Maths Conf 9 bought with it my first ever trip to the city of Bristol. The conference was hosted at City Academy school which was a great setting as expected.
The day began as usual with Mark and Andrew Taylor from AQA discussing the day and explaining the processes. It is always inspiring listening to Mark talk about teaching mathematics and he makes it all seem so simple. His message came across very effectively.
Speed dating bought with it some good conversation about raising morale, discussing interleaving and talking about Harkness to anyone that would listen. Please do talk to me about/come and see the teaching philosophy if you are at all interested. A familiar feeling then ensued where I would have liked more time to talk with fellow maths teachers but time meant we moved on to listen to the first speaker of the day: Michaela’s Dani Quinn.
Drill and Thrill (@danicquinn)
Firstly, I must say I really enjoyed listening to Dani talk and I was captivated by her energy, passion and clear desire to be a better educator. Her students are incredibly lucky – I look forward to coming and visiting the department as well as the school.
Dani was talking about “drilling” students with a particular focus on pre-year 9. She explained the processes used and the point behind them with a clear link to the relevant research. The underlying messages were:
- If teachers don’t have to think about it, students shouldn’t have to
- Children enjoy getting stuff right
- A speedy mathematician isn’t a good one but good mathematicians are speedy (in certain facets eg. index laws)
I was keen to hear how drilling is incorporated after reading a few of Dani’s blogs. She is certainly not against conversation and engagement and lively classrooms but she was saying that when used at the right time, drilling can improve that instant decision making that we take for granted. A good example was: will this addition give me a positive or negative number? Students may have 20 questions to answer on that. There is usually some competition: quickest one or most correct in a short time. It is purposefully tense and the point is that students should be accessing their long term memory and not using their working memory.
Drilling should be used to:
- Practice an isolated decision
- override system 1 type misconceptions (I think I should add the numerators and denominators when adding fractions)
- consolidate on material already taught
Dani progressed to discuss implementation and some how to’s and how not to’s. We all make mistakes and Dani was not trying to say that Michaela are perfect by any means and she gave some advice on what a good problem sheet looks like and what a less good one might be. There are risks to drilling and again Dani addressed these with positivity and advice.
I certainly feel like I will go away and think about how deliberate practice can better be implemented in mathematics and in my classroom. I really like the idea of making an individual decision. This idea can be perfected at all levels and I will have a think over the next week or so about the best way to use “drills” in particular with my exam sets. I would like to see happy students who are happy that they “know” the cube roots and square roots for example. I’m not sure I will get them doing a mexican wave though – maybe that’s next year’s task!
The key thing to take: PRACTICE MAKES PERMANENT.
Where Y11’s will go wrong in the maths GCSE…and what you can do about it now
After Dani’s excellent opening, I was treated to one of the more omminently titled workshops I have attended lead by Craig Barton (@mrbartonmaths). One of my all time favourite twitter maths people and his podcast is excellent – well researched and heavily evidenced. I was looking forward to this after attending guess the misconception nigh on a year ago.
Craig’s website has become part of my teaching this year and student feedback is positive – this has reminded me to re-push the students after their mocks to get back and do some maths every day. Craig spoke very well, awesomely confident and as Dani had done, gave off an aura of passion and dedication to the profession. Craig highlighted the top 10 most wrongly answered questions and went into detail on three:
- y = mx + c
Throughout the three, he referred to what he and his department will do with these findings. His new look website is a staple and that links to a lot of Don Steward’s resrouces which Craig will use to commence purposeful practice.
The key from this talk was that all students benefit from purposeful practice. Purposeful practice can mean some students go from no knowledge to some; some go from some to lots; some go from lots to more. Nobody knows everything about a topic and “overlearning” has many benefits. Craig is clearly evidence-based in his decisions and he has shared his expertise with us all in attendance today. The key things with purposeful practice are:
- All students can do the same material [better students engage with it in a different way – ask why/spot connections]
- Key skills can be practised by those that need it.
