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.

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:

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:

- A different definition of some term;
- A different outlook on the purpose of education.

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:

For me, education has four broad purposes (in no particular order):

— Dylan Wiliam (@dylanwiliam) April 28, 2019

Personal empowerment

Transmission of culture

Preparation for democratic citizenship

Preparation for work

The problem is that that these four broad purposes interact, and conflict...

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.

Simplifying Surds

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 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?

5BHL Presentations

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.

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.

]]>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.

Bloom's Taxonomy

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 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).

Newsletter

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 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.

Challenge

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 ran an INSET session on Challenging All Students, which is our first Principle of Great Teaching. In summary, I talked about the following:

- "But I already do that!"
- Memory is the Residue of Thought
- Mindsets
- Pygmalion and Golem Effect
- Differentiation
- Content vs Task
- The Struggle Zone
- Success Before Struggle
- Show Them Excellence
- A Culture of Challenge
- Further Reading

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:

- You require a LOT of knowledge in a domain to be able to understand it (and so on up the pyramid);
- The amount of time spent teaching knowledge throughout school should be significantly more than the time spent on creating.

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.

Here are three posts from some of the big hitters in education with their take on the Taxonomy.

We have just started our new school year in Peru, and the kids have been back for a week, after an INSET and Preparation week. It has been tough to get back into the routine, but it doesn't take long to get back in the habit.

In the INSET week I launched our new Principles of Great Teaching document with two sessions with our staff: introducing the document in general and then focusing on the first standard, which is having an activity for students to do as they enter the classroom (inspired by Doug Lemov's Do Now). It has been accepted well by colleagues, who have commented on it being useful to track their own development, and as a guide towards great teaching. Most people were even on board with the Do Now, though we will have to see how that goes as term progresses.

In general, people were very positive about the whole week, and I have had a couple of comments about it being more useful this year than usual, even though staff had less time to prepare for their classes.

My personal focuses for this year that are taken from the Principles are:

- Checking for Understanding
- Independent Practice

In terms of teaching, I have started my classes with more clarity on my expectations for lessons with me, by producing this document which I have on my walls, and have given copies to my students.

Introducing Direct Variation with S4

In the first lesson of the year I introduced my S4 class (taking IGCSE this year) to the concept of two variables being connected by a constant factor, and linked this to previous work on proportion. I ended by showing them the notation for a is directly proportional to b.

In the first lesson of the year I introduced my S4 class (taking IGCSE this year) to the concept of two variables being connected by a constant factor, and linked this to previous work on proportion. I ended by showing them the notation for a is directly proportional to b.

We continued this work in the double on Tuesday. I started with the traditional Last Lesson, Last Unit, Further Back, but I have added a new section this year: Drill. The idea is to drill some of the most basic skills so they do not occupy space in working memory when solving more complex problems.

After reviewing a couple of bits from this, I moved on to a silent example problem pair. I used Show Call on the Your Turn problem, choosing a couple of pieces of work I noticed while circulating, one using 0.75 and the other using 3/4.

Previously I have written the examples on the SMART board, but this year I have decided to do it using the visualiser live on a copy of the booklet I give to students. This worked well as it gave them more guidance on how to lay it out (although I needed more space to keep the vertical structure I would have preferred).

I then had students complete a short exercise in pairs on the big whiteboards I have around my room. I much prefer this way of working than using mini-whiteboards, as it is easy for me to see everybody's work, and to draw attention to important points. For example, one pair started with x=ky whereas everybody else started with y=kx. I used this to identify that their values of k were different, but the final answer would be the same. As it was on a big board, it was easy for everybody to see.

After a couple of groups had finished the 10 questions, we moved on, and I had the class generate the 5 steps for the process. I insisted on them using proper vocabulary (substitute not "put in"). I followed this with a quick Pepper round (also Lemov), asking them quickfire questions on their squares, cubes and roots. This energised the room nicely before seguing into some more examples-problem pairs, where we have proportional to squares and roots. I actually decided to have students attempt Example 4 by themselves before I showed them, and several got stuck by the fact that it was asking for the value of the subject of the formula. When I then showed them, they had had a chance to think about it, and this step made more sense.

Then I used a few Diagnostic Questions to check for understanding of notation and steps. We finished with some independent practice questions taken from Dr Frost.

Next lesson we move on to Inverse Proportion.

Gratitude

I downloaded the 5 Minute Journal App towards the end of the holidays to start developing my own reflective processes. Each day I have to come up with 3 things I am grateful for, 3 things I will do to make the day amazing, and then in the evening reflect on 3 things that were amazing, and 1 thing I could have done to make it even better.

