There aren't many teachers (or indeed people in general) who would argue with the desire for education to lead to students having flexible, transferable knowledge. That is, that kids learn stuff, but are also able to transfer this knowledge into new an unfamiliar situations easily. As an example from my own subject, we want students to be able to spot when to use Pythagoras' Theorem even when it crops up in a question which has nothing to do with triangles (on the surface), or, even better, when it appears in a different subject (surely the true Holy Grail). All subjects have ideas like this (perhaps this is what we mean by concepts?) that we want students to be able to recognise outside of the narrow confines of the lesson or topic. It is worthwhile spending a few minutes thinking about some of these in your subject.
But as teachers we also know that this is surprisingly difficult to achieve, and are often astounded that students just can't see it when this concept appears somewhere new, especially when we know they can do it.
Throughout 2019 I worked alongside two teachers in my department on Checking for Understanding, but early on we diverted to thinking more about what we meant by understanding. Without going into too much detail, we settled on 6 stages of understanding, as shown below in a display I now have in my room.
This made me think about the excellent Daniel Willingham article for the AFT titled "Inflexible Knowledge: The First Step to Expertise", and how Willingham distinguishes between rote, inflexible and flexible knowledge. I would say that our stages 1-4 of our model above are a break down of inflexible knowledge (although 1 could be rote in certain contexts), and that only 5 is true flexible knowledge.
But anyway, the point of this blog was not to delve into the details of the differences between these types of knowledge (read the article above if you want that), but rather to get a bit meta on the idea that inflexible knowledge comes before flexible knowledge can fully develop, which stemmed from this tweet:
If we take the idea that we need to pass through inflexible knowledge to get to flexible knowledge (which is not universally accepted), then this has implications on the understanding of that very statement for teachers.
For teachers to be able to think flexibly about the idea that students need to pass through inflexible knowledge to get to flexible knowledge, the teachers must first pass through an inflexible knowledge of this very idea.
That is, it is completely natural for teachers to know that students need to first develop inflexible knowledge before being able to reach the heights of flexible knowledge, but for those teachers to be unable to apply this to their teaching (which would be showing a flexible knowledge).
If a teacher has passed on to flexible knowledge of the idea that inflexible knowledge is a precursor to flexible knowledge, then they will plan activities to make use of this. Perhaps this would involve using retrieval practice (with higher order questions as suggested here) or something else (this would depend on the individual teachers flexible knowledge of other areas of pedagogy). Once you start to dig a little deeper into this idea, it becomes clear that pretty much everything a teacher does is also subject to this principle. First we learn some new idea, perhaps we play around with it a little, we read more about it, and gradually, as we develop more experience we are able to incorporate it into our teaching practice flexibly.
And that includes our understanding of developing flexible knowledge. This understanding needs to pass through being inflexible before we can flexibly use it.
Thinking about that makes my head hurt, but I think it has implications for teacher professional development. It also make me feel a bit better about knowing I should be doing some things in the classroom, but not being able to do it flexibly.
This time last year I wrote a post on the Successes and Targets I had, and as the new year starts I find myself once again reflecting on last year.
My highlights/successes for 2019 have been:
What about my targets from last year?
And looking forward to 2020, I have decided to follow the advice I got from the coaching course, which was to work on one target at a time. So these targets are what I shall work on in my teaching ine the respective bimester. I detailed some things I wanted to work on after reading Making Every Maths Lesson Count.
On top of targets for my teaching, I have some targets for my role as T&L Coordinator.
So there it is. Some highlight from 2019, progress against my targets from last year, and some targets for 2020.
Today I saw this tweet.
If this tweet was intended as a self-depreciating ironic statement, then perhaps what I am about to say should not be directed at the author. But if it is meant as a passive aggressive jibe at "traditional" teachers, then I have a few things to retort.
My first issue with the whole thread is that the main argument is that traditional teachers fall for confirmation bias, actively seeking out research, blogs, books that confirm their beliefs. Whilst this is almost certainly true, we are all susceptible to confirmation bias, and this particular attack would be just as well placed at the "progressive" educator. Everything that is said could easily be turned on to the other side of the debate.
On top of this, by drawing comparisons to outlandish ideas, the author is heavily implying that "traditional" teachers are stupid, and will believe anything they read. Obviously, devoid of any critical thinking skills, and unable to make judgements for themselves
Throughout this I am going to stereotype the progressive educator as the author has stereotyped traditionalists, to draw certain parallels between the arguments. I am not intending to say that all "progressives" are like this, just as I am willing to admit that there are "traditionalists" as described. My main point is to say that every attack that has been made against the "traditional" teacher could equally be made against the "progressive" teacher, and as such, show that the arguments given are not logical. Despite being a more traditional teacher myself, I think that the variety of experiences that students receive in school are important, and having a mixture of pedagogies across teachers in beneficial for the system as a whole.
