731
Views
0
CrossRef citations to date
0
Altmetric
Articles

Measuring early mathematics knowledge via number skills and task types

ORCID Icon, , , &

References

  • Aunio, P., Hautamäki, J., Heiskari, P., & Van Luit, J. E. (2006). The early numeracy test in finnish: Children’s norms. Scandinavian Journal of Psychology, 47(5), 369–378. doi:10.1111/j.1467-9450.2006.00538.x
  • Aunio, P., & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(5), 427–435. doi:10.1016/j.lindif.2010.06.003
  • Aunio, P., & Räsänen, P. (2016). Core numerical skills for learning mathematics in children aged five to eight years – A working model for educators. European Early Childhood Education Research Journal, 24, 684–704. doi:10.1080/1350293X.2014.996424
  • Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency? Journal of Experimental Child Psychology, 117, 12–28. doi:10.1016/j.jecp.2013.08.010
  • Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102(39), 14116–14121. doi:10.1073/pnas.0505512102
  • Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339. doi:10.1177/00222194050380040901
  • Bonny, J. W., & Lourenco, S. F. (2013). The approximate number system and its relation to early math achievement: Evidence from the preschool years. Journal of Experimental Child Psychology, 114, 375–388. doi:10.1016/j.jecp.2012.09.015
  • Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56(2), 81–105. doi:10.1037/h0046016
  • Chu, F. W., vanMarle, K., & Geary, D. C. (2015). Early numerical foundations of young children’s mathematical development. Journal of Experimental Child Psychology, 132, 205–212. doi:10.1016/j.jecp.2015.01.006
  • Clarke, B., Doabler, C. T., Fien, H., Baker, S. K., & Smolkowski, K. (2012). A randomized control trial of a tier 2 kindergarten mathematics intervention (Project ROOTS). (USDE; Institute of Education Sciences; Special Education Research, CFDA Num: 84.324A, 2012–2016, Funding Number: R324A120304, awarded $3,338,552).
  • Clarke, B., Doabler, C. T., Smolkowski, K., Baker, S. K., Fien, H., & Strand Cary, M. (2016). Examining the efficacy of a tier 2 kindergarten mathematics intervention. Journal of Learning Disabilities, 49, 152–165. doi:10.1177/0022219414538514
  • Clarke, B., Doabler, C. T., Strand Cary, M., Kosty, D. B., Baker, S. K., Fien, H., & Smolkowski, K. (2014). Preliminary evaluation of a tier-2 mathematics intervention for first grade students: Utilizing a theory of change to guide formative evaluation activities. School Psychology Review, 43, 160–177.
  • Clarke, B., Gersten, R. M., Dimino, J., & Rolfhus, E. (2011). Assessing student proficiency of number sense (aspens). Longmont, CO: Cambium Learning Group, Sopris Learning.
  • De Smedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278–292. doi:10.1016/j.jecp.2010.09.003
  • Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82(1), 64–81. doi:10.1348/2044-8279.002002
  • Doabler, C. T., Clarke, B., & Fien, H. (2012). Roots assessment of early numeracy skills (RAENS) ( Unpublished measurement instrument). Center on Teaching and Learning, University of Oregon. Eugene, OR.
  • Duncan, G. J., & Murnane, R. J. (Eds.). (2011). Whither opportunity? Rising inequality, schools, and children’s life chances. New York, NY: Russell Sage Foundation.
  • Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). Washington, DC: National Center for Education, Evaluation, and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website http://whatworks.ed.gov
  • Geary, D. C., & Moore, A. M. (2016). Cognitive and brain systems underlying early mathematical development. Progress in Brain Research, Advanced online publication. doi: 10.1016/bs.pbr.2016.03.008
  • Gersten, R. M., Beckmann, S., Clarke, B., Foegen, A., March, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (Practice Guide Report No. NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/practiceguides/.
  • Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394–406. doi:10.1016/j.cognition.2010.02.002
