This year I am teaching IB Higher Level for the second time. My approach to teaching has changed a fair amount in the last three years since I last taught the course, and in particular I am now much more focused on breaking down ideas and giving examples across the range of types of questions. However, with this being a Higher Level class, I am also acutely aware of the Expertise Reversal Effect, and the fact that my students are further along the expertise spectrum than all of the other students I have taught in the last 3 years.
There are some elements of my teaching I have kept, such as the weekly quizzes. I run these in our single lesson that is after lunch each week. I use past paper questions mostly, with the odd drill style activity (recently we have been doing trigonometry, so have been drilling the exact values), and try to keep to 30-35 marks in the 40 minutes period.
I started the year with the Last Lesson, Last Unit, Further Back starters as well, but have found that there is too much of a time pressure to include these and the quizzes. Given that students are significantly more focused in the quizzes (there is a little bit of stake there as they do count minimally towards their grade), I have moved away from the longer starters, often just using a single exam question to start the double period, and a prior knowledge priming question in the singles. I am considering going down the route of quick retrieval of key facts and terminology as a starter.
But the biggest change is that I have started teaching through lesson sheets. Well, more appropriately, skill sheets. I have focused on breaking each of the units down into the individual skills that students need to master. On each of these I give a starter (which is really just a link to prior knowledge), and then a space for notes. This is followed by a series of examples and your turns on the sheets, and then an exercise (usually just the page numbers from the textbook and 2 ebooks).
With the examples and your turns, I am much less specific about the your turn being very similar to the example, as these kids are good mathematicians, and that would be patronising for them and would not invoke them to think. I even have them one after the other, rather than side by side as I have done with other classes. Below is an example of a set of example and your turns for the Trigonometric Double Angle Identities. As you can see, the jump from example to your turn is significant. Indeed, I have found that often the students need a little help with the your turns, and I will address this with individuals and pairs as I walk around the room.
One of the great things about having lesson sheets is that I can go through and "do" the sheet as part of my planning. This includes thinking carefully about the notes, both what I want them to write down, and annotations of what I want to say. I also do the examples before class to ensure there is nothing that is going to trip me up, but also to give me the answers to the your turns so I can easily check student work. This is a good example of what Doug Lemov calls Standardize the Format, making it easier to quickly check work as it is in the same place for all students.
In the lesson I model live using my visualiser. In the notes section I will write the key points that they should definitely copy down, but I also expect them to keep notes of the things I am saying as well. I then model the example on the sheet using the visualiser.
I have also given students folders to store the lesson sheets, quizzes, formula booklets and challenge sheets (UKMT Mentoring sheets). I have a folder with my notes versions too. This means students have an easy set of notes and examples to return to in revision. When we do questions from the textbooks or other exercises, students do these in their books. In reality we do very little of this in class due to time constraints, and they are having to do a lot of that as homework. They are getting practice through the your turns, but not enough to really cement the ideas, and this is a problem I am struggling to overcome at the moment. They do get some practice as part of the weekly quiz.
At the end of each week, I take all the lesson sheets that I have written on live under the visualiser to the library where I scan then in, along with the solutions for the quiz. I then upload them to our class website, where I have a section for each unit. In each unit there are links to the blank lesson sheets, the completed version, the notes from the last time I taught the course (which are similar but a pdf of a smart board file), and any links to other worksheets. There is also a page with links to all the quizzes and solutions.
I have found the process of breaking units down into individual skills to be useful for me to really think about the content. It has also made students more aware of the individual skills they need to work on. When the idea of atomisation has come up on the Mr Barton Maths Podcast a couple of times, Craig has asked how they then pull it all back together. For me this comes in the retrieval practice they get in the weekly quizzes and starters.
The resources are really popular with my students, who have a folder full of organised revision material with links to pages of questions in the textbooks.
Last week I also asked for student feedback, and one of the things they said was they wanted more feedback on their progress, and I have produced Skill Tracker sheets where they can record each time they answer a question correctly on a skill to show their own progress.
The big change for me has been not using a presentation software. I have used both Powerpoint and SMART Notebook successfully for many years now, and this is quite different. Whereas I used to place things I wanted to show them in the presentation, I now have to switch to them from the visualiser. On the other hand, the visualiser gives me the ability to quickly and easily Show Call student work (the Your Turns, for example) and to comment on their answers.
Do you use lesson sheets? What do you include in them? How do you put them together? How do you find using them?
I have been thinking a lot about my approach to teaching. It has changed dramatically over the last few years, but with having an IB Higher Level class for the first time in a few years, I have been forced to reconsider as their level of expertise is much higher. That being said, there is still some in the class who need the explicit instruction of this difficult content.
So yesterday I decided to have a chat with my class about how the course is going so far. I started by asking them two questions:
1. Would they prefer to get rid of the weekly quizzes, or change them to every other week?
2. Do they find the lesson sheets I produce (future blog post on these coming) a useful resource that is worth the time they take to produce?
The answers to both questions were unanimous: keep doing what I am doing.
The students were very happy with the weekly quizzes (a couple did mention they were a little too difficult, so I am going to ensure there are more easier questions in future), and they definitely seemed to be won over by my constant hammering on about the importance of retrieval practice. They could see the benefits of having regular chances to retrieve their knowledge and practice applying it to exam questions.
