The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Institutions of higher education are having a difficult time filling positions requiring a doctorate in mathematics education. This study reports that about one half of the 83 national searches by institutions for mathematics educators for the 2005-06 academic year were unsuccessful. Salaries for assistant professors were slightly higher in…

Explores some of the possible contributions of complexity science to discussions of the teaching of mathematics. Focuses on the use of the vocabulary of complexity in the re-description of mathematical communities and the application of principles of complexity to the teaching of mathematics. Highlights compatible and complementary discussions…

Explores the way that mathematics and secondary education mathematics majors read and reflected upon student-generated arguments purported to be proofs of a single theorem. Suggests that such undergraduates tend to focus on surface features of arguments and that their ability to determine whether arguments are proofs is very limited. Discusses…

Introduces crossdisciplinarity as a strategy for highlighting the discrete notions of learning that psychology thus far has succeeded in coherently articulating. This strategy positions teachers to consult their own values, interests, and strengths in defining their own teaching priorities while at the same time marshaling accessible, theory-based…

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Uses situated abstraction to understand nurses' conceptions of intensive quantity of drug concentration. Explores nurses' conceptions to undertake a pointed examination of the degree of situatedness of nurses' knowledge and reasoning. Demonstrates that nurses' conceptions were abstracted within their practice when they coordinated mathematical…

Studies four preservice elementary teachers during a field-based mathematics methods course to investigate elements of mathematics teaching and learning that teachers found problematic and how they resolved those problems. Concluded that teachers exhibited concerns about classroom context, pedagogy of mathematics, children's mathematical thinking,…

Examines the value of concept maps as instruments for assessment of conceptual understanding, using the maps to compare the knowledge of function that experts and two groups of students (N=28)--traditional and nontraditional--enrolled in university calculus classes hold. Discusses the differences between the student and expert groups as well as…

Presents a study of the beliefs and belief structures of four preservice secondary mathematics teachers as they progress through a four-quarter sequence in mathematics education that includes student teaching. Concludes that the various ways in which the teachers structured their beliefs helped account for the fact that some beliefs were permeable…

Explores the strategies used by prospective secondary mathematics teachers (N=13) to develop and validate functions as mathematical models of real-world situations. Uses a grounded hypothesis on strategy selection. Concludes that strategy choice was influenced by task characteristics and interactions with other student modelers. Contains 38…

Reviews literature on mathematics achievement trends and discusses relevant population trends. Examines the literature on mathematics achievement by demographic group-race, class, gender, and language proficiency. Also highlights important findings including the improvement of all demographic groups in basic mathematics skills over the last 15…

Reviews the four sections of the two-volume set, "International Handbook of Mathematics Education," with specific comments on various chapters contained therein. Suggests that this handbook be used as a general resource for specific topics. (AIM)

College students (n=32) in their first abstract algebra course were asked to list elements and find the product of 2 elements in the dihedral group D4. Most students found solutions using a combination of visual approaches and analytic strategies. Proposes an alternative model, the Visualizer/Analyzer model, which assumes visualization and…

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)