I spent yesterday at the Royal Armouries in Leeds, a beautiful building next to where I lived during my first year of Uni, across the river from where I lived during my first and second years of teaching and from where I teach now. It may surprise you that I've never step foot in the Royal Armouries until today, but it's the truth.
I arrived early, mooched around the exhibition area picking up a few things and went to take a seat in the main hall. I sat for a while, did some admin and was joined by @MissBLilley, whom I'd never before met, but I follow on Twitter. We said we'd share notes via blogs, so here's my half of that agreement...
00 - La Salle/AQA/Mike Askew
After the normal MathsConf stuff from Mark McCourt and Andrew Taylor (this was my second, so I assume it's normal), they welcomed Mike Askew to the stage (@mikeaskew26). I enjoyed listening to him. particularly to research-based recommendations. The first of which was to '
space learning over time'. This resonated with me as I recently 'liked' a tweet that suggested that starters/settlers should be binned as they waste learning time. I didn't argue at the time, but my thoughts around this are that students require regular repetition of subjects in order to consolidate their understanding - as a result, each and every lesson starts with a 3 - 5 question long settler activity on things they've studied in the past. I'd previously raised this as a concern with SLT prior to our move to 100 minute lessons, reducing the number of opportunities for repetition, and I'm still unsure of this 35 weeks into the school year.
The next was to '
interleave worked examples with problems to solve' whilst students are working independently. Question 1 might look like 'Solve 5 + 3x = 20', with question 2 being 'Here's a solution for ..... Study each step. Can you improve your previous solution?'
3 and 4 could be different problems, with 5 being a solution to a harder question, and so on and so forth. I'll look to try this, but potentially as a part of my cover work for when I'm on residential over next week.
The third suggestion was to '
connect abstract and concrete learning', taking from Guy Claxton's 'Intelligence in the Flesh' and Lackoff and Johnson's 'Metaphors we live by' (apparently) and is something I'm probably quite good at - my takeaway was that the way I would go about teaching area and volume scale factors (bringing students back to a 1 x 1 square and enlarging by a scale factor, and highlighting the increase in area by that scale factor squared and volume, cubed) is a thoroughly effective way.
Quizzes (to introduce a topic, or to re-expose students to a key concept at a later date) reared their heads, and I'm aware that this is a part of the White Rose Maths Hubs suggestions in schools and something that I'll look to work on with the new GCSE and years 10 and 11 over the next academic year.
The final suggestion was to '
ask deep explanatory questions'. Always ask 'why?' and 'how?', use problem solving and reasoning, and Askew stated that 'mathematical reasoning is more important than knowledge of arithmetic'. I agree, and see this so clearly in a year 10 boy whose arithmetic is outstanding, but he struggles to apply it to basic concepts like volume, and as a result one of my takeaways that we could probably use a problem for all topics as a part of our schemes of work to help develop reasoning skills.
The whole presentation made me think of the advice from the Maths Hub that our department were given in September last year - 'plan for what you want students to think, not what you want them to do', and to plan for students to develop proficiencies rather than plan for exercises and doing.
The next piece of advice was something I've written down as a 'meeting idea', as I'd like to make more use of departmental meetings for teaching, and have teachers bring the activities that their students have worked through over the past week or two, and ask 'are they good enough?', 'what is their purpose?', 'do they develop proficiency?'. The research suggested that whilst many tasks are developed to promote proficiency and deeper thinking, two thirds of the activities declined into routine within the first five minutes when students encountered difficulty and teacher responses declined to 'Just use the formula' and spoon-feeding. Take away: press for reasoning, and don't let it go. Don't give students an easy way out because they want it.
The next part of his presentation centred around the ABC of problems. Authentic (problems and solutions), Believable or Curious Challenges. Problems should be something that students might encounter or that they might never encounter, but is interesting (If Bolt's latest race was ran against his world record time, how far behind his record setting self would he finish?). Problems should also never have an image that contradicts a narrative, or a narrative that doesn't add to the picture, and we looked at an open problem using a box wrapped up with string (1m of string, a 300mm bow, dimensions of the cuboid?) - a low threshold/high ceiling activity - differentiated through the use of prompts and supporting materials and stretch materials, with an opportunity at the end for consolidation (How much string would I need for a 20cm by 15cm by 100mm box with a 300mm bow?).
