13 Mathematical Learning

Educational Psychology

  1. Richard Lehrer PhD1,
  2. Richard Lesh PhD2

Published Online: 26 SEP 2012

DOI: 10.1002/9781118133880.hop207013

Handbook of Psychology, Second Edition

Handbook of Psychology, Second Edition

How to Cite

Lehrer, R. and Lesh, R. 2012. Mathematical Learning. Handbook of Psychology, Second Edition. 7:13.

Author Information

  1. 1

    Vanderbilt University, Department of Teaching and Learning, George Peabody College, Nashville, TN, USA

  2. 2

    Indiana University, Department of Learning Sciences, Bloomington, IN, USA

Publication History

  1. Published Online: 26 SEP 2012


Mathematical practices are the cornerstone of mathematical learning, so it is critical for researchers and educators to understand their ontogenesis. In this chapter we trace the ontogenesis of three forms of mathematical practice. The first, argument, represents a discursive view of learning, originates in everyday conversation, and culminates in specialized forms of discourse, such as proof. The second, inscription, represents a view of learning as co-originating with written expression. It begins with scribbles and culminates in systems of notation, especially those that are digital and dynamic. The third, modeling, is inaugurated by metaphor and analogy, especially those involving the body. As it progresses, it encompasses argument and inscription for the purpose of creating mathematical systems for describing the world. Although each draws on native resources and dispositions, each of these forms of practice also relies on contexts that encourage their development. Accordingly, we focus on the intentional design of classroom ecologies that promote these forms of development, especially the knowledge and practices of teaching that influence student learning. We conclude with implications of this practice view of mathematical learning for research in mathematics education.


  • mathematical learning;
  • practice;
  • argument;
  • inscription;
  • model