<![CDATA[Interactive Maths - The Interactive Way to Teach Mathematics

<![CDATA[Interactive Maths - The Interactive Way to Teach Mathematics - Blog]]>Thu, 23 Apr 2026 21:08:26 -0500Weebly<![CDATA[Tree Diagrams...A Brain Wave]]>Fri, 23 May 2025 06:33:23 GMThttps://www.interactive-maths.com/blog/tree-diagramsa-brain-waveI had a brain wave mid lesson today.

I introduced my year 8 class to tree diagrams today. I have developed an approach that I find works really well for this, with one minor issue (which I will come back to).

I start with just basic tree diagrams with two options at each stage and two stages. I keep the structure the same each time to start with to help them build confidence around where things go on the diagram. For example, we start with this question

"Fill in the probability tree below to display the outcomes of flipping a fair coin twice"

We compare this to the sample space method, but I discuss the limitations of sample spaces (e.g. how they don't work for more than 2 trials, and how large they can get for lots of outcomes)

Then they have a go at this one.

"Draw the probability tree to display the outcomes of spinning a fair five sided spinner twice, for getting odd or even."

Some of them start drawing 5 branches and need reining in, but they all get there pretty quickly.

We do a couple of counters from bags examples WITH REPLACEMENT, and then we look at this one:

"The probability that it will rain on Monday is 0.2. The probability that it will rain on Tuesday is 0.3. Draw a tree diagram to show this."

I have chosen the examples carefully to showcase different types of questions that lead to the same underlying structure. But this one always throws them. Most of the class put Monday and Tuesday at the ends of the branches. And some students have always struggled with what to choose to put at the ends of the branches in cases like these. Many students just 'see' it, but I had always struggled to break this down for those that didn't. Until today!

Back to my brain wave today.

It is about the language of the question. A tree diagram is broken down into the vertical strips representing the trials, and the outcomes at the end of the branches. But this language just trips some kids up. So today I tried this.

WHEN it is Monday (trial - title at top) WHAT could happen (outcomes - end of branch)

Before, the 'Monday/Tuesday' question always stumped them. But with 'WHEN it is Monday, WHAT could happen (rain or not rain)? WHEN it is Tuesday, WHAT could happen (rain or not rain)?' it clicked.
Then I realised this always works

WHEN I first flip the coin, WHAT could happen (heads or tails)?
WHEN I draw the first counter, WHAT could happen (red or blue)?
WHEN they play the tennis match, WHAT could happen (win or lose)?
WHEN I eat the first chocolate, WHAT could happen (milk, dark or white chocolate)?
WHEN the bus comes, WHAT could happen (late or not)? WHEN I get to work, WHAT could happen (late or not)?

This structure of thinking about it really helped students to see what needed to go where in the diagram.

As an aside, the rest of the sequence of lessons then introduces WITHOUT REPLACEMENT, but still in the same structure of 2 outcomes and 2 trials. I follow this by looking at different structures (3 outcomes, 3 trials, terminating trials). And finally bring it together to look at finding probabilities of events that combine different outcomes (e.g. exactly two counters the same colour).

]]><![CDATA[Teaching Significant Figures]]>Thu, 05 Aug 2021 20:22:14 GMThttps://www.interactive-maths.com/blog/teaching-significant-figuresTeaching rounding to significant figures is a topic I have never felt that I have done particularly well. In the past I have used explanations like "3 significant figures means 3 non-zero digits". I have never felt completely happy with that, nor the way I have taught it in the past.

This year, as part of the White Rose Year 7 scheme, I had to teach rounding to 1 significant figure. I approached it differently to in the past, and it went really well. So I thought I would share (for me to refer back to next year, if nothing else!)

I started by confirming that all students could round to the nearest 10, 100, one, tenth, etc. We had been working on this in previous lessons, but just to make sure this was secure.