The lesson sheets were really popular. The comments were that they helped them organise themselves and were great for looking back at for revision. I am glad to hear this since they take a long time to produce, but it is worth it if they are appreciated and helpful.
These were both affirming results. I believed that doing them was beneficial for the students, but it was good to hear they also see the benefits.
After that I turned to some comments they had raised on a recent survey I sent them as part of our Maths Department review. The two main issues that were raised in the survey were that there was too little time for practicing, and that the feedback I give was not detailed enough.
First I addressed the issue of practice. This is something I have been concerned about for a little while myself, and was something I reflected on as a target for this year. We went down from 8 periods (40 minutes each) to 6 periods last year, and this had a huge impact on the amount of practice students get in class. They were given more study periods with this extra time, so I have been assigning more homework than I used to. I explained this to the class, and made the suggestion that we could fit more practice in class time, but I would have to stop doing my tangents on the non-curriculum side of Maths. Thankfully they all (bar one) said they would rather have those and practice at home. It would have been difficult to cut those out, so I am glad they went that way!
I did also explain my main principles for teaching, which are the four quotes I have printed and stuck on my walls:
1. Memory is the Residue of Thought
2. Practice makes Permanent
3. Working Memory is limited
4. Learning occurs over time
I said that I try to give them lots of opportunities for 1 in class through the Your Turns, address 3 through the examples and lesson sheets, and the weekly quizzes and starters are aimed at 4. We left it at 2 was their responsibility if they wanted to learn the material properly, though obviously they do get some practice in class.
For feedback I was a little more contemplative before the lesson. This was not a comment I was expecting, so I took it to heart. I only take in and mark one piece of work a week (the weekly quiz) which is our departmental policy. For homework I expect them to check answers in the back of the textbook, and I will do a walk around checking for any issues they had. But I do not review them. I have decided that I need to be more focused on giving individual feedback whilst they are working in class on the Your Turn questions, and also that I need to make sure I Show Call their answers for these too.
But we talked about how they could become more aware of the areas they need to work on, and I suggested I create a grid which has a row with 4 boxes for each of the skills we learn. They could then tick one of the boxes when they answer a question successfully on that skill, in either the weekly quiz, the starters, exams, or indeed practice at home. That way they could generate a visual of the topics they are doing well at, and see it grow over time. And if they comment when they get it wrong, they can also see the ones they need more practice on. I will review these with them every couple of weeks to get a picture of which skills and topics I need to drop into the quizzes and starters.
I have also been thinking about making use of learning maps as I have read about them in High Impact Instruction by Jim Knight (one of the books we got on the instructional coaching conference I attended in April). They idea of these is that they show the entire unit in simple terms at the start, but that students add to them over the course of the unit. I had a think about one for the upcoming statistics unit, and I am going to try that out. I hope this will also give students a chance to see how they are progressing.
Overall, the conversation with the students was useful. I got some confirmation, but also some ideas to try going forward. I am going to have a similar conversation with my GCSE class next week.
We started a new term a few weeks ago, and I led a couple of INSET sessions on Monday to kick it off. We started by exploring the second standard of our Principles of Great Teaching. The wording of this is:
All students are expected to participate in questioning sessions, with the use of a "no hands up" policy.
We watched a few clips to spark discussion around why asking for hands up is not a great strategy, and then groups shared a few strategies they use to question students. In the last 20 minutes I talked about Doug Lemov's Cold Call technique.
If you are interested you can download the powerpoint I used here.
After that we had some optional workshops on offer, and I ran one on MARGE (which I have talked about before here). We had 45 minutes, so it was a whistle-stop tour through the 5 principles with some time to reflect on what they meant for classroom practice. I tried really hard to build in the 5 principles to the presentation to model the ideas, and at the end I pointed this out to the group, making the metacognitive explicit. It seemed to go down well, and I think I am slowly getting more people to think about the science of learning. It is a slow process, but my incessant going on about it seems to be making people think.
You can find that presentation here.
Finally we all came back together to start looking at the Principles of Great Teaching in more depth. My plan has always been to create a document to support the poster front sheet, and I wanted everyone to be involved in creating that document. The purpose is to make the Principles more explicit through explanations and examples. The first stage towards this was to create a rubric for each principle. I started by creating an example one for the first Principle (Challenges All Students) which you can find here. I shared this with all staff, and split them into 15 groups to start putting together rubrics for the other Principles.
The purpose of the rubric will be for self-assessment of our teaching. I envisage teachers going through the rubric for a Principle and highlighting the descriptors they feel they are meeting, and using this to inform their target setting. It will also build into the coaching programme we are starting.
By the end of that session we had a starting rubric for most of the Principles. In a future session we shall come back to those, review them in departments, adjust and amend them, so that for the start of 2020 hopefully we have a complete (but not finalised) document.
My High Five
An idea started by Ben Gordon, here are My High Five.
T&L Newsletter Issue 11
Last week I published the 11th issue of our T&L Newsletter. You can find the issue here, and the full back catalogue here.
