We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Second and third graders from six Dutch elementary schools (N = 168) solved two sets of almost identical addition and subtraction sums at a two-week interval. Inconsistency in strategies, which characterized half the subjects, was related to unfamiliar sums and resulted in misinterpreted errors. (TJH)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

Mathematics 30 is a 12th-grade mathematics course for students in Alberta, Canada. This document is the final test for the course. Intended for administration during June 1989, it contains 45 multiple-choice questions, 7 open-ended machine scorable questions, and 3 written-response questions. Two-and-one-half hours are allowed for completing the…

This report attempts to discover how students think about and use mathematics in open-ended questions. Part I, "Open-ended Questions in Mathematics," describes the rationale for adding open-ended questions to the grade 12 mathematics test of the California Assessment Program (CAP). Part II describes the findings from students' responses…

Investigates the development of concepts and processes associated with computational estimation. Twelve students at each of grades three, five, seven, and nine were interviewed. The older children understood better than the younger children what was asked but were uncomfortable with estimation processes and outcomes. (Author/YP)