Mathematics provides a language by which man can explore, and describe precisely and profoundly, any possible set of characteristics or relationships in nature. Discussed in this article are several mathematical topics including some historical perspectives in mathematics and new pioneering in hypernumbers. Supplementary sections include…

The concept of even and odd integers is explored through the use of fractions. (JT)

The author examines certain areas of confusion which arise in the teaching of linear equations for lines. (SD)

Several approaches to the teaching of matrices are discussed. (SD)

Several examples through which the Klein 4-group can be introduced are offered. (SD)

Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

The method of finite differences is discussed with some applications. The method is described in detail, with illustrative sequences, and several problems are presented. (MNS)

Discontinuing use of the term "negative" in reading -x is suggested; rather, "the opposite of x" is suggested. A definition is given, plus two worksheets to help students understand the meaning. (MNS)

A problem on speed of travel is stated in general terms to provide practice in algebraic manipulation while maintaining a sense of real-world usefulness. A computer program is listed. (MNS)

Much can be learned from a study of rational functions and the behavior of their graphs, so their inclusion in secondary school mathematics textbooks is urged. Analysis of reciprocal relationships and when they don't apply, asymptotes, and the graphing technique are each included in the discussion. (MNS)

Algebraic and transcendental curves are discussed, with attention focused on computing the area of some special regions bounded by the curves. (MNS)

The reversal phenomenon was studied with nearly 1,000 Australian students in grades 9-12. The insertion of a multiplication sign in an equation tended to lower the incidence of reversals, but switching from initial letters to other letters made little difference. (MNS)

The relationship between the historical evolution of algebraic ideas and their conceptual development is examined. A study with secondary school students indicates a possible parallelism between algebraic evolution and conceptual development and indicates how historical analysis can guide teaching. (MNS)

Explains an application of matrix algebra which involves probability matrices and weather predictions. Using probabilities of sunny or cloudy weather students can determine the effect weather on day one will have on subsequent days. (DH)

The author's adaptation of a mastery learning program to a Beginning Algebra course is described. Test score averages clearly increased. (MNS)