Some Algorithms of Mathematics Teaching

Abstract

An algorithm is a step-by-step procedure designed to achieve a certain objective in a finite time, often with several steps that repeat or “loop” as many times as necessary. The most familiar algorithms are the elementary school procedures for adding, subtracting, multiplying, and dividing, but there are many other algorithms in mathematics. The place of algorithms in mathematics is changing. One reason is the widespread availability of calculators and computers. It is clear that proficiency at complicated paper-and-pencil computations is far less important today than in the past. An even more serious problem with the mathematics teaching is beliefs that mathematics symbols and rules have little to do with common sense, intuition, or the real world. These inaccurate beliefs lead to negative attitudes. How the university mathematics curriculum should adapt to this new reality is an open question. Reducing the emphasis on complicated paper-and-pencil computations does not mean that paper-and-pencil arithmetic should be eliminated from the high school curriculum. The time saved by reducing such computations can be put to better use on topics as problem solving, estimation, data analysis and etc. Exploring algorithms can also build mental mathematic skills and help students see mathematics as a meaningful and creative subject. Students are more interested in what they can understand. This new approach to computation – algorithmic thinking will be described in more detail during presentation. The Risch algorithm for the calculus operation of indefinite integration will not be discussed at all. The own algorithms of differentiation (i.e., finding derivatives) using key – „cabbage“ image and indefinite integrals integration (i.e., finding antiderivatives) using key – „monetary reform“ image will be discussed. The algorithms transform the problem of integration into a strong step-by-step procedure