 Most teachers and school leaders think they know what makes great teaching, but they don't;
 Most teachers and school leaders think they know what it takes to improve teaching, but they don't;
 Most teachers and school leaders think that teaching in their classroom/department/school is good enough, but it isn't.
I have just finished reading The Teaching Delusion by Bruce Robertson, and it hit all the right notes for me. I found myself nodding along, lapping up what Robertson says, constantly thinking "This is exactly what I think, but said so much more eloquently." In fact, I am thinking of copying a few extracts to give to people when I can't put into words my own thoughts! I jest, of course. There were plenty of insights in the book that I had not thought about before, and a couple of things I disagreed with. The main premise is that no matter how good teaching is, it can always be better. This has been a point I have made at the start of each new school year since getting the job of T&L Coordinator, and my most recent phrasing has been "It is both our right and our duty to continue to improve our teaching". I use this wording carefully, to instil the idea that it is our right to want to continue to improve ourselves, get better at our jobs, and become better teachers. This aligns with Robertson's idea of a Professional Learning Culture. On the other hand, we serve a community of children and their parents (who, in my case, pay a fair amount of money for our services), and it is also our duty to them to do the best job we can, which includes continually improving our teaching. Our duty to the parents who pay, yes, but mainly our duty to the young people we have the pleasure of working with, whose future depends so much on what we say and do, how we make them feel, and what they learn from us. Robertson asserts that The Teaching Delusion is made up of three factors:
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End of a Semester We are approaching the end of our first semester, and so have a two week holiday coming up. After teaching online since March, with only a week break, I have to say that this is very much welcome. We (teachers and kids) are all tired and having two weeks away from Zoom will be a beautiful thing. We are not allowed to do any travelling as kids under 14 are still quarantined in Peru, so it will be spent at home and going for walks, but I am glad to have some time away from work for a little bit. I have been getting to spend more time with my son as I work from home, which is amazing, but I am looking forward to doing this without nagging feelings in my head about work that needs finishing. IB Key Skills I have been using my new IB AA SL Key Skills Generator to create retrieval starters for my lessons. I am using this in conjunction with the Spacing Spreadsheet which tells me which skills to do each week. With the lockdown still continuing here in Peru, we switched all classes to double periods, and so I only see the class twice a week, so I do a key skills like the one above on a Monday, and then a shorter definitions/facts recall on Thursday where I simply ask them to define the important words and concepts, and state some important facts. I have also just finished working on the Binomial Expansion questions, which I am quite proud of. In particular, I went for two different ways for presenting the solutions, based on a conversation on twitter. Anki I listened to the recent Mr Barton Podcast with Daisy Christodoulou last week, and one thing that intrigued me was Anki. I had previously downloaded it to my phone as I had heard Ollie Lovell talk about it, and thought it was an easier way to go than the old fashioned flash cards I was using to learn some Spanish, but I never actually got round to setting it up. I will get on this in our two week break that is coming up. But what really caught my attention was using this with kids. I am thinking about setting up an Anki deck of the key terms and skills that I was recording in the spreadsheet, and then sharing this with kids. They can then do this as the starter, giving them recall practice that is a bit more individualised to what they need. Hopefully this will also get them using Anki to study other things. And then each lesson I can get them to add new stuff to their deck too. As Craig said at the end in his reflection, it would be great to be able to combine this with randomly generated questions. This is definitely not something I am up to coding myself (mine is largely just a hobby), but it would be interesting. I am thinking a workaround could be to use my IB Key Skills Generator and get students to put a reference to a question in their decks. Then, when it comes up, they go to the site, do that question, and then mark it as right or wrong on Anki as they would a normal flashcard. I think you can even insert a link directly into the card, so that could take them straight to the page. I will be having a play around with this when we come back in August.
