The Diagnostic Testing and Prescription model, developed by the Center for Talented Youth at Johns Hopkins University (MD), was implemented in seven sixth-grade classes at three Brooklyn schools. The selected 165 students were provided an accelerated curriculum (covering arithmetic, prealgebra, and in some cases, algebra) and completed from 1-2.5…

Gives a lesson plan for a mathematics activity using balloons which shows connections between the algebraic concepts of slope, linear functions, and power functions and the geometric concepts of circle, sphere, volume, and pi. Includes reproducible student worksheets. (MKR)

Presents an activity in which students draw a picture, analyze each line and curve, and write the symbolic equations represented by the graph. Includes reproducible student worksheets. (MKR)

Characterizes algebra as a way of reasoning involving variables/functional relationships, generalization/modes of representation, and mathematical investigation/argument. Examines curricular goals; considers contributions of technology to reconceptualize algebra; and suggests directions for future development of tools and models, research agendas,…

Presents five lessons to demonstrate how graphing calculators can be used to teach the slope-intercept concept of linear equations and to establish more general principles about two-dimensional graphs. Contains a reproducible student quiz. (MKR)

Explores abundant numbers and presents a proof that abundant numbers of every order exist. Readers are encouraged to use the included computer program to explore abundant numbers for themselves, look for patterns in the output, and consider further questions. (Author/MKR)

Discusses the use of technology to investigate what graphs represent as well as how to interpret graphs. (MKR)

Presents algebraic and geometric solutions with surprising twists to a word problem involving linear functions and postal rates. (MKR)

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

Study examined the effect of frequent testing on eleventh grade algebra students' performance. One group was tested weekly and another biweekly for two months, then the testing schedule was reversed for two months, over eight months. Results indicated definite performance improvements during weekly versus biweekly testing. Students preferred…

Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)

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)

Part I describes the presentation of six different proofs of the Pythagorean Theorem by groups of three students in a party atmosphere. Part II delineates the analysis behind a student conjecture concerning the area of certain closed polar-coordinate figures. Part III proposes a categorical worksheet for determining when to apply the proper rule…

The recursive model presented here involves the study of drugs in the bloodstream and their subsequent elimination from the body. Both a basic and a more realistic model are presented and discussed in terms of an algebraic approach, a recursive approach, the graphical representation, and other extensions and connections particularly with models…

Describes the Geometer's Sketchpad, a geometric construction kit composed of three manipulatable, dynamic, linked, multiple representation environments: the coordinate system, formulas, and graphs. Examines the use of the environments for studying parameter effects of linear and quadratic functions and for solving linear equations. (MDH)