It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

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 article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…

Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…

There is a new wave going on in the Dutch Adult Education, similar to the ideas of Open Learning Centers in Further Education in Great Britain. The intention of this movement is to structure adult education in a way that it fits everyone. That means: more flexible programs, more individual education, more teacher independent learning, and more…

Introduces the idea of using computer microworlds--interactive software for exploration of specific concepts--for mathematics education, the theme of this issue's articles. Discusses their development and the advantages of their use. Suggests that they can be successfully used for interactive teaching or for interpreting mathematics textbooks,…

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

In this article, the author argues that coordinate geometry and all its trappings should be banned from key stage 2 in English schools. To explain why he makes such a strong statement, he discusses geometry problems tackled by the Ancient Greeks, showing how meaningful problem solving can occur without the use of coordinates and the corresponding…

Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…