This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

This study looked at student difficulties with fractions by focusing on understanding of part/whole relationships. The sample consisted of two sixth-grade and two eighth-grade classes. A lack of substantial improvement from sixth to eighth grade on many fraction tasks was noted and viewed as cause for concern. (MP)

This study investigated whether there was a difference in achievement by first graders between their ability to solve open sentences presented in vertical form and in horizontal form. It was recommended that the horizontal form be avoided in grades one and two. (MP)

Instructional techniques are given for the use of calculators in (1) finding prime numbers, (2) solving trigonometric equations, and (3) solving polynomial equations. (CP)

Presents 12 problems for students to investigate the relationships involving properties of numbers by using BASIC language. (YP)

Gifted students attending a week's summer mathematics program completed problems involving elementary number theory ideas and extensions. The sequence of these problems and strategies used are presented to help teachers looking for topics to enrich the mathematical experiences of students in middle grades or older. (JN)

Presents activities utilized with primary teachers to alleviate instructional concerns about using calculators and provide reasons for using calculators in their mathematics instruction. Activities address the topics of estimation, number sense, numeration, whole number and fraction operations, probability, and problem solving. (MDH)

Presents results of 46 randomly selected children's performance measurement and partitive division problems when remainders are zero, nonzero but not used in the solution, and nonzero and used in the solution. Results indicate that children demonstrate an understanding of division prior to formal instruction. (MDH)