By highlighting the curriculum modifications that lead to maintaining, or enhancing, the mathematical quality of an algebra lesson introducing the substitution method for solving systems of equations from an algebra textbook, we present an analysis of how a teacher and her students impact how the mathematical ideas unfold across the lesson and how…

This paper describes "The Migration Method," a new technique for graphing a quadratic function (one of the major foundations of undergraduate mathematics) and finding its zeroes. The method promotes a higher degree of conceptualization, reinforces the concept of symmetry, encourages mental visualization, and strengthens the ability to…

Reports a case study set in the context of a "function" curriculum approach to introductory algebra. The expectation that the teacher's actions would reflect the philosophy implied in the curriculum was not supported. The teacher gave priority to curriculum content coverage, emphasized methods and procedures, and adopted teacher-focused…

Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

A sequence for teaching quadratic equations is presented. Considered are: multiplying arithmetic binomials, multiplying algebraic polynomials, reversing the process, missing terms, perfect squares, other special forms and diagrams, quadratic equations, completing the square, systematizing the process, the general form, graphing equations, and…

Discusses the relevance of teaching algebra to all students. Issues examined include the desperate need for reform in the algebra curriculum, developing a curriculum for a broad range of people, and rethinking how mathematics courses are structured and taught. Concludes that teaching algebra to students previously unsuccessful in mathematics will…

This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials…

Discusses representations in the context of solving a system of linear equations. Views representations (concrete, tables, graphs, algebraic, matrices) from perspectives of understanding, technology, generalization, exact versus approximate solution, and learning style. (KHR)

This report investigates recent tenth-grade algebra achievement, after first suggesting there are good reasons for maintaining algebra in the syllabuses for grades nine and ten. Results indicate the students studied have mastered such algebraic skills as "collecting like terms" and "substitution in formulae." It is noted that…

Examples are provided which demonstrate the use of the computer as an instructional aid for the algebra curriculum. While the basic content of an algebra course would remain intact, computer technology can enhance and expand methods of algebra instruction. (JN)

Discussed are the rationale for, and the benefits accrued from, the use of graphing calculators within all aspects of the secondary mathematics curriculum. Examples are included that highlight specific features of graphing calculators. (JJK)

The development of the new mathematics curriculum of the late 1950s is examined in light of current calls for changes in the instructional program. Thoughtful, imaginative reform that offers radically new models of approach to teaching mathematics is called for. (MP)

The aim of this unit is to assist teachers in the presentation of integers and the combining of like terms in algebra in a more interesting and meaningful way. This program was developed for use in mathematics classes, grades 7-12. The unit is a descriptive module on the teaching of integers using bingo chips to develop a concrete approach to…

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)