Two units are developed that provide the student with experience in constructing auxilary lines that are often needed in formulating geometric proofs. (MP)

The problem-solving processes of seven upper-division college students working a series of problems that could be solved by the application of one or more heuristics are described in detail. (MP)

Three approaches to the same geometrical problem are presented to demonstrate the role of intuition in mathematics and to clarify the concept of insight. (MP)

A programed unit on triangle constructions using an information processing prescriptive model was compared to a traditional model. The experimental group scored significantly higher on a retention test. (MP)

A technique is given for solving problems involving a balance scale and a number of coins which are to be sorted in a certain number of weighings. (MP)

The results of an analysis of incorrect strategies used by students in solving mathematical problems are reported and explanations offered. (MP)

Investigates the extent to which children's number sense and novel problem-solving skills govern their problem-posing abilities in routine and nonroutine situations. Children who participated in the program appeared to show substantial developments in each of the program components in contrast to those who did not participate. Contains 66…

When permitted, children frequently devise approaches to solving problems that are distinct from those typically used by adults. Presents examples of children's thinking from Project IMPACT which illustrate the crucial interplay between a teacher's instructional decisions and children's thinking while confronting mathematical misconceptions.…

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)

Instead of teaching his fifth-graders a formula, a teacher leads them to discover an important mathematical concept on their own. Learning through discovery is probably the very essence of meaningful understanding and retention. (Author/MLF)

Presents a series of questions designed to help convince students that mathematics is useful, current, and newsworthy through solving systems of linear equations in real world contexts. (KHR)

Replies to Hiebert et al. (1996), who proposed that curriculum and instruction be guided by the basic principle that students problematize their subjects, arguing against the notion of problematizing mathematics. Considers the nature and range of mathematical content pursued in classrooms and the related question of student participation and…

Describes an experimental approach to determining the speed of light in water using some simple observations and Fermat's principle. Enables students to integrate mathematical techniques and encourages mathematical exploration in which the students have control over what mathematics and technology to use and when to use them. Presents extensions…

Endorses the projects approach to learning as helping students acquire contextual, personal knowledge rather than learning only isolated bits of content information. Describes the five-step process for doing projects which includes productive thinking or generating ideas, the planning or organizing of ideas, decision making, communication or…