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Fractions and algebra are critically important components of the mathematics education of the youth. Unfortunately, however, students have typically struggled in these areas. For this reason, teachers and researchers have focused their attention on these topics for at least the past century. This article discusses what research shows regarding fractions and algebra, particularly, on issues related to when fractions should be taught, how fractions should be taught, and how competence with fractions affects the transition from arithmetic to algebra will be considered. Suggestions for teacher practice are included throughout the article.

Pattern recognition is a critical component of success in mathematics. Students at all levels should be provided with opportunities to investigate and uncover patterns throughout their mathematical careers. Further, they should be allowed to explore situations in which pattern recognition plays a vital role in the construction of important mathematical knowledge. This article will discuss a lesson that introduces arithmetic sequences through a simple, yet rich exploration of a pattern. This lesson has been taught in a methods course for secondary mathematics teachers to provide them with a model of a constructivist lesson that they will be able to implement in their own classrooms when they begin teaching. It is, also, beneficial to this group as it affords them an opportunity to participate in a cooperative learning activity that lends itself to a wide variety of solution methods. (Contains 4 figures.)

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

Investigated the effects of mathematics methods courses that used manipulatives, technology, and cooperative learning on preservice mathematics teachers' meaningful mathematical content knowledge and attitudes toward mathematics. Pre- and postintervention student teacher surveys indicated that there were significant increases in content knowledge and improvements in attitudes for preservice elementary teachers and insignificant increases for secondary teachers. (SM)

Finds that an elementary mathematics-methods course provided preservice teachers with important knowledge and experience concerning the use of manipulatives. Notes that the preservice teachers learned mathematical content through the use of manipulatives in the course, and that they were concerned that difficulties might impede their ability to use manipulatives. (SR)

The article presents an analysis of students' difficulty with fractions using a twenty-five-question test of concept knowledge and computational fluency. The error analysis revealed that most of the students have a fragmented understanding of fraction concepts and operations and opted to use algorithm in test items that could be solved by applying a concept. The time for fractions spent before grade 6 should be devoted to develop a conceptual base of fraction relationships.

This article explores the concept of expected value within the context of a gambling proposition known as Royal Match wagering. Royal Match wagering allows the better to win money when dealt cards of the same suit. The game is named for the hand yielding the maximum payoff, a king and queen of the same suit. Specifically, this article: (a) explains the rules of this game; (b) calculates its expected value using a standard deck of cards; (c) investigates the effects of various deck compositions on the expected value; (d) considers implications for bettors; and (e) discusses advantages of using Royal Match to teach expected value. [ABSTRACT FROM PUBLISHER]