Teaching for problem solving is something I do, but don't do well and don't really have a real plan for. Here's my new one:
Choose the task (with a particularly skill in mind).
Set it up (tell a story, show a picture).
Orchestrate the discussion of solutions (the bit I struggle with). I need to give 'private talk time' and 'public talk time', a chance for students to talk in pairs, and then with others, before asking them to share their solutions publicly. Students need to repeat, revoice, rephrase, build on and agree/disagree with each other's statements, and I'm thinking that I should invest in a visualiser to aid my lessons here. I'll choose the solutions that move the discussion on and show great understanding and a variety of methods.
Above all, my largest take away here was '
Teachers need to select tasks so that over time students experiences add up to something important'. It might be that small tasks don't seem beneficial, but it's important that over time the diet that students receive develops their fluency and reasoning skills.
01 - Mark McCourt - Reducing non-teaching activity workload and improving subject knowledge and pedagogy.
I signed up for this session with our department in mind, and it dawned on me prior to Mark starting his presentation that I'd basically signed up for an advert for Complete Mathematics. That said, I have a few takeways.
The
DfE expectation for the coming academic year is that:
A fully resourced, collaboratively produced, scheme of work should be in place for all teachers from September.
Teachers should consider the use of externally produced and quality assured textbooks and teachers guides. This one has always bothered me. I know teachers who look down on other teachers for handing our textbooks, and advocate the use of worksheets. Well, I hate to break to this to those people, but textbooks are just worksheets glued together. If you have a selection of worksheets collated for use, and an exercise is appropriate for your learners, go ahead and use it!
Staff should engage in collaborative planning instead of spending a great deal of time planning individual lessons. We've done that this year, and the results are mixed. We started this to support our Year 7 and 8 teachers, of which I am not one, but became a part of the joint planning. I spent a good hour putting together a worksheet on perimeter that increased in difficulty between questions 1, 2 and 3 and within questions 1, 2 and 3, suiting the lesson I had planned perfectly. Unfortunately, another (number of) colleague(s) had thrown something together and added a CorbettMaths workbook as the worksheet. The objective was the area of triangles (if I recall correctly) and if you've seen the area of triangles workbook from CorbettMaths, it's not just area of triangles for Year 7! Joint planning is wonderful in theory, but when two people are asked to plan a lesson together, and they each plan half and throw it together it isn't collaboratively planned, and when teachers teach 20 hours a week and can't find the time to plan collaboratively, they go back to the same routine that they find themselves in day-to-day, and their collaborative planning matches the issues that we're trying to avoid.
The DfE has said that 'if your current approach is unmanageable, stop. If you're spending hours every night marking books, you need to ask yourself what the marking needs to achieve for the pupils and strip that back'.
The bit that made me laugh was how Mark has been in to schools and seen schemes of work where Year 7s always study position-to-term rules for sequences first. He knows that that SOW isn't fit for the students in that school because he wrote it, years ago, for the year 7 cohort he had that year. Your schemes of learning need to suit the students in front of you, and quoted a school that has 40 schemes of work in place. Of course, all that means is that they have 40 classes and each class works on different things at a different pace, probably because they have different abilities and starting points.
02 - Kris Boulton - The genius of Siegfried Engelman: a comprehensive theory of how to teach pretty much everything.
This session made my head swim, a bit. It was very dense, but useful and may well transform how I approach some things in lessons.
The session was about the difference between facts, processes and concepts, and how many facts require a good grounding in many concepts. Learning that '2 is the smallest prime number' requires you to understand the concept of the number 2, the concept of something being the smallest, and the concept of a prime number. Knowing that 'the Earth is a sphere' requires conceptual understanding of the Earth, and what a sphere is.
These concepts need to be taught well in order for students to understand facts and develop fluency. We've all had that student who has seen an irregular 5-sided shape and responded with 'What shape is this?!' 'Well, count the sides' 'That's a pentagon?!' They know what a few pentagons look like, but don't really understand what a pentagon is. As an aside, the L-shape, that compound shapes typically look like, is a hexagon. Tell this to your classes and observe their responses - confusion and realisation that they've been lied to, probably.
