In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative…

In an effort to reduce the engineering student withdrawal rate due to mathematics, The University of Alabama developed a unique, informal, interactive, and interdisciplinary five-week summer residence program called the Engineering Math Advancement Program (E-MAP). The program aims to increase retention by preparing students to be successful in…

Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

In the popularization course of higher education, students entering into the higher colleges are not those excellent students with excellent achievements in the senior school, so the teaching of college mathematics in higher colleges should transform from the learning emphasis to popularization emphasis for traditional excellent higher education.…

To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

The revolution of technology in education has heralded a new wave of learning styles and in some cases total dependence on technology. Yet, statistics reveal no significant improvement in student performance in Mathematics and a downward trend in basic algebra skills. The major impediment in the learning process is lack of understanding of the…

In this article, the authors discuss the importance of unexpected graphs as a vehicle for encouraging critical classroom dialogue. By examining such graphs more critically, teachers and their students can reexamine beliefs about the authority of technology in their classrooms. (Contains 15 figures.)

Calculus at the secondary school level has traditionally represented the peak of school mathematics in Australia, and has been available only to the most capable students. Until recently, many calculus curricula have focused on developing standard techniques, such as those concerned with differentiation and integration, with an emphasis on…

This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.)

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

Study was conducted on how the students were made to think meaningfully and widely within and across the representations in solving and identifying functions in precalculus, without the usage of the vertical line test. It was concluded that the "no vertical line testing" method proved to be easily accessible by all students and also made them…

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

The purpose of this study was to investigate how modeling-based instruction combined with an interactive-engagement teaching approach promotes students' problem solving abilities. I focused on students in a calculus-based introductory physics course, based on the matter and interactions curriculum of Chabay & Sherwood (2002) at a large state…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

In this article we focus on university lecturers' approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers' calculus courses. The findings show that lecturers' approaches to…