My argument would be that an excellent teacher-led classroom (which is what I am assuming the author means by traditional, as they later refer to lectures) involves just as much (if not more) planning than a student centered one as the teacher has to carefully craft examples and explanations, and think deeply about the sequence of the curriculum. In a student centered classroom, the teacher can plan an activity without any of this extra thought (necessarily). Similarly, in the classroom, the progressive teacher can allow students to work in their groups, not being actively involved, whereas the traditional teacher is questioning students, checking work and giving feedback on the spot, and marking work.
Of course, the reality is that on both sides of the spectrum there are lazy teachers and there are those who work incredibly hard to give their students the best education they can (within their belief system). Laziness is not an inherent property of a traditional method to education, but rather one of human kind.
Lecture is the best way to teach
This is like saying that student-centered approaches are rubbish because teachers just let the kids do what they want. It is a lazy stereotype of a methodology. Done well, either methodology is far superior to the other done poorly.
That is ignoring the "Being insane" comment that is obviously trying to ruffle some feathers.
But the real issue here is that traditionalists are opposed to change. Many of the "traditional" teachers I know were trained in "progressive" methodologies, and told that too much teacher talk was bad, to use VAK, that you had to be active to learn, etc. And many of these people, myself included, have changed what they believe based on new information. To say they are not open to change goes against the fact that they have changed to become who you say cannot change. A true logical contradiction.
Of course, again, there are those who are set in their ways, and have done this just because they were shown that way. But, again, this can just as easily be said of the "progressive" teachers who are just doing what they are told.
This is the one point where the tweeter accepts there is a problem on both sides. Anyone who pushes an agenda at the expense of others, or worse, the children we teach, is an issue in my opinion, no matter where they fall on the spectrum of pedagogy. But again, the jibe with saying that "traditionalists can be worse" is clearly implying that one end is of lower quality
If this was meant as a bit of fun (which I presume it must be), then perhaps I have overreacted. Perhaps I am lacking a sense of humour about this. But as somebody who still hears people saying that we should not tell kids stuff, I think this type of material is dangerous, as some will interpret as "traditional is bad", falling, ironically, into their own confirmation bias
Wholesome Leadership by Tom Rees is a whole approach to school leadership. It is based around the model of the heart, the head, the hands and the health of school leaders, and goes into detail as to what successful leaders in schools do in each of these categories.
Throughout the book, Rees tells personal stories of how he has developed as a leader in the different aspects, as well as giving specific examples of his experiences. This personal touch really helps the book feel more authentic, as you can tell it is written by somebody who has lived these experiences. This is balanced nicely by the interviews with others who are (or have been) involved in leadership in education, each giving their own perspective on one of the aspects of the Wholesome Leadership model.
Before delving into the nitty gritty, Rees shares a handy planning tool, which he calls the Five Fives, for managing change, a big part of being a school leader. Throughout the book he refers back to this tool, providing a template at the end of each chapter to encourage leaders to engage in planning their changes.
Also at the end of each chapter are a series of reflection questions for leaders to use to ascertain what areas they would like to work on in their leadership/school. Combining these with the Five Fives planning tool is an excellent way for leaders to take action after reading the chapter.
Illustrated by Oliver Caviglioli, the visuals add to the whole experience of the book. Each chapter starts with a summary of key quotes which gives the reader a nice taster of what is to come. The highlight of the visuals are the WalkThrus for Learning Walks, Appraisal, CAP Meetings and Review Mornings.
Each of the four parts of the Heart, Head, Hands and Health model is broken into 3 linked chapters. Although it is an easy book to read all the way through, it is also designed so you can jump to a particular chapter that you are interested in. I can see myself popping back to chapters on a regular basis to reacquaint myself with the ideas, now that I have read the whole thing.
I have created a summary document of the book. The image is below, but you can find the PDF version here, which can be printed up to A2 (it also works pretty well in A3). Some more details on each chapter are below that.
Next week we have our taster lessons for the new IB cohort. The IB syllabus has changed this year, and there are now four options that students can choose from.
I will be teaching the AA SL course next year, and for the taster classes we wanted to choose a topic that would show the difference between the courses. We (well I wasn't actually in the meeting, but I agree) chose to use proof. This will make good use of algebra skills, ensuring students know this is a pre-requisite for this course, but also gets to the heart of Mathematics.
In preparing for this I have put together a couple of documents.
