Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based…

Forty 4th and 9th grade students participated individually in tutorial interviews centered on a problem-solving activity designed for learning basic algebra mechanics through diagrammatic modeling of an engaging narrative about a buccaneering giant burying and unearthing her treasure on a desert island. Participants were randomly assigned to…

A key learning outcome in problem-solving domains is the development of flexible knowledge, where learners know multiple strategies and adaptively choose efficient strategies. Two interventions hypothesized to improve flexibility in problem solving were experimentally evaluated: prompts to discover multiple strategies and direct instruction on…

"Principles and Standards for School Mathematics" (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaning-making through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. In this article, the author…

To discover a generalization from a pattern of data, students need to know how to analyze the data. This is a description of how high school students can find a formula to predict the number of spherical fruits in a piling by using differences. (JP)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

Presented are three methods to enrich the mathematics classroom. The first introduces an activity allowing students to discover the law of sines. The second gives eight distance-rate-time problems of value for their counterintuitive or elegant solutions. The third poses multiple answer questions that promote student interaction and communication.…

Presented is a teacher's guide for a hands-on activity challenging students to develop problem-solving behaviors by exploring the construction of a right-cylinder of maximum volume from an m x n sheet of metal. Reproducible worksheets leading students through the activity are provided. (MDH)

Presents activities which highlight major concepts of linear programming. Demonstrates how technology allows students to solve linear programming problems using exploration prior to learning algorithmic methods. (DDR)

College algebra is currently being taught using graphing calculators such as the TI-81. This document presents exploratory and problem solving activities that have resulted from classroom experiences with the TI-81. The activities have been designed to enhance the learning of some standard college algebra topics through the easy access to…

Utilizes LOGO to teach the concept of inequalities by programing the turtle to take random walks in the coordinate plane restricted to predetermined regions defined by inequalities. The students task is to discover the inequalities that define the illegal areas into which the turtle must not move. Provides examples and corresponding computer…

Described is a study that used LOGO to improve the proportional reasoning ability of students enrolled in mathematics classes for students poorly prepared for college-level mathematics. Included are the methodology, procedures for using logo, and a discussion of the results. (KR)

The International Group for the Psychology of Mathematics Education (IGPME) was founded in 1976 at the Third International Congress for Mathematics Education, to promote international contacts and the exchange of scientific information in the psychology of mathematical education. The goal was to further a deeper and more correct understanding of…