Describes a college geometry course centered around challenging, open-ended problems that invite students to draw upon their experiences and share their understandings. Includes discussion of sample problems; writing assignments; classroom dialog; student comments and insights about geometry, mathematics, and themselves and mathematics; and…

Introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. Describes components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies. (Author/MM)

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…

This article describes explorations using The Geometer's Sketchpad for algebra and calculus content.

The interpretive framework for the study of learning introduced in this article and called "commognitive" is grounded in the assumption that thinking is a form of communication and that learning mathematics is tantamount to modifying and extending one's discourse. These basic tenets lead to the conclusion that substantial discursive change, rather…

In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

Mathematics is both a beautiful language and the simplest systematic discipline men ever created. The simplicity of mathematical concepts almost guarantees that the facts it establishes about those concepts will also be elemental. Despite this simplicity, most people complain about the difficulty of mastering the subject and shun the study of…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

Presented are practical activities relevant to teaching mathematics in the American Indian culture that can be used in the non-Indian classroom. Discussed are tessellations, exercises that allow for artistic creativity and geometric exploration. The use of Pascal's triangle is included. (KR)

Several times a week I walk by a metal chair that is fastened to a flat concrete slab at an outdoor bus stop here in Boulder. One day I noticed on the concrete a nice shadow image of the woven metal seat of the chair (Fig. 1). The seat and back of the chair are formed from 3.8-cm wide strips of metal spaced 3.8 cm apart. The seat is about 39 cm…

This study was designed to evaluate the effect of the use of mathematical logic in high school geometry on (1) achievement of students in geometry, (2) achievement of students in reasoning in geometry, (3) critical thinking of students, and (4) attitude of students toward logic deduction, and proof in mathematics. The experimental group of six…

The plans for a field test of teaching tenth grade plane geometry through transformations is described. Text and homework materials have been written, and teachers have been trained. Eight intact classes are now being taught utilizing the materials. Data to be collected will include: (1) teacher descriptions of the course via questionnaire; (2)…

The author argues that sine, secant, and tangent should be taught as the three basic trigonometric functions rather than sine, cosine, and tangent. (SD)

Many Waldorf methods charter schools are opening up in California today. They are publicly funded schools bringing Waldorf methods into public education. In today's political climate all public schools must pass the state's bar of academic success measured by their Adequate Yearly Progress (AYP). Because these scores are based largely on…