Discusses the use of computers to teach proofs. Presents some possibilities of computer use in teaching proofs. (ASK)

Emphasizes the importance of proofs and offers examples and ideas that might help educators develop students' mathematical reasoning skills. (ASK)

Examined the evaluation and implementation of standards-based curricular materials by middle school mathematics teachers over two years. Data from classroom observations, conferences, field notes, surveys, and interviews indicated that teachers' experiences, professional knowledge bases, work contexts, and personal theories on effective teaching…

Investigated the effects, on 7th graders' mathematical reasoning, of: cooperative learning embedded within multilevel metacognitive training (MMT), cooperative learning embedded within unilevel metacognitive training (UMT), and whole-class learning with no metacognitive training. Students exposed to MMT significantly outperformed students exposed…

Describes the refinement of a conception in the domain of linear functions. Examples show how students refine their use of the x-intercept in equations of the form "y=mx+b" by narrowing problem contexts, making connections between conceptions, using a mathematical procedure, and refining verbal descriptions. Resources that teachers can draw on to…

Describes a consumer-math-skills project in which students make geometric shapes using pretzel sticks and gumdrops, then start a shop to sell them. This requires counting costs, pricing items, setting up shop, using money, making change, and understanding profits. Students reflect on the experience and write lists of the math they used to create…

Presents a program in the United Kingdom that trains every serving teacher and trainee teacher how to use Information and Communication Technology (ICT) to teach their subjects more effectively. Discusses mathematics education related to this part of the program. (ASK)

Describes an experiment designed to change prospective teachers' views of what constitutes a good explanation of a mathematics topic, presenting examples of participants' explanations at three stages of the experiment using a "levels of subject-matter understanding" framework, and suggesting that to effectively teach a topic, teachers'…

This paper introduces technology-based teaching ideas that facilitate the development of qualitative reasoning techniques in the context of quadratic equations with parameters. It reflects on activities designed for and used with prospective secondary mathematics teachers in accord with standards for teaching and recommendations for teachers in…

This article describes an activity in which students plot collections of ordered pairs according to prescribed set conditions. The coordinate plane sets can have rich variety, and their construction fosters critical thinking, attention to detail, and algebraic reasoning. (Contains 3 figures.)

This article describes geometry-oriented problem-solving tasks that can encourage students to develop a positive attitude toward mathematics. The tasks concern working with polyominoes, two-dimensional shapes that consist of squares joined fully at the edges. (Contains 7 figures.)

This article describes the use of commercial games in mathematics to help teach algebraic reasoning, spatial sense, and multistep problem solving. It also provides a description of how one teacher implemented the use of games.

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

This article describes partner quizzes, presents a process for using them in classrooms, and discusses the work of several students on such a quiz. (Contains 7 figures.)

This paper presents an examination of the use of Rasch modelling in a major research project, "Improving Middle Years Mathematics and Science" (IMYMS). The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates…