A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

Eight techniques for studying mathematics that can be taught during regular classroom instruction are presented and discussed with illustrations of their classroom use. (MNS)

A variety of tips about problem solving are included, with the focus on helping students recall an image. Manipulative materials and models using grids are included in most of the activities. (MNS)

Students compose original stories that incorporate nonroutine problems which contribute logically to the plot of the story. Examples and suggestions from work with fifth graders and preservice elementary teachers are given. (MNS)

The focus is on the ability to create and relinquish hypotheses in problem solving. Given are activities that illustrate how to stress the importance of producing and evaluating new ideas. A hidden rule game, microcomputer software, and an attribute game are described. (MNS)

Different uses of numbers in natural language and mathematics is argued to have consequences for children's learning of numbers and for primary-grade textbooks. A study using particular properties of Hebrew indicates a crossing of the two language systems in children's reading of an arithmetic textbook. (MNS)

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)

A problem from a course called "Introduction to Gambling" is described. A flowchart and a computer program are included. (MNS)

The contribution to learning that can be made by students' questions is considered. Some questions asked by middle school students and the activities selected by the teacher to answer their questions are presented. Questions involve predicting, judging reasonableness, measuring, finding an average speed, and multiplication. (MNS)

This study addressed the problem of how a prospective mathematics teacher's active engagement in a scientific inquiry can deepen the meaning of her extant mathematical concepts. We used a constructivist framework to analyze a 2-hour interview with a prospective mathematics teacher as she solved an open-ended problem of graphing a 3-D landform. We…

This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

This volume contains the proceedings of the 7th international conference on Adults Learning Mathematics--A Research Forum held in July, 2000 in Massachusetts. It includes posters and short oral reports under these section headings: (1) Research into Practice; (2) Large- Scale Issues: Frameworks, Standards, and Assessment; (3) Theoretical…

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

Can textbook exercises be transformed into problem solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a routine problem from different angles or perspectives. In this process, students…

Current mathematics education emphasizes the importance of a problem solving mindset in the classroom. Students need to know how they are going to use what they are learning in real life. The purpose of this study was to determine the effect of anchored problem solving instruction on middle school students' mathematical abilities. The researcher…