I downloaded the 5 Minute Journal App towards the end of the holidays to start developing my own reflective processes. Each day I have to come up with 3 things I am grateful for, 3 things I will do to make the day amazing, and then in the evening reflect on 3 things that were amazing, and 1 thing I could have done to make it even better.

I am finding it difficult to come up with new gratitudes each day, but it is slowly becoming easier. I have built it into my morning and evening routine now, so I am remembering to do it. I am starting to feel generally more positive about situations, and I am hoping that this will help me become more charitable in my interpretations of what people say, as well as making me more aware of my own good fortunes. It is very easy to focus on the negatives, and this will hopefully stop me from doing that so much.

Team Teaching

My colleague and I who are both teaching IB Mathematical Studies, have decided to combine our classes and team teach this year. It is the second year of the course, and we always have a few students leave school at this point (it is only compulsory until 17 in Peru), so we both have small classes (less than 10). We figured this will allow us to provide more support, especially during independent practice. We are going to see how it goes, and I will reflect more on it as we progress, but I am excited to give this a go.

My colleague and I who are both teaching IB Mathematical Studies, have decided to combine our classes and team teach this year. It is the second year of the course, and we always have a few students leave school at this point (it is only compulsory until 17 in Peru), so we both have small classes (less than 10). We figured this will allow us to provide more support, especially during independent practice. We are going to see how it goes, and I will reflect more on it as we progress, but I am excited to give this a go.

Sets Notation Matching

We started the new year with a unit on Sets and Probability with the final year IB Mathematical Studies classes. Sets is something they have encountered several times before, and it is on the IGCSE that we do. However, the notation is always something that causes confusion. To start the unit we decided to do a matching activity with the symbols, the names and a brief description.

We started the new year with a unit on Sets and Probability with the final year IB Mathematical Studies classes. Sets is something they have encountered several times before, and it is on the IGCSE that we do. However, the notation is always something that causes confusion. To start the unit we decided to do a matching activity with the symbols, the names and a brief description.

The activity was done in pairs, and there was lots of good discussion and questions about some of the notation and words. They had not seen the words Order, Disjoint or Ellipsis before, so these threw a lot of them, even though they had an idea of what the symbols meant. This gave us a pretty good idea of which were the problem areas (subset vs proper subset).

]]>With this is mind, I have designed a new PD programme for our teachers to engage in throughout the 2019 school year. The starting point of this programme is a document that I put together with several of my colleagues last year, which was then put through SMT, and is titled "The Principles of Great Teaching". In putting this together, I referred the focus group to several articles and bits of research, and I discuss the process in more depth in __this post__.

The final product has 16 principles, broken into two categories: 4 core principles that we think underpin every instance of great teaching and will be a part of all learning opportunities; 12 principles that are called upon over a period of great teaching, though may not be a part of every single lesson. Important to me from the outset was the idea that these are principles for great teaching NOT great teachers.

Some of my colleagues struggled to see what I meant here, but this is the crux of the first sentence of this post. Great Teaching is something everybody is capable of doing and is more objective. However, being a Great Teacher is seen as an innate trait and seems more personal. When talking about somebody's teaching you are talking about something they have the power to improve. When talking about somebody's qualities as a teacher you are talking about their personal qualities, something that is much more difficult to change and also more unique to each individual. It is the same principle as when we talk about the behaviour of a child when reprimanding them rather than assigning a quality to the student ("Punching somebody is unacceptable and the consequence is..." vs "You are a naughty child for punching them").

I also wanted the principles to be things that we could give examples of and model in INSET sessions. These are the knowledge of great teaching, and as such must be concrete ideas rather than abstract ones that teachers are not sure how to interpret. Although they are principles I want to develop a set of possible techniques and strategies for implementing these principles in the classroom. As part of the CPD Programme for this year, I am going to ask departments to discuss each of the core principles in detail, and make some suggestions on what they might look like in their departmental context.

Finally, I wanted most of the principles to be linked directly to the learning of the students, as this should always be our focus in developing ourselves as teachers. If we are not doing it to improve student learning, then it is probably a waste of time. This was a very important aspect of the whole process for me, and has been confirmed as essential as I have recently been reading Unleashing Great Teaching by David Weston and Bridget Clay.

A side benefit of the principles was to be the formation of a set language that can be used throughout the school when talking about teaching and learning, to help us all communicate more clearly about what we do and how we can improve. This will hopefully enable staff to have more productive discussions about teaching and learning.

Below you will find the 16 principles, along with a graphic version I put together.

