nLab mathematics education






The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms



μαθησις\mu\alpha\theta\eta\sigma\iota\varsigma - Learning (Gr.)

This page will discuss approaches to teaching of mathematics (as it is usual in the subject, with emphasis on the pre-university level, where the care in didactical aspects is the most relevant) and the outstanding sources of the relevant materials about teaching.


Pedagogically well written introductory books in mathematics, rather than about pedagogical matter, are also of our concern, but they will preferably be posted under elementary mathematics, introductions to mathematics?, elementary geometry? and related pages.


Most traditionally, teaching methods were improvized adaptations of communication of subject matter from the knowledgeable teacher to a learner.

Modern educational theory is greatly influenced by the works on child psychology. In particular, it has been investigated which cognitive aspects can be achieved at certain age, or within certain educational or other cognitive experiences.

It is now commonly accepted that the advanced and long term knowledge is better achieved if the learner is also a discoverer. This means in mathematics that the emphasis on procedural knowledge should be replaced by wider experience in which a student discovers her own ways to approach the problems which make up the subject. The teacher and the learning environment hence have to anticipate and foster also specific processes in learning the subject rather then only the goals and supposed content matter. Many authors however acknowledge the importance of balance with more traditional coaching and somewhat standardized procedural techniques (micromanagement being counterproductive). While in most educational taxonomies application of knowledge comes only at very hi stages in taxonomy, applying and experiencing concepts in practice, applications and in interaction with technology is considered necessary even at initial steps, and lower degrees of learning the subject. This should be therefore taken into account when creating the goals of mathematics curricula.

References and online materials


Organizations and initiatives in math education

Individual educators and their work

  • Liping Ma, Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)
  • Guy Brousseau and at French wikipedia
  • Harold W. Stevenson (educational psychologist), Mathematics learning in early childhood, NCTM, 1985
  • John A. Van de Walle et al. Elementary and middle school mathematics. Teaching developmentally, Pearson 2004, 2007, 2010, 2013
  • J. Mayberry, The Van Hiele levels of geometric thought in undergraduate preservice teachers, Journal for Research in Mathematics Education 14 (1): 58–69 (1983) doi jstor
  • Hans Freudenthal, Why to teach mathematics so as to be useful, 1968, pdf
  • (on Hans Freudenthal‘s school) Marja van den Heuvel-Panhuizen, Paul Drijvers, Realistic Mathematics Education, pdf

Opinion articles

  • Elizabeth Green, Why Do Americans Stink at Math?, New York Times opinion story (moral: good ideas in the reforms never materialized in practice)
  • Ralph A. Raimi, Whatever Happened to the New Math?
  • Richard Askey?, Good intentions are not enough, pdf
  • Mariya Boyko, The “New Math” Movement in the U.S. vs Kolmogorov’s Math Curriculum Reform in the U.S.S.R., html
  • R. Balian, A. Connes, Bismut, Lafforgue, Serre, Les savoirs fondamentaux au service de l’avenir scientifique et technique, pdf, a text lamenting the current state of the scientific part of education in France

Other references

  • wikipedia: mathematics education, Van Hiele model
  • G. Ziegler, Teaching and learning “What is mathematics?”, in Proc.ICM 2014, Seoul, vol. 4
  • Alexander Karp, Bruce R Vogeli (eds.), Russian mathematics education, 2 vols, World Sci. Publ.
  • Lingguo Bu, Robert Schoen (eds.), Model centered learning, Pathways to mathematical understanding using geogebra, vol. 6 of Modeling and simulations for learning and instruction
  • Jennifer A. Kaminski, Vladimir M. Sloutsky, Andrew F. Heckle, The advantage of abstract examples in learning math, Science Magayibe 2012 pdf

Discussing elementary mathematical notions avoiding “pleasure principle” in education:

  • Carl E. Linderholm, Mathematics made difficult, Wolfe Publishing 1972

The following epistemiology of math article offers also discussion on educational issues and has related bibliography

Cognitive, linguistic and cultural aspects of mathematics (which are of relevance for learning) are emphasized in

category: education

Last revised on June 2, 2024 at 08:23:57. See the history of this page for a list of all contributions to it.