Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…

This paper provides an overview of a book entitled "Adults Count Too: Mathematics for Empowerment". The introduction to the book details why the author spent three years writing about adults learning mathematics, and outlines the shape and structure of the book. A chapter from the book, entitled "A Matrix of Factors," is presented as an example of…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

The teaching of negative numbers poses problems at the school level. A historical account of the intellectual difficulties in the evolution of negative numbers and a method of viewing negative numbers as an extension of the number system to help overcome these difficulties are presented. (MDH)

Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH)