Interactive Online Exercises of Basic Mathematical Functions

In this paper, a system is described for serving online exercises of mathematical functions for high-school students. The system uses web browsers running on students' computers for displaying questions, answers, and explanations. Although recent developments of electrical worksheets and symbolic computing programs like Mathematica make it easy and quick for a student to draw graphs, it is only half the way to understanding. Because the drawing is automated and includes minimal guesswork, the student does not necessarily get ideas about, for example, the effect of a coefficient value on the shape or the position of a graph. The only rigid knowledge he has is how he operates the program. The online exercises provide the other half. The first thing a student does in the exercise is to make a guess trying to describe the given graph correctly. There are no instructions for expressing the graph, nor hints before the first guess. After the first guess is done, then comes the hint or comment which helps him to make the next guess. This makes a kind of experiment on the desktop. A series of experiments tells him the behavior of graphs in detail and the relation to expressions. Adding to that, because the evaluations are done symbolically using Mathematica functions, wide varieties of expressions are allowed, which is easier to accept for the average student. The exercise provides the students with opportunities to learn from their mistakes and to build their own theory about mathematical functions.