College students having a poor high school mathematics background or returning to school after many years may want concrete tips and procedures to help them improve their grades in mathematics. This book provides those tips and procedures proven effective in improving a student's ability to learn mathematics and take tests. Pre-test study skills…

The ability to think critically in the presence of arguments with essential quantitative elements, most often graphical elements, will become an essential skill for educated citizens in the future. This paper takes one specific graphical display, a narrow series of observational and interpretational tasks related to a graph, and using a small set…

This study compared the performances of college mathematics students on mathematics problems stated in three different contexts: in arithmetical form, in the form of algebraic expressions to be simplified, and in the form of practical situations stated in words. Both single-step and multi-step problems were used. For all three contexts, there were…

This paper is a discussion of algebraic factoring. It is suggested that factoring is frequently presented in textbooks and by teachers without specifying one of the great values of this technique; that is, finding some of the factors of any number that can be generated by a particular polynomial. Concrete examples can help students understand the…

This ex-post facto, quasi-experimental study was conducted to determine whether students taught nursing math in the classroom did better than students who did not take the nursing math course in the classroom. First-year students enrolled in the Long Beach City College Associate Degree Nursing Program were selected as the treatment sample. Thirty…

Teaching students to think mathematically or to apply mathematics to the solution of real-world problems has become a national priority. This paper explores a method of developing the basic problem-solving skills in a remedial mathematics course at the college freshman level. The first part of this paper describes some basic problem-solving skills…

In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (1) the learners' mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present; and (2) the kinds of knowledge that learners may be building (including…

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Examined is the performance of men and women undergraduate students in mathematics using multiple-choice, relationship analysis, and true/false questions. Sex differences were reported. Implications of this research are suggested. (Author/YP)

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

Discusses the use of the mathematics classroom for discovering the relationship among computers, mathematics, and real-world problems. Provides three probability problems and compares the results of three methods, actual trial, computer simulation, and mathematical solution. (YP)