Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…

More than 2,200 years ago, Eratosthenes, who was a Greek astronomer, geographer, and mathematician, used a simple proportion involving the distance between two ancient cities and measures of shadows cast in those cities during a summer solstice to estimate the circumference of Earth (Nicastro 2008, 25-28). Today, middle school students can use…

An iPad® can be used to teach students to graph parabolas with ease and grasp vocabulary quickly. Parabolas come to life for students in this easily implemented activity described in this article. Teachers can use this tool in a fun and interactive way to not only address these graphing and vocabulary concepts but also introduce and explore…

Discusses computer solutions for factoring problems. Includes listing for (1) a program that multiplies two user-chosen factors (X-R times X-S) and allows subsequent multiplications by more linear factors and (2) a program which computes P(X)/(AX plus B), where P(X) is a user-chosen polynomial and AX plus B is a user-chosen divisor. (JN)

Cognitive psychology, artificial intelligence, and computer technology have advanced so much that it is feasible to build computer systems that are as effective as intelligent human tutors. Computer tutors have been developed for teaching students to do proofs in geometry and to write computer programs in the LISP language. (JN)

This article examines the difference made in computing when one school switched from a terminal with a telephone link to a computer, to a complete microprocessor system. (MK)

Presents a set of classroom activities and a computer program that have been used to help students intuitively grasp, in a minimum of instructional time, such fundamental concepts as hypothesis testing, random sampling, statistical inference and p-values. The lesson shows students how statistical thinking and microcomputers can be used in…

Discusses a structured approach to teaching computer programing in secondary schools. The approach can be used in an introductory computer programing (literacy) course or as a method to teach computer programing in traditional mathematics courses. Two sample lesson summaries (related to temperature conversions) are included. (JN)

Promotes the use of the microcomputer in mathematics instruction, reviewing approaches to teaching nonlinear equations. Examples of computer diagrams are illustrated and compared to textbook samples. An example of a problem-solving program is included. (ML)

Algebraic and computer solutions are offered for a problem on time payment scheduling. The problem, falling within the scope of high school algebra, could focus only on the algebraic methods, but including the computer brings out the relationship between the power of algebra and the power of modern technology. (JN)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

Discusses uses of calculators and microcomputers in mathematics education with particular reference to their impact on the teaching and learning of mathematics in Hong Kong schools. Indicates that teacher training in software design and production is essential because of the lack of adequate, well-designed mathematics software. (Author/JN)