What Is Or What Might Be the Benefit of Using Computer Algebra Systems in the Learning and Teaching of Calculus?
Advantages and disadvantages of the use of Digital Technologies (DT) and especially of Computer Algebra Systems (CAS) in mathematics lessons are worldwide discussed controversially. Many empirical studies show the benefit of the use of DT in classrooms and there are also many useful examples concerning their use. However, despite these inspiring results and the countless ideas, classroom suggestions, lesson plans and research reports, the use of DT—and especially CAS—has not succeeded, as many had expected during the last decades see Hoyles & Lagrange, (2010). The thesis of this article is that we have not been able to convince teachers, lecturers at university and parents of the benefit of CAS in the classrooms in a sufficient way. What are the arguments that justify the use of CAS in the classroom? The article gives examples of a fruitful use of CAS with regard to the generally accepted goals or standards of mathematics education—like fostering students’ abilities in problem solving, modelling, proving or communicating—and to the subjects taught in high school. The basis of the argumentation is a competence model which classifies the relation between contents or topics: sequences and limits, functions and equations; representations of DT or CAS: static isolated, static multiple, dynamic isolated and dynamic multiple representations; and classroom activities: calculate, consult, control, communicate and discover.
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