The underlined words are those which will hopefully form the basis of our shared language. The bold phrases are the principles themselves, and the sentence after provides a small justification of the principle. The idea is that over the next year this document will become backed up by a larger document detailing what we mean by each of these principles in our context, and provide some examples of what they look like in the classroom (hopefully with video clips of our teachers demonstrating different aspects of each principle).

At the end of this document we have also decided on three Standards of practice at our school. These link to multiple of the principles above, with a focus on the core principles. These are a bit more specific than the principles, and are designed to give a little more structure to the learning environment of the students. The idea here is that if these three standards are used in every lesson, we will be lowering the cognitive load on students to do with expectations of behaviour for learning, allowing them to spend more time focusing on the content, skills and concepts they will be learning.

I hear you asking, how am I planning to implement these principles and standards? Well, this is my plan...

In our INSET week in February I will introduce all colleagues to the document. This will include time to discuss what we mean by each of the principles. In this week I will also do a session on the first standard, where I will use Doug Lemov's idea of Name It, See It, Do It. After briefly describing the standard, we will look at examples of how it can be done effectively, then give departments time to work on designing their own activities. I will use this format in a similar session on each of the other two standards at the start of each term.

We also have a 40 minute INSET twilight in the middle of each term, so I will be using these to introduce the 4 core principles in more detail (we have four terms), which will be followed by a Departmental T&L session a week later, where departments will be given the task of discussing what that principle could look like in their subject. The minutes from these meetings will inform the larger document of examples.

The final aspect is that each department will have a second T&L meeting each term. In the first of these, the department will decide on 2-3 of the principles which they would like to focus on for the year, and in the other sessions they will discuss how they are working towards these, and share ideas on how to improve. Teachers will then focus some of their own development on this departmental targets, and through observations and reflection , teachers will decide how best to incorporate the principles into their teaching.

The aim for this year will be to get all staff to be familiar with the principles, in particular the core principles. By the end of the year all teachers should also be working towards implementing the standards in their teaching. Hopefully, by the end of the year, we will have several examples of our own teachers implementing the standards and core principles in their own ways. The following year we will look at the other principles in more detail.

Alongside this, we are also trialling an instructional coaching programme this year. To start with I will be acting as a coach, working with 12-15 staff throughout the year. The idea is that this will be expanded in the following year, with more coaches being trained, with an end goal that every member of staff will go through a coaching cycle of 8 weeks over a 3 year period (120 staff in 3 years is 40 each year, giving 10 per 8 week term).

My plan is that this document will form the basis of the coaching programme too. So when staff are thinking of aspects of their practice they would like to work on, they will, mostly, be choosing from these. I am on an intense training course in April, so we will be launching the coaching programme after that when I have had a proper chance to do it properly.

]]>I finished reading the excellent ebook MARGE, and immediately saw links to the EBC model I was introduced to in the Science of Learning course I did earlier in 2018. I wrote this post comparing the two models, which has been one of my most popular posts.

I have recently finished reading the book Why We Sleep by Matthew Walker (

There are correlational studies between lack of sleep and a whole host of health problems (cardiac problems, diabetes, etc). There are also links with many mental health disorders (see

But the most relevant to us as teachers was the impacts on learning. When we are awake certain toxins build up in our brain, and when we sleep these are cleared away. Without adequate sleep these toxins build up and prevent us from learning new things. Even worse, one of the main purposes of sleeping seems to be consolidating the learning from the previous day, so with insufficient sleep we get a double whammy on our ability to learn: we will forget the things we learned the previous day; and we will be in a worse position to learn new things as our brain is full of toxins.

Another interesting point for (secondary) education is the natural sleep cycles of teenagers, which are later than those of adults. In fact, teenagers naturally sleep in until later (I know, we all know this), but the important thing is that this is not them being lazy, but rather their biology is forcing this upon them. Whereas adults naturally sleep 10pm - 6am (give or take), teenagers naturally sleep 12am - 8am. This is important when considering school start times, as starting too early can actually be very detrimental to the learning experience of teenagers who will probably be sleep deprived if required at school before 8:30 am (

The book truly was a sobering and enlightening read, and I would highly recommend it to anyone (not just educators). As educators I think it is our responsibility to teach and promote good sleep hygiene to our students.

IB Results

This year the first cohort of students that I taught the IB Mathematical Studies course to finished their course. I was very happy with their results, all of them except 1 achieving or surpassing their target grade.

This year the first cohort of students that I taught the IB Mathematical Studies course to finished their course. I was very happy with their results, all of them except 1 achieving or surpassing their target grade.