The second book by Craig Barton (well, ignoring the non Maths teaching ones) is everything a sequel should be: it builds upon the greatness of the first, but has its own tale to tell. It gets into the nitty gritty of the story, focusing on one of the smaller parts of the first. And yes, it is a bit controversial. I am not going to write a summary here. I thought I was, but that would not be able to do any justice to the book. If you are a Maths teacher, you should read the book. Craig is open throughout about not trying to tell you what to do, but rather telling what he does, why he does it, and provoking you to think about how you could adapt those things to work for you (if indeed you find them valuable in the first place). But even if you disagree with everything Craig has to say, then you will still learn a lot from reading the book. If nothing else, if you do all the sequences of questions he provides, you will be giving your subject knowledge a good servicing! Here I am going to share a few of my main takeaways, and what I want to incorporate into the book. In my teaching In the very last chapter of the book, Craig gives some advice on "Making it work", and the first thing is to choose one thing you want to try. Well, I am going to ignore him on that! Well, not completely. I am going to choose one thing that is new, and 3 things that I currently do but want to adapt after reading the book. Reflect, Expect, Check, Explain  this is the new one. I have been using some sequences of questions from Craig's www.variationtheory.com website, as well as making some of my own, but, honestly, they have really just been a set of questions. They have allowed me to direct student attention to certain things, but I have not been systematic enough in my approach to develop their mathematical thinking in the way Craig describes. Since starting the book I have been adding some elements, in particular the reflect stage, but I want to make more of this. So I am going to try the full structure, and use the Prompt Questions that Craig suggests (available on his website: http://mrbartonmaths.com/booklinks/). I think I will need to use a template to help them structure the process too. My plan is to try this with my first year IB class, though I need to think carefully about what topic to do this with. We have some recap of indices and logarithms coming up, so that seems like a good fit. I will blog again on this when I give it a go. I have been using some sets of questions with them (such as the one below on Binomial Expansion), and have made short references to the ideas of reflecting on what has changed, but will need to be more explicit about this. Another aspect that I have not been building in that Is important is the idea of Fluency Practice before the intelligent practice. I used to do too much fluency practice, now I am not doing enough for students to get the most out of these sequences of questions. For students to develop the mathematical skills, they need to be more confident with the method they need to apply first, Atomisation  this is something I have been exploring, in particular with putting together the IGCSE Booklets and IB Lesson Sheets, but the systematic way Craig approaches it grabbed my attention. Going through the small atoms that make up a new idea and ensuring they are all secure first is something I want to look into further, but think that will definitely need to be a collaborative project. I am also thinking about how I could do some of that in the "flipped" model with IB classes. Example problem pairs  just a minor adaption to my current process, but I need to find a consistent way to get all their attention on the example. I print examples and your turns in the booklet/lesson sheet, so the easiest way seems to be to get them to shut their booklet when I go through the example. Even go as far as put it on the floor if necessary. Then they can open their booklet once I am done to try the Your Turn. I also make scans of the sheets available to students after they are complete, so I might get students to NOT copy the example in class, and then get them to do the example as a homework, where they can check against my version. This would give them another exposure pretty soon after the first, and give them instant feedback on it. Rule  I have been playing around with Frayer Diagrams for a year or so too, and the Rule sequence is a nice structure to lead into these. So far I have been using them to introduce the definitions, but this has not really been successful. Flipping this and getting students to fill them in themselves after seeing a sequence of examples, nonexamples and boundary examples is a much better approach. In out department I also want to get my department thinking more deeply about the questions we offer students and the experiences they get of thinking mathematically. I am hoping to get some time with the whole department to get them to do some sets of questions over the coming months, and then start building some of our own sets. I think I will start with the Reflect, Expect, Check, Explain cycle. It is difficult as we are still in lockdown from Covid, but I think we can make it work via breakout rooms in Zoom. Thoughts and plans are coming together…
We have moved to using the White Rose schemes of learning this year. In the current unit on place value, I was surprised to see the inclusion of Range and Median as Small Steps in their guidance. But when I thought about it more, it makes perfect sense. Separate these similar ideas from mean and mode. Both these require students to write a list of numbers in ascending order, which has been covered a couple of steps previously, so they get more practice. We then move on to ordering decimals, so we can come back to range and median in that context, and again later when we hit negative numbers. But when I was looking for some tasks for students to do to practice these skills beyond the worksheets that White Rose provide, I realised nearly all resources either cover just one, or the whole mixture of averages. So I went ahead and adapted a few resources to fit what we have covered. The first is a set of questions that I put together to try to get students thinking about what it means when the data set changes and only one of the median or range changes. It is meant to lead them towards the idea that both a measure of position (median) and spread (range) are necessary when looking at data. The second is a More Less Same grid (check out this website for more). The third and forth are a pair of Maths Venns tasks. The final is an Open Middle style problem. The PowerPoint file that contains all 5 is here.
