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

Fundamentals of elementary mathematics

Fundamentals of Elementary Mathematic

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

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