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Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2011

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

Descriptors: Secondary School Mathematics, Mathematics Education, Knowledge Base for Teaching, Colleges

Pournara, Craig – For the Learning of Mathematics, 2009

The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…

Descriptors: Mathematics Education, Mathematical Concepts, Mathematics Teachers, Spreadsheets

Huillet, Danielle – For the Learning of Mathematics, 2009

This paper analyses how the mathematical knowledge needed by a teacher has been described by several mathematics educators, all based on Shulman's notions of Subject Matter Knowledge and Pedagogical Content Knowledge. In particular, it looks at the notion of Mathematics Knowledge for Teaching, as elaborated by Ball and her research group. It then…

Descriptors: Mathematics Education, Anthropology, Knowledge Base for Teaching, Foreign Countries

Chick, Helen – For the Learning of Mathematics, 2009

Examples play a central role in mathematics learning and teaching. Although they involve specific situations, their purpose is to exemplify more general mathematical principles. A critical task of teaching, therefore, is to choose appropriate examples and implement them in pedagogically productive ways. This study considers the examples used by…

Descriptors: Mathematics Education, Mathematics Instruction, Mathematics, Mathematics Teachers

Towers, Jo; Martin, Lyndon – For the Learning of Mathematics, 2009

In this paper we explore the growth of understanding of a group of preservice teachers, and their instructor, as they work collectively together on what we describe as a "mathematics for teaching" task. Through drawing on elements of improvisational theory, in particular the notion of the "better idea," we analyse how the preservice teachers'…

Descriptors: Student Teachers, Knowledge Base for Teaching, Mathematical Concepts, Preservice Teachers

Davis, Brent; Renert, Moshe – For the Learning of Mathematics, 2009

We report on a two-year "concept study" in which a cohort of middle school teachers collectively deconstructed and reconstructed the concept of multiplication. Defining concept study as a collaborative structure through which mathematics educators identify, interpret, interrogate, invent, and elaborate images, metaphors, analogies, examples,…

Descriptors: Mathematics Education, Middle School Teachers, Mathematics Teachers, Mathematical Concepts

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2009

Mathematical knowledge used in teaching has attracted the interest of many researchers, but was mainly explored considering teaching at the elementary school level. This paper attends to mathematical knowledge used in teaching at the University level. We present a story about a student suggesting reconsideration of Cantor's diagonal method and the…

Descriptors: Mathematics Education, Mathematics Teachers, Classroom Environment, Pedagogical Content Knowledge

Even, Ruhama – For the Learning of Mathematics, 2003

When asked to give a talk at a mathematics teacher conference that focused on research in mathematics education, Ruhama Even viewed the invitation as an opportunity to address the meta-question: what can teachers learn from research in mathematics education? The reason for her view was her way of feeling, as a researcher and teacher educator, that…

Descriptors: Mathematics Education, Educational Research, Epistemology, Inquiry

Peer reviewed

Winicki-Landman, Greisy; Leikin, Roza – For the Learning of Mathematics, 2000

Addresses the concept of mathematical definition as well as the definitions of different mathematics concepts. Focuses on the possibility of defining a mathematical concept in several ways based on logical relationships between different mathematical statements related to the concept. The choice of one of these statements as definitional plays a…

Descriptors: Definitions, Geometric Concepts, Learning, Mathematics Education

Peer reviewed

Cooney, Thomas; And Others – For the Learning of Mathematics, 1985

An overview to a session at the Fifth International Congress on Mathematical Education is given. Papers on research by Cooney, curriculum development by Goffree, reform in mathematics education by Stephens, and a summary by Nickson are included. (MNS)

Descriptors: Curriculum, Development, Educational Research, Elementary Secondary Education

Peer reviewed

Dreyfus, Tommy; Eisenberg, Theodore – For the Learning of Mathematics, 1986

Appreciating the power and beauty of mathematical thought should be an integral component of a student's mathematical education. The meaning of aesthetics in the realm of mathematical reasoning, the relationship of aesthetics to problem solving, the results of two studies, and recommendations for developing aesthetics are included. (MNS)

Descriptors: College Mathematics, Educational Research, Higher Education, Mathematics Instruction

Peer reviewed

Barnes, Mary – For the Learning of Mathematics, 2000

Investigates magical mathematical moments in order to seek to understand what they are and how they happen, to look for examples, and to reflect on their impact on students' mathematics learning. Describes magical moments as they appear in references in the literature and characterizes those moments. Provides examples from classrooms. (Contains 27…

Descriptors: Elementary Secondary Education, Learning, Mathematics Instruction, Teaching Methods

Peer reviewed

Graf, Klaus-Dieter; Hodgson, Bernard R. – For the Learning of Mathematics, 1990

The kaleidoscope is presented as a suitable topic for a preservice mathematics teacher's first contact with a nontrivial mathematical phenomenon. Included are historical notes on the kaleidoscope, explanation of the inner mechanisms of various kaleidoscope designs, and suggestions for further student investigations. (JJK)

Descriptors: Computer Software Reviews, Elementary School Mathematics, Geometric Concepts, Higher Education

Peer reviewed

Neubrand, Michael – For the Learning of Mathematics, 1989

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

Descriptors: College Mathematics, Higher Education, Mathematical Formulas, Mathematical Logic

Peer reviewed

Gerdes, Paulus – For the Learning of Mathematics, 1985

Reflecting the author's experiences in Mozambique, some conditions and strategies for mathematics education in underdeveloped countries are suggested. How mathematics education can be used for emancipation is discussed, with extensive comments on problemising reality in classroom situations and creating confidence. (MNS)

Descriptors: Creative Thinking, Cultural Background, Developing Nations, Mathematical Applications

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