The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

A common activity in school mathematics is to derive a function from a table of values. There are two general strategies one might adopt to determine the function f. First, one might try to determine a connection between a particular n and f(n), and then evaluate whether it holds for other values of n. An alternative strategy would be to look for…

In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

This article discusses two sequences of activities that were developed to support middle school students' and preservice teachers' construction of algorithms for dividing fractions. One sequence is intended to promote understanding of the common-denominator algorithm; the other sequence is intended to promote understanding of the…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

For the thirty-first year, the Research and Theory Division of the Association for Educational Communications and Technology (AECT) sponsored the publication of these Proceedings. Papers were presented at the annual AECT Convention in Orlando, Florida. This year's Proceedings has two sections--Section 1 includes research and development papers and…

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…