ICT provides a rich and flexible learner-centred environment in which students can experiment and take risks when developing new understanding (link)
To a certain extent I think that this is true. As a maths teacher-to-be I love how advances in graphic calculators in the last decade have made certain areas of mathematics so much more accessible to students. Students no longer have to work an equation (linear, quadratic, cubic, exponential…) out the ‘hard’ way – the calculator, if asked correctly, will solve for whatever variables you require. This of course allows far more complex equations to be worked with and useful practical applications to be more readily achieved. However this all comes at a cost: during my teaching rounds I have seen students of all year levels punching things into their calculator without fully understanding what they are doing, and losing the ability to evaluate whether an answer is reasonable or a mistake has been made.
I see students in the early years of high school automatically turning to their calculators for simple addition and multiplication problems, and in later years solving financial arithmetic problems without knowing what they are actually calculating. We provide the students with the ability to take shortcuts so it would of course be hypocritical to blame them for taking them. Not only this but the scope of mathematics that is taught in schools is constantly expanding – to spend too much time on laborious by-hand calculations would be inappropriate, out-of-touch and inefficient. I do however wonder if it is possible to find a way of ensuring that students’ actual understanding of the mathematical processes they are carrying out is not completely lost when we provide them with these shiny tools…? I’ll admit I don’t know the answer.
The situation is further complicated by a tendency among students to see calculators as tools, not opportunities: just because they can or have been provided with the opportunities to ‘experiment and take risks’ is no guarantee that they will have an interest in doing so. And again, this is fair enough – why should a student be fascinated by moving a parabolic function around a graph? Those who already love mathematics will see the appeal but for the majority of students, maths can be trying enough without being encouraged to experiment or take risks; such students will be perfectly content with knowing how to get the correct answer to set questions. However, it is impossible to cure a maths teacher of wanting to develop understanding, not just rote learning. As such I think it is vital to keep on encouraging students to play around with their calculators – to see what effect it has on an equation to move a parabola around a screen – to help them to see this technology as the opportunity it is to develop solid foundations, cement ideas and explore possibilities. There is no easy way to do this but to keep on doing it, to let our enthusiasm shine through, to integrate technology into our lessons as often and naturally as possible.