FUTURE TEACHERS’ BELIEFS AND CONCEPTIONS ON THE USE OF TECHNOLOGY,
MATHEMATICS, AND MATHEMATICAL PROBLEMS VS EXERCISES
Antonio Codina*
CINVESTAV, México,
U. Granada, España.
acodisan@yahoo.es
Jose Luis Lupiañez*
CINVESTAV, México,
U. Granada, España.
jllupianez@yahoo.com
Manuel Santos
CINVESTAV, México.
msantos@mail.cinvestav.mx
Recent changes in curricula have considered that problem solving and the use of new technology can be utilized as a frame in the teaching and learning of mathematics. In this context, the role of teachers is now seen as a dynamic, critical, reflexive, agent who now has a greater responsibility in the teaching-learning process of mathematics. This study aims to report some conceptions and beliefs endorsed by future teachers concerning the use of new technology, the notion of mathematical problem vs. exercise and the nature of mathematics. We designed a questionnaire with three open-ended questions. The study sample consists of 43 students of the last semester of the undergraduate degree in mathematics at the University of Granada (Spain), the main job perspective for these students was teaching. The questions were:
1. When calculators, computers or other technologically advanced instruments are used, is mathematics being done? Explain your answer:
2. For you, what are the five main characteristics of mathematics?
3. State the main criteria that differentiate a
problem from an exercise in mathematics.
Illustrate with an example, if necessary.
The analysis of the written responses provided by the subjects helped us identify that mathematics is being done when new technology is used, since it lends itself to conjecturing, exploring, doing calculations etc.; that mathematics is logical-formal; and that there is a clear distinction between problem and exercise in mathematics. Moreover, the group of subjects who believe that mathematics is not being done when new technology is used state that the main characteristics of mathematics are its “aesthetic and beautiful” character as well as its practical usefulness, without ignoring its logical-formal characteristic.
*Acknowledgement: Supported, in part, by Project ALFA, net FIEMAL from UE.