The values of a polynomial with integer coefficients can be computed using a graphing calculator, but it is impossible to see the formula itself. Suggests finding this formula from numerical data and describes the unusual way to solve this problem with one calculation only. (Author/NB)

Introduces the concept of function using graphs or pictorial representations of functions. Presents four activities for grade levels 8-14 that use the natural progression from qualitative graphs to quantitative graphs to tables to equations for introducing the theme of distance from an object as a function of time. (Author/NB)

Poses the question, How can one find a polynomial function that agrees with a given input-output table? Describes one method that leads to some interesting mathematics. (Author/NB)

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

Uses cryptography to demonstrate the importance of algebra and the use of technology as an effective real application of mathematics. Explains simple encoding and decoding of messages for student learning of modular arithmetic. This elementary encounter with cryptography along with its historical and modern background serves to motivate student…

Uses the spot problem to illustrate the importance of inductive and deductive reasoning and the connections among algebra, graph theory, geometry, and combinatorics. (Author/NB)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Students use the relationship between the speed of a ball and the time that a player has to react to it to understand uniform motion problems. Includes activity sheets. (Author/NB)

Characterizes those numbers that are the sum of consecutive natural numbers and counts how many such representations a given number has. (Author/NB)

What initially appears to be a standard maximum-minimum problem presents, with a particular independent variable, a wealth of calculus and algebraic subplots. Uses graphing calculator technology to reinforce the "pencil and paper" solution and open the problem to lower level mathematics courses. (Author/NB)

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)

Investigates meaningful assessment to give teachers information on students' understanding of mathematical ideas and how their understanding changes over time. Presents examples collected from a teacher-made quiz, the Advanced Placement calculus test, and the SAT-I Mathematics test. Illustrates both the inherent subjectivity of these methods and…

Describes how a 3-inch by 5-inch card can be used to develop properties of similar triangles and prove the Pythagorean theorem. (MKR)

Gives a short biography of George Polya and a summary of his suggestions for teachers. (15 references) (MKR)

Describes the Recognizing and Recording Reform in Mathematics Education Project created to monitor the implementation of the NCTM Standards and monitor a broader program of research and development. Discusses key issues in mathematics reform and describes the methodology of the project. (Contains 10 references.) (MKR)