Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…

For many the phrase "teaching math online" evokes a vision of teaching and learning that is not based in physical classrooms. Perhaps teachers and students are even interacting asynchronously. In math classrooms in the United States, the increasing availability of devices (e.g. laptops, Chromebooks™, smartphones, and tablets) and…

Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…

In Part Three, the author reviews the basic ideas presented in Parts One and Two while arguing why the traditional equation-solving developmental algebra curricula is not a good choice for implementing neural response strategies presented in the first two parts. He continues by showing that the developmental algebra student audience is simply…

When taking mathematics courses, students will sometimes ask their recurring question, "When will I ever use this in real life?" Educators are often unable to provide a direct connection between what they are teaching in the classroom and a real-life application. However, when such an opportunity does arise, they should seize it and…

Most mathematical functions can be represented in numerous ways. The main representations typically addressed in school, often referred to as "the big three," are graphical, algebraic, and numerical representations, but there are others as well (e.g., diagrams, words, simulations). These different types of representations "often illuminate…

This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the…

The chain rule is one of the hardest ideas to convey to students in Calculus I. It is difficult to motivate, so that most students do not really see where it comes from; it is difficult to express in symbols even after it is developed; and it is awkward to put it into words, so that many students can not remember it and so can not apply it…

Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f(x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's…

Discusses mathematics as analogous to a tree with many branches. Contends that technology, especially the graphing calculator, can help students see the sun and sky through the many branches and leaves. (MKR)