Read part 1 here first!
Straight after workshop 2 was a pretty special guest speaker: Simon Singh. He played us Led Zeppelin’s Stairway to Heaven backwards several times. The first time it was just noise, but the next time there were words about Satan on the board and we could hear these within the reversed extract! – our brains tricked us into hearing something that wasn’t there because we were expecting to hear it. This was a real eye-opener that encourages us to continue to question what’s around us and always seek evidence.
Simon gave us a whistle-stop tour of his four books, starting with ‘The Code Book’ which includes a history of making codes and breaking them. Linking in with the Stairway to Heaven, ‘The Code Book’ talks about the Bible code; allegedly the Bible makes over 3000 “predictions” within the original Hebrew text, although there are also over 3000 “predictions” in Moby Dick too! With so many possible permutations you’ll find anything that you want.
‘Big Bang’ is mostly about cosmology. Lemaitre, a priest as well as a physicist, sought to find a day without a yesterday. Simon explained that that physicists will accept anything if it’s backed up by evidence!
‘Fermat’s last theorem’ demonstrates that maths can be just as emotional and passionate as anything else. I don’t think I knew that it was his last theorem because it was the last one that anyone could prove. Simon showed us a short video clip from a documentary on Andrew Wiles who worked on the proof in secrecy for 7 years. It’s on available on BBC iPlayer here.
Simon’s most recent book ‘The Simpsons and their Mathematical Secrets’ sounds like a great way to engage students! Lots of the writers are mathematicians so they hide maths in the show, including Euler’s identity amongst loads of other cool stuff. If Bart can do maths, our students definitely can. There are lots of slides that you can use with your classes here.
At lunch, I thought I’d help out Rob with selling some raffle tickets for Macmillan Cancer Support, in between running the MA stall so he could get lunch too. I didn’t ever appreciate how much work Rob does at these things! I didn’t even have time to get any cake! Imagine if he had his tuck shop too?! Second pledge to myself: help Rob in the future too.
After lunch I was in a problem-solving workshop with Claire Dackombe that was so full I at next to Kathryn on the floor. Claire opened by saying that we want all of our students to become masters of problem solving in maths. She handed out several tasks and asked us to discuss whether or not the tasks counted as problem solving tasks. Delegates share lots of definitions of problem solving including that they must be challenging yet attainable. Claire suggested that her definition was that they must be challenging to the individual learner, not have immediately obvious solutions and involve independent thought and creativity (although a single task doesn’t have to meet all three criterion).
Claire listed a variety of things to consider when involving problem solving in lessons, including cognitive load, surface structures and deep structures, growth mindset and resilience, generic problem-solving skills and topic-specific problem-solving skills. She mentioned Polya’s work on “how to solve it” and the four stages he outlines are needed in order to solve a problem: understanding the problem, devising a plan, carrying out the plan and then looking back to reflect.
Kathryn spoke about some problem-solving bookmarks she had made that list strategies that can be used for problem-solving and I discussed how I use problem-solving starter packs to help students become more familiar with processes.
Session four was fantastic – Craig Barton spoke about intelligent variation and how to use it in lessons. Forming an expectation is vital for students because it’s either realised and they experience satisfaction or it’s not realised and they experience cognitive shock. Craig listed the three phases of using variation: REFLECT – EXPECT – CHECK. This is (thankfully!) what I’ve been doing with my classes without realising this, but not all of my students are on board. Craig suggested making it an explicit part of the activity so students cannot avoid this vital part of variation.
Craig introduced Jess from Minimally Different Exercises to talk about the first possible activity that could incorporate variation: example. Jess discussed how she used to use “more of the same” questions and students would get the answers right. But it was boring and they would forget it quickly. Instead, she started to write questions that were minimally different from question to question, and used lots of fractions and negatives, so students were less likely to be panicked when they encounter them later on. Jess also reinforced that REFLECT – EXPECT – CHECK needs modelling explicitly. She discussed that to begin with she went “variation crazy” but that it doesn’t work all the time for every lesson, other activities are also needed. To help students become more mathematically minded, we can ask students what question might come next, or what they could do to change a question. I thought Jess spoke brilliantly, and still use her website loads.
Ben Gordon spoke about the next type of activity: rules. By using examples and non-examples to help students to identify what the rules are and what they are not. He uses choral response to ask his class all at once, after a 3-2-1 countdown whether they think an answer is correct or not (I love this idea and will be stealing it – thanks Ben!). He emphasised how “students remember what they attend to” and that it’s important to not talk when you’re expecting them to think. Subject knowledge is vital to create these carefully chosen examples – you’ve got to identify and address common misconceptions and make sure that students understand that mistakes are ok.
Ben showed us this fantastic summary slide which perfectly summarises how to use variation with examples and it’s truly brilliant as infographics go!
The third activity is patterns, but more importantly breaking those patterns. Logical patterns can make a difference but it’s important to have a “gap of understanding” – something that breaks the pattern and forces the students to look at the structure. Use this repeated practice then mix it up a little more, still changing something small, to really deepen students’ understanding.
The fourth activity is demonstration, which involves going through one example in detail, them keeping that one example static on the board, and show students another varied one. Having something to compare to will help then to understand what difference that minor variation makes.
Craig went through a list of FAQs at the end with possible answers. He spoke further about how to ensure students REFLECT – EXPECT – CHECK and that other activities were needed in between these varied tasks – variation is very important but only forms part of students’ diet of maths. Finally, although it may look boring, “the sequence of questions should be magical”.
Now Craig being Craig, he just can’t help but be a legend. He reminded us of his two new and awesome websites, www.mathsvenns.com and www.ssddproblems.com, then unveiled his new website that Ben and Jess have supported him with over the last couple of months: variationtheory.com. He really is incredible. Thank you so much!
The closing remarks at the end of MathsConf15 reiterated his thanks to all delegates, exhibitors and sponsors. We had raised £800 in raffle ticket sales which Mark “doubled” (questionable maths?!) to £2000. Another amazing conference in which I learnt so much. As always, thank you so much to Mark, Tom, Josh and the rest of the La Salle team and all of the brilliant speakers. I’m looking forward to using those variation questions this week, along with plenty of other tasks obviously!