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…

The purpose of this study was to determine if college students could benefit from the use of visual and manipulative aids while studying a mathematical topic. A sample of 33 freshmen were pretested for mathematical ability, divided into ability levels by means of ACT composite scores, and randomly assigned to one of three treatment groups for a…

Sixty Japanese children ranging in age from 3 years 4 months to 7 years 5 months were individually interviewed with three Piagetian tasks. Children's levels of representation were assessed by asking for a graphic representation of 4 dishes, 6 pencils, 8 small blocks etc. A conservation-of-number task was then given to assess children's level of…

Reports survey results on proof conceptions. Presents an overview of responses at the end of year 8 (age 13 years) and year 9 (age 14 years). Distinguishes three strategies--empirical, focused-empirical, and focused-deductive--that represent shifts in attention from an inductive to a deductive approach. Indicates some progress from year 8 to year…

Discusses Vygotsky's theories about concept formation, his distinctions between everyday and theoretical concepts, and how empirical generalizations can lead to misconceptions. Examines the implications of these theories for mathematics instruction and its relationship to the current mathematics reform. (34 references) (MDH)

Presents research findings and teaching implications of mathematics as reasoning and students' reasoning abilities in mathematics. (20 references) (MKR)

Describes four projects that support the transition from an abstract to a concrete notion of the effective use of technology in the secondary school classroom: The Interactive Mathematics Program, Systemic Initiative for Montana Mathematics and Science, University of Chicago School Mathematics Project, and Connected Geometry. (MKR)

Discusses the historical, cultural, and pedagogical roots, as well as reasons inherent in mathematical thought that may explain U.S. students' resistance to learning mathematics. Concludes that bridging the gap between theory and practice can be facilitated by a hands-on approach that employs experiments and model making. (PR)

Shares the results of a study in which 204 first grade students were interviewed. Interprets the findings in light of Piaget's emphasis on abstraction. Concludes that children represent ideas at their respective levels of abstraction. (Author/ASK)

Describes the different types of reasoning in scientific research activity. Outlines three different but complementary ways to integrate history into the presentation of science. Considers and illustrates the close historical relationship between mathematics and physics. (Contains 50 references.) (ASK)

Proposes that children progressively recognize deeper and deeper similarities between their physical angle experiences, and classify them firstly into specific situations, then into more general contexts, and finally into abstract domains. Indicates that the standard angle concept first develops in situations where both arms of the angle are…

Presents a theoretical framework based on interviews with undergraduate students and written questionnaires to study how undergraduate students cope with abstract algebra concepts. Indicates that students' responses can be interpreted as a result of reducing the level of abstraction. Examines the theme of reducing abstraction based on three…

Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…

This paper presents the results of the second class to participate in the fast-paced mathematics program begun by the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University. Fast-paced mathematics classes were established to meet the needs of highly gifted junior high school students. Thirty-three students participated in the…