Not Just IQ: Patterning Predicts Preschoolers’ Math Knowledge Beyond Fluid Reasoning

References

• Baddeley, A. D., & Logie, R. H. (1999). Working memory: The multiple-component model. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 28–61). doi:10.1017/CBO9781139174909.005
   Google Scholar
• Baker, F. B., & Kim, S.-H. (2004). Item response theory parameter estimation techniques (2nd ed.). New York, NY: Marcel Dekker.
   Google Scholar
• Bates, D., Maechler, M., & Dai, B. (2008). The lme4 package version 0.999375-26. Retrieved from https://cran.r-project.org/web/packages/lme4/lme4.pdf/
   Google Scholar
• Briars, D., & Siegler, R. S. (1984). A featural analysis of preschoolers’ counting knowledge. Developmental Psychology, 20, 607–618. doi:10.1037/0012-1649.20.4.607
   Web of Science ®Google Scholar
• Burgoyne, K., Witteveen, K., Tolan, A., Malone, S., & Hulme, C. (2017). Pattern understanding: Relationships with arithmetic and reading development. Child Development Perspectives, 11, 239–244. doi:10.1111/cdep.12240
   Web of Science ®Google Scholar
• Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37, 87–115.
   Web of Science ®Google Scholar
• Carroll, J. B. (1993). Human cognitive abilities. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Cattell, R. B. (Ed.). (1987). Intelligence: Its structure, growth, and action. New York, NY: Elsevier Science Publishers Company, Inc.
   Google Scholar
• Charles, R. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Educational Leadership, 73, 9–24.
   Google Scholar
• Cho, S.-J., & Rabe-Hesketh, S. (2011). Alternating imputation posterior estimation of models with crossed random effects. Computational Statistics & Data Analysis, 55, 12–25. doi:10.1016/j.csda.2010.04.015
   Web of Science ®Google Scholar
• Clarke, B., Cheeseman, J., & Clarke, D. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18, 78–102. doi:10.1007/BF03217430
   Google Scholar
• Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In Douglas A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 420–464). New York, NY: Macmillan Publishing Co, Inc.
   Google Scholar
• Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). New York, NY: Routledge.
   Google Scholar
• Collins, M. A., & Laski, E. V. (2015). Preschoolers’ strategies for solving visual pattern tasks. Early Childhood Research Quarterly, 32, 204–214. doi:10.1016/j.ecresq.2015.04.004
   Web of Science ®Google Scholar
• Common Core State Standards. (2010). Retrieved from http://www.corestandards.org/Math/
   Google Scholar
• Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.
   Google Scholar
• Duncan, G. J., Claessens, A., Magnuson, K., Klebanov, P., Pagani, L. S., Feinstein, L., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. doi:10.1037/0012-1649.43.6.1428
   PubMed Web of Science ®Google Scholar
• Economopoulos, K. (1998). What comes next?: The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5, 230–233.
   Google Scholar
• Fyfe, E. R., Evans, J. L., Matz, L. E., Hunt, K. M., & Alibali, M. W. (2017). Relations between patterning skill and differing aspects of early mathematics knowledge. Cognitive Development, 44, 1–11. doi:10.1016/j.cogdev.2017.07.003
   PubMed Web of Science ®Google Scholar
• Fyfe, E. R., Rittle-Johnson, B., & Farran, D. C. (2019). Predicting success on high-stakes math tests from preschool math measures among children from low-income homes. Journal of Educational Psychology, 111, 402–413. doi:10.1037/edu0000298
   Web of Science ®Google Scholar
• Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
   Google Scholar
• Ginsburg, H. P., Lin, C., Ness, D., & Seo, K.-H. (2003). Young American and Chinese children’s everyday mathematical activity. Mathematical Thinking and Learning, 5, 235–258. doi:10.1207/S15327833MTL0504_01
   Google Scholar
• Greenes, C., Ginsburg, H. P., & Balfanz, R. (2004). Big math for little kids. Early Childhood Research Quarterly, 19, 159–166. doi:10.1016/j.ecresq.2004.01.010
   Web of Science ®Google Scholar
• Hammill, D. D., Pearson, N. A., & Voress, J. K. (1993). Developmental Test of Visual Perception: DTVP-2. Austin, TX: Pro-ed.
