Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Describes a beginning algebra course that places stronger emphasis on learning to solve problems and introduces topics using real world applications. Students learn estimating, graphing, and algebraic algorithms for the purpose of solving problems. Indicates that applications motivate students by appearing to be a more relevant topic as well as…

Discusses solving inequality problems involving linear programing. Describes the usual and alternative approaches. Presents an intuitive approach for finding a feasible solution by maximizing the objective function. (YP)

A Holt, Michigan, high school's recent shift toward conceptual understanding and demonstrated performance inspired one math teacher to develop a panel performance-assessment process. For their midsemester and semester exams, students in algebra II and precalculus discuss before a panel of judges the solutions to complex problems. Panel assessment…

Clapping music for two performers provides the basis for a series of mathematical problems in combinatorics and group theory. A discussion provides insight about how to avoid overlooking global extrema in constrained max-min problems when solving systems of algebraic equations. (JJK)

Mathematics portfolios need not be limited to problem-solving efforts. When California algebra teacher asked students what portfolio contents would show their effort and learning, they suggested daily notes, personal budget and lottery projects, scale drawing, their best and worst tests, weekly problems, daily class notes, and homework. Students…

Describes the experimental intelligent computer algebra system STRAMS which can solve problems using a set of methods and techniques traditionally taught, learn new mathematical problem solving methods, and generate different kinds of explanations. Analyzes these features of STRAMS to give reasons for its potential applicability in building…

This article describes the authors' experiences using clock arithmetic to help students understand key structural properties in algebra, such as identities and inverses. (Contains 10 figures.)

In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

The purpose of this exploratory study was to investigate the impact of writing during mathematical problem solving. The study involved an analysis of ninth grade algebra students' written and verbal descriptions of their mathematical problem solving processes. Through this comparison, a better understanding of the connection between problem…

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

The What Works Clearinghouse (WWC) reviewed interventions to promote middle school students' math knowledge and skills. Because there is some variation in how school districts organize middle school, we considered curricula aimed at students in grades 6 through 9, covering one or more of the following content areas: numbers and operations,…