IB HL Just For Fun
I have decided to continue to open up the world of Maths to my IB Higher Level class. They all did presentations last term on a topic of their choice, and I am planning on doing that again later in the year. But for now, I have also decided to do a Just For Fun lesson at the end of each unit.
As we are finishing of a unit on Trigonometry, I am going to talk to them about the etymology of the trig words, why it is called the CO-sine, and the tangent. And why secant is the reciprocal of cosine not sine (as much as students wish the first letters would match).
The next unit is on exponentials and logarithms, and I am planning on introducing them to fractals and Hausdorff dimensions. I have some other ideas for later units, but I am eager to hear suggestions too
I read Memorable Teaching by Peps Mccrea, which was excellent, and have written a short reflection here, with a sketch note.
I have used a couple of the tasks from mathsvenns.com this week when teaching quadratic functions. I have used them before, but kind of forgot about them, and they are just such an amazingly rich task. In trying to find the functions for each of the regions, students have to think deeply about the ideas. I want to build more of these into my lessons over the next few weeks and months to try to embed the practice of using them. Since I am now doing weekly quizzes with my classes, the need for the Last Lesson, Last Unit, Further Back starters has kind of diminished as they are getting regular retrieval in the quiz. So I am thinking that Venn diagram tasks could become a feature of my starters (on a previous topic so there is some retrieval going on, and time for the maturation of ideas to help in the process).
I have started having 20 minute coaching style conversations with my colleagues about what they are aiming to achieve this year. They have been positively received so far, and it has been an interesting experience for me. I am also trying to set a time when I will catch up with them in a few weeks to see how things are going.
This comes from my delving into the world of coaching, but also thoughts about leadership. I want to have one-to-one conversations with all staff, and really listen to what they have to say. Hopefully this will be informative for the T&L Programme.
This is a response to this post about what schools need to do to prepare students for the 4th Industrial Revolution.
The underlying argument is that students will need to be educated differently to survive in the new world. However, as far as I am aware, the brain structure of children is no different now than it was 4,000 years ago, which would suggest that effective learning happens in the same ways as it always has.
Many of these ideas are comprehensively argued against by Daisy Christodoulou in her excellent book 7 Myths about Education.
But lets take a look at each of the 8 ideas presented in the post.
1. Redefine the purpose of education
The premise of the argument is that we should stop educating children to work in factories and have a single job for life, but rather educate them to be adaptable when they go to work. But that is NOT changing the purpose of education. It is still saying the purpose of education is to prepare students for a life of work. I have come across very few teachers who have such low aspirations for their students.
We do not teach them so they can get jobs. We teach them to give them an education that will allow them to have options later in life. We gift them the knowledge and skills that have been useful to the development of society over hundreds (or more) years. We give them the chance to explore beauty in nature, in art, in science. We provide opportunities for them to find themselves, and learn to work with others. Are some of these things useful in our working lives? Maybe. But that is not why we teach them.
Mark Enser argues this point well here.
2. Improve STEM education
I am a Maths teacher, so of course I think Maths is important. But is it more important than languages or arts? To some students, maybe. But, as I argue above, the purpose of education is to provide a broad insight into the world.
But, the author barely argues this point, but rather goes on to say that we should be teaching humanities as well (which is what we already do) and then further changes tact saying we should teach critical thinking and collaboration, citing this rather famous WEF Report. Blake Harvard does a good job of breaking down this report here. And I refer back to my argument above again. This suggests we should teach things that employers want, not what is best for students. Perhaps if employers want these skills, they should invest in training their employees.
Anyway, what a whirlwind. From stating we should improve STEM teaching we end up at teaching creativity and collaboration. All in one paragraph. A muddled argument at best.
3. Develop Human Potential
With machines able to do all the manual and repetitive labour, we need humans to be more creative and do the things machines can't do. So the argument goes. But creativity is hugely domain specific, and requires a large amount of background knowledge. Schools do teach students to be creative, by teaching them enough content and skills that they can be creative. As an Art teacher once said to me, "You need to know the rules to be able to break them". He was describing the work of Pablo Picasso, and how he had spent years learning the basics of drawing and painting before being able to create the masterpieces we now celebrate him for. We need to go through those steps to be able to become the creative and adaptable thinkers able to compete with the machines.
And don't even get me started on what happens when the machines learn enough content to become creative!
4. Adapt to lifelong learning models
"The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn and relearn." - Future Shock, Alvin Toffler.
What nonsense. Those who cannot read and write will not be able to "learn, unlearn and relearn" (at least not as effectively as those who can). And we can all learn, unlearn and relearn naturally anyway. Everyone of us is in built with the ability to learn. What makes us more able to learn, is knowing lots of stuff. The more we know, the more we can learn, and the more we learn, the more we will know. This is the Matthew Effect.
And then we hear that we need people to be lifelong learners as the jobs of the future don't exist yet. Another old argument that has been argued against many times (e.g. here). But again, this supposes that schools are not teaching kids to be lifelong learners. That is one of the primary aims of many teachers. I want my kids to be successful in whichever path they choose, and the best way to do that is to give them a broad education of the stuff that has helped generations of previous thinkers to advance society.
5. Alter Educator Training
Finally one I agree with. We need to incorporate more cognitive science into teacher training so that teachers are aware of how the brain works and learns.
