This article describes one teacher's efforts at creating a differentiated mathematics program in her multi-age first- and second-grade classroom. The author describes challenges encountered and successes met in this process, as well as the structures she uses to meet a variety of student abilities, including open-ended problem-solving tasks,…

Theories that explain the gender discrepancy in mathematics almost universally explain why boys are "better at math" than girls while failing to adequately account for girls' higher grades in math classes or better performances on tests of computational ability. This article develops a new, more comprehensive theoretical model that explains girls'…

An account is given of the importance and role of trust in motivating teachers to understand students and develop instructional approaches. Three examples of student actions, teacher learning, and instructional change that resulted from understanding students' goals are presented, as well as guidelines for teacher reflection. (Contains 3 figures.)

Play, particularly children's sociodramatic play, is the cornerstone of early childhood classrooms in the United States. Early childhood educators learn and expound mantras of "the value of play," "play-based programs," "children learning through play," and "play as child's work." They strive to promote the importance of making a place for play in…

A century ago, John Dewey proposed educating children through a curriculum rich in real-life problem-solving experiences. While many traditional schools have been slow to adopt such methods, experiential learning is making a significant impact in alternative education, youth development, and treatment settings. Challenge and adventure activities…

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

This article discusses ways to integrate reading into mathematics using environmental print or real-time text. (Contains 2 tables and 4 figures.)

We present an approach of defining certain transcendental functions as solutions to initial value problems or systems of such problems. This material is suitable for use in a second-semester one-variable calculus course.

As the topic of relativity is developed in a first-year physics class, there seems to be a tendency to move as quickly as possible to the fascinating ideas set forth in Einstein's special theory of relativity. In this paper we linger a little with the Galilean side of relativity and discuss an intriguing problem and its solution to illustrate a…

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…

A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the…

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying…

The author builds on arguments he has made elsewhere that good commercial video games foster deep learning and problem solving and that such games in fact promote mastery as a form of play. Here he maintains that some good video games engage players with an important type of play, namely of play as discovery, of play as surmising new possibilities…

Just as comprehension strategies have helped millions of students learn to read like proficient readers, they can also help students think like effective test-takers. The authors show how students can use background knowledge, mental images, synthesizing, monitoring, inferring, questioning, and determining of importance to understand the genre of…