Kokol-Voljc identifies three-steps that are required for the successful adaptation of CAS into the classroom, foremost a change of teaching styles is required. This is further broken down by Kokol-Voljc as "from teacher centered to student centered group work and from deductive to inductive learning." The second step is identified as "refocusing on the teaching goals" and finally the third step is to "change the mathematical problems" including in-class activities, homework, and exam questions.
The article then goes on to identify the two types of exam questions: "theory oriented and application oriented questions." These two exam question types can be further reduced into "CAS insensitive questions and questions changing with technology" or in other words questions where "CAS - or any other calculation tool is of very limited help" and questions where the focus will change drastically due to the use of CAS respectively.
I believe the Kokol-Voljc really hits home the point here:
Without CAS, the solving of such problems was (is) strenuous because they involve a lot of mechanical calculations, or because they require “complicated” multi-step solving strategies. For many students, such craftsmanship activities outshine the actual point (goal) of the problem, hence they often forget to answer the original question after successfully completing the necessary calculations.
In a traditional paper and pencil environment tasks such as solving equations, finding derivatives, and computing integrals require most of the time used for answering these questions. Therefore for both teachers and students the feedback centers on testing the performing of operations. When using CAS, the time needed for such questions is reduced drastically, hence the significance of these questions for providing feedback for teachers and students changes as well.
I wonder however, as educators embracing new technology and changing the way mathematics is taught at a secondary level, if we are doing a disservice to the next generation? We are delivering them to a university environment where, speaking in generalizations, technology is not openly embraced and the teaching environment is still VERY teacher centered. Are we setting up our students to fail by allowing them to rely on a device, foregoing these strenuous and time consuming "mechanical calculations" which have governed mathematics educations for years? In some ways, yes.
Great, so we've created a new generation of critical thinkers! The problem is students are inclined to use the minimal brain activity required to achieve the desired result. As educators, WE are responsible for creating activities which challenge students to learn and develop a better understanding of the underlying mathematical concepts while....emphasis on WHILE, ensuring out students are intelligently utilizing technological aids. So, am I sold on the CAS for the classroom environment? No. Do I believe there is potential for something great? Yes. But we have to remember, a computer is only as intelligent as its user - Garbage in, garbage out.
References:
Kokol-Voljc, V. Exam questions when using CAS for school mathematics teaching.
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