Postdoctoral Training in Children’s Mathematics Learning
The Postdoctoral Training in Children's Mathematics Learning at Carnegie Mellon University provides fellows with the opportunity to develop their understanding of contemporary theories and methods of cognitive development, and the opportunity to actively participate in research that focuses on experimental methods for testing interventions to improve learning. Participants in this program work with faculty on projects which seek to identify the components of interventions shown to be highly effective in increasing the numerical knowledge of low-income preschoolers; use microgenetic methods to understand the sources, paths, rates, breadth, and variability of learning through interventions; examine whether and how teacher aids influence learning; and determine whether the combination of overlapping waves, statistical learning, socio-cultural, and dynamic systems theories can produce insights into learning of fractions given middle school students previous learning about whole numbers. The experience of the fellows focuses on identifying key topics for investigation, planning, designing, conducting, and analyzing data from the studies, publishing in journals, presenting at conferences, and writing grant applications.
Siegler, R.S., Fazio, L.K., and Pyke, A. (2011). There is Nothing so Practical as a Good Theory. In J.P. Mestre, and B.H. Ross (Eds.), The Psychology of Learning and Motivation, Volume 55: Cognition in Education (pp. 171–197). San Diego: Elsevier Academic Press.
Journal article, monograph, or newsletter
Bailey, D.H. (2014). What's the Point of Teaching Math in Preschool?. The Brown Center Chalkboard (Brookings), 88.
Bailey, D.H., Siegler, R.S., and Geary, D.C. (2014). Early Predictors of Middle School Fraction Knowledge. Developmental Science, 17(5): 775–785.
Bailey, D.H., Watts, T.W., Littlefield, A K., and Geary, D.C. (2014). State and Trait Effects on Individual Differences in Children's Mathematical Development. Psychological Science, 25(11): 2017–2026.
Bailey, D.H., Zhou, X., Zhang, Y., Cui, J., Fuchs, L.S., Jordan, N.C., Gerstene, R., and Siegler, R.S. (2015). Development of Fraction Concepts and Procedures in US and Chinese Children. Journal of Experimental Child Psychology, 129: 68–83.
Fazio, L.K., and Siegler, R.S. (2013). Microgenetic Learning Analysis: A Distinction Without a Difference: Commentary on Parnafes and DiSessa. Human Development, 56(1): 52–58.
Fazio, L.K., Bailey, D.H., Thompson, C.A., and Siegler, R.S. (2014). Relations of Different Types of Numerical Magnitude Representations to Each Other and to Mathematics Achievement. Journal of Experimental Child Psychology, 123: 53–72.
Fazio, L.K., DeWolf, M., and Siegler, R.S. (2016). Strategy Use and Strategy Choice in Fraction Magnitude Comparison. Journal of Experimental Psychology: Human Perception and Performance, 42(1): 1–16.
Siegler, R.S., Fazio, L.K., Bailey, D.H., and Zhou, X. (2013). Fractions: The New Frontier for Theories of Numerical Development. Trends in Cognitive Science, 17(1): 13–19.
Nongovernment report, issue brief, or practice guide
Fazio, L., and Siegler, R. (2012). Teaching Fractions, Volume 22 of Educational Practices Series. Geneva: UNESCO's International Bureau of Education.