In a previous post I wrote about how Computer Algebra Systems (CAS) are really useful tools for teaching when writing questions: http://digitalmathematics.blogspot.co.uk/2011/08/using-cas-for-writing-questions.html This focussed on teachers using them for preparation but not necessarily exploiting them in the classroom.
Many teachers are reluctant to use them in lessons when they aren’t allowed in examinations. There is also the view that the purpose of mathematics lessons is for students to learn processes and therefore a tool that can perform those processes will hamper students’ progress.
CAS is out thereThere are free tools available online that have CAS built into them such as websites like Wolfram Alpha, and software such as Geogebra and Microsoft Mathematics. If students find these they can use them when set basic algebraic tasks. A series of questions on factorising quadratic equations can be performed very quickly on Wolfram Alpha!
Once students are aware of these then the standard tasks set to them may appear pointless. They may also question why the school subject of mathematics is not using a widely available tool that everyone has access to. This could be the driver that leads teachers to think about how CAS can be used effectively in the teaching of mathematics, as opposed to ignoring it or banning it.
When to use CAS
A parallel can be drawn with four-function calculators and arithmetic. If a problem required students to divide two numbers I wouldn’t always want them to demonstrate that they could divide these numbers with a pencil and paper method, especially if the numbers were large or given to a lot of decimal places. I would often be looking for them to know that division was need and that they could give the answer to a suitable degree of accuracy when found using a calculator. That is not to say there is or there isn’t a place for students learning a pencil and paper method for division but that is a debate for another time.
If the same logic is applied to students who have access to a CAS calculator this would mean that problems could be set where I would be interested in whether students could select the correct process and give a suitable answer. For example, in a question that required a derivative I would want the students to know that a derivative was needed and to be able to work with the expression for the derivative obtained using CAS but not demonstrate that they could find this by pen-and-paper (such as using the quotient rule). Again, this is not to say that there isn’t a place for learning the quotient rule.
A lot of the decision as to whether to use CAS comes down to an individual’s perception of what mathematics is. For those who perceive maths as a series of processes where the mechanics of them are important then CAS can appear like cheating; for those who see it as the relationship between objects then it can be a useful tool for freeing-up students to investigate these relationships.