I then spent some time focusing on what a significant figure is. I settled on any digit after, and including, the first non-zero digit in a number. I used this excellent task from the Variation Theory website to help demonstrate what counted as a significant figure.

To check their understanding further, I asked them to show me a number with 5 significant figures (in Zoom chat as we are still remote teaching), then extended the idea as below. This was an idea from the excellent book Thinkers from the ATM.

This really got them thinking in more depth about what counted as a significant figure.

I followed this up with another task from variationtheory.com as below.

Happy that they could all identify the number of significant figures, and, more importantly, identify a given significant figure, I moved on to rounding to 1 significant figure.

I used the WR resources as inspiration here, and developed them.

Round 4,271 to 1 significant figure.

Identify the first significant figure (4).
What is the place value of this figure (thousands).
So we are rounding to the nearest thousand.
Is 4,271 closer to 4,000 or 5,000? (we used number lines to visualise this, though most could do it easily without by this point as they were secure with rounding to thousands)

Round 427 to 1 significant figure.

Identify the first significant figure (4).
What is the place value of this figure (hundreds).
So we are rounding to the nearest hundred.
Is 427 closer to 400 or 500?

Round 0.0427 to 1 significant figure.

Identify the first significant figure (4).
What is the place value of this figure (hundredths).
So we are rounding to the nearest hundredth.
Is 0.0427 closer to 0.04 or 0.05?

The explanation of the steps was, I felt, much clearer than I have given in the past. And student success suggested this to be the case too. Only 1 significant figure is in the scheme of work at this point, but I did stretch some with ideas of 2 or 3 significant figures, and the explanation holds up (identify the second significant figure,...)

They then did the WR worksheet in pairs, to great success.

I pulled them back together to look at this question

Finally we used a more-same-less grid

How do you explain rounding to significant figures?

]]><![CDATA[Graph Transformations in Zoom]]>Tue, 13 Apr 2021 19:36:13 GMThttps://www.interactive-maths.com/blog/graph-transformations-in-zoomThis week I had a breakthrough on how I could teach transforming functions to my IB AA SL students, which as with many of the best ideas, happened almost completely by accident!

The lesson was on combining different transformations to draw complicated functions. The end point for the lesson was questions like this where you have a function f(x) and have to draw something like g(x) given below (f(x) was defined earlier in the example, and is shown in the graph).

But from the previous lesson I knew that several students were still having issues with vertical and horizontal stretches, especially when the factors are negative, so I wanted to practice these first. I decided to use my IB Key Skills question generator to create 3 questions of increasing difficulty. We started with the ones shown below.

This is nothing new. I often do this when I know there are problems for some students. It gives us a chance to discuss as a class the approach to different questions.

But what I realised whilst doing this was that I could ask students to annotate on the screen to show their answers. I can't believe it has taken me this long to think of this, but it was equivalent to getting students to the front to draw on the board! Anyway, after kicking myself for not thinking of this earlier, I realised I could do a lot more with it.

For starters, I had three students working at a time, and I chose students to work on the level of difficulty that I thought was appropriate for them based on the previous lesson. I asked the other students to work out what their answers would be.

When a student had finished their question I asked the rest of the class to use the stamps built in to the Annotate function of Zoom, to either tick, cross or ? each answer. This gave me a feeling of what the class thought (and because I could see the names as they annotated, who was right or wrong). The ? was good too, as it allowed students to show they still weren't sure. For those that disagreed with an answer I asked them to explain why.

After we had all three answers done, I pushed the answer button to show the answer. And what worked REALLY well, was when I then scrolled down, the annotations don't move. Usually this is a pain, but in this instance it was perfect, as the graphs they had drawn slid on top of the answers, clearly showing if they were right or not (all of them were by this point).

This short recording gives an idea of the whole process. I made it after the lesson, so it looks like I am annotating, but in class it was students names that appeared.

Of course, the benefit of randomly generated questions is that then I could create 3 more instantly and get 3 different students to have a go (this time choosing those who I knew had struggled last lesson, and had intentionally avoided in round 1). I only needed to do this twice, but I could keep going if I needed.