New Year Website Reminder

As the new year started I tweeted a thread showing some of the things that my site__http://generator.interactive-maths.com/__ can do.

As the new year started I tweeted a thread showing some of the things that my site

As you head back to school, check out my site which creates random questions on more than 50 #maths topics.https://t.co/D1z3LA46VF#mathschat #MTBoS #mathchat pic.twitter.com/e3lxaugIJJ

— Dan Rodriguez-Clark (@InteractMaths) January 4, 2019

Review of Last Year's Highlights

I also posted a thread on some of the highlights of the blogs/tweets from 2018.

I also posted a thread on some of the highlights of the blogs/tweets from 2018.

THREAD As 2019 starts, here is a reminder of some of the things I have blogged/tweeted about this year:

— Dan Rodriguez-Clark (@InteractMaths) January 8, 2019

Simon Singh Retweeted Crypto Corner

This made me very happy as Simon Singh is a legend, and I love all his books. The Code Book was one of the reasons I became so interested in cryptography in the first place, so for him to recommend my site (__https://crypto.interactive-maths.com/__) was awesome.

This made me very happy as Simon Singh is a legend, and I love all his books. The Code Book was one of the reasons I became so interested in cryptography in the first place, so for him to recommend my site (

Something for maths teachers (and others). May help introduce maths into the classroom. https://t.co/mCLZOc209Z

— Simon Singh (@SLSingh) January 13, 2019

I have previously talked about the excellent Fractal Christmas Tree, though I did not have time for that this year.

I have previously done a DESMOS pumpkin challenge, and I changed this into a Christmas Tree challenge this year. I started by showing students this DESMOS page as inspiration, and quickly talked through the way to set domains, ranges and shade using inequalities.

I then directed students to DESMOS, and off they went. Some started by copying what I had done. One found an image online and pasted it in and then added lines to reproduce it. I then added a couple of baubles to my tree, like below.

At this point, many of the students started adding loads of baubles in different places (they quickly learned how to move them). Some started adding stars to the tops of their trees. One student asked me how to create an ellipse to create a shadow. Below are a few images of ones students created.

In the end I finally added an extra layer to my tree on the board, as below.

And my favourite finished one:

I challenged a couple of classes to find the total number of presents given to me by my true love in the famous carol. All students started by finding how many presents I received on the twelfth day, not in total, but with some further prompting, they all answered the actual question. I then challenged them to do the same for 20 days, or 100 days, generalising their ideas.

In my S3 class (15 year olds), most groups were able to find the nth term for the triangle numbers, which gives the formula for working out how many presents you will get on the nth day. One student was able to work out the total number of presents you would get in the 20 days, and did identify that it was a cubic sequence, but we ran out of time to really explore this.

With my IB HL class, we have been doing taster lessons on proof by induction, and so I decided to start with them proving the following two identities.

Then I gave them the same challenge, but also asked them to prove their results using induction, and with the expectation they would use sigma notation to make a conjecture. I have been giving my HL students lesson sheets, and the one for this activity can be found here.

]]>In particular I have done two free online courses:

- The Science of Learning through FutureLearn
- Learning How To Learn through Coursera

And on top of those I have been reading around the subject. Recently I finished reading the excellent MARGE: A Whole-Brain Learning Approach for Students and Teachers by Arthur Shimamura, which I discovered through this post by Tom Sherrington.

In this post I want to compare and contrast two of the models offered through these experiences: MARGE from Arthur Shimamura and EBC from the FutureLearn course.

First a brief overview of each model.

MARGE

MARGE is the acronym used by Shimamura to stand for Motivate, Attend, Relate, Generate, Evaluate. In the ebook, Shimamura gives both an overview of this model and goes into detail for each of the aspects. He also discusses the brain functions behind each of these.

MARGE is the acronym used by Shimamura to stand for Motivate, Attend, Relate, Generate, Evaluate. In the ebook, Shimamura gives both an overview of this model and goes into detail for each of the aspects. He also discusses the brain functions behind each of these.

I created this sketchnote summary of the main ideas on how they apply to the classroom (PDF available here).

In short, we must be MOTIVATED to learn before starting any learning session for it to be an optimal learning experience. When learning new information we must ATTEND our focus on what we want to learn, and make a conscious effort to RELATE this new information to knowledge and concepts that are already embedded. Once we have encountered information, the best way to strengthen our memories is to GENERATE the information in our own words (that is retrieve from memory rather than rereading notes), and we must regularly EVALUATE our learning by testing ourselves to see what we have actually learned, and what is merely familiar to us at any given time.

