Describes an inquiry into students' uses of graphics calculators in the Tertiary Entrance Examination of Calculus in Western Australia for 1998. Discusses a comparative analysis of boys' and girls' performances. Indicates that the main areas of difficulty for students are interpreting graphing calculator outputs and knowing when use of graphing…

Describes the Treisman model which involves supplemental workshops in which college students solve problems in collaborative learning groups. Reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses at Oregon State University over five academic terms. Reveals a significant effect on…

Reports on the responses of students using a computer algebra system (CAS) called DERIVE in an introductory calculus course at undergraduate level. Indicates that the use of this technology was a catalyst for students to use three types of learning strategies: (1) regularly using multiple representations, (2) discussing meaning with peers and…

Discusses experiences teaching mathematics courses in a lecture-free, discussion-based seminar format at all levels of the traditional undergraduate mathematics curriculum. Presents methods for motivating, instructing, and supporting student efforts toward independent reading of mathematical text. Provides a non-scientific assessment of the…

The purpose of this study was to determine the causal ordering (predominance) between attitude toward mathematics and achievement in mathematics in secondary school (grades 7-12). Structural equation models were employed to analyze data from the Longitudinal Study of American Youth. Results showed that achievement demonstrated causal predominance…

An interdisciplinary activity in which students can see how a famous author, Leo Tolstoy, metaphorically applied the integration steps from calculus to illustrate his ideas about how history should be studied is described. The activity provides a startling and energizing conclusion to a unit on applications of integration and provokes students'…

The backdrop of the calculus reform movement created a fertile movement for the creation of overlap between general chemistry and precalculus as many of the goals emphasized key concepts from the chemistry lab. By using the graphing calculator in both precalculus and chemistry laboratory enhanced the students' comfort and competence with the…

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

Many undergraduate students have difficulty with the transition to proof-based courses in mathematics. This paper discusses students' beliefs about proof and justification in mathematics just prior to entry into such courses. The paper is based on in-depth interviews with students. The data suggests that some students have beliefs that may in part…

This paper describes a sequence of lessons from two Calculus I classes for teaching the epsilon-delta definition of a limit. In these lessons, the author elicited students' misconceptions and perceptions of this definition through a reading/writing lesson and then used these student ideas to design a lesson aimed at addressing these misconceptions…

This article is a discussion of some geographical problems related to geographic and population centers of the U.S. The focus is on modeling, using concepts from calculus.

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

Several formulae for the inradius of various types of triangles are derived. Properties of the inradius and trigonometric functions of the angles of Pythagorean and Heronian triangles are also presented. The entire presentation is elementary and suitable for classes in geometry, precalculus mathematics and number theory.

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…