Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)

Discussed are a review of related literature, a review of other programs, a survey to determine the actual learning environment of the other programs, a review of student demographics, the group decision process (a Delphi exercise), and the evaluation of the program components. (CW)

Discusses a student project visualizing the surface of a function using computer graphics. Describes topics to complete the project, function and its domain, scaling, coordinate axes, projection of the surface, sketching the graph, plotting, changing the viewpoint, and rotating the axes. Provides a BASIC program using the rotation of the axes and…

Outlines an instructional plan working within the existing structure of most colleges that produces higher levels of student achievement through the manipulation of time. Described are the objective-based unit design, group instruction, initial test, corrective procedures, and retest. Lists 10 references. (YP)

Presented are three cases for intuitive understanding in secondary and college level geometry. Four ways to develop the intuition (physical experience, mutable manipulatives, visualization, and looking back) step are discussed. (YP)

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)

A problem-solving approach is developed for secondary or college students to estimate the number of piano tuners in a large city. The answer and method are analyzed for appropriateness. Four similar problems are suggested. (DC)

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Described is an outline for a school mathematics project dealing with the theory of equations, specifically solutions to polynomials of the third and of the fourth degree. Cardano's method for solution of cubic equations and Ferrari's method for solution of quartic equations are included with examples. (JJK)

A discussion of mathematics anxiety and learned helplessness in mathematics focuses on student failure and avoidance in college mathematics learning. It explores possible causes and suggests classroom activities to foster students' interest and success. (MSE)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

The four-color theorem stating that any map in a plane can be colored using no more than four colors represents a problem suitable for the liberal arts student. Presented is an algorithm for coloring familiar maps through the temporary removal of states bordering three or fewer states. (MDH)

Described is an approach to the derivation of numerical integration formulas. Students develop their own formulas using polynomial interpolation and determine error estimates. The Newton-Cotes formulas and error analysis are reviewed. (KR)

Described is an activity that works to attract and retain more women in mathematics. Women who do mathematics and information about particularly noteworthy women mathematicians are brought into the mathematics classroom. A list of women mathematicians is included. (KR)