Describes an activity for making the connection between triangle ratios and graphs of circular functions which helps middle school students understand the concept of a sine curve. (ASK)

Presents an activity on fractions and explains how students obtain different fractions having different patterns when they are represented by their decimal expansions. (ASK)

Describes a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos. Focuses on the use of a dynamic model to promote habits of mathematical reasoning, conjecturing, and graphing analysis that support mathematics learning across grade levels. (ASK)

Presents an activity using quilts for many mathematical investigations. Benefits arising from the use of quilts include being useful, visually appealing, steeped in history, and an integral part of many cultures. (ASK)

Presents situations from geometry classrooms resulting from observations of five geometry teachers and their classes. Concludes that some teachers are influenced by their beliefs, professional development experiences, and views about their own teaching. Contains 11 references. (ASK)

Discusses how important it is for teachers to think deeply about what it is to know mathematics and their own understanding of fundamental mathematical ideas. (ASK)

Discusses how different meanings can be given to the proof at different levels and branches of mathematics education. (ASK)

Presents a mathematics activity that introduces proof by contradiction in a nonformal setting. This activity has the added benefit of helping students gain a greater understanding of the electoral college. (ASK)

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

Utilizes the notion of a students' proof schemes and outlines categories of proof schemes to evaluate the justifications given by students so that teachers can plan instruction to move them toward more sophisticated ways of reasoning. Contains 22 references. (ASK)

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

Presents a set of activities in which students explore how complex models can be generated using a small and simple set of rules. (ASK)

Focuses on teaching in China, concentrating on two particular aspects of teaching: teaching students to prove in geometry and the details of what teachers do in classrooms. (ASK)

Describes teaching about proofs in college-level mathematics courses. Presents typical questions that students raise while studying proofs and offers possible answers to these questions. (ASK)

Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)