This article provides detailed analysis, from a radical constructivist perspective, of a sequence of letter-writing exchanges between a preservice secondary mathematics teacher and a high school student. This analysis shows the ways in which the preservice teacher gained understanding of the high school student's mathematics and attempted to pose…

Planning is an important phase of teaching, during which teachers make decisions about various aspects of instruction that ultimately shape students' opportunities to learn. Prior research on teacher planning, however, fails to adequately describe experienced teachers' planning decisions, and is unclear about the extent to which teachers use…

This article discusses how communication theory is used to understand the thoughts mathematics teachers employ when creating messages intended for students. According to communication theory, individuals have different premises about the act of communicating, and these thoughts, called message design logics, guide the process of reasoning from…

One dimension of mathematics learning is developing an identity as a mathematics learner. The social learning theories of Gee (2001) and Wenger (1998) serve as a basis for the discussion of four "faces" of identity: engagement, imagination, alignment, and nature. A study conducted with 54 rural high school students, with half enrolled in a…

In this narrative of teacher educator action research, the idea for and the context of the lesson emerged as a result of conversations between Shelly, a mathematics teacher educator, and Lisa, a quilter, about real-life mathematical problems related to Lisa's work as she created the templates for a reproduction quilt. The lesson was used with…

Even though there is much research related to the teaching and learning of K-12 mathematics, there are few studies in the literature related to university professors' teaching. In this research report, I investigated how three professors of mathematics education structure their graduate level curriculum courses. The results show that three factors…

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

Problem solving theory and practice suggest that thinking is more important to solving problems than knowledge and that it is possible to teach thinking in situations where little or no knowledge of the problem is needed. Such an assumption has led problem solving advocates to champion "content-less heuristics" as the primary element of problem…

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

The purpose of this study was to measure student attitudes toward and conceptions about statistics, both before and after an introductory undergraduate college statistics class. Relationships between those attitudes and conceptions, as well as their relationships to achievement in statistics, were also studied. Significant correlations were found…

Addresses the use of subjective judgment in research that involves statistical/quantitative methods with regard to four aspects of quantitative research: (1) design; (2) preliminary analyses; (3) general analyses; and (4) specific analyses. (Contains 37 references.) (ASK)

Studies the amount of attention to various kinds of activities and how students are called upon to process information in typical mathematics lessons, and whether this focus indicates a balanced program with respect to procedural knowledge, conceptual knowledge, and mathematical activity. (Contains 15 references.) (ASK)

Discusses linguistic influence on children's numerical development. Describes and reviews recent papers that address the relationship between number naming systems and children's numerical concepts. (Contains 20 references.) (ASK)

Discusses the development of new mathematics teacher-education programs in Turkey. Presents examples of curricula for elementary and secondary mathematics teachers. (ASK)

Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)