EBC

EBC stands for Engage, Build, Consolidate, and this was the model offered for the process of learning in The Science of Learning course through FutureLearn. The course goes into detail about each of these three stages, and the brain functions behind them, as well as looking at other areas of learning.

EBC stands for Engage, Build, Consolidate, and this was the model offered for the process of learning in The Science of Learning course through FutureLearn. The course goes into detail about each of these three stages, and the brain functions behind them, as well as looking at other areas of learning.

I blogged about the course giving a review of each week as I did it, and you can find these below:

In short, this model says that we need to at first ENGAGE the brain to be ready to learn before anything else. Then we need to BUILD memories of knowledge and skills in the optimum ways. Finally, in order for our memories to remain intact over a period of time, and for them to become more easily transferable to novel situations, we must CONSOLIDATE our new learning over time.

Comparing the Models

When I read MARGE I immediately saw some connections to the EBC framework I had previously seen, and as one of the techniques recommended was the 3 C's (Categorise, Compare and Contrast) to help develop schema, I thought I would do just that.

When I read MARGE I immediately saw some connections to the EBC framework I had previously seen, and as one of the techniques recommended was the 3 C's (Categorise, Compare and Contrast) to help develop schema, I thought I would do just that.

The most obvious first comparison to be made was between the two acronyms and the stages they represent.

The MOTIVATE and ENGAGE sections are covering the same ideas, and link up pretty neatly. To BUILD new knowledge we are using our ATTENTION and RELATING it to things we already know. But CONSOLIDATION also has some links to RELATING information (when you RELATE new information to old, you are consolidating the bits you already knew). GENERATING and EVALUATING are things you do once you have the new knowledge, so these pair up with CONSOLIDATE.

What is interesting about this diagram is the sizes of the sections. For MARGE each section came out as being equally important, but when making this comparison we see the increased size of the CONSOLIDATE phase. This would suggest to me that for all the new information we introduce to students we need to spend just as much time (if not more) consolidating the information in their minds.

I will now look at each of the broader sections (EBC) and look at the comparisons between what was said in each model.

The ENGAGE/MOTIVATE section of learning was made very clear in both the MARGE document and the Science of Learning course. Without engaging the brain to learn, everything we do after that is not going to be as effective as it could be.

Both talked about the brain's reward system, and the release of dopamine into our brains when we experience something pleasurable. Many highly addictive drugs stimulate the reward system in the brain, thus releasing dopamine, making us feel happy. But more importantly there is a very simple way to trigger the reward system in a classroom setting: CURIOSITY! Both models discuss the way curiosity, or being introduced to something new that sparks a question, can cause the release of dopamine.

Curiosity is, in effect, a powerful drug. And, to make this even better, we appear to remember more about things which we are a curious about before we learn them.

Curiosity is given as one way to MOTIVATE students to learn, among others, and to get students brains ENGAGED in the learning that is about to take place.

The idea of schema is introduced in this section of MARGE (and developed further in the BUILD section below), and the importance of storytelling as a MOTIVATION technique is explored, since stories contain their own schematic structure by their nature (beginning - middle - end), and usually cause us to question

MARGE also discusses the importance of having a "big picture" of the topic before starting on the details to engage MOTIVATION, as this gives students a skeleton schema on which to attach more ideas as they develop.

The Science of Learning course also looked at the negative effects of anxiety on ENGAGEMENT, and the unconscious communication from the teacher to the students. If you are not engaged in the topic, then this will "rub off" on the students through the Mirror Neuron System.

Before starting a lesson or new topic, we should do something to ENGAGE the brain or MOTIVATE the learning. There are many options for this, including:

- A starter question from a previous topic that will ENGAGE the brain to be ready for the new content (this has links to RELATE and BUILD);
- A question that sparks curiosity in the students and a MOTIVATION to learn to answer the question;
- An anecdote or story narrative which can create MOTIVATION by causing students to question ("What will happen next?");
- Give an outline of the big picture of a topic before diving into the details, to develop a sense of questioning around the specifics.

The start of the BUILD section of learning is that we have to focus on what we want to learn. That is, we have to ATTEND to the information that we want to BUILD into our existing schema of knowledge. This is achieved by the Prefrontal Cortex (the bit of the brain at the front) which acts a bit like a conductor to the orchestra that is your brain, directing which bits of the brain need to be active to ATTEND to the given stimulus.

This relates to the ideas of reducing cognitive load, so that we can ATTEND to the relevant information, and not have distracting ideas or stimuli pulling our focus away from BUILDING the new knowledge. This is because this ATTENDING to information happens in the working memory, which is very limited in the amount of things that it can process at any given time.

