Students' brains are wired to make them natural, curious learners. The mathematical world around them offers a vast classroom, filled with shapes, spaces, quantities, and experiences to discover and explore, all leading to the construction of understanding. Teachers can use this natural curiosity to tap the inborn neural mechanisms that motivate…

Beginning in 1987, a reform movement was heavily funded by the National Science Foundation (NSF) to change the teaching of calculus. Borough of Manhattan Community College (BMCC) received seven NSF grants over an eight-year period, allowing the college to: establish a state-of-the-art calculus computer lab; purchase calculators, graphing…

Describes five activities using the World Wide Web that teach students to experience searching, locating, and organizing data. Students learn to summarize statistics, analyze data, make conjectures, and communicate information. They interpret or create bar graphs, line graphs, histograms, and circle graphs. (PVD)

Current thinking of researchers from different disciplines about interaction among students in educational settings and the potential of peer interaction for learning and cognitive development is discussed. Topics of the eight papers presented include: potential outcomes of peer interaction, its nature, peer learning settings, and factors shaping…

Presents five activities to help students construct meaning for multiplying fractions through real-world problem contexts, physical or pictorial models, the recognition of patterns, and the use of calculators. In the context of a garden plot, worksheets examine various aspects of parts of plots, patterns in plots, and a maximization problem.…

Reports development and results of the Kramer Project, a two-year study of the implementation of a problem-solving, activity-based mathematics program in the elementary grades. Describes the mathematical content covered, participating teachers, instructional materials employed, inservice teacher training provided, and academic achievement gains of…

Describes 4 activities for levels K-2, 3-5, 4-6, and 6-8 and a family activity that asks students to describe their community; use coordinates to represent the 4 voyages of Columbus; write a story based on a line graph of Lewis and Clark's expedition; determine serving sizes for astronauts in space; and investigate different modes of…

Reports a case study to evaluate whether basic concepts of fractal geometry are teachable to elementary school children and to determine the effectiveness of having an elementary school student present a lesson to inservice and preservice teachers. Concludes that simple concepts of fractal geometry appear appropriate for the elementary school…

Describes the "number 2 arithmetic challenge," an activity in which students score points by creating examples using the number 2 that satisfy an unknown rule. Computers are utilized to verify and record examples. Conflicts with computer responses create situations to explore negative numbers, fractions, mixed numbers, the order of…

Proposes the method of student-generated story problems to supplement textbook problems, generate student interest, and bring real-life situations into the mathematics classroom. Gives steps to initiate the method that incorporates small groups and peer teaching to develop problem-solving and problem-posing abilities. (MDH)

Presents a discussion illustrating student reasoning while using LOGO to draw tilted squares and rectangles. Suggests that teachers recognize that many students use visual imagery to reason and discuss visual reasoning with students. Gives examples of tasks to promote discussion. (MDH)

Presents the results of a survey of 165 seventh grade students asked to respond yes, no, or maybe to 21 metacognitive statements about their cognitive activity on a mathematical word problem. Suggests how to use the responses as a basis for developing classroom activities. (MDH)

Focuses on connections between mathematics and environmental concerns. Activities were designed to make students aware of, and increase their knowledge of, the various materials people ordinarily use and discard and ways to use materials more conservatively. Each activity includes data gathering, graphing, and interpreting data. Activity sheets…

Reports results from a project designed to bring about student conceptual change by using multiple modeling and representation as well as links to other areas. Students developed rules as conveniences and meanings for symbols, were active in learning, made interpretations, and had confidence in their thinking. (MKR)

An exploratory study assessed the degree to which 13- and 14-year olds (n=100) adjusted assumptions of direct proportionality suggested by surface structure of word problems. Virtually no errors were made on "straightforward" items, but many students showed no adjustment for realistic constraints on complex items. (Contains 21…