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…

Discusses the limitations in the explain-practice and active learning methods of teaching mathematics. Proposes that problem-centered learning is a teaching method that encourages student reflection, and presents examples demonstrating that encouraging reflection results in greater mathematics achievement. (MDH)

As universities strive to produce the best mathematics teachers possible through both graduate and undergraduate programs, teacher educators must constantly work towards helping teacher candidates create their own conceptual understanding of mathematics. This pilot study examined the effect teaching in a constructivist manner had on teacher…

This research focused on students' learning of mathematical rules with reasoning. A small group of students (age 11-12 yrs) was observed closely by the first author as she taught them fraction rules. The area of focus was fractions and activities were designed pertaining to the four rules of fractions: addition, subtraction, multiplication, and…

An investigation-based course on teaching strategies for in-service science and mathematics teachers has been developed. The purpose of this course was to learn how to teach science or mathematics from the constructivist perspective. The course development was based on constructivism, especially social constructivism. Major adjustments concerning…

Reports on case studies of three secondary school teachers who were implementing the University of Chicago School Mathematics Project (UCSMP) for the first time. The research examined whether innovative textbooks and curriculum materials can play a role in the process of change in instructional practice. Data from field observations, interviews,…

Is educational technology effective in increasing student learning? If technology is an effective tool in the classroom, how can teachers best be trained to use it appropriately? An experiment was conducted to determine the effectiveness of a constructivist math class utilizing computer technology as well as other tools. The study occurred in a…

This digest describes an interdisciplinary approach to instruction based on the relationship between reading, writing, and arithmetic. Questions related to which language learning strategies apply to mathematics, the perspectives of the National Council of Teachers of Mathematics (NCTM) regarding this approach, the impact of reading on…

Examines research on computer-based mathematics learning in the context of constructivist learning and the National Council of Teachers of Mathematics Standards. The reviewed studies examined the effectiveness of computer software in the three categories of programming, computer-assisted instruction, and mathematical tools. Future research is…

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

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…