Then with a quick change of settings we got these questions.

After a few of those, we pushed into combined transformations with these questions, and I showed them the answer for the first one. I asked them to put their answers in the chat, and they all got it correct. We had to talk about the importance of the order of the transformations later, but that wasn't on my mind just yet.

Then we moved on to look at this example together as a class (available in the lesson sheet for this topic).

Which I colour coded as below

Then I sent them off to try two Your Turn questions in pairs, suggesting they use the annotate function to communicate with each other as they worked through the problem.

Finally, as the lesson came to a close, I wanted them to quickly check their answers, so I whipped up a desmos file to reveal the answers.

]]><![CDATA[Solving or Understanding Problems]]>Tue, 13 Apr 2021 12:05:02 GMThttps://www.interactive-maths.com/blog/solving-or-understanding-problemsPut yourself in these situations:

A colleague is talking at lunchtime in the staffroom about having trouble with a particular student. They do the bare minimum, but won't do any extra even though they could do really well in the subject if they just applied themselves a little bit.

After a day visiting your parents, your partner is upset about something your father said. This is not the first time, they have had a tumultuous relationship at best. You just want them to get along.

You are a middle/senior leader, and an area of concern/improvement in your area of responsibility has been identified from some data.

What is your default reaction to situations like these?

Mine has always been to go into problem solving mode. Certainly as a Mathemacian, that is what I do: solve problems. But recently I have noticed that I do this in all areas of my life, both professional and personal. If I get involved in a problem, then I am aiming to solve that problem.

I took stock of this position a couple of times over the last few years. The first time I really thought about it was when I started training as an instructional coach following the Impact Cycle by Jim Knight. I was fortunate enough to go to the Instructional Coaching Institute in 2019 to be trained by Jim himself, and it was am incredible experience, not only to be surrounded by 99 other people who were coaches, but to listen to Jim himself.

There was so much to take away from that week. But one thing that really hit me was that a coach is not there to solve the teacher's problem, but rather to understand the problem and help the teacher solve their own problem (though not in a facilitative way assuming the teacher knows what to do, but in a constructive conversation as partners).

Since then I have been fortunate enough to have many coaching conversations and have worked for an extended period with several teachers as their instructional coach. I feel that in these conversations I am actually quite good at not trying to solve the problem. But it seems to be mostly limited to the structure of a coaching conversation.

In reading Kicking the Solution Habit recently, I was suddenly confronted with a behaviour I exhibit most of the time. I try to find solutions. In the post, Matthew Evans basically has one big message: before trying to find a solution to a problem, make sure you understand what the problem is.

And this is the sticking point for many people, in my experience. It is quicker and easier to make your own interpretations of the problem and solve those, than to actually spend the time investigating the true causes of the problem and addressing those. The quick fix is easy in the moment (even if it doesn't last), whereas actually solving the problem takes a lot of time and energy to explore what the true problem is.

So, whilst I find myself able to do this in the confines of a coaching conversation, it is the structure of that conversation that acts as my cue to behave that way.

When in another situation, be it an impromptu chat with a colleague or a conversation with my wife about our children, I fall back on my problem solving ways, trying to fix the problem instead of understanding it first.

One area where this has been very evident is in my role as lead for teaching and learning. Early on in my time in this role, I wanted to enact quick solutions: an inset on this topic, a collaborative professional development day. But as I have gained experience, reflected and gotten better at the job, I have realised that if you want to implement anything, you have to take it slow, not just to get buy in (though that is important), but to make sure you are actually addressing the real problem, and not some surface detail that is really just a symptom.

I want to improve at this. I want to be better at uncovering the real problem, and listening intently to people before trying to solve the problem. But I have a ways to go. I need to change a lifetime habit, and that is difficult. I need to work out some cues for myself to put me in the right frame of mind. I know I can do it, I just have to transfer what I do in a coaching conversation to other situations.

