The foreknowledge that a given school mathematics problem might have no specific solution or no solution at all affords students the challenge of investing careful consideration in the explicit problem conditions, as well as in the problem's unstated assumptions. Hence, the implication is that mathematics teachers, rather than speaking to their…

Prior to college-level mathematics coursework, students are not routinely provided with the opportunity to engage in the kind of sustained mathematical thinking necessary to solve complex, multistep problems, most likely because of the difficulties that school mathematics teachers face in communicating problem settings and contexts that are…

Teachers of mathematics are leading a nationwide effort to bring about a complete redesign of both school and college mathematics programs by setting new and more demanding standards for what students must learn about mathematics, as well as for what teachers themselves must accomplish as professionals in the classroom. This brief document is…

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

This monograph is the first in a series of three dealing with the curriculum and evaluation standards for grades K-4 as promulgated by the National Council of Teachers of Mathematics (NCTM). The publication of the standards marks a new guidepost in the evolution of mathematics education and signals the impact of the information society upon all…

This monograph is the second in a series of three dealing with the curriculum and evaluation standards for grades K-4 as promulgated by the National Council of Teachers of Mathematics (NCTM). The publication of the standards marks a new guidepost in the evolution of mathematics education and signals the impact of the information society upon all…

This monograph is the third in a series of three dealing with the curriculum and evaluation standards for grades K-4 as promulgated by the National Council of Teachers of Mathematics (NCTM). The publication of the standards marks a new guidepost in the evolution of mathematics education and signals the impact of the information society upon all…

The projection of shadows task developed by Inhelder and Piaget was used to identify error patterns and solution strategies used by diverse populations in a sequence of proportion tasks. In Study A, two group tests were administered to 607 students from science and mathematics classes in grades 9 and 10. A sub-sample of 69 students was involved in…

This second volume of a review prepared for the Cockcroft Committee of Inquiry into the Teaching of Mathematics in Schools in Great Britain reflects a sociological research basis in which neither mathematics nor mathematics teaching is the essential focus. Rather, as the introduction indicates, the concern is with the constraints (institutional…

This study investigated: (1) the relationship between the development of information processing capacity and certain Piagetian logical reasoning abilities; and (2) how the development of these cognitive abilities related to acquisition of certain measurement concepts. Forty first-grade children were individually administered tests of conservation…

One of a series of activity guides designed to aid teachers in developing the thinking skills of intermediate grade students, this publication offers a variety of learning activities and resource materials. The activities and resources include: a calendar which lists important days and birthdays in September, October, and November; poems; word…

One of a series of activity guides designed to aid teachers in developing the thinking skills of intermediate grade students, this publication offers a variety of learning activities and resource materials. The activities and resources include: a calendar which lists important days and birthdays in March, April, and May; poems; word puzzles and…

This teacher's guide is the ninth in a set of 20 activity booklets for teaching mathematics to children in grades 1-8. The 20-level curriculum embodies carefully delineated areas of learning arranged in progressive stages, eliminating grade restrictions and permitting continuous growth according to the individual's ability and rate of learning.…

The materials in this publication were originally prepared for a set of conferences on Equity in Mathematics, organized by the National Council of Teachers of Mathematics with funding from the National Science Foundation. It is suggested that these materials may assist supervisors, teacher trainers, administrators, and teachers to design and…

These instructional materials were produced as part of the project, Developing Computational Estimation Materials for the Middle Grades. The introduction to these seventh grade materials covers the following: why teach estimation; how the materials were developed; and how the lessons are organized. The 15 lessons that follow are designed to teach…