misalignment related to constraints in the environment. For example, in a school in which student progress is solely measured by low-level, multiple-choice standardized tests, teachers’ practices might not reflect their beliefs that students’ conceptual

### Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa

### Louis J. Chatterley

A university mathematics department plans and tests a precalculus course.

### Patrick W. Thompson

Twenty fourth-grade children were matched according to performance on a whole-number calculation and concepts pretest and assigned at random to one of two groups: wooden base-ten blocks and computerized microworld. Instruction in each group was designed to orient students toward relationships between notation and meaning. Instruction given the two groups was based upon a single script that extended whole number numeration to decimal numeration, and emphasized solving problems in concrete settings while inventing notational schemes to represent steps in solutions. Neither group changed in regard to whole-number notational methods. Blocks children understood decimal numerals as if they were funny whole numbers; Microworld children attempted to give meaning to decimal notational methods, but were largely in a state of disequilibrium at the end of the study.

## A Design with Disks

### little problems with big solutions

### Pamela J. Wells and Annie Perkins

To elicit creative student thinking, this open-ended problem asks solvers to create shapes that have certain constraints.

### Edited by Annie Perkins and Pamela J. Wells

Each problem asks you to create shapes that meet certain constraints and to compare the shapes you made.

### Ralph E. Mahan, James K. Bidwell, Jan McDonald, Dennis J. Riordan and Judy Freier

We welcome letters from readers, and will publish them to the best of our ability within the constraints necessarily placed upon us.

### John C. Scheding and Walter J. Sanders

We welcome letters from readers, and will publish them to the best of our abillity with in the constraints necessarily placed upon us.

### Joseph A. Troccolo

Given a box of squares and a box of triangles. you are to build convex polyhedrons. With the constraints, how many polyhedra are possible and how are they constructed?

### J. Louis Tylee

For beginning calculus courses, it is often helpful to have real-world applications that use derivatives. This article presents two such applications related to computing the distance required to stop an airplane. This problem is important because this distance must be within the constraints of the runways where an airplane might land.

### Nadine L. Verderber

Teachers of elementary calculus are familiar with problems requiring their students to maximize or minimize certain quantities subject to certain constraints, Representative of these problems is the problem of minimizing the surface area of a tin can that has a fixed volume. A noncalculus approach using a program written in BASIC has previously appeared in this journal (Inman and Clyde 1981).