  • Ginsburg, H. P., & Baroody, A. J. (2003). Test of early mathematics ability-third edition (TEMA-3). Austin, TX: ProEd.
  • Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development it is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798. doi:10.1177/0956797613516471
  • Gray, S. A., & Reeve, R. A. (2014). Preschoolers’ dot enumeration abilities are markers of their arithmetic competence. PLoS One, 9(4), e94428. doi:10.1371/journal.pone.0094428
  • Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668. doi:10.1038/nature07246
  • Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Preschool children’s spontaneous focusing on numerosity, subitizing, and counting skills as predictors of their mathematical performance seven years later at school. Mathematical Thinking and Learning, 17(2–3), 155–177. doi:10.1080/10986065.2015.1016814
  • Howell, S. C., & Kemp, C. R. (2010). Assessing preschool number sense: Skills demonstrated by children prior to school entry. Educational Psychology, 30, 411–429. doi:10.1080/01443411003695410
  • IBM Corp. (2011). IBM SPSS Statistics for MacIntosh, Version 20.0. Armonk, NY: Author.
  • Jordan, N., Glutting, J., & Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In A. Dowker (Ed.), Mathematical difficulties: Psychology and intervention (pp. 45–57). San Diego, CA: Academic Press.
  • Jordan, N. C., Glutting, J., & Dyson, N. I. (2012). Number sense screener (NSS) user’s guide, K-1. Baltimore, MD: Paul H. Brookes Pub.
  • Jordan, N. C., Kaplan, D., Nabors Oláh, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175. doi:10.1111/j.1467-8624.2006.00862.x
  • Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “math talk.”. Developmental Psychology, 42, 59–69. doi:10.1037/0012-1649.42.1.59
  • Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York, NY: Guilford Press.
  • Krajewski, K. (2008). Vorschulische förderung mathematischer kompetenzen. In F. Petermann & W. Schneider (Eds.), Enzyklopädie der Psychologie, Reihe Entwicklungspsychologie Bd. Angewandte Entwicklungspsychologie (pp. 275–304). Göttingen, Germany: Hogrefe.
  • Krajewski, K., & Schneider, W. (2009). Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103(4), 516–531. doi:10.1016/j.jecp.2009.03.009
  • LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753–1767. doi:10.1111/j.1467-8624.2010.01508.x
  • 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, 1309–1319. doi:10.1037/a0019671
  • Libertus, M. E., Feigenson, L., & Halberda, J. (2013a). Is approximate number precision a stable predictor of math ability? Learning and Individual Differences, 116, 829–838. doi:10.1016/j.jecp.2013.08.003
  • Libertus, M. E., Feigenson, L., & Halberda, J. (2013b). Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities. Journal of Experimental Child Psychology, 116(4), 829–838. doi:10.1016/j.jecp.2013.08.003
  • Lipton, J. S., & Spelke, E. S. (2005). Preschool children’s mapping of number words to nonsymbolic numerosities. Child Development, 76, 978–988. doi:10.1111/cdev.2005.76.issue-5
  • Mack, N. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32, 267–295. doi:10.2307/749828
  • Manfra, L., Dinehart, L. H. B., & Sembiante, S. F. (2014). Associations between counting ability in preschool and mathematic performance in first grade among a sample of ethnically diverse, low-income children. Journal of Research in Childhood Education, 28(1), 101–114. doi:10.1080/02568543.2013.850129
  • Mejias, S., Mussolin, C., Rousselle, L., Grégoire, J., & Noël, M.-P. (2012). Numerical and nonnumerical estimation in children with and without mathematical learning disabilities. Child Neuropsychology, 18, 550–575. doi:10.1080/09297049.2011.625355
  • Mix, K. S., Levine, S. C., & Huttenlocher, J. (1999). Early fraction calculation ability. Developmental psychology, 35(1), 164–174. doi:10.1037/0012-1649.35.1.164
