Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

Two-Way Immersion (TWI) programs have demonstrated positive outcomes in students' academic achievement in English, yet less is known about content teaching and learning in the non-English language in these programs. This study uses math instruction as a lens to identify pedagogical strategies and challenges in the teaching of math in Korean to…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

Presents an activity using fractal cards--eye-catching pop-up cards--by applying simple iterative processes to single sheets of paper. This activity incorporates the concepts of measurement, number systems, sequences, series, limits, recursion, iteration, self-similarity, and fractional dimensions. Contains 12 references. (ASK)

Presents activities developed for teacher training courses for the middle school level that integrate mathematics history with the selected topics of number systems, fractions, and geometry. The activities seek to give relevance to history and to motivate and deepen students' understanding of the evolution of mathematical concepts. (MDH)

Provides a bibliography of children's literature exploring mathematical concepts: classification; place value and numeration systems; counting, addition, and subtraction; multiplication and division; fractions; estimation; big numbers; geometry; measurement; and games and puzzles. Highlights one book for each concept, suggests class activities,…

Annotated listing of research summaries, articles, and dissertations in mathematics education reported in 1993. Grade or age levels are indicated for each citation. Articles and dissertations are indexed by mathematics education topic. Includes a list of the journals searched. (427 citations) (MKR)