First is this learning map which shows an overview of proof as a topic. They will only need to do Direct Proof and Disproof by Counter Example in the AA SL course (though Induction and Contradiction are in AA HL), but I think giving them a broader picture is important.
I will reveal this a step at a time, as the powerpoint builds up slide by slide (something like in the gif below).
I also put together a lesson sheet for the topic. I have talked before about how I have started using lesson sheets in IB and booklets in IGCSE. This lesson sheet includes examples and plenty of your turns for the students to have a go at, to test their skills in proof.
We will see how the lessons go next week, and I will post an update.
In Better Conversations, Jim Knight briefly talks about the power of assumptions. We all have different core beliefs and assumptions, and often disagreements that we have are based on differing assumptions that we hold. This is true in all aspects of life, including our views on education.
The problem with assumptions is that we tend to defend them aggressively when we feel they are being attacked. By sharing our underlying assumptions we can help each other see why we disagree, which should help conversations be more constructive.
If we do not know the assumptions our conversation partner holds, then we are liable to think they are stupid for what they are saying, as we are judging their comments against our own assumptions.
These assumptions (or beliefs, values, opinions) feed into everything we say and do, so helping others to understand them will help others to understand our points. Similarly, by finding out the underlying assumptions of others, we are in a better position to understand their points.
So, here are some assumptions I hold about education.
1. Conversations should focus on the learning
There are a lot of things going on in a school, but the primary purpose is to give students the best learning opportunities that we can. For this reason, conversations we have in schools should focus on the learning of the students as much as possible. By keeping a relentless focus on learning within meetings, we don't waste precious time talking about things that will not affect student learning.
Just like Willingham suggests we plan by thinking about what students will be thinking at each stage, when in meetings we should always be thinking about how this will impact student learning. If the answer is "Not Much", then we need to consider if we could be talking about something more impactful.
I get frustrated when conversations become focused on details that have little impact on student learning, and I will always try to bring it back to what I think is the most important thing for us to be discussing. Of course, that doesn't mean we should agree on everything about learning, but focusing our discussions on this will give us the biggest chance of having the best impact we can.
I recently read the excellent Making Every Maths Lesson Count by Emma McCrea. Like the original, it is an engaging read, but I really liked the subject specific ideas that this version had to offer over the original. In this post I am going to identify 1 idea from each chapter that I am going to work on over the next year or so.
The rule in my IB Higher Level class is that if they forget to add +c for an indefinite integral then they have to bring cake to the following lesson. I call this +Cake (and will write this on any pieces of work I collect without it).
On Monday morning I had two students turn with cakes to pay for this.
The excellent Ritangle competition started last week, and I introduced it to my IB HL students as a starter activity. I am going to use the problems to start lessons for a few weeks, but then will set them off to do it in their own time. We set up a team of the whole class with the team name +Cake!
If you haven't seen the competition before, it is worth a look.
We are in the final term of our year, and in preparation for launching a small scale instructional coaching programme next year, this term I am working alongside 4 colleagues to develop them as instructional coaches.
In April of this year I went to the Instructional Coaching Institute in Kansas with Jim Knight, and since then I have been doing little bits of coaching with some colleagues. But for next year we are making the programme a little bigger, and I have the role of 'training' the new coaches. Of course, I am certainly no expert in the process as I have been looking into it for only about a year, but I have some insight into the coaching cycle (more than others anyway).
I have put together a 9 week programme of training, where we will explore the fundamentals of Better Conversations (see below), through the Impact Cycle advocated by Jim Knight, and then delve into the depths of gathering data, setting goals and developing an instructional playbook.
Each week I am setting the group some pre-reading as well as a task to complete (such as recording themselves teach), and meeting with the whole group to discuss the reading and next bits, and then meeting individually to talk through individual concerns and how the task went.
It is still early days, but the setup seems to be working well. We are going to get into the actual coaching cycle next week after doing some background stuff on conversations and partnerships in the first two week.
As part of our Principles of Great Teaching we have 3 Standards that we expect to be implemented in lessons:
Over the year we have done various sessions on each of these to introduce the ideas, and for the third one groups of teachers designed their own acronyms to represent what we feel shows good listening (think SLANT style).
After getting 20 ish different versions, I put them into a Google survey for teachers to vote on which they felt was the best, and the winner is below.
I blogged briefly about Better Conversations by Jim Knight, and produced these images on the main ideas.
Whole Class Feedback Sheets
People have been going on about whole class feedback a lot lately, so I decided to actually try putting together a template to structure it. I often write brief comments on a post it note, but thought it was worth trying a template structure.
