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…

In this paper, the application of fuzzy logic in mathematical education is viewed from the perspective of pre- school education. The aim of the paper is to give a brief overview of examples from the literature related to fuzzy logic and to point out the presence of fuzzy linguistic variables in the everyday life of a preschool child, as well as…

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…

A theoretical model of metacognition in complex modeling activities has been developed based on existing frameworks, by synthesizing the re-conceptualization of metacognition at multiple levels by looking at the three sources that trigger metacognition. Using the theoretical model as a framework, this study was designed to explore how students'…

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…

The interest in developmental sequences and learning hierarchies is growing. One approach to the study of such sequences is to gather data on several variables, each of which corresponds to a stage, step, or phase in the sequence and to examine the associations between the variables as displayed in a contingency table. If the variables are…

PIAGET'S THEORETICAL FORMULATION OF THE DEVELOPMENT OF CONSERVATION OF CONTINUOUS QUANTITY WAS EXAMINED. CONTROL SUBJECTS IN EACH OF TWO AGE GROUPS (5 AND 6 YEARS) WERE GIVEN A COMPLEX TASK SITUATION THAT IS TYPICAL OF PIAGET'S WORK. THESE SUBJECTS WERE ALSO GIVEN ANOTHER TASK, A MEASURE OF CONSERVATION OF QUANTITY THAT IS INDEPENDENT OF PIAGET'S…

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)