'Everybody can learn what we need them to learn, if we find the find the right way to teach it to them'. This reminded me of a film released in the early 2000s (I think) called Road Trip. They travel to see one of the character's girlfriends, or something, and find that she's traveled to see him (I think!). They find out that one of them has been lied to about a final assessment at college and he becomes concerned that he doesn't know anything about the subject as they make their way back. One of the characters claims that he can teach Japanese to a monkey in 46 hours, and that the key is just finding a way to relate the material to that monkey. In this case, he compares ancient philosophy to the WWF (wrestling, not World Wildlife Fund) and he goes on to pass.
Concepts were put into five categories. For
categorical concepts, Kris showed a rectangle and said 'This is not a triangle', a quadrilateral which was almost a triangle and said 'This is not a triangle', a right-angled triangle 'This is a triangle', an equilateral triangle 'This is a triangle', a scalene triangle 'This is a triangle', and another quadrilateral less like a triangle 'This is not a triangle'. By showing these, students are now considering what a triangle is and what the shapes have in common, how can they be categorised? This can be followed by an activity on saying whether shapes are triangles or not, and in his experience, this has been largely productive and positive in results. The same can be done with surds, showing root 3 (a surd), root 4 (not a surd), root 5 (a surd), root 14 (a surd), root 15 (a surd), root 16 (not a surd), before asking students what surds are and whether certain numbers are surds. When approaching 'What is a prism?' this way, Kris realised that he had made a mistake when learners identified a sphere as a prism, and quickly realised that he hadn't given a non-example where the shape was convex or concave between the congruent ends and students had assumed that a prism only needed congruent ends, and didn't need to have a congruency cross-section throughout the shape.
The basis is, begin with a 'non-example', then show a minimally different non-example, an example, a maximally different example, a different non-example and a different example. Give students a chance to show their understanding, and orchestrate a discussion allowing students to articulate their learning. Just because a student can't articulate their understanding, doesn't mean they don't understand, and lower ability students in particular may not understand worded descriptions, but will develop understanding based on the non-examples and examples, even though they can't get the words out.
Fuzzagorical concepts are not exactly applicable to me, but
comparative ones are. Kris started with the understanding of the word 'gradient', which was defined as 'It's how steep the line is' and carried on, before realising that students had no idea what the word 'steep' means. 5 images, one after the other, showing a line with a fractional gradient (no information, just the line), a line with a greater gradient, a line with the same gradient, a line with a greater gradient, and a line with a lower gradient. As you flash the images up, 'This line has a gradient', (next image) 'Did the gradient go up?' or 'Did the gradient change?' or, for higher attainers, 'What happened to the gradient?'. Do the same with the area of shapes - images with (and my own example) 2 squares next to each other, 4 squares in a row, 4 squares in a 2x2 grid. 'Did the area go up?', 'Did the area change?' or 'What happened to the area?'. The diagrams, and particularly the change between the second and third are important, as the area doesn't change, but the perimeter does, and it's important that students know the difference. How about showing two shapes and asking 'Which shape has the greatest area?', to check that we are indeed understanding what area is and not looking for perimeter.
Transformative concepts will change, and the best examples here were showing 2(5x + 7) = 10x + 14 and 3(-5x + 7) = -15x + 21, saying 'This is factorised, and this is expanded' and having students realise the link, but this will only work simple procedures and probably wouldn't work for (2x + 1)(5x + 17) = 10x^2 + 19x + 7, but potentially could for (2x + 1)(5x + 17) = 2x(5x + 7) + 1(5x + 7)
The final category was
correlated concepts. Show an image with a blue, red, green on, and then an image with two blues, a red and a green. 'The probability of picking a blue has increased because the relative frequency has increased'. Show an image with two blues, a red and two greens. 'The probability of picking a blue has decreased, because the relative frequency has decreased'. Show an image with four blues, two reds and four greens. 'The probability of picking a blue has not changed, because the relative frequency has not changed'. Do the same with different images and ask 'Has the probability changed? How do I know?' and ask students to echo your wording to develop an understanding of relative frequency and its link to probability.
I left with a lot to think about and enough to share with others. But having typed that up, I think I have more questions than answers.
03 - Ben Ward - Developing Leadership Potential
I've never considered going into leadership roles before this year. I have a TLR, but it's more classroom based, and I didn't like the idea of being too involved and knowing too much. This year has changed that, though, and I'm hoping for greater responsibilities within the department sooner rather than later. I attended this session in the hope of getting some ideas about what I may need to do over the summer should the opportunity arise. The following are just sub-headings and some thoughts...