Oh wait. No. We need to become facilitators. That is not altering educator training. That is what most teacher training currently is. Both initial training and training we receive later in our careers.
"Failure needs to be embraced as an essential step to learning." Another dangerous idea. Whilst we can learn from mistakes, they are not what we want to happen, and they are not essential. They are likely to happen, and can be used to in ways to remove misconceptions. But a 'perfect' explanation with examples and models can lead to learning with no mistakes. The danger in this phrase is that mistakes will happen, and we want students to learn from their mistakes. But we should not be aiming to make mistakes.
6. Make schools makerspacesHonestly, I do not know enough about this to make an informed comment. But my gut feeling is that these makerspaces could be useful, unless they are taking away time from other stuff (like teaching of classes), which I suppose is the implication.
7. International Mindfulness
I actually do agree with this one. Although I think many teachers and schools do already do this.
8. Change higher education
I am not sure how this is something that schools are supposed to do. But the argument once again boils down to colleges being a place to prepare people for work, and schools prepare you for college, so the people in charge of businesses should decide what they want and schools and colleges should fit in with giving them the mindless drones (who are all very creative about things they know nothing about) that they want.
Memorable Teaching by Peps Mccrea is an excellent short read as an introduction to some of the big areas of cognitive science.
After a brief overview of the architecture of Long Term Memory and Working Memory, and how they interact to create Deep and Durable learning, Mccrea launches into an explanation of his 9 Principles of Memorable Teaching.
Each Principle is described concisely, with descriptions and key ideas, and further reading on the topic.
I created this sketch note summary of the key points for me.
There are lots of links to things I have been working on over the last few years, such as: removing most of my displays and streamlining my resources (Principle 1); thinking about the cognitive load by breaking tasks down (Principle 4); ideas from variation theory and examples and non-examples (Principle 6); desirable difficulties and especially spaced retrieval through low stakes quizzes and starter activities (Principle 7).
Over the last few weeks I have been thinking about Mark McCourt's idea of the Teach->Do->Practise->Behave model of learning, which links in with Principle 8.
One area I want to work on more is making my students elaborate more. I am using Cold Call a lot more now to do this, bouncing answers from one to the next, but I still need to work on priming their minds and tethering to their prior knowledge in a more deliberate way.
Ben Gordon suggested this idea, and started it off on his "Teach Innovate Reflect" blog. Peter Mattock picked up the mantle in his blog too, as did some others. Ben has collated the posts here. I am going to use the same format that Ben suggested, which can be seen below:
I have grown to think it is really important that we seriously reflect on what we do and why over the last few years, as well as thinking hard about what we read and the implications it has on our teaching. This is why I have been doing semi-regular Personal Reflections posts. I am planning on building in some dedicated T&L time later in our year (southern hemisphere, so we are only a third of the way into our year) for staff to quietly reflect on their targets and how they have progressed towards them. But it is also important for teachers to take control of their own professional development, and writing blogs has always been that for me.
So here are my High Five for this year (well actually a High 7, but I hope you will indulge me!)
What I learnt: The stages of learning that we as teachers need to be aware of consist of Motivate, Attend, Relate, Generate, Evaluate.
Source: Arthur Shimamura's paper MARGE; found through Tom Sherrington's blog post.
Implications: When planning a sequence of learning we need to build in opportunities for students to partake in all five aspects of learning. We should help students to MOTIVATE their minds so they are primed for learning. The use of creating curiosity was a big take away for me, as well as building in anecdotes and stories. Getting students to ATTEND to their new learning is really important (Willingham's "memory is the residue of thought") and we often have to direct students attention to the important aspects as they are unable to do this themselves as novices. Students should have lots of opportunities to RELATE what they are learning to what they already know, with Shimamura recommending the 3Cs (Categorize, Compare, Contrast) and using graphical organisers. We need to give students lots of opportunities to GENERATE their new knowledge (also known as retrieval practice) to strengthen the connections. And finally we should allow students to EVALUATE their learning (this seems to be linked to metacognition to me), especially after some time has elapsed (to check for learning not performance).
I find this acronym useful to bear in mind when planning a learning sequence, so I can try to ensure I give students opportunities to do each of these things. The ones I have recently been incorporating a lot more of are GENERATION through weekly quizzes and Last Lesson, Last Unit, Further Back reviews at the start of lessons, and I use Example Problem pairs to help students ATTEND to what they need to. In the next bit I share one way how I might try to help students RELATE more.
I did an INSET session on MARGE and you can find the presentation here and I also compared the model to the EBC model I was introduced to on a Future Learn course.
2. Sequencing Examples and Non-examples
What I learnt: The sequence of examples we give can help students construct their own meaning, and so providing a faultless communication through examples can help ALL students succeed.
