Before judging a student's diagram correct or incorrect, the mental associations made by the student between his diagram and the problem should be known. This is a follow-up to the author's article in the November 1970, Arithmetic Teacher." (RS)

A programing language called DYNAMO, developed especially for writing simulation models, is promoted. Details of six, self-teaching curriculum packages recently developed for simulation-oriented instruction are provided. (MP)

This study illustrates a process for selecting a preferred model in the validation of hierarchical learning scales. The test performance of 100 8-to 11-year-old children on subtraction tasks involving variations in borrowing are examined. Goodman's response scaling technique is illustrated. (Author/GDC)

Discusses some mathematical games concerning the packing of squares. (HM)

Reports on the results of a project that involved experienced K-12 teachers in mathematical modeling, using variables and functions in a fundamental and intuitive context, while investigating the appropriateness of spreadsheet solution methods across a broad range of grade levels. (14 references) (LZ)

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

Discusses diagrams and problem solvers' constructions of a problem situation, how the way of drawing changes during the problem-solving process, and the meaning and sense of diagrams. (Contains 15 references.) (MKR)

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…

In administrative inquiry, the scientific tradition is utilized less frequently than the humanistic tradition. Such imbalance in perspectives may be a cause of the acknowledged poverty of the knowledge base. Departments of educational administration should encourage the existence of proponents of both perspectives within their ranks. (Author/WM)

This study investigated the problem representations formed by college students while solving mathematics problems. Problem representation characteristics indicative of understanding were identified by analyzing audio-tapes and written work of sixteen subjects, ages 16 to 24, who solved mathematics problems using the think-aloud technique. These…

Five methods are given for computing the area of a regular octahedron. It is suggested that students first construct an octahedron as this will aid in space visualization. Six further extensions are left for the reader to try. (LS)

The advantages of the Delphi Technique are that it relies on collective expert judgment, prevents the excessive influence in decision-making of those in positions of status, and encourages consensus. The technique consists of five steps: (1) asking experts to list items relevant to a topic; (2) returning the list to the participants and asking…