Working with a group of aspiring entrants to the teaching profession is always an interesting opportunity. They still have the open mindedness about this noble profession that allows for certainties to be challenged and opportunities explored. The reality is that dialogic teaching supported by dynamic technology (meaning both parties: student and teacher, have control over how the narrative plays out) is a very rare event in schools. The mass of technology is either already booked out so kids can be trained to use MS office 2003 or is pre-programmed for zombie teachers to press the next button on their MyMaths lesson.
My argument is that if you can get dynamic maths software into the hands of students, then they can explore mathematical ideas and develop their own mathematical thinking. That needs a teacher who has thought through the maths and has a coherent map of how it all fits together. There is a story to tell (the narrative) for example, moving from the idea that numbers can either be written as the product of other numbers (rectangular numbers) or they cannot (prime numbers), then on to writing all rectangular numbers of products of primes (prime factorisation) and that there is only one way to do this for any number. This is a big idea (the fundamental theorem of arithmetic). We got to this point in a one hour lesson with a mixed ability group of year 8 students in an ordinary East London comp, simply by handing out a graphing calculator, with a factor command which for example reports factor 24=23x3. We knew where the story was going and went round the class asking students to explain what they had noticed and how they knew that some numbers had an output from the factor command which was just the number itself. Giving these numbers a special name (prime) seemed reasonable to the students who had seen that they were pretty special and that they were the only numbers which appeared in the factor output of other numbers make the term prime factorisation seem appropriate. In the end, of course, they told us how to do it, we didn’t need to. (That was me running the lesson and the class’s normal teacher with me). We used TI-nspire CAS machines that day, but it works just as well with an HP40GS which has a computer algebra system (CAS) as well.
This week’s PGCE students were convinced (I think) that the technology provides some pretty rich teaching opportunities (I did mathematically modeling with cooling curves and matching a person walking to a distance time graph with live data logging as well as instant statistical analysis with live data and much more). However, the debate afterwards, suggests that the fuss of getting the machines organised means this will rarely happen. Keeping the narrative in the hands of the teacher (with software on a laptop) is credible, but student access much less so. This completely accords with my experience,with unbookable computer suites and sets of laptops with flat batteries, it is the student who never gets their hands on dynamic maths software and yet a half class set of graphics calculators (perfect for keeping students talking … one each is much worse!) would be £600. Schools are not short of money, they just choose to spend it differently. In France, parents buy them at massive discounts in the supermarket.
So, come on schools, get technology into the hands of students and let them develop their own mathematical thinking. Five years is long enough to do this AND to get good at passing GCSE exams! And please, get proper maths software, notice how reports of the smartphone revolution never say what software was being used, because (and this from an early iPad adopter and serious fan) the maths software for learners hasn’t even started the journey of usefulness, but we’ll flesh that one out another day …