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…

The subject of buffer solutions in chemistry is a challenging concept for students to learn due to its abstract nature. The difficulties that students face in learning about buffer solutions can lead to poor performance and alternative conceptions about the topic. The development of successful conceptual understanding to solve buffer solution…

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…

Use of the calculator to create a series of iterations to approximate i to some desired degree of accuracy is illustrated with three problems on interest rates. (MNS)

Many problems and activities which can be worked with a calculator are contained in this booklet. The problems include: pattern recognition, combinations of operations, estimation, squares and square roots, rate problems, area, and volume. Chapter topics include: getting to know the calculator, single-step problems, using formulas, and…

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,…

Uses conic sections, trigonometric functions, and polar coordinates to solve the problem of determining the shape of a baseball outfield fence, given the distances along the foul lines and to straightaway center field. Graphing programs and calculators are utilized to plot different solutions. (MDH)