On Saturday I was lucky enough to be invited to a course that Ed Southall was running for his ITE students at Huddersfield Uni. This was being led by Don Steward. If you’re sat there reading this and saying “who?” you need to go and look at his excellent MEDIAN website which is full to the brim of challenging and rich activities ready for use in the classroom. Why are you still here? Go. And. Look. You back? I know! The best thing since sliced bread, right? No need to thank me. Needless to say Saturday was amazing so I wanted to jot down some thoughts.
First things first, Don may have developed a bit of a cult Twitter following but he’s just a very normal, very lovely, very passionate educator. Don talks sense but above and beyond that he possesses the creative gene that I lack to think outside the box and come up with so many great ideas to challenge and enrich the classroom experience. He said so many things I agreed with throughout the course of the day I wanted to record some of them here and then I wanted to talk about a few Eureka moments I had (there were lots), I’ll finish up by sharing a few problems I have on my list to complete as homework. Don talked us through some of the resources from his site but I’ll leave you to explore that on your own.
Words of Wisdom
“Good lessons wiggle”
This was Don’s way of saying that the best way to differentiate is through the questions you ask of the pupils in front of you from questions so hard that most struggle to answer to easy questions all can answer and everywhere in between.
“Every maths lesson should have algebra; get it established, get them comfortable and confident”
Don said that he felt there wasn’t enough emphasis on the language of algebra in Year 7; actually deconstructing expressions and being able to interpret them as a series of operations. He said he throws some algebra into every lesson so that pupils gain confidence in it as a language.
“Every shape we can think of is a rectangle in disguise”
This was fascinating but as someone who isn’t very visual made my head hurt. Big thanks to Em for patiently talking me through it. Don gives pupils confidence with more complex shapes by relating them back to rectangles. This is something we probably all do with parallelograms (slice a triangle off move it to the other side…hey presto but he went much further; more on that later.
“All ratio and percentage questions are effectively the same”
Don praised the merits of the box method which can be applied to ratio, percentage and more complex topics such as Trig ratios. He said the idea initially came from the Shell Centre resources but I can’t locate it. I like this idea and I think it’s similar to the Bar Model idea which seems popular at the moment; a routine procedure which can be adapted to help you solve a variety of problems across many topics. Don’s resources on Boxes are here.
Where to start!
Eureka One: Transforming Calculations
Don began by telling us Maths was all about transformations. So if we want a pupil to work out 7.00 – 0.57 they’ll probably get lost with carries in the calculation. How do we get round this? We teach them they can change it by shifting back 0.01. Suddenly we have 6.99 – 0.56 which is a much simpler calculation to carry out.
I probably haven’t told you anything new. Hang in there. Here it comes:
Do this with negatives and 3 – (-6). Can also be shifted, let’s us a +6 shift. Woah. There it is 9 – 0. Wow. I’ve actually written OMG in my notes. I may just be a really poor teacher but why have I never thought of doing this in over a decade teaching?
Eureka Two: Trapeziums
More things I’ve never thought about. I always prove the formula for area of a trapezium by using 2 to create a parallelogram. Something I’ve never seen done is splitting it into triangles;
That’s probably really easy too! Why have I missed such obvious things? Feeling very stupid.
I also spent my lunch break tying to prove the area of a trapezium formula by cutting a small triangle from the top of another triangle. I’ll leave that for you to try yourself.
Some things I still want to look at/ try in the classroom
- These star polygons which will be great when teaching angles in polygons
- These what’s the question ratio problems which I’ll be using with Y11 before their exam
- This division cycling problem (which everyone else seemed to grasp much quicker than me. (@melmaths was off like a rocket!)
- What numbers have exactly 5 factors?
- I want to look deeper into the shape problem which made my head hurt. Can’t find it on the site but it was simply this “Show how to transform a regular pentagon into an isosceles triangle of equal area” and when you get there it is BEAUTIFUL.
How to “do a Don”
Don talked us through his 4 ways of creating challenge in his classroom. These are going on the wall near my desk:
- Reverse the question
- Greater generality
- Seek or exhaust all possibilities
- Look for alternative methods
Many thanks to Ed for the kind invitation couldn’t think of a better way to spend a Saturday morning (really!). Thanks to Don for sharing his pedagogical genius. Don’s full presentation is available here.