Based on a few I had seen on twitter, I put together this one.
On using it a couple of times, the biggest thing I have immediately noticed is that it has made me think more specifically about the actions I should take for each error/misconception. Straight away I was more deliberate about the questions I put in my retrieval starters, for example.
I will continue to use them and see how it goes, but my first impression has been positive.
Over the last year I have started working as an instructional coach in my school, and this term I am training 4 other teachers to work as instructional coaches next year. As part of this I have gone back and read various books by Jim Knight, to clarify some of the details that he shared in the Instructional Coaching Institute I attended in April.
One of these books is Better Conversations, which is not directly about coaching, but rather about having productive conversations. Obviously, this is a key skill of the good coach.
Knight starts by exploring the issues around communication in today's world, and what he refers to as the "radical brokenness" in many of todays conversations, which often focus on persuading an "audience" to agree with you. He contrasts this to a Better Conversation, or a dialogue, where both parties learn from the conversation.
Knight does not sell himself as an expert, but rather somebody who wants to improve his own conversation skills. The book is his way of collating the stuff that will be useful to his own development, and he has very generously shared what he has discovered.
The philosophy of Better Conversations is that they are based on a set of 6 Beliefs.
These 6 beliefs are easy to agree with, but Knight goes one step further to say that we need to demonstrate these beliefs through our actions, and to do this we can internalise a set of 10 Habits.
The main bulk of the book is exploring each of these habits, what they look like, and how we can become better at them. Each chapter ends with a series of reflection forms to use to analyse how you currently live up to the habits and to plan how you will make the next steps.
I agree with the premise that many conversations that take place do not fulfil the requirements of a dialogue (a learning conversation where both partners are there to learn). This is as true in schools as it is in the wider world. But these skills are not only applicable to coaches: they are a vital part of developing anything, including a school or education system.
Just imagine a world where everybody was willing and eager to learn from each other, and our conversations were not an attempt to convince or belittle others, but rather to truly understand what the other believes and learn from them.
You can get a PDF version of the above images here.
I have done a few sessions with students recently on the importance of sleep, as lack of sleep has become a chronic problem for our sixth form students. They are staying awake into the small hours of the morning to complete work that they have left to the last minute, thinking that sleep is a luxury that they can do without.
But that is simply not true.
Based on my reading of Why We Sleep by Matthew Walker, I have been being more explicit about the dangers of a lack of sleep, but also the benefits of getting enough sleep. I have been particularly focusing on the way sleep relates to learning, but have also been talking briefly about the other health concerns.
I have started with a brief introduction to the importance of sleep for the learning process, and I have cobbled together an analogy that I think sums it up quite well.
Our brains act like a sponge, absorbing lots information throughout the day. As they day progresses the sponge gets more and more full. When we sleep, it is like squeezing the sponge into a bucket: the new learning is safely stored into our long term memory (the bucket). Day after day we keep adding more stuff to our bucket. Of course, when we squeeze the sponge some of the water splashes out and misses the bucket, and we lose that water, but most of the water is makes it into the bucket. When we wake up, the sponge has been completely emptied, and is ready to absorb a new set of learning the following day.
I have been using this analogy to highlight the two benefits of sleep towards learning: firstly it helps consolidate our learning from the previous day by transferring ideas from our pre-frontal cortex into our long term memories; and secondly, it leaves our brains in a more receptive state to learn the next day.
Of course, when we do not get enough sleep, we do not fully squeeze the sponge, so not everything makes it to the bucket, and we do not have as much ability to soak up new knowledge the following day as the sponge has not been fully emptied.
Or if our sleep is of low quality (such as when we drink alcohol or take sleeping pills), when we squeeze our sponge it is like having a shaky hand, and much less of the water makes it into the bucket.
This analogy works for the deep sleep cycles, and seems to get the point across.
But it does not work as well for the importance of the REM cycles. This phase of sleeping is also vitally important to learning, as this is the time when our brain starts to make connections. As many mathematicians know (and I am sure many from other walks of life) when we are stuck solving a problem, one of the best things to do is to go away and come back the next day. Part of this is due to the power of the REM cycles of sleep, where the brain continues to work on the problem, accessing that deep bucket of knowledge you have stored away in the daily sponge cleansing.
Having talked about the importance of sleep for learning, I then share some of the startling facts and figures that Walker shares:
Many students bemoan that they just don't have time to sleep as they have too much work to do. I point out to them that if they were getting enough sleep then the work would take far less time as they would not be trying to do whilst cognitively drunk, and that, more importantly, their health is far more important than any piece of work.
I finish with some recommendations for sleeping better:
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.