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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

Tillema, Erik – For the Learning of Mathematics, 2010

I propose that attending how symbolizing activity functions for teachers and students helps to characterize student-teacher communication, and allows for an investigation of how symbolizing activity contributes to learning. I begin this discussion by articulating four ideas-schemes, symbolizing activity, communication, and learning. Then I propose…

Descriptors: Student Participation, Teacher Student Relationship, Data Analysis, Classroom Communication

Burgess, Tim – For the Learning of Mathematics, 2009

This paper first reports on the methodology of a study of teacher knowledge for statistics, conducted in a classroom at the primary school level. The methodology included videotaping of a sequence of lessons that involved students in investigating multivariate data sets, followed up by audiotaped interviews with each teacher. These stimulated…

Descriptors: Investigations, Research Methodology, Teacher Attitudes, Statistics

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

Biza, Irene; Nardi, Elena; Zachariades, Theodossios – For the Learning of Mathematics, 2009

This paper explores secondary teachers' views on the role of visualisation in the justification of a claim in the mathematics classroom and how these views could influence instruction. We engaged 91 teachers with tasks that invited them to: reflect on/solve a mathematical problem; examine flawed (fictional) student solutions; and, describe, in…

Descriptors: Feedback (Response), Mathematics Instruction, Beliefs, Didacticism

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

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

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

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

Zazkis, Rina; Liljedahl, Peter; Sinclair, Nathalie – For the Learning of Mathematics, 2009

We introduce Lesson Play as an imaginary interaction between teacher and students presented in a form of a dialogue or play. We suggest that lesson plays are a valuable professional development tool in preparing for teaching that can be juxtaposed with, or used as a replacement for, traditional lesson planning. The article begins with an…

Descriptors: Lesson Plans, Student Evaluation, Concept Formation, Teacher Student Relationship

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

Dickinson, Paul; Eade, Frank – For the Learning of Mathematics, 2004

The curriculum for eleven-year old students in the United Kingdom, currently adopted by most schools, includes solving linear equations with the unknown on one side only before moving onto those with the unknown on both sides in later years. School textbooks struggle with the balance between developing algebraic understanding and training…

Descriptors: Foreign Countries, Teaching Methods, Mathematics Instruction, Problem Solving

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

Castro, Fernando – For the Learning of Mathematics, 2003

The author shares a story of how Luis González, an iron artisan, helped the author build a wooden and iron toy truck. The knowledge required to build the skeleton for the parallelepiped in the construction of the truck is not in the mathematical high school curriculum in Venezuela. Although Luis never received a degree beyond high school,…

Descriptors: Metallurgy, Geometry, Geometric Concepts, Mathematics Skills

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Skovsmose, Ole – For the Learning of Mathematics, 2000

Critical mathematics education cannot be translated into principles. Aims to search for a working philosophy of mathematics for critical mathematics education. Concludes that aporism attempts to consider mathematics in its social, cultural, and political complexities, and to express uncertainties about mathematics' possible role as an educational…

Descriptors: Cultural Influences, Educational Philosophy, Elementary Secondary Education, Mathematics Education