Recently there seems to be a bit of a backlash against using technology in lessons. Examples include @Katie_s_Ashford’s humorous tweets of what can go wrong using technology, concerns over Glasgow Council’s £300 million iPad splurge, and reminders of Michaela School’s reluctance to use some technology in lessons. I recognise the dangers, downsides and pitfalls of using technology in lessons. Like many others, I reject the claim that technology will revolutionise the classroom anytime soon.
However, as is usually the case, it is different in maths. Maths teaching needs technology. Not for games on the iPad, aimless Googling or elaborate voting routines, but for mathematical understanding. Understanding concepts can come from a variety of sources and looks different across subjects. I imagine that a student’s geographical understanding would come from physical observations, and a musician’s deep understanding comes from her experience of hearing and playing music. Maths teachers and students often live in the abstract and we have developed a body of knowledge which is not easily seen or understood in the physical world. However, mathematical ideas are not useless, random, disconnected facts. All of maths makes sense even if the reasons to explain why are not always communicated. Technology gives us the opportunities to show why.
- Why does the equation x2 + 7x + 12 = 0 have exactly two solutions?
- How does varying b effect the equation ax2 + bx + c = 0 ?
- Why is cos 45 equal to sin 45?
- Why is the derivative of a function equal to zero at its stationary points?
Students need to know the answers to these questions. Perhaps we could explain these concepts using a whiteboard and a series of diagrams. However, a dynamic geometry package such as Geogebra, Desmos or Autograph makes it make sense quicker and better. We can see visually and dynamically why the maths behaves as it does. We can see the connections between the algebraic form and the graphical form. We vary variables to see their effect. We consider and test boundary cases. These insights are crucial in developing students’ conceptual understanding.
The DfE agrees. The subject guidance for A level Mathematics and Further Mathematics (2016) states:
“The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics.”
At its most basic, the teacher can show a short animation such as this one at the front of the class. No technological skill, time or effort is required to do this. More ambitious is to use a class set of computers. This gives students the opportunity to explore the maths themselves. My personal experience is that chromebooks are the best way to do this. (I find phones tend to be a little small and not available to all, and iPads I find too fiddly although they may be better recently?). Yes, we need to have some spare when they don’t work, yes someone always forgets his password and yes sometimes the internet is down. However, an effective IT support team and good student behaviours and habits means that these annoyances are minor compared to the benefits.
Of course, teachers need support in order to get the best out of technology for maths teaching. I recommend starting with having a little play around with Geogebra, Desmos or Autograph. There are tutorials and online courses. There are also some excellent course run by MEI which provide more depth. I am yet to meet a maths teacher who is not immediately impressed with the power of such dynamic graphing tools. We need more of us to use such software so that the joy of understanding maths is passed to our students. I read a tweet which said that ‘technology disrupts learning’. Replace ‘disrupts’ with ‘enhances’ and add ‘maths’ at the end of the sentence and I would agree.