Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Describes a process for creating a more diverse set of experiences for undergraduate students in mathematics by focusing on linear algebra. Emphasizes that the diversity of the activities is generated in part through the use of a taxonomy that addresses the nature of the activities rather than a hierarchy of levels of difficulty. Contains 13…

In standard mathematical notation it is common to have a given symbol take on different meanings in different settings. Shares anecdotes of how this symbolic double entendre causes difficulties for students. Suggests ways in which instructors can clarify these ambiguities to make mathematics more understandable to students. (Author/ASK)

Presents four related problems that provide examples of ways to include justifications of interesting mathematics in courses taught prior to a geometry course. (ASK)

Examines the status of Broward County (Florida) Public Schools high school students, who must satisfy the district's algebra requirement in order to graduate. Data indicate that the majority of district students are meeting the new, higher standards; 80% of seniors in school year 1998-99 had previously completed the algebra requirement. (MLH)

Investigates secondary mathematics teachers' use of the graphing calculator in their classrooms. Examines whether algebra teachers are currently using this technology in their classrooms, their perceptions toward the technology, and any changes in the curriculum or instructional practices. Indicates that the use of the graphing calculator is still…

Describes investigative choices made and strategies used by students to solve problems in classrooms that provided access to a computer algebra system (CAS). Reports that technology-neutral mathematics questions were attempted by approximately equal numbers of students using CAS and traditional paper and pencil. Reveals that students who used the…

Produces algebraic solutions by reducing the problems to equations and arithmetic solutions that do not use variables. Investigates how the arithmetic solution helps students better understand the problem before they approach it algebraically and how logic used in solving the problem arithmetically can be directly linked to the algebraic…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Reports the results of research conducted to investigate the relationship between involvement in learning mathematics and achievement as measured by test scores and course grades. Finds that attendance is the one measure of effort most closely related to success in developmental mathematics. Indicates that academic autonomy was consistently…

Presents the story of a mathematics teacher's transformation that resulted from her engagement in collaborative action research. Discusses issues related to the broader study of collaborative action research in the mathematics classroom that are connected to teachers' transformation. (Contains 31 references.) (Author/ASK)

To allow variable amounts of time for students to complete Algebra I, a gateway course, schools must address four issues: curriculum, instructional methods, assessment, and scheduling. The Algebra I curriculum should be divided into four parts; assessments should be designed to measure students' mastery of each part. Also, a two-period block of…

Describes an approach to algebraic thinking based on an extension of the problem-solving tasks typically investigated by elementary and middle school students. Demonstrates how elements of algebraic thinking may be developed in a systematic and coherent way through problem-solving experiences. States that students' pattern-building capabilities…

Describes an experiment using applications and projects to motivate students in college algebra. Provides a few illustrative examples of the applications/projects used and shares some student comments. (Author/ASK)

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)