Event Detail

Event Type: 
Department Colloquium
Monday, January 9, 2012 - 08:00
Kidder 350

Speaker Info

Laplace Institute, Argentina

The main objective in teaching Calculus is the understanding of concepts. In this work I propose a FAS philosophy to learn Calculus; that is, a way of reaching the concepts from an equidistant equilibrium between a traditional and a reformist point of view. Because of its structure, this system may be as traditional and instructive (of the cookbook-recipe type) or as reformist (cutting out or taking different approaches) as you wish, thus stimulating logical and creative thinking.
The system is aimed at the fast self-learning of Calculus, offering flexibility and interaction similar to one-on-one tutoring. It also collaborates with and complements and/or supplements syllabi developed by teachers.
The philosophical key to FAS is based on access to knowledge by means of a set of different approaches, each of which has been carefully designed to be independent from each other. Graphically, we may picture each approach as lying parallel to each other like the ends of a fork. The idea is to gain understanding of the concepts using a strategy that surfs between the different approaches, consolidating the process of comprehension and so generating a way of thinking.
Due to the independence of each approach, every single one may be considered as a book in itself. The new information provided by each approach is added into the cognitive structure and associated to pre-existing knowledge. Each approach is used not as an end in itself but as a means to trigger a disintegration of the cognitive structure and its subsequent automatic restructuring.
To illustrate the FAS we take up the concept of solving ordinary differential equations.
1. The system is aimed at teaching Calculus to those who need it as a work tool, when knowledge is needed promptly. For example, engineers who wish to recall or broaden their knowledge on some matters.
2. It is also aimed at High School and College students, who are benefited by the self-acquisition of knowledge for better academic performance, eventually allowing them to save money on tutoring.
3. On the other hand, it is aimed at instructors who wish to turn the relationship with their students into a beneficial symbiosis.