nLab mathematics education

Idea

$\mu\alpha\theta\eta\sigma\iota\varsigma$ - 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.

Scope

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.

Overview

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

• wikipedia: mathematics education, Common Core State Standards Initiative, New Math, Moore method, modern elementary mathematics, Van Hiele model
• 13th International Congress on Mathematical Education, Hamburg Aug 24-31, 2016
• Douglas A. Grouws ed., Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics, Macmillan Library Reference 1992
• GreenApples – resources for new math teachers

Related $n$Lab pages

• New Math
• elementary mathematics
• foundations

Software

• geogebra.org, wikipedia: geogebra

Organizations and initiatives in math education

• NCTM National Organization of Teachers of Mathematics
• Common Core math standards
• Next Generation Science Standards <http://www.nextgenscience.org>
• ICMI International Commision on Mathematical Instruction (founded in 1908, now under IMU)
• websites of math education and math teacher associations (a list maintained at ICMI)
• International Mathematical Olympiad, official site

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)
  • Liping Ma, A critique of the structure of U.S. elementary school mathematics, Notices AMS, Oct 2013 pdf
  • Liping Ma, webpage
  • blog opinion What Does Liping Ma REALLY say?
• 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

• 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

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

• Zbigniew Semadeni, The triple nature of mathematics: deep ideas, surface representations, formal models, article

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

• George Lakoff, Rafael E. Núñez, Where mathematics comes from, Basic Books 2000, xviii+493 pp. MR2001i:00013 (cf. also wikipedia: George Lakoff#Mathematics)

category: education