Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

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…

This paper reports on data from investigations on learners' understanding of inclusion relations of quadrilaterals, building on the ideas from our earlier study (Fujita & Jones, 2007). By synthesising past and current theories in the teaching of geometry (van Hiele's model, figural concepts, prototype phenomenon, etc.), we propose a theoretical…

Niche construction is the modification of components of the environment through an organism's activities. Humans modify their environments mainly through ontogenetic and cultural processes, and it is this reliance on learning, plasticity and culture that lends human niche construction a special potency. In this paper we aim to facilitate…

This paper argues that design fixation, in part, entails fixation at the level of meta-representation, the representation of the relation between a representation and its reference. In this paper, we present a mathematical model that mimics the idea of how fixation can occur at the meta-representation level. In this model, new abstract concepts…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

Two studies address the sequence of understandings evident in preschoolers' developing theory of mind. The first, preliminary study provides a meta-analysis of research comparing different types of mental state understandings (e.g., desires vs. beliefs, ignorance vs. false belief). The second, primary study tests a theory-of-mind scale for…

Comments on van Geert's mathematical model of Vygotsky's zone of proximal development, in this issue. Supports van Geert's use of a nonlinear model, noting that linear statistical models overlook variability in psychological phenomena. Discusses the time asymmetry in van Geert's model, which does not account for a subject's "developmental…

This paper explores the public awareness that there presently exists a crisis in mathematics education and a "dumbing down" of the curriculum, examines the nature of this crisis and argues that there has been a lowering of cultural, pedagogical and cognitive expectations with respect to most learners. The notion of cognitive development in…

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)

Notes advantages of using dynamic models to understand cognitive functioning: (1) they are specifically intended to represent changes that systems undergo as they evolve; (2) they can capture change in a continuous fashion; (3) they can account for development of behavior that appears orderly at times and disorderly at others, and (4) chaotic…

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)

Presents a unified theoretical approach to children's false-memory reports that deals with both spontaneous and implanted reports. Details false recognition and misinformation models that allow researchers to determine the impact of identity judgment, nonidentity judgment, and similarity judgment in false memory reports. (LBT)

Notes that there has been far less mathematical modeling of children's memory than of adults' memory. Explores the flaw in fuzzy-trace model, and maintains that situations in which partial verbatim information is used along with partial gist information fall outside the boundary of this type of model. Suggests refining the concepts of and…

Notes that a multitude of studies have demonstrated that misleading postevent information affects people's memories. Contents that the fuzzy-trace theory is a positive step toward understanding the malleability of memory. Discusses fuzzy-trace theory in terms of three primary areas of study: altered response format, maximized misinformation…