Our students are currently heading towards their mock examinations, and usually at this time of year I do an assembly with them to talk about effective revision. But this year we are all on lockdown due to COVID19, and it seems unlikely that we will be back in school any time soon. So I decided to do something I have meant to do for quite some time: put together a brief guides for students and parents on how to revise effectively. I wanted to build in the elements that I usually present, which are all evidence informed, and present it in a way that would help students identify both why it is important and what they should actually be doing. I have seen other similar ideas before (a couple are linked in the Further Reading section), and there is nothing groundbreaking in what is included. Mine is just another example that people might find useful to share with their students, parents and colleagues.
I have been working on what I call the Aspects of Teaching, which is designed to underpin our Instructional Coaching Programme. The purpose behind this is to give coaches and teachers some broad areas of what we do to talk about, but also split it up a little bit to direct conversations to the most important parts that teachers want to work on. Below is the Aspects of Teaching. It should start automatically, and takes about a minute to play through the whole animation. There is a static image version here. Hopefully it is fairly self explanatory, which is why I have produced it in an animation form. But by splitting what we do into the 4 big Aspects, and then focusing on a particular detail within one of these, I am hoping to help create useful conversations. For each Aspect there will be a set of strategies taken from various sources, including
I have just finished reading A Compendium of Mathematical Methods by Jo Morgan. It is a book directed at Maths teachers and has a simple purpose: sharing different methods that are used to perform some common processes that we teach. For each of 19 topics, spanning the whole of secondary maths, Jo goes into depth on a variety of methods, always using 2 well chosen examples to show some of the subtleties you might otherwise miss. Accompanying this are some of her own notes, and excerpts from historical textbooks to show how these were approached in the past. Jo stays neutral throughout the book, never saying one method is the best, but rather presenting them as they are. A few concerns about some methods which rely on following a procedure rather than developing understanding are raised, but not in a judgemental way. The tone throughout is one of trying to start a conversation about mathematical methods. When we come out of lockdown, I am going to take some of the chapters to my department to discuss. I think it is a great idea to talk about the merits of different methods, and looking at ones we don't use will help teachers develop their own subject knowledge too. I am also a fan of being consistent across the department in the main method we teach. I think this has benefits when students change teachers, and allows for more continuity. As we are a 318 all through school, we could even extend this to the primary school to discuss how we teach the foundation skills. In terms of sharing methods with students, it is also nice to have a few other methods "up your sleeve" for those situations when they do not understand the primary one you use. Or with those who need an extra push, asking them to see if they can understand why different methods are actually the same can push their understanding. Perhaps using a method comparison example like Emma McCrea discusses in Making Every Maths Lesson Count could be used. One thing that the book has made very clear to me is that we need to move to an area model of multiplication. It is a versatile and easy to understand method for multiplication, that can easily be extended to more complex topics such as algebraic expansion and factorising. I will be taking this to our department soon as I think this is something we should be consistent about. It is a great read for any Maths teacher. It is not something that you need to read in one go, and perhaps is better read by chapter when you want to look at a particular topic. And I am with Jo. Let's talk about methods.
I am writing this as we are in the middle of the global Covid19 pandemic. This has shut schools across the globe, leaving most children to be taught remotely. I have blogged before about how I have used Online Live Teaching in this situation. But one of the things that seems to be on everybody's mind is how do we get students to engage in this type of teaching. Without having students in the class it is much more difficult to judge engagement, and for some it is even difficult to ensure they are present and doing the work. This raises the debate over what we actually mean when we talk about engaging students. As a younger teacher, I firmly fell into the camp of believing that lessons should be fun in order to motivate students to be engaged in lessons. I would spend hours designing activities, be it card sorts, bingos or jigsaw activities to keep the students busy and active throughout the lesson. My thinking behind this was that if they were kept busy, then they would be engaged in the lesson. Well, if I am being honest, I do not really mean "my thinking" in that last sentence. I mean "I was told/led to believe". Not necessarily directly, but certainly through the types of activities we were shown in my teacher training. These were the activities that were modelled to us, and so these were the types of activities that we employed in our teaching. And it was all about that holy grail of education: student engagement. For those first few years of my career my job was to engage the students in the lesson, usually by making it fun in some way. Perhaps that was through the way I "performed", or through the activities I prepared. But my main concern was that students enjoyed lessons. But now I see things differently. I still believe in engagement. We know from plenty of research that it is vital that students are engaged with the learning in order to learn the material (for example, check out MARGE by Shimamura). But there is a subtle but important difference in the language. You may not have noticed it. At the start of this post I referred to students being engaged in the lesson. Now I am saying that students are engaged with the learning. And that is the crux of the issue when it comes to discussing engagement. Is our job to create engaging (fun) lessons? Or is it to make the content that students need to learn engaging? These are very different things. You could argue that the former is easier (though the workload was killer!) in that it requires far less thought on everybody's part. But again, that is the problem. As Willingham says, "memory is the residue of thought", and if we want students to remember things, we have to get them to think deeply about those things. And interestingly, this normally piques their interest and gets them engaged in the lesson. So in this time of remote teaching when we are all concerned about keeping students engaged in their school work, think about this: do you want students to have fun, or do you want them to learn something? If it is the latter, perhaps you would be better off thinking hard about the content you want them to know, and, more importantly, how you can get the students to think really hard about it. Engage them in the learning, and they will be engaged in the lesson.
