Presents a study to determine students' concept of slope carried out in three classes of the second form before introducing the notion of derivative. Discusses the meaning of conceptual framework and reviews literature on slope. Analyzes student responses to a questionnaire for mathematical content and expression and interprets the results. (MDH)

Kindergarten (n=30) and grade 1 (n=15) students of contrasting socioeconomic backgrounds were interviewed to assess their knowledge of number word sequences and spatial patterns and their ability to recognize numerals and use counting to establish numerosity of visible and screened collections. Findings indicate greater variation in abilities…

The facets of teachers' views of mathematics include their personal views, how they view mathematics for their students, how they view the mathematics curriculum, and how they view mathematics teaching. This paper reports a pilot study to examine how elementary school teachers view mathematics both personally and for their students. A coding…

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)

Written descriptions by students in grades 3-7 (n=274) of common 2-dimensional geometric shapes were examined to compare the level descriptors of the van Hiele Theory and the SOLO Taxonomy. Results indicate that descriptors associated with the SOLO Taxonomy more accurately describe the quality of student thinking. (MDH)

Reviews research on (1) schemata acquisition while learning mathematics and techniques for detecting schema in mathematics learners; and (2) assessment of the distribution of cognitive resources while learning mathematics that lead to the design of instructional techniques to facilitate schema acquisition. (26 references) (MDH)

Inservice teachers (n=180) participating in seven mathematical problem-solving workshops were asked to define problem solving. An item analysis of the written responses indicated that 67% of the responses were conceptually or terminologically vague. Precise definitions fell into three categories: strategy-based (12%), skills-based (9%), and…

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…

It is generally accepted that mathematical reasoning, like language acquisition, is part of normal cognitive development. This paper proposes that other variables must be considered when explaining the differences in the acquisition of mathematical reasoning skills in young children. Considered is some of the evidence that suggests that certain…

The relationship between teachers' and students' personal constructs regarding intrinsic motivation in the mathematics class were examined in this study. Participants were six middle-school mathematics teachers and 30 students from 5 classes. Videotape, direct observation, individual interviews, and repertory grid tasks focused on the ways in…

Classroom boredom in the secondary mathematics classroom is a problem that can be addressed from knowledge of the intrinsic motivational variable of "interestingness." The lack of a theoretical model of interest is an obstacle in research that investigates this variable. This paper describes the three stages in the development of a model…