Source: The Theory of Instruction by Siegfried Engelmann; www.variationtheory.com
Implications: Direct Instruction (and scripted lessons) is something of a taboo subject in many education circles. After reading The Components of Direct Instruction, I decided to start reading The Theory of Instruction to get a better picture of what it really entails. I am about a third of the way through it at this point, and so far we have been looking at (in incredible granular detail) how examples can help students to understand new ideas. The idea of juxtaposing minimally different examples to highlight what effect variables have seems sensible. But the biggest takeaway for me has been the importance of non-examples of concepts. I need to think hard about how this fits in to a whole host of mathematical ideas. I can see how it works with simple concepts such as definitions, but I am still not sure about more abstract ideas such as processes we follow. I am planning to think about making some sets of non-examples (hopefully in conjunction with my team) for some of the concepts we introduce, as well as making use of https://nonexamples.com/ and trying to incorporate the use Frayer Models more regularly (I suggest some Thinking Activities here).
3. The four phase model of learning a skill
What I learnt: When learning new ideas and concepts we go through a four stage model of Teach, Do, Practise, Behave.
Source: Mark McCourt: The Return on the MrBartonMaths Podcast
Implications: Since we all go through these phases when learning, it is of interest to me both as a teacher and as the person running the CPD programme at my school. As Mark states in the podcast, most lessons only cover the Teach and Do phases, as this shows performance ability. Of course, these are vital steps in the journey. But I have found that I am not incorporating as much independent practice into my classes as I would like. Or maybe I am? I do retrieval starters (though Mark would not like these as they break up the learning episode), and weekly quizzes. This cover topics in a mixed order, but do not focus on a particular skill. I think I need to build in more time for intelligently designed sequences of questions on a topic.
I am making a bigger effort to include ideas from the behave phase at an appropriate time (Mark suggests 2 years after initial teaching), and I do this mainly through the weekly quizzes and the Further Back questions in my starters. These are usually out of context exam questions. But perhaps I need to build in more problem solving questions from the likes of NRICH and UKMT.
And what about CPD? Teachers need to go through these phases too when improving their practice. We know that one off sessions don't lead to improvements (though they might be a useful starting point). But most CPD only utilises the Teach phase. No chance for teachers to Do. When running sessions I will endeavour to build in more opportunities for teachers to actually Do the strategy in a role playing environment. But the real power of this model will be in the coaching programme (discussed below).
4. The importance of sleep
What I learnt: Sleep affects so many aspects of our lives and wellbeing. In particular, sleep is an essential part in the learning process where new ideas are consolidated.
Source: Why We Sleep by Matthew Walker and Learning How To Learn MOOC.
Implications: Many students do not sleep enough (e.g. here). It is so easy for them to become distracted that sleep seems like something that can be pushed aside. Many of our students claim the workload of the IB means they have to choose between working and sleep (so they choose to work). Of course, whilst there are high demands in the IB, this is not true. It is all the other things that take up time they should be getting rid of. The myth of multitasking probably leads many of them to being less efficient than they could be.
But maybe if they knew the damaging effect that lack of sleep can have on them, they would take it more seriously. Increased risk of heart disease, cancer, car crashes, anxiety, depression, and a host of others. We need to start educating students in the importance of sleep for healthy lives. We talk about diet and exercise. But rarely is the importance of sleep discussed.
And from a teachers perspective, I need to be aware that this lack of sleep might be playing havoc with what students remember from day to day. If they are not getting enough sleep, they are probably not consolidating the new learning effectively. However, whereas accepting that students will forget between lessons due to the forgetting curve can help us teach better (as we can incorporate spaced retrieval, for example), we should not accept that lack of sleep is the way it is. Whilst not being surprised by it, I will still try to educate the students to make sleep a priority in their lives.
5. Instructional Coaching is an effective form of professional development
What I learnt: there are different forms of coaching and instructional coaching is placed well to lead to improvements in teaching.
Source: The Impact Cycle and the Instructional Coaches Institute.
Implications: Instructional Coaching positions coach and teacher as partners (in accordance with the partnership principles). Whilst the teacher is the decision maker about their goals and what they will do, the coach enters a dialogue with them to help find a way forward. As this is a dialogue, the coach will offer suggestions and support (different from a facilitative model), but will not force their methods upon the teacher (different from a directive model).
The benefits of coaching are that it is sustained over a period of time and individualised. Each teacher gets support in the area they want to focus on, and coach and teacher work together until the teacher is successful. The sustained nature also allows teachers to not just go through the Teach phase, but also the Do phase (practising before using it in class) and the Practice phase (as they use it in different contexts over a few weeks). The behave phase will come later, after the coaching cycle has finished, but this puts teachers on the path to success.
6. Think of the introverts
What I learnt: Between a third and a half of people are introverts, but many of our school systems are built for extroverts.
Source: Quiet by Susan Cain
Implications: I am an introvert. I have started reading this book, and it has already had some profound impacts on me. Introverts react differently to stimulation than extroverts. They actually are more receptive to stimulation (from social stimulation, to caffeine stimulation). Which means they require less of it. Indeed, they are much more easily over stimulated than extroverts, who need more stimulation to stop them from becoming under stimulated and bored.
This is something I experience daily. When in a group of people I literally cannot focus if more than one conversation is going on. I am being over-stimulated by the multiple conversations. And it is tiring. It is not that I don't enjoy these conversations. In fact, the ones that give me something to think about are great. But afterwards I need some time to decompress.