   Google Scholar
• Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850–867. doi:10.1037/a0014939
   PubMed Web of Science ®Google Scholar
• Kidd, J. K., Carlson, A. G., Gadzichowski, K. M., Boyer, C. E., Gallington, D. A., & Pasnak, R. (2013). Effects of patterning instruction on the academic achievement of 1st-grade children. Journal of Research in Childhood Education, 27, 224–238. doi:10.1080/02568543.2013.766664
   Google Scholar
• Kidd, J. K., Pasnak, R., Gadzichowski, K. M., Gallington, D. A., McKnight, P., Boyer, C. E., & Carlson, A. (2014). Instructing first-grade children on patterning improves reading and mathematics. Early Education and Development, 25, 134–151. doi:10.1080/10409289.2013.794448
   Web of Science ®Google Scholar
• Lee, K., Ng, S. F., Pe, M. L., Ang, S. Y., Hasshim, M. N. A. M., & Bull, R. (2012). The cognitive underpinnings of emerging mathematical skills: Executive functioning, patterns, numeracy, and arithmetic: Cognitive underpinnings. British Journal of Educational Psychology, 82(1), 82–99. doi:10.1111/j.2044-8279.2010.02016.x
   PubMed Web of Science ®Google Scholar
• Lipkus, I. M., & Peters, E. (2009). Understanding the role of numeracy in health: Proposed theoretical framework and practical insights. Health Education & Behavior, 36, 1065–1081. doi:10.1177/1090198109341533
   PubMed Web of Science ®Google Scholar
• MacKay, K. J., & De Smedt, B. (2019). Patterning counts: Individual differences in children’s calculation are uniquely predicted by sequence patterning. Journal of Experimental Child Psychology, 177, 152–165. doi:10.1016/j.jecp.2018.07.016
   PubMed Web of Science ®Google Scholar
• Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21, 10–32. doi:10.1007/BF03217543
   Google Scholar
• Miller, M. R., Rittle-Johnson, B., Loehr, A. M., & Fyfe, E. R. (2016). The influence of relational knowledge and executive function on preschoolers’ repeating pattern knowledge. Journal of Cognition and Development, 17, 85–104. doi:10.1080/15248372.2015.1023307
   Web of Science ®Google Scholar
• Mix, K. S., Prather, R. W., Smith, L. B., & Stockton, J. D. (2014). Young children’s interpretation of multidigit number names: From emerging competence to mastery. Child Development, 85, 1306–1319. doi:10.1111/cdev.12197
   PubMed Web of Science ®Google Scholar
• National Association for the Education of Young Children. (2014). NAEYC early childhood program standards and accreditation criteria. Washington, DC: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Reston, VA: Author.
   Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42, 237–269. doi:10.5951/jresematheduc.42.3.0237
   Web of Science ®Google Scholar
• Pasnak, R., Schmerold, K. L., Robinson, M. F., Gadzichowski, K. M., Bock, A. M., O’Brien, S. E., … Gallington, D. A. (2016). Understanding number sequences leads to understanding mathematics concepts. The Journal of Educational Research, 109, 640–646. doi:10.1080/00220671.2015.1020911
   Web of Science ®Google Scholar
• Purpura, D. J., & Lonigan, C. J. (2015). Early numeracy assessment: The development of the preschool early numeracy scales. Early Education and Development, 26, 286–313. doi:10.1080/10409289.2015.991084
   PubMed Web of Science ®Google Scholar
• Quinn, P. C. (1987). The categorical representation of visual pattern information by young infants. Cognition, 27, 145–179. doi:10.1016/0010-0277(87)90017-5
   PubMed Web of Science ®Google Scholar
• Quinn, P. C., Brown, C. R., & Streppa, M. L. (1997). Perceptual organization of complex visual configurations by young infants. Infant Behavior and Development, 20, 35–46. doi:10.1016/S0163-6383(97)90059-X
   Web of Science ®Google Scholar
• Quinn, P. C., & Eimas, P. D. (1986). On categorization in early infancy. Merrill-Palmer Quarterly, 32, 331–363.
