Yesterday was the seventh national maths teachers conference held by La Salle Education, super conveniently for me, it was held in the Royal Armouries in Leeds, so I didn’t even have to travel far (a massive bonus in my mind!). I’ve only attended one of the conferences before, that was the one in London at the same time last year, it went down as one of my favourite CPD events, as I met so many amazing Maths Teachers, it was like a really cool day of meeting your heroes… Yesterday there were not as many heroes… where were you all?! However I did still get to meet some of them 🙂 the first person I met was the friendly person I sat next to in preparation for the opening speeches… He “creepily” (his words not mine!) stalked me on twitter after introductions 😉 and I soon realised it was the lovely Mr Taylor @taylorda01. We realised that we were both attending completely different workshops, and so we agreed that we’d share our blogs to give good coverage (genius, I know).
Mike Askew @mikeaskew26
The first part of the day was listening to Mike Askew talking about some research on effective teaching, he stated there were 7 key points. At this point I’m kicking myself for not taking down where the research was from! (Sorry).
1 – Space learning over time – absolutely makes sense, all about not teaching a topic once and never returning to it, all the research points in the direction of little and often, much like the ideal way of eating! Repetition is the way forward.
2 – Interleave worked examples and problems to solve. Sweller and Cooper did some research in 1985 (Got this one!) in which they have one group of pupils one worked example and then asked them to do 8 practice questions on their own. The second group was given a worksheet with one worked example followed by a problem, followed by a worked example then another problem, etc., until there were 4 questions they’d answered. They found that not only had pupils in the second group understood the topic better, but also retained more at a later point. I thought this was rather interesting, I suppose the only thing you need to make sure of is that pupils are reading carefully through worked examples and using them to attempt their own questions (something they can easily get into the habit of doing).
3 – Combine graphics and verbal descriptions – this was a really interesting one actually, this was about how you can’t put something on the board that is an image of something not completely related to what you are talking about. Nor can you have an image accompanied by lots of text. I suppose it’s essentially distracting pupils, and they’re then not taking in what you’re talking about, and should be more of a useful link of the visual and verbal memories.
4 – Connecting the abstract and concrete representations – during this, Mike discussed the book “Metaphors we live by” and how we talk about temperature a lot. But not necessarily in a weather related way, but also when we talk about other things such as giving a person a cold shoulder, how we greet someone with warmth, and this can be used to our advantage because we understand how temperature works, if we can link some of what we are doing to metaphors we use regularly then pupils can find it easier to understand the abstract.
5 – Quizzes – should not be underestimated, use them to introduce, to re-expose. They don’t need to be tests, but they can be very useful.
6 – Deep explanatory questions – speak for themselves I feel.
7 – Don’t end lessons all wrapped up and solved. Mike said that leaving a lesson with a question at the end will mean that pupils continue to think about it when they leave the room. If the questions have all been ended then why would they carry on thinking of it? The human mind will niggle at pupils and they might then be more enthusiastic to look at solving it the next day, and they’ve been trying to solve it inbetween.
I found the talk really interesting, of course there were some bits we already know and do but I found the cliff-hanger type ending a really good idea and found the metaphors quite intriguing too, definitely things I’ll be looking to use in my own lessons in the future.
Wow I almost finished it off then but realised that Mike went on to discuss Problem Solving and Reasoning (how did this squeeze into 45 mins?!).
The initial point was that actually it has been found that having mathematical reasoning abilities is more important in later maths use than demonstrating arithmetic abilities.
We looked at the “Objects of Learning” – not Objectives, I have spelled it correctly J This was about looking at the direct and indirect. The direct is the topic area you are teaching, however the indirect is looking at fluency, problem solving, and reasoning proficiencies. We should be aiming to promote these in all lessons.
A particularly valid point was that when you do problem solving, don’t give it to the pupils and then give up and tell them how to do it, that’s not going to help them in the long run. Actually it’s much more important to keep them at it and thinking about it. Thinking carefully will help much more. One teacher he mentioned would get the pupils to shout they are confused after first looking at a problem. After that they would get on, and be relieved they’d got their confusion out in the open first. I suppose once you’ve accepted you’re confused, it’s much easier to overcome the barriers.
One sentence I’ve written is “Sustained pressure for explanation and meaning”… I’m going out on a limb here, I feel like this is something that is definitely good for pupils. If we ask them what they’re doing, why, what does it mean, then we’re on to a winner, and we need to keep it up. Always. That will be good for them. They should be into the practice of us doing that, then pupils always know where they’re at.
We also need to provide problems with an emergent mindset, which means they can be solved in multiple ways, rather than the engineering way, where there is one way to solve it, and that’s going to be the only way you let pupils access it.
