How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

The development of probability judgment is explained in terms of working memory, composed of four types of storage operations and three types of processing operations. Age changes in probability judgment were related to changes in frequency retrieval, which stem from changes in constraints on work-space capacity. (Author/RD)

Category theory concept of a commutative diagram was used to construct a model of the way in which symbolic processes are applied to problem solving. It was shown that several different levels of thought can be distinguished within the basic model. Two experiments testing the theory are reported. (Author/RD)

A general theory of how children learn conservation concepts is presented. The acquisition process is described at an abstract level in terms of a rule-sampling system, implying a three-state Markov model with identifiable parameters. Three experiments testing the model's quantitative predictions about conservation learning experiments are…

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

The causal relationship between metaphonological skills (sound blending and segmentation) and reading/spelling was investigated in two studies of first graders. One tested causal models using data from a longitudinal study of 46 dyslexics and 44 control children. The other studied the effects of metaphonological training versus general language…

A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the…

The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…