Much of the world today, including schools, is designed for extroverts. But many of the greatest inventions and discoveries through history came from introverts working in solitude (Newton and Gravity, Wozniak and Apple computers). They are the often over looked leaders (the introverted Rosa Parks compared to the extroverted Martin Luther King Jr).
A few things come to mind:
1) how can we utilise the power of the introverts in our classrooms, both as individual thinkers and leaders? And how can I ensure that all students can benefit from the power of thinking deeply (links back to the independent practice from above).
2) how can we ensure we are not over stimulating introverts, and giving them the time they need to decompress? If they are always in environments where they are expected to work in groups, or there is lots of chatter going on, they will become exhausted (and probably not aware of why).
3) how can I as an introvert be more aware of my own personality, and use this to my advantage.
4) Don't use phrases like "He needs to be more active in class" in reports. For introverts, that is just not how they learn. They work by thinking hard to themselves, unlike extroverts who think openly and require input from others. Saying things like this just perpetuates the myth that we should all aim to be extroverted.
7. The Power of Cold Call and Show Call
What I learnt: Cold Call and Show Call are excellent ways to check for understanding and build a culture of accountability in class.
Source: Teach Like a Champion 2.0 by Doug Lemov
Implications: This book is a must read for all teachers. It is full of strategies that we can all use in our classes to enhance the learning of our students. But it was Cold Call and Show Call that had the biggest impact on me. By using Cold Call I have students not only answering the questions more regularly (as they know they could be asked) but also I benefit from a better understanding of what they can each do at any point in time, and they benefit from hearing explanations as to why and how things work from their peers more often.
Similarly, with Show Call, I can show students work to the whole class. I do this using a visualiser (my favourite bit of kit at the moment). We can dissect errors and misconceptions. I can show off exemplary work.
Instructional Coaching course
Earlier in the month I attended the Instructional Coaching Institute in Lawrence, Kansas. This institute is designed to give an overview of The Impact Cycle as developed by Jim Knight, and how this is an integral part to the instructional coaching model. I produced the Summary Map below of the main ideas to share with my management team, which includes some links to further reading and videos available online.
I am convinced that a model of instructional coaching is the way forward for us as a school to develop teaching practice. It is a personalised model where each teacher works on what is important for them, but provides scaffolded expertise in implementing teaching strategies, as well as somebody to help support teachers in meeting their goals.
I am really excited to start coaching a couple of teachers next bimester, and further learn how this approach can make a difference to the lives of our students. It is going to be hard work, but I am up for the challenge. I will be reflecting both on my teaching and my coaching in the future.
Teach Like a Champion
Knowing that I was going to the Instructional Coaching Institute, and being aware of the importance of the 'instructional playbook', as Jim Knight calls it, I decided to read through Doug Lemov's Teach Like a Champion 2.0 from cover to cover. I had previously dipped into various of the techniques, but never read it all the way through. I go into detail on my takeaways of this amazing book here.
Purpose of education
Blake Harvard (@effortfuleduktr) recently posted a blog titled The Most Important Question in Education. In it he talks about the reasons we tend to have disagreements when discussing education, and says they mostly boil down to one of two things:
But the bigger issue for me is the latter of those two causes. We all have different reasons for going in to teaching. We all have different experiences of education (both as students and teachers). And we all have different expectations as to what education should provide for our young people. Dylan Wiliam, in response to Blake, suggests the following:
Personally, I lean more towards the second of these, though I do think the first and third are also important. For me, the main purpose of education is to create socially functioning and responsible adults. Adults who can engage in conversations with others, on a wide variety of topics, but also know their own limitations. To do this, I believe, we have to teach students the accumulated knowledge of the human race (well, a broad overview of many aspects, with depth of a few important parts). As a species we have discovered/created so many things, and this is the cultural heritage of every single one of us. We all deserve to know as much of this as possible, and education is about enabling students to access this wealth of knowledge.
However, I recognise that my opinions on this matter are not the same as others. In several of our INSET sessions this year I have been dropping this idea to our staff: We all have different opinions, but it is the variety that ensures our students get the best possible education. Of course, there are many purposes to education, and if we all championed the same one, then the others would get left behind. It is our differences that actually push the education system to achieve all of the purposes. It is our arguments and disagreements that enable the system as a whole to keep improving.
So, yes, as Blake says, it is important that we recognise what our personal beliefs are with regards to the purpose of education. But it is equally important that we also realise that there is no one correct answer, and sometimes when we get into a disagreement, it is worth reflecting on the fact that this is probably caused by a fundamental difference in opinion. When we can accept that, we stop arguing to try to convince the other of the truth, and start arguing to improve the education system, utilising all of our strengths.
I had a cover lesson for a colleague where he wanted me to introduce simplifying surds to his low achieving class. I did this in a slightly different way to how I have in the past.
I started with the question and the black numbers on the board. I just asked students to find a product of two numbers for each, where one was a square number (I had to add the not 1 comment after an excellent point).
After a few minutes, I took answers from pairs, which I added in blue (including multiple possibilities). I intentionally wrote the square number first (even if they said it the other way round) and asked them if they noticed anything about the order that I wrote them (which they did).
We then talked about what they had previously learned, the fact that root(2) * root(3) = root(6), and I reversed it saying that root(6) = root(2) * root(3).