It is important to select tasks carefully and set them up effectively. Another teacher he had seen had enabling and extending prompt cards in their pocket to hand out to pupils when doing problem solving. This meant that he could pop the card down and a pupil could begin to access something which may help them to think about solving the problem in a more lateral way, or extend their understanding.
Another point was it is important to allow pupils to talk privately, and also publicly. So allowing pair discussions before opening out to the class for discussion makes pupils more confident in contributing, this means if they are unsure, you can just ask what their partner had said and the pressure is alleviated slightly.
Finally, pupils do really like to demonstrate their own work and how they’ve attempted a problem. However, pupils do not like to listen to others, therefore it is important to ask pupils after to add to what has been demonstrated, repeat it, do they agree, disagree and to explain in their own words, helping them to take it in and engage another pupil’s explanation.
Speed Dating Resources
Admittedly I forgot about this until 2am the night before. The first resource I thought to share were my times table grids – I have laminated, completely times table grids, particular for use with lower ability groups, helping them to think about the problem at hand and use their working memory for that rather than struggling with it. My second idea to share was my padlock lessons, (I shared these last time too), you have a set of questions on the board. Each one is one number of the combination padlock. When they have the answers, they unlock the padlock to get another set of questions which will unlock the next padlock. In total there are 5 padlocks, and as many questions as you like (you can put on provisos such as the 3 lowest answers of 6) and it’s a competition to get to the end first.
Mr Taylor told me about his whole school academic sports day equivalent, where one year group at a time competes in an academic competition, his words were “sports day for the kids who can’t do sports”. I thought this sounded so fun! I bet the kids really get into it. I might see if I can set something similar up in my school 🙂
The second resource someone shared with me (I didn’t catch your name I’m sorry!) was homeworks that are set across the department (originally designed for Year 11s), which have a number of topics on and also include the mathswatch video clip number, that way no pupil can say they’re confused as an excuse for not doing homework. A great idea 🙂 I also liked the idea for the fact it was standardised homeworks, so that everyone is doing similar things, and it takes away additional question finding 🙂
The last resource came from Janet, who told me about using a slide situation for decimals, they cut out a piece of paper with the decimal point and then they can a number behind it to see that the numbers stay in the same order, etc. She also told me about Numeracy Ninjas, which I still have to look at but sounded great for low ability!
Can Technology Make A Difference? Douglas Butler – @douglasbutler1
I was quite mindblown by this to be honest! Firstly it was about A Level type work so perhaps I should’ve prepared myself! He was telling us about the different things available on www.tsm-resources.com and then demonstrating the cool things you can find on Google Earth. On Google Earth he showed us where the world’s biggest hexagon was, the world’s biggest hexagon and parabola! (All genuine things you can see on the satellite images)
He told us all about how the numbers on runways come about (bearings so you know!).
Douglas told us about a cool tool called Jing, which records your computer screen and even your voice as you explain what you’re showing. Too cool.
Most of all he demonstrated how to use Autograph, something I haven’t actually used yet, but now I’ve seen how amazing it is I intend to use it almost all the time!
My two favourite demonstrations were looking at a 3D graph of Pythagorean triples, and also looking at derivatives of y = x n onto y = 1/x. Really cool, seriously. You should’ve been there, I cannot possibly give it the justice it deserves.
Developing Problem Solving Skills – Dominic Hudson – (no Twitter!)
Dominic started us all off considering
“What do you want pupils to be when they leave school?”
Answers ranged from Problem solvers, resilient, enthusiastic about maths and then thinking about what we do to enable that to become the reality rather than the intention.
We looked at the difference between traditional maths questions and the non-routine ones that are now our problem solving work. A good way to cope with our new problem solving intentions is more to embed the concepts within the problem solving, allowing even more time for problem solving and investigations 🙂
He discussed bolt-on maths. I’m not sure what this is… It sounded as if it could be a set of resources maybe? (If you’re in the know please let me know! I could just be being inexperienced and it could be a term I haven’t heard before).
At Dominics school, they give 2 weeks for Year 7 to all have a go at the same problem, so it’s a good length and activities can then span all abilities.
Strategies in the classroom to begin the problem solving activities are:
2 mins at the beginning to silently read through
5 mins to turn the sheet over, and recall to partners what the problem was (I imagine this then leads to a good discussion about how they can begin solving each part)
After the 5 mins, discuss as a class
Then allow silence to write down how they are going to begin attempting the problem.
He handed out some cool problem solving activities such as he uses:
They also use a form for pupils to fill in if they’re struggling – asking what are they doing, why are they doing it and what will they do next? They can also look at their partners work and answer the same questions.
