S., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology = Revue Canadienne de Psychologie Experimentale, 54(2), 105–115. https://doi.org/10.1037/h0087333
   PubMed Web of Science ®Google Scholar
• Le, V. N., Schaack, D., Neishi, K., Hernandez, M. W., & Blank, R. (2019). Advanced content coverage at kindergarten: Are there trade-offs between academic achievement and social-emotional skills? American Educational Research Journal, 56(4), 1254–1280. https://doi.org/10.3102/0002831218813913
   Web of Science ®Google Scholar
• Lyons, I. M., Bugden, S., Zheng, S., De Jesus, S., & Ansari, D. (2018). Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners. Developmental Psychology, 54(3), 440–457. https://doi.org/10.1037/dev0000445
   PubMed Web of Science ®Google Scholar
• Munn, P. (1998). Symbolic function in pre-schoolers. In C. Donlan (Ed.), The development of mathematical skills (pp. 48–71). Psychology Press.
   Google Scholar
• Mussolin, C., Nys, J., Leybaert, J., & Content, A. (2016). How approximate and exact number skills are related to each other across development: A review. Developmental Review, 39, 1–15. https://doi.org/10.1016/j.dr.2014.11.001
   Web of Science ®Google Scholar
• Muthèn, L. K., & B. O, M. (1998–2019). Mplus user’s guide (8th ed.). Muthèn & Muthèn.
   Google Scholar
• NCES. (2000). America’s kindergartners (NCES 2000070). National Center for Education Statistics, U.S. Government Printing Office.
   Google Scholar
• Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M. (2016). Non-symbolic approximate arithmetic training improves math performance in preschoolers. Journal of Experimental Child Psychology, 152, 278–293. https://doi.org/10.1016/j.jecp.2016.07.011
   PubMed Web of Science ®Google Scholar
• Sarama, J., & Clements, D. H. (2009a). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
   Google Scholar
• Sarama, J., & Clements, D. H. (2009b). “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.
   Web of Science ®Google Scholar
• Sarama, J., & Clements, D. H. (2011). Mathematics knowledge of low-income entering preschoolers. Far East Journal of Mathematical Education, 6(1), 41–63.
   Google Scholar
• Sarama, J., & Clements, D. H. (2016). Physical and virtual manipulatives: What is “concrete?” In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (Vol. 3, pp. 71–93). Springer International Publishing. https://doi.org/10.1007/978-3-319-32718-1_4
   Google Scholar
• Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108(3), 662–674. https://doi.org/10.1016/j.cognition.2008.05.007
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11(5), 655–661. https://doi.org/10.1111/j.1467-7687.2008.00714.x
   PubMed Web of Science ®Google Scholar
• Skoumpourdi, C. (2010). Kindergarten mathematics with ‘Pepe the Rabbit’: How kindergartners use auxiliary means to solve problems. European Early Childhood Education Research Journal, 18(3), 299–157. https://doi.org/10.1080/1350293x.2010.500070.
   Web of Science ®Google Scholar
• Thorndike, E. L. (1922). The psychology of arithmetic. Macmillan.
   Google Scholar
• United States Census Bureau. (2018). CPS historical time series tables on school enrollment. Retrieved April 11, 2019, from Author: https://www.census.gov/data/tables/time-series/demo/school-enrollment/cps-historical-time-series.html
   Google Scholar
• Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
   Google Scholar
• Whyte, J. C., & Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Developmental Psychology, 44(2), 588–596. https://doi.org/10.1037/0012-1649.44.2.588
   PubMed Web of Science ®Google Scholar
• Wu, H.-H. (2011). Understanding numbers in elementary school mathematics. American Mathematical Society.
   Google Scholar
• Zhang, X., & Lin, D. (2015). Pathways to arithmetic: The role of visual-spatial and language skills in written arithmetic, arithmetic word problems, and nonsymbolic arithmetic. Contemporary Educational Psychology, 41, 188–197. https://doi.org/10.1016/j.cedpsych.2015.01.005
   Web of Science ®Google Scholar