Discusses a new approach to mathematics education that moves away from methods that tell students what to do and toward methods that help students build mental representations of mathematical concepts. Contrasts the previous and emerging views and examines aspects of the new approach. (26 references) (MDH)

Presents a unit to review geometric concepts and problem solving by having students work cooperatively to discover geometric shapes constructed from two congruent right triangles obtained from cutting a rectangle along its diagonal. Students report their findings both orally and in writing. (MDH)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Describes a mobile computer lab set up in a converted bus that is used by fourth graders as part of the math curriculum. The program, which emphasizes problem solving and spatial visualization, also addresses gender differences and in-service teacher training. The physical arrangements, including provisions for computer security, are described.…

Described are activities that use a hundred chart to improve student abilities to recognize and describe number patterns, to use variables, to make and informally prove conjectures, and to communicate mathematical ideas to classmates. Included are the directions, four reproducible student sheets, the answers, and extensions. (KR)

Discussed is how the concept of equivalence can relate various segments of a mathematics program and help students develop an appreciation of the unity of mathematics. Activities and examples of equivalence at all grade levels are included. (KR)

Developed is an examination to determine a student's visualization capabilities. This examination has two versions, both developed to measure visualization ability, time to visualize, and reaction time. This test indicates the learner's ability to visualize complex three-dimensional objects from six principal views. Included are the results from a…

Described is a course that offers students the opportunity to learn the graphics language of computers in conjunction with the traditional engineering design graphics concepts. The course objectives, course description, course administration, and advantages to using the dual approach are included. (KR)

A project in which students designed environmentally responsible food packaging is described. The problem definition; research on topics such as waste paper, plastic, metal, glass, incineration, recycling, and consumer preferences; and the presentation design are provided. (KR)

The components of archeological research, including the low and high tech tools employed in its pursuit, are described. Archeology appeals to students because of its sense of mystery and is rich in cross-curricular possibilities. Activities based on the Anasazi people (prehistoric people of southwest United States) are included. (KR)

Presents activities to teach the formula for the area of a rectangle that require students to determine the cost of refurbishing their school's tennis courts. Students collect their own data, organize information, and make decisions individually and as a group to solve the problem. Worksheets are provided. (MDH)

Presents two spreadsheets for middle school students applying Polya's heuristic to help develop number sense, reasoning abilities, and problem-solving skills. Spreadsheet 1, "the coin problem," allows students to vary coin quantities to total $8.32. Spreadsheet 2, "ratios," develops number relationships while finding 3 3-digit…

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)

Presents and discusses assumptions for a general-mathematics problem-solving curriculum that incorporate the belief that all students can do algebra, geometry, and trigonometry, that mathematics must be presented in problem situations, and that students should work cooperatively. Worksheets provide exemplary problem-solving activities. (MDH)