When ATTENDING to new information, students also have to be active in the process of BUILDING the new knowledge. This does not mean they have to be moving around the classroom, but rather active learning is that where students do not just passively listen, but rather do some mental work to incorporate the new information in a meaningful way to their prior knowledge.

This is where BUILDING new learning links to the idea of RELATE, as we need to RELATE new information to things we already know to BUILD a bigger schema of connected ideas.

Both models give an example on the importance of chunking to demonstrate the limitations of working memory, and hence the importance of this in BUILDING new memories.

First try to remember this list of letter strings

TVC IAY MCAJ FK

Now try to remember this string of letters

TV CIA YMCA JFK

Even though both strings are identical, it is easier to remember the second one since it is grouped into meaningful units (or chunked). These chunks are things we already know, and so by RELATING the list to these things it becomes easier to remember the new information.

Interestingly, the Science of Learning course pointed out that the prefrontal cortex of children is still developing (up until late teens, even early into the twenties), so we need to help direct students to make these connections, as they are sometimes unable to do it for themselves. Even though they have the prior knowledge, they are less able to make the connections, so we need to make the prior knowledge they have explicit to them, so they can RELATE the new ideas to the old.

MARGE discusses some other ways to help structure new information, and create RELATIONS between content, such as:

- Using acronyms (such as MARGE)
- Creating visual imagery
- Using the 3C's (categorise, compare and contrast, which is what I am attempting to do in this post)
- Make use of elaborative-interrogation (asking yourself "how" and "why" questions when studying)
- Using metaphors and analogies to RELATE new ideas to old ones
- Using conceptual hierarchies (to create an inbuilt schema for the information)

We need to help create environments where students can ATTEND to new information and RELATE it to prior knowledge in order to BUILD new knowledge. We can do this by:

- Keeping the limited working memory of our students in mind, and removing unnecessary distractions (see Cognitive Load Theory for more on this);
- Focus students ATTENTION on the information that you want them to learn by insisting on silence when introducing new content;
- Get students thinking about the content as soon as possible;
- Help students to CHUNK ideas, by building meaningful models for them;
- Get students to RELATE new content to things they already know (and make this explicit for them)
- Have students use the 3C's, analogies, metaphors, concept maps, etc to help RELATE new information to prior knowledge

The process of CONSOLIDATION is about making material that we have seen long lasting AND more easily transferable. Physiologically, what happens is that the areas that are activated when we think about consolidated knowledge as opposed to new knowledge is that the active areas are further back in the brain. This "frees up" working memory in the prefrontal cortex to focus on other aspects of a problem or on learning even more new knowledge.

The only way to achieve CONSOLIDATION is through practice, and it is best if in that practice we are GENERATING the material ourselves from memory (that, retrieval practice). When we do this we should try to elaborate on what we mean, RELATING it to other bits of knowledge and schemas.

Simply saying the name of somebody back to them when they introduce themselves to you can improve your memory by 30-50% (according to MARGE).

However, it is even better if when we GENERATE information we do so in our own words, rather than just "rote memorisation".

By using different variations of how we GENERATE the known information, we can RELATE it to other areas of knowledge, and thus CONSOLIDATION helps make later GENERATION easier and more successful. The more often you GENERATE something the better you will "understand" it.

The process of CONSOLIDATING our knowledge will also involve EVALUATING if we know something. It is common to think we know something, when really we don't. Consider the student who comes out of an exam thinking they have aced it, when the reality is much different. They were unaware of how little they knew and could not EVALUATE their own performance effectively. This is a problem of being familiar with material (such as when you have first studied it, or recently looked at it) and the ability to recollect it (or GENERATE it by yourself with no cues). This is known as an illusion of knowing, and combating these is important.

One way to truly EVALUATE if you know something is to try GENERATING it after some time has passed since you last saw it. This is known as spacing, and it is the opposite of cramming (which will usually lead to illusions of knowing, allowing you to be successful in the immediate test, but then forgetting everything immediately after).

The true benefit of retrieval practice (especially spaced retrieval) is that it involves GENERATING the information, RELATING that information to new cues (especially if you use elaborative-interrogation) and EVALUATING your knowledge objectively so you don't fall prey to illusions of knowing.

The Science of Learning course also talked about the importance of sleep in the consolidation process, in "moving" information to different areas of the brain. In fact, a lack of sleep affects our learning in two profound ways:

- We are unable to consolidate the new things we have learned during the day;
- We are not in the best state to learn new things the next day.