Online Teaching I feel like I am in the routine of teaching online now, after 8 weeks. It is not ideal, and I would rather be in the classroom, but given the situation I think I have found my flow. There are still some things I need to focus on improving:
Key Skills I have been thinking a lot about the key skills of my students, especially those I am teaching in the IB AA Standard Level course this year. I have started to put together a generator with these key skills at different levels, which I can use as a starter, to create worksheets, or at this time, get students to use it independently to keep overlearning these key skills so they can do them fluently. Reflect, Expect, Check, Explain A full post will come on this once I have finished reading the whole thing, but as I get close to finishing Chapter 1 (which could be a full book in its own right), I have already been struck by the amount of thought that Craig has put into this process. I am planning to ask my HOD to bring the Estimated Means sequence of questions to a departmental Zoom meeting soon so we can all do them and discuss the benefits of these kinds of connections. The structure of Reflect (what has changed), Expect (what do you expect to happen), Check (do the algorithm to see if your expectation was correct), Explain (can you explain the relationship) is a really helpful way to think about mathematical thinking. This is the behaviour we go through when answering questions, so we need to explicitly teach our students this behaviour too. I am excited to try some elements of this out in the next few weeks. CPD There is soooooo much CPD available at the moment. Seneca Learn courses. ResearchEd Home videos. The usual blogs and articles. Books piling up. Complete Maths webinars. Inner Drive Academy. And with a 2 year old at home and teaching a full timetable via Zoom, I am not managing to get much done (other than slowly working my way through books). Keeping track of all the opportunities is difficult, and I want to do them all, but I just need to file them and come back to them when I have the time. Instructional Coaching and Playbook
We launched our new instructional coaching programme in February this year. 3 weeks later, the whole of Peru went into lockdown, and coaching hit the backburner as we all got our head around teaching from home. But now I am trying to restart the programme in some way. It is difficult to get people on board when you can't go and speak to them directly about the possibility of being coached. I am relying on people letting me know when I keep mentioning it. But whilst I am waiting for somebody to coach, I have made a start on putting together an instructional playbook (as Jim Knight calls it). This is the set of instructional strategies that the coaches become experts in so they can share them with teachers. I will be pulling on three books to bring it together: High Impact Instruction by Jim Knight; Teach Like a Champion 2.0 by Doug Lemov; Teaching WalkThrus by Tom Sherrington and Oliver Caviglioli. But before pulling the actual strategies together, I have started by thinking about how I want to break them into groups. Each of these books does this, and I thought hard about our context and what groupings would work for us. I came up with this model, which also fits with our Principles of Great Teaching. Teach Like Nobody's Watching by Mark Enser is a call for teachers to take control of their teaching, rather than pandering to outside entities (be it Ofsted, SLT, parents). It is based on two underlying principles: that we should do what is effective (do things that work) and what is efficient (don't do things the long way if there is a shorter way). It is the antidote to the fads of education: things that either don't work (teaching to learning styles), or have been morphed from what does work in such a way to make them useless (plan lessons in three parts), or they do (partially) work but are not worth the time investment in most cases (discovery models of learning). Efficiency, as the author points out, is a term that is often viewed with disdain in education. "There is no place for efficiency in schools" is something I have had said to me, implying that efficiency is about stripping back and reducing the level of education. But that is not what efficiency is about. It is about reaching the same level with the least possible resources wasted. Those resources are not paper or electrical devices. Enser is talking about time costs of certain tasks. Every minute of teachers time spent doing something that could have been achieved in less time is time not used to prepare lessons, feedback to students, improve their own practice. Being efficient is about using our time wisely to achieve the best results, in the shortest time. And Enser argues that an efficient and effective teacher follows four stages. He compares these to "real world teachers", such as driving instructors, who follow these stages naturally. There are a lot of benefits to having a simple structure around which to base your teaching: it is easy to remember, meaning you are more likely to do it; it cuts out unnecessary stuff that has little impact on student learning; it reduces teacher stress and workload, and so makes them better at their job. In Part 1 of the book, Enser goes into detail on each of these four aspects of effective and efficient teaching, linking to research and classroom practice. There are some suggestions for activities, but mostly it focuses on why