   Web of Science ®Google Scholar
• Ramirez, G., Chang, H., Maloney, E. A., Levine, S. C., & Beilock, S. L. (2016). On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies. Journal of Experimental Child Psychology, 141, 83–100. doi:10.1016/j.jecp.2015.07.014
   PubMed Web of Science ®Google Scholar
• Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24, 1301–1308. doi:10.1177/0956797612466268
   PubMed Web of Science ®Google Scholar
• Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2017). Early math trajectories: Low-income children’s mathematics knowledge from ages 4 to 11. Child Development, 88, 1727–1742. doi:10.1111/cdev.12662
   PubMed Web of Science ®Google Scholar
• Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31, 101–112. doi:10.1016/j.ecresq.2015.01.005
   Web of Science ®Google Scholar
• Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14, 376–396. doi:10.1080/15248372.2012.689897
   Web of Science ®Google Scholar
• Rittle-Johnson, B., Zippert, E., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46, 166–178. doi:10.1016/j.ecresq.2018.03.006
   Web of Science ®Google Scholar
• Sarama, J., & Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189. doi:10.1016/j.ecresq.2004.01.014
   Web of Science ®Google Scholar
• Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.
   Google Scholar
• Shapka, J. D., Domene, J. F., & Keating, D. P. (2006). Trajectories of career aspirations through adolescence and young adulthood: Early math achievement as a critical filter. Educational Research and Evaluation, 12, 347–358. doi:10.1080/13803610600765752
   Google Scholar
• Siegler, R. S., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8, 144–150. doi:10.1111/cdep.12077
   Web of Science ®Google Scholar
• Spiegelhalter, D., Thomas, A., Best, N., & Lunn, D. (2003). Winbugs user manual. Retrieved from https://www.mrc-bsu.cam.ac.uk/wp-content/uploads/manual14.pdf
   Google Scholar
• Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99–120. doi:10.1016/j.ecresq.2004.01.002
   Web of Science ®Google Scholar
• Steen, L. A. (1988). The science of patterns. Science, 240, 611–616. doi:10.1126/science.240.4852.611
   PubMed Web of Science ®Google Scholar
• 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, 352–360. doi:10.3102/0013189X14553660
   PubMed Web of Science ®Google Scholar
• Wechsler, D. (2003). Wechsler intelligence scale for children (4th ed.). San Antonio, TX: Harcourt Assessment.
   Google Scholar
• Wechsler, D. (2012). Wechsler preschool and primary scale of intelligence-fourth edition. San Antonio, TX: The Psychological Corporation.
   Google Scholar
• Weiland, C., Wolfe, C. B., Hurwitz, M. D., Clements, D. H., Sarama, J. H., & Yoshikawa, H. (2012). Early mathematics assessment: Validation of the short form of a prekindergarten and kindergarten mathematics measure. Educational Psychology, 32, 311–333. doi:10.1080/01443410.2011.654190
   Web of Science ®Google Scholar
• Wijns, N., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Young children’s patterning competencies and mathematical development: A review. In K. M. Robinson, H. Osana, & D. Kotsopoulos (Eds.), Interdisciplinary perspectives on early mathematical minds (pp. 139–161). Springer.
   Google Scholar
• Zippert, E., Clayback, K., & Rittle-Johnson, B. (2019). Examining the link between patterning, math, and numeracy beyond IQ. doi: 10.17605/OSF.IO/HETD5
   Google Scholar
• Zippert, E., Douglas, -A.-A., & Rittle-Johnson, B. (2019). Measuring repeating patterning skill in Kindergarten. Education in global contexts: Evidence on teaching and learning in early childhood education. Presented at the Society for Research in Educational Effectiveness, Washington, DC.
   Google Scholar
• Zippert, E., Loehr, A. M., & Rittle-Johnson, B. (2018, February). A new teacher-based assessment of preschoolers’ patterning skills. Poster presented at the Society for Research on Educational Effectiveness, Washington, DC.
   Google Scholar
• Zippert, E., & Rittle-Johnson, B. (2018). The home math environment: More than numeracy. Early Childhood Research Quarterly. doi:10.1016/j.ecresq.2018.07.009
   Google Scholar