I was invited speak at the Maths Mastery conference in London last month. My essential brief was to engage with using technology to support mathematics learners. I have increasingly wanted to take a wide view of things so I interpreted technology very liberally. Having trained teachers in using graphing calculators for both TI and HP for many years, I am well versed in the language of multiple representations. The possibility is there to see a function represented graphically, symbolically and as a table of values and to swap quickly between them and to see how each representation gave you different insights into the nature of the function.
For example, a linear function has a particular algebraic form, it has a straight line graph and a table of values with a common difference. We exploited all of these in our Pizza project, showing that the natural tendency when watching change over time (the declining temperature of a cooling pizza) is to look for a linear change. The difference is roughly equal over the minute intervals we used, for the 10 minute length of the experiment. This is forcefully confirmed visually when a real time graph being drawn is very nearly a straight line. So, we feel empowered to hypthesise a linear function which symbolically can be used to calculate extrapolations. It is these that undermine our initial thoughts (put time = 24 hours into the function and we quickly see there is something wrong). Then we can go back to the graph and change the axes to see the nature of the slight curve and look again at the nature of the differences from equal differences, which themselves have a pattern.
Continue reading The Mastery of Multiple Representation
The ATM/MA london Branch was treated to on of Peter Ransom’s barnstorming performaces last Saturday. A big message that we share with our PGCE students is that teaching is a performance art and ensuring that your lessons have a good dose of theatre will bring students in to your message. Well, Peter brings avery big dose of theatre. Right down to the brilliant stand-up touches … is he really going to drop the cannon ball? Well, yes, naturally. We got through transformational geometry, force functions in suspension bridge chains, cannon ball stacking sequences and the destructive impact of cannon balls by linear and quadratic scaling. So, no messing maths. Please come back soon to see the photos … and come to our next session which will be 10:30 Saturday 24th March (King’s College London, the Franklin Wilkins Building on Stamford Street, SE1, just down from the IMAX cinema), which is the Danny Brown maths Workshops. Read all about it at Danny’s site: www.makemaths.com
At higher level GCSE, it is possible to get a grade B having got 60% of the paper wrong. Since this is the benchmark for moving on to an A level course, there could be a concern that students could decide, say to avoid learning algebra and concentrate on geometry and statistics in order to get the B (or vice versa). In the main, the questions that they choose will have one or two steps at most to a solution, or if more are needed then guidance will be offered in the form of question structuring. In these circumstances, more extended A level questions, where the mathematics required may cover more than one area, would prove a significant culture shock. Continue reading Maths Puzzles: Sustaining Activity