Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)

Presents a series of 5 reproducible worksheets for grade levels 5-10 that provide hands-on activities to help develop the concept of slope. (MDH)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

Introduces the concept of maximum and minimum function values as turning points on the function's graphic representation and presents a method for finding these values without using calculus. The process of utilizing transformations to find the turning point of a quadratic function is extended to find the turning points of cubic functions. (MDH)

Among 1,453 male and 1,133 female academically talented 7- to 11-year-old students, boys performed better overall than girls on mathematical reasoning. Gender differences appeared as early as second grade, varying according to mathematics subskills. Male performance was better on tasks requiring application of algebraic rules and understanding of…

Presents an extended activity consisting of a sequence of tasks organized so that students can visit several mathematical concepts concurrently and explore connections among them. Students build solids using bendable straws to form the skeletons of various polyhedra. Topics covered include tables and charts, algebraic expressions, surface area,…

Discussed is the use of a program called MathCAD which allows students to solve higher order polynomial equations and geometry problems. The use of cooperative learning is emphasized. Included are graphs and part of a printout generated while solving problems with MathCAD. (KR)

Demonstrates how to construct rational, exponential, and sinusoidal functions that appear normal on one scale but exhibit interesting hidden behavior when viewed on another scale. By exploring these examples, students learn the importance of scale, window size, and resolution effects in computer and calculator graphing. (MAZ)

Explores the concept of extraneous roots in radical equations using an alternative to traditional algebraic methods. Using calculator- or computer-based graphs, accounts for extraneous roots by examining the four possible cases of systems of equations that can produce the solution to the radical equation. (MDH)

Describes and illustrates the Monomial Sums Approach, a graphical learning strategy, facilitated by microcomputer capabilities that allow easy manipulation and exploration of graphical representations of polynomial functions. Reduces emphasis on memorized rules in favor of qualitative understanding of functional behavior, visualization of…

Presents an account of the historical evolution of the definition of variable and the way the concept is currently treated in textbooks. Shares activities to promote student discussion on the use of variables as constants, as quantities that vary, and as parameters. Provides a reproducible worksheet. (MDH)

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Describes three activities to teach mathematical concepts involving probabilities related to outcomes using "Sicherman" and other dice; geometric representations of algebraic identities; and the volume of a cone. (MDH)

Collections of small objects have often been used in mathematics programs to develop classification and patterning skills. This book synthesizes that body of experience to create a new and original sequence of activities that build upon each other in order to draw out the greatest possible educational richness from the treasures. Treasure Boxes is…