Presents an activity for demonstrating the area of five geometric figures--the square, the rectangle, the parallelogram, the triangle, and the trapezoid--that is based on a simple tangram puzzle. Suggests ways in which this activity can be used at several different levels. (ASK)

Devised a model that hypothesized that students, in discriminating relevant information in mathematical story problems, search for values of semantic categories that match those in the problem. Two experiments assessed the validity of the model. Results indicated that the model was an accurate predictor of discrimination performance for successful…

This paper describes first-year results of a project in Cleveland (Ohio) that was funded by the National Science Foundation. Cleveland's Problem Solving Infusion Program (PSIP) was designed to help teachers implement new mathematics standards and to empower them to make curricular decisions. In particular, the study examined whether urban teachers…

A study examined the effectiveness of the Title 1 Middle School Summer program that provided students at two middle schools in the Columbus, Ohio public school district with background experiences to help them connect learning to living. Mathematics and literacy lessons were developed around travel experiences to museums, zoos, baseball games, Sea…

It is known from many international studies that Japanese students do well in mathematics. This paper describes a typical lesson from a Japanese fifth-grade classroom, and discusses the lesson in terms of problem solving, including: embedding of the problem, spending 35 minutes or more on one problem, acting out the problem, multiple solutions,…

Items in the North Central Regional Educational Laboratory's (NCREL) School Development Library series are multimedia packages consisting of print, video, and CD-ROM resources designed to support educators in their efforts to improve classroom instruction. This particular set consists of a 40-minute video and a printed booklet focusing on Dwight…

This investigation is part of an ongoing, larger study which is looking at joint activity and appropriation of new understandings in an inquiry mathematics classroom setting. Instances of help-seeking which occurred while children were endeavoring to solve non-routine problems at home were analyzed. Considered in this study were (1) the kind of…

This pilot study examined the form or nature of the more highly organized knowledge structures used by successful problem solvers and whether there are experiences that would encourage their development. Previous related research and a theoretical framework are discussed. The small-group problem solving mode was used, with "A Problem with…

This document contains teaching modules based on 20 objectives in grade 5 mathematics. The modules may be used for program evaluation and curricular planning as well as detailed outlines for classroom activities. Each module has eight section: (1) "Objective"; (2) "Explanation of Objective"; (3) "Prerequisite Skills";…

The purpose of this study--which was a part of the Flexible Learning Environment project at the University School of Nova University in Florida--was to determine if there was a difference in learning to solve mathematics word problems between groups using computer assisted instruction and groups taught by teachers. Fifth-grade students (N=31) were…

This study examines in detail a sample of widely used teacher guides in order to describe a picture of instruction as it is represented in these guides and to compare it with classroom practices. Mathematics and social studies were selected as the subject areas because of observed differences in classroom practices. Six questions guided the…

A nonequivalent control group design study, with a math unit on ratio and proportion as the treatment, was conducted to examine the validity of some written tasks as a measure of formal reasoning. Subjects in the study were 68 fifth grade students who enrolled in two classes in a small urban school. The experimental group learned a 12-lesson math…

This document is the answer key for level 4 of the teacher-developed mathematics curriculum for New York City schools. Approximately 235 performance objectives are listed, with reference to the appropriate worksheet(s) for each. The answers are typed in the appropriate space on each sheet; when varied answers are possible, this is noted. (MNS)

This document is the answer key for level 5 of the teacher-developed mathematics curriculum for New York City schools. Over 250 performance objectives are listed, with reference to the appropriate worksheet(s) for each. The answers are typed in the appropriate space on each sheet; when varied answers are possible, this is noted. (MNS)

This paper describes a research and development project in teaching designed to examine whether and how it might be possible to bring the meaning of knowing mathematics in school closer to what it means to know mathematics within the descipline by deliberately altering the roles and responsibilities of teacher and students in classroom discourse.…