I then added the green square root symbols to the started activity. Commenting on the fact that, because we chose one number to be a square number, we can simplify that part.
We discussed the two where there were multiple answers, and which gave us the "simplest form".
Then they did some questions.
It seemed to work quite well (though I will never get to follow it up as it was a cover lesson). I have always used a variation of the spot a square number approach, but felt my explanation was clearer this time because of the way I laid it out.
How do you teach simplifying surds?
Over the last few years I have become obsessed with the Science of Learning, cognitive science and evidence informed practice. I have become a much more explicit teacher, planning my examples and explanations clearly. I rarely use discovery learning any more.
Whereas my focus used to be almost solely on inspiring students to love Maths, now I focus on getting students to be good at Maths (which does, eventually, lead to a love of Maths). However, have I swung too far in the other direction?
I have been considering the Mode A + Mode B model as explored by Tom Sherrington, and how I can reintroduce a little more of the Mode B style of teaching to my practice. One thing that I thought about was an experience I remember from when I was at school. When studying for Additional Maths at GCSE (we did the GCSE in Year 10, and the Additional Maths course in Year 11), our teacher challenged us to go away and research an area that was not on the curriculum to present to the rest of the class. I chose to do complex numbers. I do not remember the actual presentation, but I do remember the feeling of being the expert in the room about something none of my peers knew, and I remember it being really interesting to research something independently.
So, this year I have decided to do the same with my IB Higher Level class. I have set them the same challenge to go away and find an aspect of Maths from beyond the course to present. I emailed them a couple of links with ideas (https://www.numberphile.com/ and https://ibmathsresources.com/maths-ia-maths-exploration-topics/).
Some of the topics they have chosen are: Graham's Number; Euler's Identity; solving a Quintic equation; Viete's Formula; Stellar Numbers; the birthday paradox.
Simplifying Algebraic Fractions with S4
I have had a great unit on Algebraic Fractions with my S4 class these last couple of weeks. I have made extensive use of example problem pairs and the whiteboards I have around my room. I talk in more depth about one aspect of the unit here.
I blogged about my view on the famous pyramid, and how I think it has been misinterpreted but still has value. Interestingly, since I posted this, Pooja Agarwal has released an article linking retrieval practice to Bloom's Taxonomy (https://www.retrievalpractice.org/strategies/2019/3/27/blooms-taxonomy).
I published the first issue of our T&L Newsletter of 2019 last week. We have a couple of new sections linked to our school focuses for the year, and links to 8 blogs that I hope people will find useful. I also blogged about using objectives effectively as part of our focus on the Principles of Great Teaching.
I ran an INSET session on Challenging All Students, which is our first Principle of Great Teaching. In summary, I talked about the following:
I have been teaching algebraic fractions to my S4 IGCSE class. I am about halfway through the unit, and I wanted to take some time to reflect on how it was going so far.
I started the unit by getting students to answer a serious of questions on cancelling fractions and equivalent fractions. I generated these using my website as I wasn't concerned about the order of questions as it was all stuff they had done before. However, in reviewing this, I decided to talk explicitly about what we are doing when simplifying a fraction. I was very deliberate with my wording "We are looking for common factors in the numerator and denominator that we can cancel". In saying this I broke the numerator and denominator into a product of factors, as shown below.
We then extended this, with me saying "To simplify algebraic fractions we find common factors in the numerator and denominator which we can cancel."
Following this I ran through a series of Example Problem Pairs (shown below). I have started doing this using my visualiser so students can see the layout I use in the booklet they have to copy the examples into. I broke up the numerators and denominators into the factors, then cancelled them (I have always taught spotting these before). There are 9 example problem pairs, showing different types of simplifications they may come across. As this was quite a lot of examples, I didn't want to spend ages going through them all, so I decided to do it quickly.
For each example, I called students attention to the board ("Eyes on the board" - I have been working with them for 6 months on how to behave during examples, so this is all that is needed most times), and then I worked the example on my copy of the booklet. They are watching the screen, not talking and not writing. In this case I did not feel the need to narrate after doing the example. As soon as I was finished I said "Your Turn", and all students copied down the example and attempted the corresponding problem. I then Cold Called a student to give the answer to the Your Turn, making an effort to congratulate them for getting it right. In one instance the student wasn't sure, so I asked them to tell me the first step, which I wrote down in the Your Turn box (Your Turn 5), and they finished the explanation by themselves without further prompting.
I then sent students to my big whiteboards that I have around my room to work in pairs answering the following set of questions from the textbook. After a few minutes, they had all made really good progress (much better than when I have them work at their desks). During this time I had been able to quickly see the work of every student as they were all on display to the whole class.
This was followed by another quickfire round of example problem pairs, where there were factors in brackets. I made a big deal to refer to them as factors throughout.
Then back on the whiteboards for some more practice.
I followed this same pattern through simplifying algebraic fractions that needed to be factorised first, and here is where my over emphasis on the need for factors paid off. Another set of example problem pairs on linear expressions, with time on the boards, and then quadratic expressions. Students spent 25 minutes working individually in their books on the questions for these, as I explained to them that they were more difficult and they would need to give it their full attention. For a class that are generally quite chatty, they worked pretty much in silence for 20 straight minutes on difficult algebra problems. I was in shock (in a good way!)