- Methods can be shared by more able students
We must cover key concepts before we can expect students to get better at exam questions.
Craig mentioned this towards the end of the talk and it reminded me of something I heard a few conferences ago: “nobody gets cleverer by being tested”. This is absolutely true (“Minimal guidance doesn’t work”) and we cannot throw past papers at students and expect them to get better. This was great advice at this time of the academic year and has made me refocus my mind on how best to use the remaining teaching time. There is some merit in past papers but don’t just throw them at students and expect results to improve. Learning is not happening.
A fascinating session with Craig and the bar has been set superbly high from the morning. I am now looking forward to lunch and then sessions this afternoon with Andrew Taylor and Kris Boulton.
New GCSE Maths Exams (@aqamaths)
It takes a certain sort of someone to enjoy a session about exams and what constitutes which mark and why questions are how they are. I am that sort of person so I had a great 50 minutes listening to Andrew Taylor discuss the new GCSE exams and why AQA have taken the decisions they have.
Andrew eloquently went through the different types of problem encountered at GCSE and discussed where marks can be gained and what we would expect to see for those marks. There is an emphasis on finding marks not taking them away and rewarding students. This means that some notation mistakes aren’t penalised and examiners are expected to translate without something necessarily written down word for word.
The big decision taken by AQA with the new spec is that there are less marks for doing numeracy or carrying out basic operations. For example, in a problem solving question, the markw ould be for getting to 4x + 1 = 13 and no extra mark for 4x = 12. There will be other questions which tackle this skill.
At Wellington, we teach to the Edexcel board but there is lots to be gained I feel from talking about the final assessment. There are also some awesome questions written by all the different boards and it cannot be a bad thing to see more of these!
The key message from this sessions was that:
- Marks are accessible throughout the GCSE papers. The final questions are harder but marks can be gained
- Words of explanation during methods will help both the student and the examiner
- Most marks in the paper are for using the correct method.
Discuss methods with students and ensure they understand what a correct method looks like and why that is so.
One more hit of caffeine and then on to listen to Kris Boulton (@kris_boulton) – another of my favourite tweeters.
Most of the things you think are processes probably aren’t
I have read a lot of Kris’ work on Engelmann and his thoughts but have never heard him talk about him and how he uses the theory of instruction in his own teaching. After listening this afternoon, I wish I had! Kris always speaks well and this was certainly no exception. He explained the theory well and it was easy to see why continuous conversion and minimal difference will work in many contexts.
Today’s discussion was centred around a type of concept which Engelmann calls “transformation”. Simply put, this is any concept which takes an input and something happens to create a new output. Kris used examples of the distributive concept of multiplication and finding the area of shapes. At a basic level, the students see your answer to the question you are asking multiple times and then infer a correct answer to a new question based on patterns. I can see how this works in all creation of resource and I don’t think it has to be done in the explicit my turn, your turn way that Kris modelled (although this looks hugely effective). For example, in our Harkness books, we have examples of showing examples and then ask students to complete a similar problem. The next sheet can then be initial assessment. The next sheet would then be the expansion phase and seeing the same concept in different scenarios. The key here is that differences must be minute. As small as changing one number.
Towards the end, Kris mentioned two things which will sit with me forever.
The phrase: Logico Empirico. Loosely this refers to think of something, try it, adapt it, try it, adapt it. If I could sum up my approach to teaching, it would be this.
The sameness and difference principles related to maths problems.
Sameness relates to questions which look markedly different. The cognitive discussion students have is to find the similarities. Difference then is questions which look really similar, students ask what is different and how does this affect the output?
Thank you very much, Kris, for an inspiring finish. Not sure where I will find 180 quid for Engelmann’s book though!
And that was that. The final curtain on another wonderful day. Many thanks to La Salle and Mark McCourt. Thank you to City Academy. Thank you to everyone I listened to and everyone I had a conversation with about teaching maths. Every single moment was a learning opportunity. I will go home now with a head full of ideas and a lot of stuff to read up on.
Well done all!