This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

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…

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.)

Procedural evaluations of limits of functions provide invariably better understanding of the limits than the approximations using a calculator. The purpose of this article is to demonstrate that better understanding can be promoted if mathematical understanding precedes the impulse to use calculators. The note clarifies the stages when the…

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

The Mathematics Department at Borough of Manhattan Community College (BMCC) (New York) has been actively involved since 1988 in a serious and successful program to improve instruction, understanding, and retention for women and minority students in calculus courses. One result of this work has been students creating calculus animations using…

Presents a project that explored student choice of a solution method for quadratic inequalities. Students were first instructed in the use of the case, critical-number, and graphical methods using the graphing calculator. The majority of students chose graphical methods of solution. (DDR)

Gives a general description of reformed calculus efforts and describes experiences with two reformed calculus programs together with traditional calculus. Also provides comparisons between these three programs using teaching evaluations and student journals. (Author/MKR)

Illustrates three examples usually delayed until sufficient terminology, concepts, and methods have been developed unless using calculators or computers. The three examples are on exponential growth, triangle construction, and end behavior of certain function. Discusses the advantages of technology-enhanced mathematics teaching. (YP)

Describes how to develop students' communication skills, regular study habits, basic mathematics skills, and a talent for logical thinking in a calculus class. Eight references are listed. (YP)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

A growing number of mathematics professors are asking their students to keep journals, write papers, and answer essay questions on tests, arguing that students learn mathematical concepts better by articulating them. This is part of a trend toward teaching mathematics for understanding rather than by rote. (MSE)