We need to provide time for students to CONSOLIDATE their new knowledge into their long-term memory, by giving them plenty of opportunities to GENERATE the material and RELATE it to other things they know. We can do this by:

- Giving students opportunities to teach others about what they have learned;
- Using quizzes as learning tools;
- Using interactive tools such as Kahoot and Quizlet to engage students in retrieving;
- Have students use the 3C's and other techniques, but from GENERATED material.

We also need to help students be better at EVALUATING their own knowledge, by:

- Using questions to identify missing knowledge;
- Leaving time between GENERATING material;
- Mixing up their study of different topics.

Contrasting the models

The EBC model is all about the general processes involved in learning new material whereas MARGE is about the specific things we as teachers (and our students) should be doing to improve learning. The overlap is that the aspects of MARGE help us do each of the principles from EBC.

The EBC model is all about the general processes involved in learning new material whereas MARGE is about the specific things we as teachers (and our students) should be doing to improve learning. The overlap is that the aspects of MARGE help us do each of the principles from EBC.

What was made very clear in the Science of Learning course was that EBC should NOT be seen as a three part lesson plan (Starter - Main - Plenary), and that these three stages of learning could all take place at the same time within the same activity, or be spread over a long period of time for a given learning objective. MARGE does not talk about the whole structure of planning, but does give some ideas for teachers and students for each of the five aspects.

The Science of Learning course was a 5 week online course, and so covered many more aspects of learning as well. The most important one of these (which was also a key point in the Learning How To Learn course) is that sleep is absolutely vital to the process of learning. Without getting enough sleep, it does not really matter what else we do, we will struggle to learn new things effectively. This is such an important aspect of learning (I am also currently reading Why We Sleep by Matthew Walker which I thoroughly recommend to anybody interested in the importance of sleep both to learning and our general wellbeing), that we should be making a big deal of this to our students. How many students stay up into the small hours of the morning playing computer games, on social media, or even just doing their homework, which means they do not get adequate sleep to prepare them for the next day, or consolidate the learning from that day (it should be noted that, as Walker points out, teenagers have a natural sleep rhythm which is later than adults, but I fear many are now going well beyond this)?

So which is the better model?

I actually think both models have a lot to offer to help teachers (and students) to understand the processes we go through to learn new things. Both in terms of the biological functions (what happens where in the brain) and the implications on what we should do. EBC offers an overriding set of principles that we need to consider when planning out long term units: how will we ENGAGE students in the learning; how will we BUILD the new knowledge; how will we CONSOLIDATE this in long term memory? And MARGE gives us some advice on how to achieve these things successfully; MOTIVATE through curiosity and questions; make sure students ATTEND to the new information we want them to learn; have students RELATE the new knowledge to what they already know; provide as many opportunities as possible for students to GENERATE the knowledge in their own words; and help students EVALUATE their own learning so they can avoid illusions of knowing and fix any gaps in their knowledge.

I actually think both models have a lot to offer to help teachers (and students) to understand the processes we go through to learn new things. Both in terms of the biological functions (what happens where in the brain) and the implications on what we should do. EBC offers an overriding set of principles that we need to consider when planning out long term units: how will we ENGAGE students in the learning; how will we BUILD the new knowledge; how will we CONSOLIDATE this in long term memory? And MARGE gives us some advice on how to achieve these things successfully; MOTIVATE through curiosity and questions; make sure students ATTEND to the new information we want them to learn; have students RELATE the new knowledge to what they already know; provide as many opportunities as possible for students to GENERATE the knowledge in their own words; and help students EVALUATE their own learning so they can avoid illusions of knowing and fix any gaps in their knowledge.

Ollie Lovell wrote this short thread about MARGE which is an excellent summary of the main ideas.

Previously, I've shared the short booklet 'MARGE' by Prof Arthur Shiamura. It's a booklet on memory and learning using an acronym for Motivate, Attend, Relate, Generate, Evaluate. I wanted to share some takeaways, as summarised by @teacherhead in https://t.co/cmYtoMHRg0 pic.twitter.com/EHgBgoFnBB

— Oliver Lovell (@ollie_lovell) December 11, 2018

In particular, I like his comparison of MARGE with the model offered by Efrat Furst here.

Image from Ollie Lovell.

]]>My 4 targets this year:

— Ben Gordon SLE (@mathsmrgordon) November 6, 2018

1. Use exit tickets to assess performance using hinge questions

2. Use SSDD questions to help students improve procedural knowledge

3. Increase wait time when I pose a question

4. Deliberately interleave and space content more often

I recently saw this tweet and it made me stop and reflect on what my successes were for this year, and what I want to work on next year.

