This study aims to establish a theory for planning and practicing mathematics instruction that enables children to actively construct mathematical knowledge. Four types of constructive interactions are recognized on the basis of teaching practice. Processes of the constructive interactions and the requirements for realization of effective…

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the…

Describes a method for teaching multiplication of fractions based on Piaget's constructivism. Instead of teaching the algorithm of multiplying the numerators and denominators, students are presented with many problems and ask to invent their own ways of solving them. (DDR)

Examines and identifies students' mental models of an abstract mathematical concept regarding intuition. Observes how students think reflectively on their mental models in a whole-class discussion in terms of logical thinking. (DDR)

Examines the performance of children in different grades as they attempt to solve simple equations involving addition and subtraction of integer numbers. The extended task involves creating a story that matches the equations. (DDR)

By the age of 4, children typically have separate schema for relating events in the physical world and for relating events to associated mental states. Generally, these schema cannot be coordinated until around 6 years of age, when the ability to use them together yields a structure for assigning intentionality. This intentional structure develops…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…