25 research outputs found
Interactions between “Structure-of-Intellect” Factors and Two Methods of Presenting Concepts of Modular Arithmetic: A Summary Paper
Tasks to assess children's perception of the size of a fraction
Behr MJ, Post TR, Wachsmuth I. Tasks to assess children's perception of the size of a fraction. In: Bell A, ed. Theory, research and practice in mathematical education: 5th International Congress on Mathematical Education, Adelaide, South Australia, August 1984. Nottingham: Shell Centre for Mathematical Education, University of Nottingham; 1984: 179-185.The question of how children perceive the "bigness" of rational numbers is of importance. Addition of fractions like1/3 and 3/5 does not make sense to a child without a quantitative notion of each addend. In order for children to perceive the size of a fraction, it seems necessary that they perceive the ordered pair such as 3/4; as one conceptual entity. This note describes, and summarizes results from several tasks the Rational Number Project has used to investigate children's perception of fractions, and especially of the size of a fraction. The Rational Number Project has involved fourth- and fifth-grade children in extensive teaching experiments. The teaching milieu of these experiments is especially manipulative rich, concept oriented, and involves small groups of children
Rational number learning aids: transfer from continuous models to discrete models
Behr MJ, Wachsmuth I, Post T. Rational number learning aids: transfer from continuous models to discrete models. Focus on learning problems in mathematics. 1988;10(4):1-18.This paper is concerned with how well children who have head instruction about rational number concepts based on a continuous manipulative aid are able to transfer their knowledge to accomplish tasks based on a manipulative aid which can be interpreted as discrete. The aid used was an egg carton which, if the subject views the holes as salient, is discrete; if, on the other hand, the subject focuses on the proportion of total area enclosed by the edges of each of the holes, then it is viewed as a continuous entity
Interactions between Structure-of-Intellect Factors and Two Methods of Presenting Concepts of Modulus Seven Arithmetic: A Follow-up and Refinement Study
Brief Reports: Interaction between Structure of Intellect Factors and Two Methods of Presenting Concepts of Logic
Rational number learning aids: transfer from continuous models to discrete models
Behr MJ, Wachsmuth I, Post T. Rational number learning aids: transfer from continuous models to discrete models. Focus on learning problems in mathematics. 1998;20(1):63-81.(selected for retrospective reprint from Focus 10(4), 1988, 1-
18)
This paper is concerned with how well children who have head instruction about rational number concepts based on a continuous manipulative aid are able to transfer their knowledge to accomplish tasks based on a manipulative aid which can be interpreted as discrete. The aid used was an egg carton which, if the subject views the holes as salient, is discrete; if, on the other hand, the subject focuses on the proportion of total area enclosed by the edges of each of the holes, then it is viewed as a continuous entity
Children's quantitative notion of rational number
Wachsmuth I, Behr MJ, Post TR. Children's quantitative notion of rational number. ERIC Document No. ED 229 218. 1983
Construct a sum: a measure of children's understanding of fraction size
Behr MJ, Wachsmuth I, Post TR. Construct a sum: a measure of children's understanding of fraction size. Journal for research in mathematics education. 1985;16(2):120-131