But that is difficult. It isn't a quick fix.

I am making headway. I have spent time identifying what the real problem is (I like to problem solve) where in the past I would have put the blame for failed fixes on the other person (they clearly didn't do it right). I am making progress. But I need to keep analysing the problem.

Are you a problem solver? Are you always looking for a solution, rather than trying yo understand the problem?

]]><![CDATA[2020: The Good, The Bad and The Ugly]]>Sun, 03 Jan 2021 01:45:25 GMThttps://www.interactive-maths.com/blog/2020-the-good-the-bad-and-the-ugly2020 will go down in history books as the year that COVID-19 swept around the world, disrupting every aspect of life as we knew it. The impact was different in different countries, as governments decided upon how extreme the measures they needed to take. For many this year was the worst ever. But for me, there were many positives to be taken from 2020.

The Good

2020 was the year our second son was born. As if to brighten up our whole year, Mateo arrived in December.
2020 was the year I was able to spend more time with my son because I was working from home, and so could manage my time in different ways.

2020 was the year my first son developed his English (Spanish had been his main language before this).
2020 was the year I reconnected with some old friends, who I had allowed distance to separate me from.
2020 was the year I read more books than any other year.
2020 was the year I learned a whole new host of skills around teaching that I never imagined would be needed.
2020 was the year I realised that family comes before work.
2020 was the year we bought a car, enabling us to visit the Zoo and go to the beach.
2020 was the year my website quadrupled its average monthly hits.
2020 was the year I gave my first CPD webinar to teachers from outside my school.
2020 was the year I was first able to attend a MathsConf (as it was virtual).
2020 was the year we were able to save a substantial sum of money to put aside for our sons futures.

The Bad

2020 was the year we had to live through the panic of not being able to get food due to shortages.
2020 was the year we weren't allowed to leave the house for over 3 months.
2020 was the year my son got to attend his first day of school , only for it to be closed for the rest of the year the very next day.
2020 was the year I had to walk to the supermarket, suitcases in hand, wearing a mask, visor and gloves, in the middle of a very hot Peruvian summer.

The Ugly

2020 was the year my great-grandmother passed away (not COVID), before learning she was going to be a great-great-grandmother for the second time.
2020 was the year our son was taken into neonatal intensive care at birth (all fine now), and put us through the most difficult 24 hours of our lives so far.
2020 was the year we tried to make up for the lack of social interaction our son was getting by spoiling him and buying him too many new toys.
2020 was the year my trusty PS3 died.

]]><![CDATA[Introducing Differentiation]]>Thu, 03 Dec 2020 19:44:11 GMThttps://www.interactive-maths.com/blog/introducing-differentiationI have previously blogged about some of the activities I use to help students to understand what differentiation tells us (that is what the derivative is), but today I had a great lesson on introducing the actual process of differentiation.

After exploring the idea of the derivative, I explained that differentiation is an algebraic way to find the function, rather than a graphical way.

I started by using a set of examples and asked students to use the Reflect-Expect-Check idea from Craig Barton. I showed them the first couple, then I asked them to reflect on what had changed in the question, expect what the answer would be and then check when I wrote the correct answer. I also made the different parts a lot more explicit than I normally do, as you can see below. The full set of questions is on pages 2 and 3 of this document.

As we went through we stopped at various points, talked about expectations, talked about the "obviousness" of the answer to y=3x (the derivative is the gradient, which is 3) and y=7 (the derivative is the gradient, which is 0) and that these fitted in with the patterns they had already spotted.

One thing I did differently in writing this sequence compared to normal is starting with the general case and showing y=x^2 as a specific case within this.

After this we then did loads of practice, but where I would normally do this via mini-whiteboards in class, since we are remote teaching, I had to find a technological solution. For most things this year, typing in the chat in Zoom has been enough, but I wanted to see the full written derivative from students.