I did make one error here when addressing prior knowledge. Although I got them to factorise a few quadratics so I could check if they were OK with this, I obviously didn't give them enough time on it, especially those with a coefficient of x2 which was not 1. This ended up distracting from the simplifying fractions, and I decided to ask them to skip a few questions to focus on the skill we were looking at today. I need to come back to reviewing more complicated quadratic expressions, and build in some algebraic fractions too.
The following lesson we moved on to multiplying and dividing algebraic fractions, and followed a similar process, though with only 2 example problem pairs (they didn’t need any more by this point). I also started this lesson with a set of questions on multiplying and dividing numeric fractions, and showed the class how to cross cancel before performing the operations (which some had never seen).
I then had them work on a challenging exercise from one of the old textbooks recommeded by Jo Morgan at Resourceaholic.
I particularly liked question 10, and once we had found the answer, I was even more convinced of the beauty of this expression. I explained to the class why it was beautiful, and challenged them in the last 5 minutes to create their own beautiful expression that simplified down to an integer.
I have now got to teach adding and subtracting algebraic fractions, and then dealing with complicated equations with algebraic fractions too. I am going to try to follow a similar process throughout the rest of the unit.
I have found the quickfire example problem pairs to be a great way to keep my lesson moving at a good pace, as I have found in the past that these can really slow the lesson down. Although sometimes that extra time is really needed to dig deep into the example and details, in this case, I think seeing lots of different examples close to each other allowed my students to make connections for themselves.
All students were able to perform in the lesson, fully able to deal with all the stuff we have covered so far. I am happy that I have laid a groundwork of success for the students before we now move into the slightly more tricky bits of the unit. Hopefully that feeling of success will run through, and students will continue to believe they can do it.
I know that them performing in the lesson is not a good indicator of their long term learning (these will be cropping up in starters and quizzes over the next few weeks and months to guarantee that), but I have never taught algebraic fractions before when all students left the room able to do it (except when I have taught the top set Additional Maths class). And this is definitely a good step in the right direction. After each of the lessons in this sequence I left the class feeling like ALL my students knew more than when they entered my classroom. On top of this, ALL the students were working for the full 40 minute period, fully engaged by both the quick pace of the example problem pairs and the use of the whiteboards for answering questions.
Overall, this is definitely something I am going to build into my teaching on a more regular basis.
Bloom's Taxonomy and the pyramid shown above are commonly known in educational settings. The hierarchy was designed to help educators push students to higher level thinking, and was intended to help with the development of cognitive abilities.
However, I feel that it is often misinterpreted in educational settings. Many people are under the impression that Bloom's Taxonomy says we should always be aiming for the top three tiers of the pyramid. These are the higher order thinking skills we want our students to develop, so these are the ones we should be practising regularly.
On the other hand, there are people who see the pyramid and immediately cast it aside, having sat through training sessions stating the above, or just having it hammered at them so often they have grown tired of it. These people argue there is no use in it as it is old (1956) or not based on a thorough research base, which is now significantly more advanced.
But I feel both camps are on the wrong track here. As far as I know, Bloom never intended to suggest that we must always aim for the top, and it is this that causes the problems (on both sides).
I actually like the Pyramid structure of the taxonomy, as to me it makes things very clear. To achieve understanding, you need a firm foundation of knowledge. To be able to apply your knowledge successfully, you need to understand it. You cannot analyze something if you cannot apply the basic ideas. To evaluate (that is justify your conclusions) you need to first analyse the material. And, finally, to be able to be creative in a domain, you have to be able to justify your opinions first.
This is the nature of a hierarchy: they build upon themselves. You have to climb to the top, and it is not possible to jump straight there without doing the ground work. This fits in with my view of creativity as the pinnacle of expertise within a domain. We can only be truly creative when we know a lot about something. As an Art teacher once told me, "You have to know the rules in order to break them" when referring to the work of Pablo Picasso.
But there is another aspect of the pyramid image that I like. Notice the size of the pieces. They are not equal. This has two implications:
I want to clarify for the second point I mean throughout school. When students arrive in our class they already have a vast amount of knowledge they have learned (both in and out of school), especially if we teach in secondary education. That means that most of that block may already have been learned, and we can move up more quickly. In general, the further through their studies of a particular subject, the more higher level thinking we should require. However, it is dangerous to assume this is the case. If there is missing knowledge, or even misconceptions, then the other aspects of higher order thinking will be built on a shaky foundation, and, inevitably, will lead to poor performance and less learning. One of our roles as a teacher is to check for understanding and knowledge before moving on to the higher levels of Bloom's Taxonomy.
And for those people who sit in the latter of the two camps described at the start? Well, I think this interpretation fits in well with ideas from modern cognitive science. For example, Daniel Willingham talks about How Knowledge Helps, which is saying that the bottom of the hierarchy is really important.
I think that there is a lot of benefit to the ideas of Bloom's Taxonomy, but, as with many things in education, when it is misinterpreted it can be killed off.
Further Reading on Bloom's Taxonomy
Here are three posts from some of the big hitters in education with their take on the Taxonomy.
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.