Focuses on culture examined in the unique context of South Africa. Makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. Also explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematics education.…

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

Examines classroom situations which allow for learning of rules of mathematical reasoning. Findings indicate that debate about mathematical rules can be generated amongst students ages 12 to 13 through the study of a mathematical problem. Argues that it is necessary for the teacher to conclude the debate. Contains 10 references. (JRH)

Investigates different types of procedures used by students (N=108) to simplify certain algebraic expressions. Findings indicate seven types of procedures including automatization, formulas, guessing-substituting, preparatory modification, concretization, rules, and quasi-rules. Contains 30 references. (JRH)

Focuses on reasons for the development of a mathematics test for admission of African students from grossly under-resourced schools as well as for placing students into a diversifying first-year curriculum. Highlights the process by which the test questions were developed and piloted. Discusses the reliability of the test and correlations with…

Reports on a study that focused on three teachers and their ways of teaching problem solving. Findings indicate that the participants unconsciously constructed personal metaphors that became the basis of their conceptualization of problems. "Community", "adventure" and "game" were the key metaphors. The outcome suggests that such metaphors could…

Investigates students' conceptions and misconceptions relating to the construction of graphs. Qualitative analysis of students' responses identified three main alternative conceptions. Quantitative analyses of the data indicated that overall students did not enter the learning situation as a tabula rasa. Discusses the theoretical and practical…

Analyzes students' productions, taking affective and social factors into account. Uses the technique of virtual monologue to reproduce the student's voice in order to describe as vividly as possible what might be going on in the student's mind during such situations. (AIM)

Presents a framework for assessing probabilistic thinking based on validated data obtained from eight third grade children who served as case studies. Major constructs were sample space, probability of an event, probability comparisons, and conditional probability. Levels of thinking appear to agree with the levels of cognitive functioning…

Discusses the difficulties observed in the transition from teaching arithmetic to teaching algebra. Future teachers (n=164) were questioned regarding to what extent they were able to shift back and forth between teaching methods within the context of problem solving. Interviews were conducted individually and in a dyad format. (AIM)

Presents to second graders the concept of an n-gon, characterized by a commutative diagram which is composed of four ways of judging a given figure. Observes that some children gave persuading arguments containing a critical idea and the concept formation corresponding to a structure-preserved transformation in the diagram. (AIM)

Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…

Describes reportedly successful treatment of deaf-mutes in China by acupuncture, and suggests that the disorders might have been more psychological than physical. The author comments that interpretation of poorly documented reports from unfamiliar cultures is extremely difficult. (AV)

A university history course in London introduced a new type of test question, similar to an essay question, based on excerpts from historical documents. The article compares scores of men and women on both types of question, and reviews student reaction to the new type of question. (AV)