Desmos comes to the rescue. I set up this assignment called My Whiteboards (copied one of the Desmos templates and added a few extra of my own). Then I paced them to the second slide so they were typing Maths. I decided to do this as they need to practice writing in Maths Type before they do their coursework next year. I then projected questions through sharing screen, and students wrote the answer in the desmos, deleting each time to write the next one.

This way I could see their answers as they wrote them, give immediate feedback and see who was participating and who was clearly unsure at any stage.

I used my website to generate the questions, starting at

And ramping up to

Slowly increasing the complexity by adding fractional coefficients, then multiple terms, then negative powers. We ran out of time to get to fractional powers, but will bring those in next lesson.

Overall, all students were successfully differentiating functions like the one shown by the end of the lesson, so I am happy with the progress they made. Unfortunately we only have one more lesson before the end of our school year, so will probably have to review a lot when we go back in March.

]]><![CDATA[Joy of Learning]]>Sun, 04 Oct 2020 17:21:26 GMThttps://www.interactive-maths.com/blog/joy-of-learningIn a recent lesson with my IB Maths AA SL class, I set them this indices question to simplify as part of the starter activity.

They struggled. A lot.

Since teaching via Zoom, I don't usually go through these retrieval based activities in class straight away, rather opting to take in their work to check through all their work, which gives me a better idea of what they can and cannot do (in a classroom it is different as I can see their work live).

Very few of them got anywhere near close to solving the problem. In the following lesson, they asked me to go through it, so I did.

After showing them how to do it, I made a passing comment about enjoying doing this kind of problem, even finding it relaxing.

Even via Zoom, I could tell the reaction of my students. Some of them even turned their cameras on to show their disbelief. How could I enjoy solving this kind of problem? How was it even remotely relaxing?

This provoked a rather interesting discussion where we talked about the things we find enjoyable. My point was that when you can do something, but it requires a bit of work, that is normally what we find fun. That is, learning is fun if you know enough to be able to learn.

We discussed how some people enjoy music or sports, and the reason why is normally they are relatively good at it. And then they enjoy getting better and doing more difficult aspects of that course.

It is the same with Maths (and anything else really). If you are constantly failing at it, you will not enjoy it. But if you can do it, with a bit of effort, normally you will enjoy it.

They could understand this point. I don't think they had ever really thought about why they enjoy some things and not others, and it helped them see how I could enjoy solving a Maths problem. I told them that my job was to help them know enough that they could enjoy solving Maths problems.

Now I just need to live up to that!

]]><![CDATA[Mathematical Diversions]]>Thu, 01 Oct 2020 18:47:38 GMThttps://www.interactive-maths.com/blog/mathematical-diversionsDue to COVID-19, we are unable to run our IB and IGCSE exams this November. Local restrictions make it impossible. It has been tough for students and teachers to have 2 years worth of work count for nothing. Our students will not get an IGCSE set this year (as an international school, no systems in place like there were for the UK). The IB students will have grades awarded purely on coursework.

The announcement that there would be no IB exams this year was made the day before I was due to finish teaching the syllabus, and my IB HL class were keen to finish that last little bit of vectors. But we still had two weeks left of term left, and with no exams, the usual rush of exam papers was pointless.

So between me and the other HL teacher we decided to offer two separate options: she taught the calculus option (we did a different option, but many students were interested in this) and I did a series of lessons on random mathematical diversions.

Here I will share those diversions, along with the resources, in case anybody ever feels like using them.

Taxicab numbers
We started by looking at this problem.

I blogged about this problem in the past here when a student brought it to me. I ran the session basically as an open problem, with students in breakout rooms in Zoom, and me popping between them.

Benford's Law
Next we took a look at Benford's Law.

