The National Council of Teachers of Mathematics [NCTM] requires students in grades nine through 12 to be able to explain inequalities using mathematical relational symbols and be able to understand the meaning of inequalities and their solutions (NCTM, 2000). Studies have shown that not only middle and high school students have difficulties with…

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

Presented is a calculation for the probability of a athletic event. Assumptions, computations, and questions to be considered in the solution of this problem are discussed. (CW)

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)

Described is a study in which elementary education students were asked to solve word problems by looking at the mathematical structure or the surface structure of the problems. Included are the methodology, data analysis, results, and discussion. The word problems used in the study are appended. (KR)

The hypothesis examined suggests that prequestions should be more facilitating than postquestions in directing students to the information necessary for a problem's solution. Fourteen problems were designed for a criterion measure, and 52 students in community college intermediate algebra classes were the subjects. Results indicated question…

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

Examines whether the embodiment of a familiar geometric system facilitates better understanding of the vector-space concept than the embodiment of a variety of unfamiliar algebraic systems. Analyzes students' responses with description, final answer, and justification of answers. Provides six problems. (YP)

Instructional methods used in a course designed to strengthen abstract thinking skills are described. (DT)

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

Provides a short list of integral triples for the design of problems employing unit fractions (so solutions will be positive integers). Also presents an algorithm whereby both primary and imprimitive sets of triples can be easily obtained and shows how to extend the algorithm to solve three-variate unit fraction equations. (JN)

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)