The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Discusses problems associated with teaching non-recursive binary searching in computer language classes, and describes a teacher-directed dialog based on dictionary use that helps students use their previous searching experiences to conceptualize the binary search process. Algorithmic development is discussed and appropriate classroom discussion…

Investigates high school students' understanding of the physical relationship of chromosomes and genes as expressed in their conceptual models and in their ability to manipulate the models to explain solutions to dihybrid cross problems. Describes three typical models and three students' reasoning processes. Discusses four implications. (YP)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

This document analyzes one chapter of a textbook for college remedial mathematics. This analysis is done by one of the textbook authors. The chapter under discussion deals with fractions. The text authors, writing from a constructivist perspective, attempted to write problems which not only developed specific conceptual and heuristic objectives…

Defines M-demand as the maximum number of schemes that the subject must activate simultaneously in the course of executing a task. Discusses the effect of M-demand on problem solving. Uses algorithms to reduce M-demand. Describes the role of algorithms in problem solving. (MVL)