My notes have not done the session justice at all. Dominic was really interesting to listen to, so I must’ve just been distracted! Apologies…
I had the pleasure of sitting next to Matt Dunbar (@mattdunbar) who is the author of Trinity Maths ( www.trinitymaths.com). He was telling me about how PixyMaths ( www.pixymaths.co.uk) have problem solving questions which they have graded for the new spec, and also about a CGP book for revision for the new spec, alongside the usual revision books, they also have one for pupils aiming for Grade 9, so they have put together Grade 9 questions for all sorts of questions. (https://www.amazon.co.uk/dp/178294415X/ref=cm_sw_r_cp_api_rUVBxb3RCTTTA) I enquired to CGP books (@CGPbooks) and they kindly sent me a free copy (and super quick!). It is a really useful tool. I’m going to be using it * A LOT* this year especially as I’ve been given top set year 11 ( 😀 ) and also just to test myself! I would definitely recommend getting yourself a copy and suggesting it to any pupils aiming for grade 8 or 9’s.
A Golden Age – Danny Brown – @dannytybrown
To be honest, by this point, my all nighter watching the referendum results plus my salsa dancing the night before was starting to catch up with me… so I don’t think I got the best out of this session at all (sorry).
Danny had put together a number of different pieces of literature to invoke discussion between us all about the pedagogy of teaching maths really, looking at the different ways children begin to develop their understanding of numbers and maths.
He told us how his department is based upon abstraction, and how they ensure they use basic level actions, such as waiting until the end of sentences before talking, and understanding that problems can have multiple solutions, therefore allowing pupils to see where their insights take them, and letting them get there more on their own than being guided towards a particular method.
Danny spoke about literature from Caleb Gattegno and Dick Tahta, and mentioned that the Maths Teacher Magazine has many articles in from Dick Tahta, and being a member means that you’re able to access all of them! Worthwhile doing when I get chance 🙂
5 Misconceptions in GCSE Maths – Craig Barton – @mrbartonmaths & @getdiagnostics
So Craig’s presentation was discussing the information that you can reap using his (and @simon_woodhead’s) Diagnostic Questions website (www.diagnosticquestions.com). There is so much! Genuinely super interesting. Initially, he went through how to use the website (for those not in the know), there are millions (I don’t even think this is an exaggeration) of questions related to GCSE subjects (not only Maths).
Each question has 4 possible options for answers. There is one correct answer, along with 3 incorrect answers that are there to alert teachers to particular misconceptions. Craig has mentioned before that he likes to use a couple of these in each lesson, so that you can easily see the misconceptions in the class and address them. In order to stretch and challenge pupils in the class, once they’ve found the correct answer, he asks them to work out the misconception for the incorrect answers, and further, they can design their own diagnostic question, with well thought through misconception answers too.
Next he showed us some cool stats about the generally worst answered GCSE Maths topics around the world, including Upper & Lower Bounds, Algebraic Fractions and 3D Pythagoras.
Then we got to play Guess the Misconception which is always good fun. Topics that came up as the 5 biggest misconceptions were:
Cumulative Frequency – surprising, we know, however when you get a funny question that is not the usual, pupil’s understanding of CF really gets tested!
Fractions to Decimals – the example was represent 2/3 on a line already drawn 0-3. The question was quite misleading, so it’s really easy to see how this can sway pupils towards the wrong answer.
Range of data – the question was reasons for a small range, most pupils leaned towards “less data”, when of course it means more consistent data, an easy to understand misconception to watch out for.
3D Pythagoras – difficult for many! It’s the visualisation that can be tricky. This question was asking which 3 corners of a cuboid created a non-right-angled triangle. Talk about tricky!
Adding negatives – the question was worded rather than in an equation, again throwing up numerous issues.
Straight-line graphs were also mentioned but I can’t remember whether this was one of the top 5 and maybe I’ve added an extra in!
Across the board, these were topics that I consider pupils to have a good understanding of, however it seemed to be a case of asking them different style questions definitely begun tripping them up, so it’s really important we try to come up with all the different weird and wonderful questions that can really test the pupils along with the typical style questions. This will be particularly pertinent in the new GCSE exams.
Craig mentioned that the topics that have been newly introduced into the spec are being answered really well, however it’s topics that were already on but have been adapted slightly that are suffering the most.
Finally, he told us about the new interactivity on the website, in September there will be interactive Schemes of Work which you can manipulate according to your teaching timetable, and then they will automatically set diagnostic questions on those topics for your class 3 weeks later as a revision type method. It sounds super useful, so I for one am excited to experiment with it!
Maths Tweet Up
How could I forget to mention this!
Mr Mattock (@mrmattock) left me in charge of a puzzle table, which had some really cool puzzles on! (See the pic below). They were awesome, some included were one to make a tetrahedron, a cube, a tower of Hanoi, and a weird cage for a cross that was really tricky! Miss Norledge dominated at some of them, while Em (@EJmaths) showed off with the cross in a cage one!
Overall, another fantastic day of CPD and networking with more absolutely incredible Maths Teachers, who just want to learn more and share with everyone J
Thank you La Salle Education!