2013 Conference Proceedings - University of Nevada, Las Vegas

the usual phenotypic assessments and to gather information about the underlying genotypeswhich are not always easily observed. By looking at students’ intellectual genotypes duringformative assessment, and thinking about what combinations of genetic material might befruitful to promote, new ways of dealing with student understandings and problems, and newways of supporting learning may be possible. A GLP approach to teaching also forces teachers tothink of learning environments not merely as places where new material can be learned, but toexplicitly promote possible combinations of existing student ideas.ReferencesAgostino, A., Johnson, J., & Pascual-Leone, J. (2010). Executive functions underlyingmultiplicative reasoning: Problem type matters. Journal of Experimental Child Psychology,105: 286-305. doi: 10.1016/j.jecp.2009.09.006Anderson, L. & Krathwohl, D. (Eds.) (2001). A taxonomy for learning, teaching, and assessing:A revision of Bloom’s taxonomy of educational objectives. New York, NY: Longman.Bassarear, T. (2011). Explorations for Bassarear’s mathematics for elementary school teachers(5 th ed.). Independence, KY: Brooks Cole.Fosnot, C. & Dolk, M. (2001). Young mathematicians at work: Constructing number sense,addition and subtraction. Portsmouth, NH: Heinemann.Gallagher, J. & Reid, D. (2002). The learning theory of Piaget and Inhelder. Bloomington, IN:iUniverse.Gould, S. (1990). Wonderful life: The Burgess shale and the nature of history. New York, NY:W. W. Norton & Company.Kamii, C., Clark, F., & Dominick, A. (1997). Teaching to facilitate “progressive schematization”or reflective abstraction? The Constructivist, 9, 9-14.Kamii, C. (2000). Young children reinvent arithmetic: Implications of Piaget’s theory (2 nd ed.).New York, NY: Teachers College Press.Kuhn, D. (1995). Microgenetic study of change: What has it told us? Psychological Science, 6,133–139.Steffe, L. (1994). Children’s multiplying schemes. In G. Harel and J. Confrey (Eds.), TheDevelopment of multiplicative reasoning in the learning of mathematics (pp. 3 – 39). Albany,NY: State University of New York Press.Thelen, E. (1997). The dynamics of motor development: Commentary on Wimmers andVereijken. In G. Savelsbergh, H. van der Maas, & P. van Geert (Eds), Non-lineardevelopmental processes. Amsterdam, The Netherlands: Edita KNAW.Thelen, E. (2005). Dynamic systems theory and the complexity of change. PsychoanalyticDialogues, 15(2), 255-283.Trowell, S. (2012). Joy’s description in a problem centered learning setting. In S. Reeder (Ed.),Proceedings of the 39 th Annual Meeting of the Research Council on Mathematics Learning.(p. 32-39). Charlotte, NC: Research Council on Mathematics Learning.Van Dooren, W., De Bock, D. & Verschaffel, L. (2010). From Addition to Multiplication … andBack: The Development of Students’ Additive and Multiplicative Reasoning Skills.Cognition and Instruction, 28(3), 360-381. doi: 10.1080/07370008.2010.488306Vygotsky, L. (1978). Mind in society: The development of higher psychological processes.Cambridge, MA: Harvard University Press.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 196