A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate. In addition, rate-related reasoning is needed to make informed…

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

Teacher played an important role in ascertaining effective teaching of mathematics. The objective of this paper was to investigate the pedagogical usability of a digital module prototype that integrated a dynamic geometry software, Geometer's Sketchpad (GSP) in mathematics teaching. The prototype was developed based on Reiser's and Dick's…

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

This randomized, controlled field trial estimated the causal impact of a technology-based geometry curriculum on students' geometry achievement, as well as their attitudes toward mathematics and technology. The curriculum combines learner-centered classroom pedagogy with individualized, computer-based student instruction. Conducted over a 3-year…

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

The third in a series of four articles, this is concerned with establishing the main properties of the general linear transformation of the plane, equations of lines, area, and change of axes. For earlier articles, see MT number 57, Winter 1971, pp. 14-19 and MT number 58, Spring 1972, pp. 49-55. (DT)

A discussion of the so-called rose curves defined by simple trigonometric functions in polar coordinates. (MM)

This article presents some easily stated but unsolved geometric problems. The three sections are entitled: Housemoving, Manholes and Fermi Surfaces" (convex figures of constant width), Angels, Pollen Grains and Misanthropes" (packing problems), and The Four-Color Conjecture and Organic Chemistry." (MM)

Conditions for congruency of triangles are investigated. (DT)