Although most calculus students are comfortable with the Cartesian equations of curves and surfaces, they struggle with the concept of parameters. A multivariable calculus course is really the time to nail this concept down, once and for all, since it provides an easy way to represent many beautiful and useful surfaces, and graph them using a…

The research presented here is a group case study of students learning calculus in a Computer Algebra System (CAS) environment which examines the following research questions: What are students' perceptions of the role of technology in their learning? What is the students' relationship to CAS? What is the effect of learning in a CAS environment on…

Most students in U.S. universities are required to take a collection of core courses regardless of their degree or major. These courses are known as "general education" courses. The general education requirements typically include at least one mathematics course. Unfortunately each year hundreds of thousands of students in the US do not succeed in…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

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…

Coming from the Macsyma system and adapted to the Common Lisp standard, Maxima can be regarded as a tool for a frequent use in the mathematics classroom. The main aim of this work is to show some possibilities of Maxima and its graphical interface through our experience as Mathematics teachers in Business degrees, although it can be easily spread…

Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian "Gymnasien"…

The GeoGebra software is attracting a lot of interest in the mathematical community, consequently there is a wide range of experience and resources to help use this application. This article briefly outlines how GeoGebra will be of great value in statistical education. The release of GeoGebra is an excellent example of the power of free software…

The purpose of this study was to determine if the use of a graphical teaching and learning approach via the graphing calculator enhances students' understanding of the formal definition of limit. College students in six sections of Calculus I participated by completing a test prior to the introduction of the definition, and completing a second…

Online homework is unable to provide the detailed feedback of paper and pencil assignments. However, immediate feedback is an advantage that online assessments provide. A research study was conducted that focused on the effects of immediate feedback; students in 5 sections of a Pre-calculus course were participants. Three sections were randomly…

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very…