The project consisted of three related series of studies, designed to (a) determine some of the underlying competencies that contribute to experts' successful problem solving performance in college level mathematics, (b) to determine what productive behaviors students lack, or what counterproductive behaviors they have, that keep them from being…

This study reports an investigation of the way in which distance students use course materials and plan their work in order to complete mathematics exercises. Two undergraduate students of mathematics and one graduate student were asked to complete a course exercise using standard course materials under distance studying conditions. They…

This report discusses how a computer was used to enhance the curriculum of a college calculus course. Problems with a calculus adjunct course in computer science are detailed, along with the nature of changes in the new program. The changes moved from student use of the computer as an automatic typewriter to use as a tool with instructional…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

NINETY FIRST GRADE CHILDREN WERE RANDOMLY SELECTED FROM 3 SCHOOLS (WHICH EACH USED A DIFFERENT ARITHMETIC PROGRAM) TO PARTICIPATE IN A STUDY TO INVESTIGATE THE EFFECTS OF 2 VARIABLES ON THE CHILDREN'S ABILITY TO SOLVE ADDITION PROBLEMS. THE VARIABLES WERE (1) THE PRESENCE OR ABSENCE OF AN EXISTENTIAL QUANTIFIER PRECEDING THE START OF THE PROBLEM,…

This student discussion guide is intended to accompany "Explorations in Mathematics," a text for teachers. The materials in this booklet relate mainly to variables, graphs, signed numbers, logic, identities, functions and matrices. The materials were designed to be used as supplementary materials with students in grades 5 through 9. (RP)

This report presents a more detailed elaboration and discussion of the mathematical content of the central concepts which have been designated as the Mathematical Strands of the Mathematics Curriculum for grades K-8. In Part I of the report there is a discussion of the pedagogical philosophy which the committee felt was to have an importance equal…

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

Hands-on mathematical activities are described for use with tricycles, Big Wheels, single-, and multigeared bicycles. (JT)

What are often missing for children in classroom instruction are experiences with numbers that stretch beyond computation skills and word problems. This lesson models such an experience for third graders. Students use small boxes of raisins in several problem-solving activities. Children apply whole number operations, estimate, consider…

Data were collected in the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems. The children were interviewed three times during the school year. The influence of problem structure on children's solution strategies appears more extensive and decisive than that…

RIDGES is a mnemonic device designed to give upper elementary and high school students a structure to follow when solving word problems. RIDGES stands for Read the problem; I know statement; Draw a picture; Goal statement; Equation development; and Solve the equation. (VW)

Cryptarithm puzzles are explained and discussed. Examples are provided and reproducible student worksheets are included. (PK)

An application of functions and their inverses is described--the coding and decoding of messages, or cryptographs. The helpfulness of computers is noted, with two programs listed. (MNS)

The regression effect is discussed, with examples from tests and from data on heights. Several problems to use in teaching about regression are included. (MNS)