This research project has generated a number of insights, including:
- Rational Number Reasoning is complex, and yields to a Learning Trajectories strand analysis;
- Equipartitioning/Splitting is a foundation for Rational Number Reasoning;
- Division and multiplication should be derived from equipartitioning/splitting, and coordinated with counting, addition, and subtraction;
- Three dominant meanings for a/b capture most of RNR reasoning; and
- Fundamental revisions are needed in the sequencing of RNR construct learning.
Confrey, J., Maloney, A., Nguyen, K., Wilson, P. H., and Mojica, G. (2008) Synthesizing Research on Rational Number Reasoning. NCTM Research Pre-Session, Salt Lake City, UT.
Confrey, J., (2008) A Synthesis of the Research On Rational Number Reasoning: A Learning Progressions Approach to Synthesis. Invited Lecture to the International Conference on Mathematics Instruction XI, Monterrey, Mexico.
Confrey, J., (2008) Engaging in Reasoning about 21st Century Mathematics: A New Approach to Rational Numbers. Plenary Address to Annual Meeting of the North Carolina Council of Teachers of Mathematics, Greensboro, NC.
Confrey, J., (2008) Learning Trajectories and Rational Number Reasoning. Workshop on Higher Cognition in Adolescents and Young Adults: Social, Behavioral, and Biological Influences on Learning National Science Foundation, Washington, DC.
Confrey, J., (2008) From Learning Trajectories to Diagnostic Assessments for K-8 Rational Number Reasoning: Defining Learning Progressions in K-8 Mathematics. Council of Chief State School Officers National Conference, Orlando, FL.
Online searchable bibliographic database of summaries and relevant catalogue of characteristics of research literature. Open-source database application code. Syntheses of research literature, by content area and identification of levels of consensus on learning trajectories.