Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

Replies to Lerman, who presented Vygotsky as an irreconcilable opponent to Piaget's genetic epistemology and von Glasersfeld's radical constructivism. Argues that Lerman's stance does not reflect von Glasersfeld's opinion of Vygotsky's work, nor does it reflect Vygotsky's opinion of Piaget's work. Establishes compatibility between analytic units…

The author defends the teaching of thinking strategies. (MK)

This critique focuses on Gagne's attempt to apply information-processing theory to mathematics education, noting that this distorts what it means to learn mathematics. This is discussed with specific illustrations. (MNS)

A methodology for exploring limits and subtleties of children's construction of mathematical concepts and operations is described. It is believed that the failure to observe children's constructive processes firsthand denies a researcher the experimental base so crucial in formulating explanations of processes. Researchers are encouraged to teach…

Examined were differential performances among categories of first graders when solving arithmetical workd problems of eight types under two distinct conditions. The categories were based on various types of quantitative comparisons which children are known to make. Several statistically significant results were obtained involving differences…

Four levels of quantitative comparisons based on Piagetian task analysis and three IQ levels were used to partition a population of 341 first grade children. Each child was then tested on a set of addition facts and a set of addition problems which varied according to the use of aids or transformation. (JG)

Stimulus conditions were found to interact with conservation level and relation type. (MM)

A study of conservation of length concepts covering the symmetric, asymmetric, reflexive, nonreflexive, and transitive relations. Their order of development was traced during the course of a 15-lesson sequence of related instruction. (MM)

Discusses constructivist teaching, students' mathematical knowledge, activating prior knowledge, hypothetical learning trajectory, and reflection in teaching mathematics, all in reaction to Simon's model of constructivist pedagogy. (24 references) (MKR)

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,…

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…

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…

Provides an interpretation of the influence of constructivist thought on mathematics educators starting around 1960 and proceeding up to the present time, including Piaget's cognitive-development psychology, a preconstructivist revolution in research, beginnings of the constructivist revolution, and how this revolution served as a period of…