Could the drive for using CAS come from students?


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 there

There 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


CAS is very powerful and used appropriately can give students access to results very quickly that they would not necessarily be able to find accurately without it, at least not without taking a lot of time.  This gives the scope for relationships to be investigated without the limiting factor of always need to perform processes by hand.

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.

Comments

Post a Comment

Popular posts from this blog

Maths GIFs: parabolas

Image
One of the fantastic features of dynamic graphing software is that you can animate how a graph changes as some aspect of it is varied. I'm particularly keen on making short GIFs of animated graphs that demonstrate interesting properties.  One advantage of animated GIFs is that they are really easy to distribute via Twitter. There are loads of them if you have a look at the hashtag #mathgif .  Parabolas I've been posting animated Maths GIFs to Twitter for quite a while now. Here are some of my favourites featuring parabolas: The midpoint of the points of intersection of y  =  x ² and y  = mx  + c lies on the line x = m /2. The tangent at point P to a parabola with vertex Q can be constructed by finding R, the point of intersection of the vertical through P and the horizontal through Q, finding the midpoint, M, of QR and then drawing the line through P and M. If the tangents at two points A and B on a parabola are perpendicular then the line AB goes through t...
Read more

The problem with Powerpoint for teaching maths

There are a lot places on the internet where the are negative opinions about Powerpoint.  I don't want to repeat these arguments here, instead I wish highlight particular problems relating to the use of Powerpoint in the teaching and learning of mathematics.  These are that: It reinforces a view of mathematics that it is a series of algorithms to be rote-learned; It can reduce the amount of student-centred use of ICT in learning mathematics; It is usually a static form of mathematics and there are many easy tools for creating equivalent dynamic forms of mathematics. Reinforcing a limited perception of mathematics Many Powerpoint presentations for mathematics feature a question with the stages of a solution presented.  This can have a negative impact of students' perceptions of mathematics.  There is a link between students' perception of mathematics and how successful they are.  Students who perceive maths a series of unrelated recipes for solving probl...
Read more

Desmos Classroom Activities: An ideal tool for remote/blended learning

Image
The past few months have been a very chaotic time for teachers and students. Many schools and colleges are now back to teaching full time but this year is likely to be very challenging and teachers want to know that they can provide opportunities for students to learn, even if the normal day-to-day routines are disrupted. For me, one tool stands out as particularly effective in ensuring that students have interesting and engaging activities that will develop their mathematical understanding: Desmos Classroom. Desmos Classroom Activities  Desmos Classroom activities are collections of screens that provide students with the opportunity to interact and respond to mathematical questions. They can feature text answers, mathematical answers, graphical features, multi-choice, card sorts and many other types of elements.  There is a large selection of pre-made activities and it's really easy to adapt these or create your own. These activities are great for supporting students in think...
Read more