So, here are 4 things that have been successful for me in 2018:

- Implementing Weekly Retrieval Quizzes and Retrieval Starters

One of my aims for this year has been to introduce more retrieval practice into my lessons. I have done this in two ways, focusing mostly on my IGCSE classes. Firstly, I have done a weekly quiz with my classes. I describe how I run this in more detail here, but they have been popular with students as a way to identify their shortcomings. The second is the retrieval starters which I talk about in this post, where each lesson students have to recall material from Last Lesson, Last Unit and Further Back. In both cases, I need to think about how I get students to act on those questions they are unable to answer, but on the whole, these two initiatives have been a huge success. I am expanding both these to my IB classes next year. - Example Problem Pairs

I have adapted all my teaching to make use of example problem pairs this year. I started dabbling with this last year, but have moved to full integration this year (see here). I am still working on how many examples to give, which depends on the level of the class. I have found I needed fewer examples this year with my S3 class than the S3 class I trialed it with last year, but this is not surprising given I have a higher set this year, and the ideas of the expertise reversal effect. Providing fewer examples gives more time for students to engage in a more thought provoking activity that will help consolidate these new ideas. I have also pushed the idea of doing silent examples in the second half of the year, discussing with my students the need to concentrate on new material. I have an IB HL class next year, who will be much further along the novice-expertise spectrum, so I will have to bear in mind the expertise reversal effect when using examples with that class. - Work booklets

Also for my IGCSE class I have produced a set of work booklets for each unit. The unit is split into the component skills, and for each skill there is a required prior knowledge question, some fill in the blank notes, the example problem pairs, independent practice exercises, and some challenging activities. At the end of the booklet there is a unit review worksheet covering all the skills. These have been very popular with students, and have saved a lot of time in them copying down questions etc. They are still expected to copy down the examples and notes, but the structure makes this quicker. It also provides students with more stuff to move on to if they finish the exercise, and gives them extra questions to use in their revision. You can find the student resources here, including PDFs of the booklets. Again, I am trialing a similar set up with my IB class next year, but it will be lesson sheets rather than full booklets. - T&L Newsletter

I started the T&L Newsletter this year as a way to communicate ideas, blog posts and other T&L news to our staff body in one monthly installment, rather than just emailing out whenever I found something of interest. The Newsletter has adapted over the year, getting a new look, and expanding to include a section on cognitive science in recent months. When a new issue is released, I often see people reading it at break and lunch, and people often come up to me to discuss something in it. One Head of Department has told me it forms a part of their departmental meetings, and other teachers have told me how they use the ideas shared. Sometimes it has sparked a debate. Overall, it has gotten teachers talking about T&L a bit more, and, for me, that makes it a resounding success.

And what about my targets for next year? Well, I want to continue to embed all these practices across all my classes, but these are some of the things I want to focus on introducing/improving:

]]>- Assessing prior knowledge explicitly using Diagnostic Questions

I started this year doing a pre-unit assessment, but this took too much class time, so it fell by the wayside. Next year I want to make use of 2-3 diagnostic questions before a new unit/skill on the required prior knowledge, so that I can address any misconceptions before moving on. I am thinking of setting these electronically as a quick homework, but have not decided yet. - Give student more time for independent practice, particularly using varied questions

This year I have felt pushed for time, and the part of lessons that has probably slipped has been giving students plenty of time to practice new skills to embed them better. I have dabbled with varied questions, but want to make more use of these, as they give students a chance to practice but also develop skills such as conjecturing. I need to focus on how I am going to implement this successfully. - Improve quality of student responses by increasing wait time, and making more use of Cold/Show Call

Giving students time to think before asking for an answer is essential if we want students to give their best answers. Giving them time after hearing another students answer to compose a response is also necessary if we want to further develop ideas. I also want to continue to develop my use of Cold Calling to engage all students in producing their best work, and Show Call (projecting student work) to show excellent pieces of work (and also address misconceptions). - To be able to offer more personalised support for colleagues, I will endeavour to drop in to more classes.

In my role as T&L Coordinator I am always looking for ways to support my colleagues in their professional development, to provide the best learning opportunities for our students and to keep teachers interested in what they do. Over the last two years I have worked hard to promote an atmosphere of discussion about Teaching and Learning, and the next stage is to start going in to more classrooms and offering direct support to teachers. This will not be in an invasive or forced way, but rather giving them a fresh set of eyes and ears to bounce ideas off of in order to further improve.