A hypothetical framework to characterize statistical knowledge for teaching (SKT) is described. Empirical grounding for the framework is provided by artifacts from an undergraduate course for prospective teachers that concentrated on the development of SKT. The theoretical notion of "key developmental understanding" (KDU) is used to identify…

The accepted framing of mathematics pedagogical content knowledge (PCK) as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains…

Explores the understanding that students who are training to be secondary mathematics teachers have of elementary concepts in mathematical analysis. Research involved probing students' conceptual understanding of convergence and continuity and associated reasoning. Concludes that even mathematically well-qualified students have difficulties with…

Focuses on one central aspect of epistemological mathematical knowledge, namely the problematique of how mathematical signs and symbols gain meaning in the interactive social processes of teaching and learning. Describes a teaching episode and analyzes it from an epistemological perspective. Identifies three components of epistemological knowledge…

This booklet is an addendum to the conference proceedings of the 20th annual meeting of the International Group for the Psychology of Mathematics Education (PME 20). It contains three reactions to the research forum: (1) "Mathematizing: The 'Real' Need for Representational Fluency" (R. Lesh); (2) "Mathematics Teacher Development: An Alternative…

Explores some of the common difficulties experienced by preservice primary teachers with mathematical word problems. Examines weaknesses in students' content and procedural knowledge, with a particular focus on how they apply these aspects of knowledge to solving closed word problems. Contains 34 references. (Author/ASK)

The broad aim of this research is to characterize the views of proof held by college calculus students and their two types of teachers mathematics graduate students and professors. The analysis is based on an examination of the ways in which people in all three groups produce and evaluate different types of solutions to a proof-based problem from…

The way teachers understand mathematics strongly influences their teaching and what pupils learn. Describes the influence of two variables on preservice teachers' performance: (1) the presence of a formal definition; and (2) previous classroom activities that addressed the concept of the altitude of a triangle. (Contains 30 references.)…

The first volume of this proceedings contains three plenary addresses: (1) "Visualization in 3-dimensional geometry: In search of a framework" (A. Gutierrez); (2) "The ongoing value of proof" (G. Hanna); and (3) "Modern times: The symbolic surfaces of language, mathematics and art" (D. Pimm). Plenary panels include:…

Mathematics professional communities were urged to make a strong, coordinated, and visible commitment to strengthening the mathematical preparation of elementary teachers. The Texas Statewide Systemic Initiative (Texas SSI) recommends that teachers complete a minimum of nine credit hours in mathematics. Texas SSI further recommends that these…

Addresses issues related to the ways teachers learn mathematics and the teaching of mathematics, and the relevance of those ways to their professional development. Mathematical experiences need to be congruous with the kind of teaching expected of the reflexive, adaptive teacher. Presents both practical and theoretical considerations of how these…

Discusses what important ideas about forms of knowing mathematics should be included in mathematics methods courses for preservice teachers. Proposes ideas related to Shulman's framework of teacher knowledge. Provides a brief discussion of the implications each idea holds for teaching mathematics, and makes some suggestions about experiences that…

This paper reports on a survey instrument designed to measure opinions regarding computer knowledge and usage among high school teachers of mathematics (N=66) and college faculty of mathematics (N=25). Findings indicate that the college faculty made reference to computer usage more often in their lectures than did the high school teachers.…

Describes changes that are being made in mathematics teachers' subject studies in order to provide students with sufficiently deep knowledge of mathematics and science and with present-day expertise in their profession as teachers. Provides an abstract algebra course as the ultimate example of a pedagogical experiment where co-operative learning…

This article addresses the question: "What are the implications for the preparation of prospective elementary teachers of 'early algebra' in the elementary grades curriculum?" Part of the answer involves language aspects of algebra: in particular, how a change in pre-service teachers' attitudes to algebra, from instrumental to relational, is…