An activity in which students use manipulative materials to help solve simple algebraic equations using the operations of adding inverses, removing opposites, and sharing equally is presented. Directions, examples, the rationale, and cautions are included. (KR)

Presents sample lab activities in algebra for representing functions in concrete, tabular, graphic, algebraic, and word format. Activities described actively involve students in hands-on models. Problem-solving techniques and technology help to form algebraic-thinking skills. (AIM)

This brochure is part of NAEPFACTS, a new series that briefly summarizes findings from the National Assessment of Educational Progress (NAEP). Course-taking is generally a powerful indicator of mathematics achievement. This occurs partially because students who are more proficient tend to take more mathematics classes and, at the eighth grade, the…

The primary purpose of this study was to evaluate the application of a process approach for the teaching of algebra with a heterogeneous class of eighth-grade students. The assessment was conducted by identifying the processes used by above-average, average, and below-average algebra students in solving standard and nonstandard problems ranging…

This paper argues that operations with negative numbers should be taught using a curriculum that is grounded in algebraic geometry. This position is supported by the results from a study that compared the conceptual understanding of grade 9 students who received the Algebra Project transition curriculum to a control group of grade 6 gifted…

This paper presents two examples in which technology, in this case a fairly sophisticated authoring system--ToolBook, was used as a tool to construct student understandings in mathematics. In doing so, students were able: (1) to successfully identify the variables (unknowns) and the information given (data) in the problem; and (2) to create…

This paper discusses the role of the culture in secondary mathematics education. A historical and philosophical look at the relationship between the real world and mathematics and mathematics education is developed. The U.S. secondary mathematics curriculum is explored both historically and philosophically to try to ascertain its changing…

This report is incorporated into "Attaining Excellence: A TIMSS Resource Kit." Released in Fall 1997, the TIMSS resource kit was developed for educators and those interested in using TIMSS data to improve teaching, curricula, and student achievement in state and local communities. This module presents information about the grade 8…

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…

Presents two activities created by preservice middle school teachers that integrate technology and real-life mathematics in algebra. (MKR)

Describes how using spreadsheets helped seventh grade algebra students develop problem-solving skills. Topics include the functional dualism of the spreadsheet as a text, uniting enactive and numeric modeling of word problems, new meanings and reciprocal learning, learning through problem "posing," higher levels of thinking, and decreasing…

Middle school prealgebra students (n=157) learned about functions in a 20-day unit that emphasized: (1) representing problems in multiple formats, (2) anchoring learning in a meaningful thematic context, and (3) discussing problem-solving processes in cooperative groups. They produced smaller pretest-to-posttest gains on symbol manipulation tasks,…

Presents 14 problems organized into three levels of difficulty. Topics include algebra, pattern identification, probability, and geometry. Includes solutions to the problems. (DDR)

Theoretical tools from cognitive science were used to put together a framework for a fine-grained theory of how students learn elementary algebra in the classroom. Developing the framework included assessing the shortcomings of current models, evaluating whether unified theories of cognition can be adapted for learning mathematics in the…