Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.

Supplementary Materials

    • Learning Trajectories and Related Learning Theory (19.2 KB)
    • Equipartitioning LT (11.3 KB)
    • Multiplicative Reasoning in K-12 Mathematics (14.0 KB)
    • Ratios Compared to Fractions (13.4 KB)
    • Unit Ratios Compared to Unit Rates (13.2 KB)
    • Algebraic Axioms (8.37 KB)
    • Simple Exponential Functions LT (585 KB)
Mathematics Teacher: Learning and Teaching PK-12
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  • Confrey, Jere. 1995. “Student Voice in Examining ‘Splitting’ as an Approach to Ratio, Proportions, and Fractions." In Proceedings of the 19th Psychology of Mathematics Education (PME) Conference. Universidade Federal de Pernambuco, Recife, Brazil, pp. I-3I-29, July 22–27, 1995.

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  • Confrey, Jere, Garron Gianopulos, William McGowan, Meetal Shah, and Michael Belcher. 2017. “Scaffolding Learner-Centered Curricular Coherence Using Learning Maps and Diagnostic Assessments Designed around Mathematics Learning Trajectories." ZDM: The International Journal on Mathematics Education 49, no. 5 (May): 71734.

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  • Confrey, Jere, Alan P. Maloney, Kenny H. Nguyen, and André A. Rupp. 2014. “Equipartitioning, a Foundation for Rational Number Reasoning." In Learning over Time: Learning Trajectories in Mathematics Education, edited by Alan Maloney, Jere Confrey, and Kenny H. Nguyen, pp. 6196. Charlotte, NC: Information Age Publishing.

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