Presents a mathematics problem that provoked an excellent classroom discussion concerning the nature of numbers and their relationships. (MKR)

This study investigated differences in achievement for control groups learning college algebra using traditional classroom instruction methods compared to experimental groups using computer algebra tutorials for three precalculus topics. Two instructors each taught one control group and one experimental group. No significant differences were…

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Explores alternative strategies to solve algebraic equations that do not lend themselves to traditional methods. Examines one nontraditional equation by a graphical approach using a graphing utility and by a numerical approach using spreadsheets. Discusses new basic skills for algebra utilizing technology. Provides a computer program to solve…

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

Clarifies the benefits of having students write about their understanding and dispositions toward mathematics. Discusses ways to manage journal writing and incorporate it into existing classes. Suggests 19 assignments students can respond to in their journals. (MDH)

Presents a method blending ideas from logic, algebra, and operators to devise discrete functions that yield the same truth values as the truth tables associated with specific logic statements. Introduces mechanisms that encourage students to discover examples of discrete functions, approximately represent logic statements, and provides examples of…

Proposes lessons for algebra students using the context of tax calculations to learn about the concepts of slope, split functions, averages, rates, marginal rates, and percents. Students explore ramifications of possible tax revisions. (MDH)

Presents a calculator method to investigate the effects of varying parameters within mathematical functions in relationship to the accompanying changes in the family of their graphical representations. Suggests that the popularity of this activity makes it equally suitable for high school second-year algebra classes, preservice mathematics…

Presents three hands-on, discovery geometry lessons based on the use of special pieces called Polydrons by a fifth-grade class to build and investigate special properties of polyhedra and to stimulate students to think geometrically. Includes reproducible student worksheets. (MKR)

Presents lesson plans for activities to introduce recursive sequences of polygons: golden triangles, regular pentagons, and pentagrams. The resulting number patterns involve Fibonacci sequences. Includes reproducible student worksheets. (MKR)

Following a short introduction on the rationale and purpose for using algorithmic structures in the teaching of algebra, two topics from elementary algebra are presented in relation to control structures from computer programing, specifically: the multiplication of polynomials defined in terms of nested loops, and the distributive property…

Presented are two ideas to improve instruction. The first celebrates the Christmas birthday of Isaac Newton with an essay assignment related to Newton and a party. The second suggests a more appropriate moment to introduce the technique of completing the square to promote greater flexibility in factoring problems. (MDH)

The effects on college students' (n=110) attitudes of using a microcomputer as a demonstration aid was investigated in an intermediate algebra class. Results suggest a significant treatment effect on students' attitude favoring the microcomputer treatment group. (16 references) (MDH)

Effects of graphic representations of algebraic functions on performance of tasks involving expression transformations were studied for 28 teachers debugging transformed expressions through syntactic manipulations (SYMs) or semantic interpretation (SEI). Those using SEI improved performance using graphs. Some positive effects of graphic feedback…