I asked students to think about a set of data. They could choose anything, but I gave some ideas like

Populations
Number of goals scored in a season
Average playing time per player
House numbers on a street
Cost of items in a weekly shop

Once they all had an idea of their data set, I asked them to think about the first digits of each data point in the set, and to decide what the probability distribution would be for them. That is, what is the probability if you choose a random point in your data set, the first digit is a 1 (or 2,3,…)

We had a brief discussion about this, with the first answer being the expected 11% each as they are all equally likely. One student suggested that they would be clumped around a number (probably the mean) value.

After a brief discussion, I told them to go away and find the data set they had thought about in the first place.

We entered them all into this Google Sheet.

And then I added the data sets one by one to Autograph.

Obviously, with any activity like this you are open to it failing dramatically, but below you will see all the data sets plotted together, and Benford's Law falls out beautifully. There is even an excellent non-example.

The non-example was of weights of NBA players, and we discussed why this did not fit the pattern (weights will all fall within the range 70 - 120 kg approximately, so the first digits will be 7, 8, 9, 1, and the mean is in the 80s, so more 8s as this is a normal distribution.

But what about the other data sets? Why do they follow this same pattern?

I finished the session by explaining Benford's Law, the percentages it predicts and the formula, and how it can be used to spot people who have made up a data set.

Exploding Dots
Exploding Dots was a part of the Global Maths Project a couple of years back, set up by James Tanton. It is definitely worth checking out the website.

However, I prefer to teach it a bit more actively, and so created a version that I can present to students, with questions for them to do along the way. You can find a blank PDF of this here.

It starts from the very beginning of school level Maths, with counting (in different bases), followed by the four operations. It introduces the idea of zero pairs to perform subtractions, and then builds up to unknown bases: that is polynomials. Within an hour you can take a group from counting to performing polynomial divisions.

I have done this with other classes before, and it went down well with this class too. By the end of the first double period we were answering questions like the one below (admittedly, they do this in the course, but we did the more traditional long division).

We took this further to polynomial division that creates infinite polynomials, and the students wondered what would happen in other situations.

It was so popular, that we did a second double period on Exploding Dots, and this was all new stuff that I hadn't done with classes before.

We looked at decimals and fractions in the exploding dots model, which allowed us to look at fractions in different bases.

Then we looked at fractional bases, and explored what they might look like.

I love the exploding dots model. The students all commented on how visual it was, an how easy it was to understand what is going on. I really need to make more of this in 'normal' teaching, and not just as an enrichment activity.

Bayes Theorem
We study this in the course, but a couple of students asked to look at it in more detail. I was fairly lazy with this one, relying on some excellent resources available online.

First I sent students to this page to read the examples. We discussed the importance of the size of the population, and then did a few of the questions at the bottom of the page.

Then we watched this excellent video from 3Blue1Brown which visualises the whole thing beautifully.

Chinese Postman
I taught D1 once before leaving the UK, but it has been a while since I have done any decision maths. I thought this was a wonderful opportunity to take a look at the Chinese postman problem. I based the lesson on the plan from the Standards Unit, and turned it into a Desmos Activity. It was a very discursive session, so I paced them through the activity to start with, and also talked about the ideas whilst demonstrating and collating their ideas on a whiteboard.

Continued Fractions
Based on a couple of articles from nrich, I put together an activity on continued fractions. We started with evaluating them (like the one below).

We quickly moved on to look at infinite continued fractions

And generalised this

We took a quick look at how we can write any rational number as a continued fraction by using reciprocals.

And then how we can use continued fractions of surds to get pretty good rational approximations for them

Finally we took a look at some of the continued fraction representations of other irrational numbers such as pi and e.

It was fun to get to explore some different aspects of mathematics with the class. I really must try to build it into my teaching more often, and not as enrichment, but as an integrated part of teaching Mathematics. If you have any go to activities like this, I would love to hear about them.

