The role of writing in the mathematics classroom is considered. Writing as a cognitive process and its relationship to problem solving is first examined. Then several long- and short-term techniques for promoting cognitive learning using writing in the mathematics classroom are considered. The Writing Across the Curriculum (WAC) program is…

The mathematics curriculum in the first 2 years of college is a tool created to assist in solving problems. The current mathematics curriculum has changed little; the same topics, tied to the engineering and science curriculum, are taught as they were being taught in 1945. The problems that students need to solve have changed however. Both the…

This paper, which addresses the issue of representation as an internal construct corresponding to an external abstract configuration, attempts to extend A. A. DiSessa's phenomenological primitives to mathematics (particularly to the notion of circle). Various acceptations of the word representation are examined, using the notion of a circle as an…

The purpose of the study was to survey self-regulation while responding to the addition facts. First graders' performance on microcomputer practice exercises was observed and recorded. Subjects could choose an analytic mode of operation using a symbolic or a finger strategy; or, they could choose a geometric mode of operation using a pictorial or…

Two methods for solving problems are presented, designed to help people overcome difficulties that often occur in the problem-solving process. One difficulty people have is in using their knowledge to reach the decisive solution idea. The proposed "method of description" for eliminating this difficulty is based on a directed enrichment of the…

Presents the pro and con of the use of calculators in the classroom. Some feel that calculators make learning mathematics more fun and when used for creative problem solving provide student motivation. Others feel that dependence on the calculators will result in students unable to do simple mathematics on paper. (GS)

The behavioristic approach to education is appropriate only to areas of skill development. To design mathematics curricula from the point of view of behaviorism is to miss the essence of mathematics as a discipline. Mathematics curricula should include strong emphasis on problem solving. (SD)

This research involved the observation and audio-recording of 30 ninth-grade mathematics students recommended as being outstanding by their mathematics teachers. Each student was presented with five different problem situations for which he or she was to make mathematical conjectures. During the interview, the students thought aloud and all of…

Computer coaching of students as an aid in problem-solving instruction is discussed. This report describes an advanced form of computer-assisted instruction that must not only present the material to be taught, but also analyze the student's responses. The program must decide whether to intervene and how much to say to a pupil based on its…

Sixteen investigations using 32 third graders, 286 fourth graders, 183 fifth graders, and 343 sixth graders, were undertaken to determine table-using proficiencies. The data indicate that: (1) upper elementary students are able to retrieve information accurately and quickly from noncomplex numerical tables over a wide range of levels of tabular…

The development of three problem-solving modules is described and the formative evaluation activities for each module reported. The modules were: (1) Using Guesses to Solve Problems; (2) Using Tables to Solve Problems; and (3) Organizing Lists. Each module consists of a student booklet and a problem deck. Each contains problems coded for…

This appendix to the Mathematical Problem Solving Project "Module Development and Formative Evaluation" contains trials 1 and 2 of the Organizing Lists quiz. Editorial feedback from teachers on the Organizing Lists booklet is given for trials 1 and 2. Editorial feedback from teachers on the Organizing Lists problem deck is given for…

This teaching guide presents six lessons on using tables to solve problems. For each lesson, the guide gives the purpose, the rationales, materials, and detailed teaching procedures. The six lessons involve making a table, completing a table, using tables to solve problems (lessons 3 and 4), reading tables, and solving problems. Each lesson opens…

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…