Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

The present study examines secondary school students' geometrical figure apprehension based on Duval's theoretical framework regarding perceptual, operative, and discursive apprehension. The aim is to explore the cognitive structure of the geometrical figure apprehension dimensions (operative, discursive, and perceptual) in three grades of…

Within mathematics education research, the responses to the Programme for International Student Assessment's (PISA's) international testing regime tend to accept its framework and results as necessary points of reference, even when offering a critical reinterpretation or challenging national policy discourses based on PISA. In this article, we…

This report describes a model for mapping cognitive structures related to content knowledge for teaching. The model consists of knowledge elements pertinent to teaching a content domain, the nature of the connections among them, and a means for representing the elements and connections visually. The model is illustrated through empirical data…

This article examines the extent to which Wittgenstein's analytical framework may be relevant to philosophical reflection on ethnomathematics. The discussion develops Bill Barton's suggestion that a philosophical basis for the ethnomathematical program should include and explain culturally different mathematics systems, and the coexistence of…

One sentence answer to the question in the title is that the ability to prove depends on forms of knowledge to which most student are rarely, if ever, exposed. Presents more detailed analysis, drawing on research in mathematics education and classroom experiences. (Contains 44 references.) (Author/ASK)

Answers Burn's question related to a previous study on the nature of knowledge about abstract algebra. Claims that a previous paper presents research that attempts to contribute to knowledge of how students' understanding of certain group concepts may develop instead of teaching abstract algebra with the computer software ISETL. (ASK)

Postulates a form of mathematical reasoning that learners engage in spontaneously that is not inherently inductive or deductive. This transformational reasoning is generated through the learner's inquiry into how a mathematical system works. (Author/MKR)

Illustrates distinctions among kinds of knowing. Distinguishes knowing-to from other forms of knowing, and explores implications of that distinction for teaching and learning mathematics. Proposes that knowing-to act in the moment depends on the structure of attention at the moment, and on what one is aware of. (Contains 75 references.)…

Examines the mathematical proof schemes of students starting their studies at the University of Cordoba and relates these schemes to the meanings of mathematical proof in different institutional contexts. Concludes that deductive mathematical proof is difficult for these students. Suggests that the different institutional meanings of proof might…

Studies knowledge of young children's partitioning strategies by setting out not only to identify new partitioning strategies, but also to develop taxonomy for classifying young children's partitioning strategies in terms of their abilities. Provides taxonomy utilizing children's informal partitioning strategies as the foundation upon which to…

New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge, knowledge of particulars, language, and rhetoric in mathematics. Highlights the importance of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in this area.…

Undergraduates in an abstract algebra course were interviewed to see how they learned the concept of isomorphism. Analysis showed students used step-by-step procedures, exhibited various degrees of personification in their language, and chose properties they perceived as simpler. (MKR)

Data from (n=4) students in grades three through six showed a consistent parallel between the types of units constructed in a geometric setting with those in a numeric context. Students who constructed abstract composite units in tiling the plane also did so in adding and subtracting whole numbers. (Author/MKR)

Views of (n=70) 16- and 17-year olds on mathematical knowledge, activity, and learning were analyzed using factorial techniques. Findings suggest there was no simple systematic relationship between beliefs about the nature of mathematical knowledge and the teaching and learning of mathematics. (19 references) (Author/MKR)