Vision - What do I want? What's important to me? How do I do that? Where do I want this go? What is not important? What doesn't NEED doing? What needs prioritising? What can wait? Is there a timeline?
Character - How do I want to be perceived? How am I perceived? How do I respond to others? How am I spoken about? How do I speak about others? Do others trust me? Do I do what I expect others to? Do I behave with consistency, or does my mood affect my leadership, the way I communicate and the way I make decisions? What do I stand for? What matters?
Skills - What am I good at? This is what I should lead on. What am I not good at? This is what I should seek help with and seek to improve. I took a personality test late last night to help with this, and to find out where I could start.
Delegation - Allow others to own their work. Delegate tasks well - be open and clear with expectations, select who to give jobs to based on their competency and capacity to do that job, communicate expected outcomes, how will it be fed back to me? is there an first draft in the interim?, have more patience - others work in different ways and at different paces, give reasons for delegation, share decision-making power if applicable, provide the resources required for the task (time, people, a support network, physical resources?). Do not delegrate your responsibilities - for example, results lie with a HoD, and that conversation if results tank is your responsibility, and blame should not be passed on.
Stretch and challenge - In the same way that you challenge your students, find a place where you and your staff are challenged, starting to gain expertise and experience, and that their fears disappear.
Look after yourself - Pace yourself, make smart decisions, what needs doing? what can wait?, your workload needs to be sustainable and so does that of your team. What will give the most impact for the least effort?
Appraisal - Make sure this is not a tick-box exercise, that objectives are useful, productive and meaningful. What are you proud of? What do you want to improve? What do you want to work on?
Coaching - Have people around you who will challenge you, who you trust and who want you (and you want) to improve. Be that person to somebody else.
Read widely, and read well - Here is a reading list shared by Ben yesterday.
Again, my head is swimming and I think I'll have to park this until I have a role to work in!
04 - Beth Smith (White Rose Maths Hub) - Teaching for Depth
I've had much of this training before, in school, when the Maths Hub visited us to do a bit of training to support out department, so my notes may be a little lacking.
The session centred around the increase in challenge and expectation of students as we move towards the new GCSE and how this filters down to younger year groups and the requirement around their learning.
The first key point was how our classrooms are centred around memorising and not around fluency and reasoning. A UK text book might have 16 questions focused on the same skill, with the same level of challenge throughout, and the idea is that we need to move away from this to a model seen in Shanghai in recent exchanges, whereby their exercises increase in challenge with almost every question. 16 questions with the same skill, or 10 questions challenging students? Their example was adding fractions with the same denominator, and where the UK text book stuck to solutions with proper fractions, the improved activity started simple, then moved on to having answers as 1, then using this fact in subtracting, and then using this to add fractions with different denominators (in pairs, so that their sum is 1). This is followed by a quick consolidation task of the same ilk, with 5 seconds on each question, with a negative fraction as an answer. At this time, a 'check list' was mentioned on our table, to make sure that exercises can be extended by introducing decimals, fractions, negatives and algebra to most tasks and concepts to extend students understanding.
The next part of the session was about how we can support all learners in the classroom with open-ended questioning. Consider three pandas eating bamboo, 51 pieces altogether, they all eat an odd number of pieces. How many do they eat each? Get as many answers as you can. As an extension, how can you be sure that you have all the answers? To support others - give them a strategy, pick an odd number and half the rest. Is that one answer? Can you find another? Try another question - using the digits 0 - 9, write a sum showing a 3-digit number and a 3-digit number resulting in a 4-digit number. To extend, is this the only answer? To support, make it 2-digit and 2-digit to make 3-digit, or provide digit cards so that they have something to hold on to. For those frustrated learners, who try to give up, give the answers (1089, 1098), and fill in the rest.
We finished by discussing the need to teach for depth and understanding, and how our teaching needs to allow students to apply their learning to problems, and how being able to memorise is great (knowing your times tables, for instance), but can't apply this (like my Year 10 student).
A good day, energising, and great to be a part of that energy despite my unwillingness to move from my seat and become involved in a greater way. I hope my notes are of use to others.
