It is shown that the symbols for the fundamental units of mechanics, namely length, time and mass, are capable of a meaningful interpretation as positive real parameters. Then a suitable parameter domain allows one to take the derived units into account. The formal manipulations usually carried out with symbols of physical quantities, involving…

In this note it is shown that the Moore-Penrose inverse of real 3 x 3 matrices can be expressed in terms of the vector product of their columns. Moreover, a simple formula of a generalized inverse is presented, which also involves the vector product.

This article describes technology-based tasks to enhance students' understanding of functions within a framework for thinking about students' development of knowledge.

Accurate and accessible expressions for the probability of having a matching birthday are obtained by using Stirling's formula and Taylor series. For interest, the results are applied to the planets of our solar system.

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

This report reviews a study of the effects of "Saxon Algebra 1/2" on the mathematics achievement of 8th-grade students and a comparison of textbook content between the intervention and comparison curricula (Crawford & Raia, 1986). Crawford and Raia conducted three analyses with different subsets of the overall sample, but only one…

Some students--and parents--think math and science are not too important for their future. As everyday life becomes more dependent on technology, most people will need a better background in math and science to succeed in today's global economy. To get high-paying jobs in some of California's fastest-growing occupations, a strong background in…

Although academic performance is a concern, African American students represent less than 8 percent of California's K-12 students, and at times get lost in California policy debates about improving student performance. Findings of this study indicate that: (1) California's African American students are concentrated in relatively few counties and…

The study investigated the effect of using mathematics laboratory in teaching on students' achievement in Junior Secondary School Mathematics. A total of 100 JS 3 Mathematics students were involved in the study. The study is a quasi-experimental research. Results were analyzed using mean, standard deviation and analysis of covariance (ANCOVA).…

College students' success in a course depends on many factors, including their ability and previous knowledge of the subject, the effectiveness of the instruction, and their motivation to work hard enough to succeed. Introductory courses, including many that satisfy general-education requirements, often pose a particular problem for students who…

This article uses one of the authors' classroom experiences to explore how teachers can create technology-rich learning environments that support upper elementary students' mathematical understanding of algebra and number and operations. They describe a unit that presents a common financial problem (the use of credit cards) to engage sixth graders…

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

This article provides the rationale for using Fermi questions with eighth graders studying algebra. It describes the students' reaction to such questions as well as their thinking processes and solutions to questions posed to them by their teacher. (Contains 1 figure.)

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…