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July 2006, Volume 37, Issue 4

FEATURES

A Report on Jobs for Doctorates in Mathematics Education in Institutions of Higher Education
Robert E. Reys

A Brief Report A Report on Jobs for Doctorates in Mathematics Education in Institutions of Higher Education Robert E. Reys University of MissouriColumbia Institutions of higher education are having a difficult time filling positions requiring a doctorate in mathematics education. This study reports that about one half


Opening Another Black Box: Researching Mathematics for Teaching in Mathematics Teacher Education
Jill Adler, Zain Davis
This article describes an investigation into mathematics for teaching in current teacher education practice in South Africa. The study focuses on formal evaluative events across mathematics teacher education courses in a range of institutions. Its theoretical orientation is informed by Bernstein's educational code theory and the analytic frame builds on Ball and Bass' notion of "unpacking" in the mathematical work of teaching. The analysis of formal evaluative events reveals that across the range of courses, and particularly mathematics courses designed specifically for teachers, compression or abbreviation (in contrast to unpacking) of mathematical ideas is dominant. The article offers theoretical and practical explanations for why this might be so, as well as avenues for further research.

Does Understanding the Equal Sign Matter? Evidence from Solving Equations
Eric J. Knuth, Ana C. Stephens, Nicole M. McNeil, Martha W. Alibali
Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using  algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of equality. This article focuses on middle school students' understanding of the equal sign and its relation to performance solving algebraic equations.  The data indicate that many students lack a sophisticated understanding of the equal sign and that their understanding of the equal sign is associated with performance on equation-solving items. Moreover, the latter finding holds even when controlling for  mathematics ability (as measured by standardized achievement test scores). Implications for instruction and curricular design are discussed.

Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks
Patricio G. Herbst
Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is analyzed in two classes with an area problem designed to bring about and prove a conjecture about the relationship between the medians and area of a triangle. The  article stresses that to understand the conditions of possibility to teach geometry with problems, questions of epistemological and instructional nature need to be asked — not only whether and how certain ideas can be conceived by students as they work on a problem but also whether and how the kind of activity that will allow such conception can be summoned by customary ways of transacting work for knowledge.

Connecting Technology and School Mathematics: A Review of The Didactical Challenge of Symbolic Calculators
James T. Fey

Review Connecting Technology and School Mathematics: A Review of The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument. (2005). Dominique Guin, Kennet