  • Morgan, P. L., Farkas, G., Hillemeier, M. M., & Maczuga, S. (2014). Who is at risk for persistent mathematics difficulties in the United States? Journal of Learning Disabilities, 47(4), 1–15. doi:10.1177/0022219414553849
  • Morgan, P. L., Farkas, G., & Wu, Q. (2009). Five-year growth trajectories of kindergarten children with learning difficulties in mathematics. Journal of Learning Disabilities, 42(4), 306–321. doi:10.1177/0022219408331037
  • Muthén, L. K., & Muthén, B. O. (2013). Mplus user’s guide, v 7.1. Los Angeles, CA: Muthén and Muthén, UCLA.
  • National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Retrieved from http://www.nctm.org/standards/focalpoints.aspx?id=282
  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education. doi:10.3102/0013189X08329195
  • 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. doi:10.1016/j.ecresq.2016.02.003
  • Noël, M. P., & Rousselle, L. (2011). Developmental changes in the profiles of dyscalculia: an explanation based on a double exact-and-approximate number representation model. Frontiers in human neuroscience, 5, 165–169. doi:10.3389/fnhum.2011.00165
  • Purpura, D. J., Hollich, G., Schmitt, S. A., & Napoli, A. R. (2017, February). The relation of vocabulary, grammatical awareness, and mathematical language to early numeracy components. In A. Truckenmiller (Chair) (Ed.), Arteries of academic achievement: Do certain malleable skills underlie multiple outcomes? Symposium conducted at the annual Pacific Coast Research Conference, San Diego, CA.
  • Purpura, D. J., & Logan, J. A. R. (2015). The non-linear relations between the approximate number system and mathematical language to symbolic mathematics. Developmental Psychology, 12, 1717–1724. doi:10.1037/dev0000055
  • 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. doi:10.3102/0002831212465332
  • Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 110–151). New York, NY: Academic Press.
  • Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2016). Early math trajectories: Low-income children’s mathematics knowledge from ages 4 to 11. Child Development, Advanced online publication. doi: 10.1111/cdev.12662
  • Rodic, M., Zhou, X., Tikhomirova, T., Wei, W., Malykh, S., Ismatulina, V., … Kovas, Y. (2015). Cross-cultural investigation into cognitive underpinnings of individual differences in early arithmetic. Developmental Science, 18(1), 165–174. doi:10.1111/desc.12204
  • Rousselle, L., & Noël, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361–395. doi:10.1016/j.cognition.2006.01.005
  • 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. doi:10.1016/j.lindif.2015.06.003
  • Sasanguie, D., De Smedt, B., Defever, E., & Reynvoet, B. (2012). Association between basic numerical abilities and mathematics achievement. British Journal of Developmental Psychology, 30, 344–357. doi:10.1111/j.2044-835X.2011.02048.x
  • Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S., Stricker, J., & De Smedt, B. (2016). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, Advanced online publication. doi: 10.1111/desc.12372
  • Segers, E., Kleemans, T., & Verhoeven, L. (2015). Role of parent literacy and numeracy expectations and activities in predicting early numeracy skills. Mathematical Thinking and Learning, 17(2–3), 219–236. doi:10.1080/10986065.2015.1016819
  • Siegler, R. S., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8(3), 144–150. doi:10.1111/cdep.12077
  • Skwarchuk, S. L., Sowinski, C., & LeFevre, J. A. (2014). Formal and informal home learning activities in relation to children’s early numeracy and literacy skills: The development of a home numeracy model. Journal of Experimental Child Psychology, 121, 63–84. doi:10.1016/j.jecp.2013.11.006
  • Toll, S. W. M., Van Viersen, S., Kroesbergen, E. H., & Van Luit, J. E. H. (2015). The development of (non-)symbolic comparison skills throughout kindergarten and their relations with basic mathematical skills. Learning and Individual Differences, 38, 10–17. doi:10.1016/j.lindif.2014.12.006

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.