Blind Trust in Authentic Mathematical Tools in Mathematics Education
- II vol, Cairo El, Y. 140-147. ZHAO
In this paper are described some features of the intensive use of math software, primarily Derive, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that includes not only course contents, but also the sequence of introduction to various topics and methodologies. For example, the use of software at the beginning of the course follows a black box strategy, in order to emphasis mathematical modeling and the discussion of theory's central problems. Also covered is the enrichment of discussion about classic problems; using CAS potentialities to demonstrate properties without the necessities of investing excessive time in technical details, avoiding long and boring calculations; design and redesign of materials that attempt to guarantee success of information technology integration; combined use of several software packages, and finally, feedback from students and assessment. In addition, examples are presented to demonstrate the support materials utility for high school Calculus. 1. Information technology as central element in the scientific work Rita Colwell, director of the NSF (National Science Foundation) of the United States, has written (Colwell, 2000) about the unifier role that information technology is playing in research in different sciences due to it allows to tie among different fields of the knowledge, and she states that no field of research will be immune to the explosion of information and information technology, however, she makes another statement that we consider very important that it is when it points that until recent years science had two components, theory and experimentation, but today it has a third component «computer simulation, which links the other two» (p.16). Colwell point out that nowadays scientific matters have grown in complexity as much as in Interdependence and it points out the specific case of the complex mathematical models that are used in biology and in social sciences, she states that many scientific achievements will be reached as far as there exists advances in information technology, «we need this computing power to put it all together: to process the volumes of data, to visualize results, and to collaborate» (p.17). 2. Mathematical modeling and Information technology In different sectors appears the perception of a fundamental change in mathematical modeling. Indeed, it’s possible to say that before the information technology birth, mathematical modeling of a physical process, could be described by the outline of the left in the following figure. Starting from the considerations of Bricio (1992) in his description of the mathematical method, the previous outline could be modify in the way that is shown in the right of the following figure.