these are important and the guiding principles of each. Part 1, which is about half the book, is, in my opinion, an essential read for all teachers. It overviews what simple, effective and efficient teaching should be based upon, and gives teachers the springboard to take control of their own practice. It celebrates the classroom teacher. Part 2 moves on to look at the curriculum and assessment. It looks at the taught curriculum and how we sequence it, the "supercurriculum" of things we want our students to know/experience/learn outside of structured lesson time, and how we can go about assessing if we have been successful at this. Again, all these are addressed from a viewpoint of being effective and efficient, and not wasting time on tasks that do not improve the learning of the students. The final chapter in part 2 is all about running department meetings and how to use them to develop one of the most important parts of great teachers: their subject knowledge. This chapter in itself is a must read for any head of department (or line manager to a head of department) as it is a treasure trove of simple ideas to help make departmental CPD time more effective, and less based on administrative tasks. Part 3 looks at the wider school, and what role school leadership has to play in allowing teachers to do their job without interference. The thorny issues of behaviour, data tracking, nonnegotiables, CPD and feedback policies are tackled, with Enser again arguing to cut these back to what is actually useful for teachers. Each of these is accompanied by a short case study from somebody in a leadership position from schools across the UK. The whole premise of the book is to allow teachers to Teach Like Nobody's Watching, and at every turn Enser brings our attention to things we do which are not essential, and the things we could be doing that would make us more time efficient in doing our jobs. Making the time to read this book (and reflect on it) would be an effective and efficient way for all teachers to keep improving what they do, and help our students do the best they can. My Takeaways The simplicity of the recap, input, application, feedback model of teaching is great. I have been guilty of overcomplicating things in the past, both as a teacher and T+L leader, and this call to simplify what we do has struck a nerve with me. My teaching does (now) largely follow this approach, though reading this has made me more aware of the importance of each stage. It can be easy to skip recap, for example, when pushed for time. But building in the stereotypical "Last lesson we..." has been something I have implemented immediately, even in live online teaching. But here are a few highlights from each chapter: Recap  importance of connecting new learning to old material explicitly; Cornwell notes; show students the puzzle box to help them fit new knowledge in the right place. Input  requires attention and good behaviour; the importance of good subject knowledge; limits on working memory; dual coding; interactive through questioning; don't rush! Application  get students thinking hard; break it down and bring it together; ensure understanding before application; make the task focus on what you want them to learn; importance of modelling; is the purpose of application to perform or to practice. Feedback  feedback is not the same as marking; reduce the need for feedback (careful input, give success criteria); reduce time (verbal, whole class); make it count (have a purpose, action points, make it specific). Programme of Study  the curriculum is the journey you wish to take your pupils on, so make it a conscious choice; build upon previous knowledge; identify and keep coming back to threshold concepts. Supercurriculum  avoid a scattergun approach and link to the main curriculum; increase cultural capital with general knowledge within classes; better than a reading list is to set reading homework and link to curriculum. Assessment  designed to make learning visible; be careful about what you are assessing (does language cause the issues); consider the types of validity (does it cover everything, would two tests on same topic produce same results, would a test on something different produce different results); benefits of rank assessments. Department meetings  develop subject knowledge (audit, address gaps, adapt practice); develop curriculum (question, map, evaluate); common culture (expectations of student work, collaborate). Leaders supporting teaching  it is impossible to teach well when there is poor behaviour; there needs to be an understanding of principles to avoid cargo cults; separate CPD from meetings and focus on why before handing to departments. In terms of leading T+L, the model has given me an idea for developing our new coaching programme, which I will write about soon. It has also made me reflect on the overly complicated nature of our own Principles of Great Teaching (...) which contain 16 different aspects. I wonder if collecting them under bigger terms would be useful? Again, building this in to the Coaching programme is on my to do list. This year was meant to be about departments going away and looking at how the Principles fit in their subjects, and what they look like, but the lockdown has pushed that back. I still need to ensure these conversations are happening when we get back.

Dan RodriguezClark
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice. Categories
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