In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

Data structures and algorithms are core issues in computer programming. However, learning them is challenging for most students and many of them have various types of misconceptions on how algorithms work. In this study, we discuss the problem of identifying misconceptions on the principles of how algorithms work. Our context is algorithm…

The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can…

Searching for an adequate method to investigate human development (especially the development of theoretical thinking) Vygotsky and his collaborators developed the causal genetic method. The basic idea of this method consists in the investigation of psychic functions and structures by their formation under controlled conditions (for instance via a…

Is it feasible and appropriate to develop a sustainability metrics which captures cosmological-spiritual dimensions of un/sustainability? Departing from the supposition that the crisis of unsustainability is a crisis of worldview and misguided cosmology which needs redirection on a cultural and global scale, this essay introduces the notion of a…

This submission contains the Proceedings of the 2008 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Universite de Sherbrooke in Sherbrooke, Quebec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

A cognitive or internal representation refers to an organized system of information which reflects certain, but not all, of the information about reality being represented. This paper considers various opinions, controversies, and debates about what representation is, how it comes about, and what forms of representation can be distinguished. The…

This study focused on the development of policy thought, or abstract thinking about policy issues. Political thought may be described as concrete thinking about political phenomena. It includes one's knowledge of and attitude toward objects, people, and events in the political sphere. Policy thought entails the abstract manner in which one…

Two groups of l4 mothers were interviewed to study how parents reason about their children's behavior. The two samples differed considerably in terms of education, age, race, and socioeconomic status. The first group, high school educated, averaged 24 years of age, and, if married, had spouses with blue-collar jobs. The second group, college…

A study was designed to investigate the nature of language proficiency and its cross-lingual dimensions. The focus of the study was on the interdependence hypothesis, that older immigrant students whose first language (L1) cognitive/academic proficiency is better developed on arrival in Canada will acquire English cognitive/academic skills more…

Using science experiments in life science, chemistry, and physics, helps ground students' understanding of abstract algebra concepts in real-world applications. Hands-on activities connect mathematics with science in a way that is accessible to teachers and students alike. Each activity explores a scientific phenomenon, connecting it to algebra…

The cognitive processes in a widely used, non-verbal test of analytic intelligence--the Raven Progressive Matrices Test (J. C. Raven, 1962)--were analyzed. The analysis determined which processes distinguished between higher-scoring and lower-scoring subjects and which processes were common to all subjects and all items on the test. The analysis…

This report summarizes research on experienced programmers' comprehension of computer programs that was carried out over a three-year contract period (1982-85). Following an extensive review of the programming skill literature, an analysis of programs based on the multiple abstractions (points-of-view) that characterize program text and design was…

The reflective judgment (RJ) model is described, along with research findings based on the model and contributions to understanding student intellectual development in higher education. The RJ model (Kitchener & King, 1981) describes a series of changes that occur in the ways adults/young adults understand the process of knowing, and…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…