Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

In this study I examined 19 preservice secondary mathematics teachers' solution processes to word problems for which the subtraction or addition of the two given numbers yields 1 more or 1 less than the correct solution. Among the aspects of their solution processes that were examined are: the modeling strategies, the type of errors, and the…

This book is intended as a demonstration that a variety of interesting problems suitable for use in the school mathematics experience of everyperson can be fabricated from available sources. It is intended to be illustrative rather than exhaustive. The problems in the book are intended to be accessible to children by the middle school years. The…

Describes a credit-card-debt activity that allows students to increase their awareness of underlying mathematical concepts relevant to the world of commerce and personal finance through learning geometric and arithmetic sequences. (KHR)

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

An empirical study was conducted in order to obtain treatment effect estimates with the Special Regression model for groups in which there was no treatment. General mathematics test scores were obtained from 730 ninth graders in city schools somewhat similar to Title I schools, but in which no special treatments were given. Hypothetical…