]]><![CDATA[The Ones We Lose]]>Mon, 31 Aug 2020 22:10:50 GMThttps://www.interactive-maths.com/blog/the-ones-we-loseYesterday was the birthday of my Grandad. When I was young this was always a day that the whole family got together, usually to have a BBQ which he would do in his garden. Me and my cousins would play around outside, maybe in the paddling pool. The adults would play some cards as the day wore on (probably start with Running Out of 7s, followed by pairs Cribbage). I am 7 years older than my next cousin, so I also remember playing along at cards. The memories of the bank holiday weekend are always good ones for me, and since his passing in 2015, it is the weekend when I most remember him.

This weekend was no different, and this year it really got me thinking about the people we lose in our lives, and the impact they have on us. In this post I want to share the impact some of the important people in my life, who I have now lost, have had on me as a person.

Grandad

My Grandad was quite a character. He was the happiest person I have ever known, and growing up seeing him every week was a joy. Even into my late teens I went tenpin bowling every week with him and my Nanny Pat (we were a team in a league). Those Tuesday afternoons were a special day, as I would go over there after school, have dinner with them, then head to the bowling alley. Even when I learned to drive, I would drive to their house first for this weekly tradition. I even blew off my friends to spend time with my Grandad and Nanny Pat. It was a highlight of my week.

My Grandad was unique. Ridiculously flirtatious, always smiling, friends with everybody he met. He was also a fixer, a people pleaser, and hated to see anybody he cared about unhappy. These are not things I actively remember about him, but things I have learned later in life. If there was tension in the family, he would make some joke to lighten the mood. He was the patriarch of the family. The glue that held us all together.

When I went to University in 2006, he drove up with me in my car, whilst my Dad followed in his van with all my stuff. When somebody knocked on the door to our student accommodation, he was the one who answered. That is how my now wife met my Grandad before she even met me! Me and my Dad were in the bedroom connecting to the internet, whilst my Grandad was flirting with the 18 year olds at the front door. He invited them in for tea. I didn't have any tea. Or coffee (I didn't, and still don't, drink hot drinks). But he was (partially) the reason I met my wife.

He and Nanny Pat came to my Graduation in 2010. I could tell they were both so proud of me. He was a plumber, she managed the business. They were so proud that their grandson had gone to St Andrews. And they would not have missed celebrating that with me for the world.

He was taken from us too early. In late 2014 he was diagnosed with cancer. Fortunately it was relatively short, and he died in April 2015. My wife and I moved to Peru in early 2014, so I did not see him whilst he was ill. I am thankful for that in many ways, as my memories of him are being healthy.

But my Grandad left me with so much more than memories. He was the personification of generosity of spirit, and I like to think that I get that from him. He was a massive extrovert. That I definitely do not get from him. He was always trying to make people happy, and, for better or worse, I follow in those footsteps. I have his hairline.

Ray Tointon was my Grandad, and he will always be in my heart.

Nanny Pat

A little over a year later, Nanny Pat passed as well. Many of my memories of Nanny Pat are intricately linked to Grandad. She was his rock, his guiding beacon. Sure he flirted, but you just had to see how he looked at her to know that she was the only one for him. I am sure she died of heartbreak.

Whilst a less obvious character than Grandad in many ways, she was the one I could talk to about things that were bothering me. She would listen. We could talk for hours. Often whilst waiting for Grandad to return from work before going bowling, we would have our chance to catch up. She was always doing stuff in the background to make sure everything was the way it should be. She wasn't a fixer like Grandad, but her ability to listen made you feel better no matter what.

She could be stubborn too. She stopped talking to her brother for years after a family drama. She would always cook, even though there was the family joke about how Grandad must have no tastebuds (her cooking left most dishes distinctly flavourless).

She was a quiet force to be reckoned with, with a quiet determination to get things done. That is what I get from her. I will get things done, but in a quiet and unassuming way. I don't like to be the centre of attention, but see myself as a vital cog to get things done. Whilst I am not as good as her, I am working on my listening. Being there for the people that matter, just to listen, was her superpower, and I do my best to emulate that.

Pat Tointon (nee Isaacs) was my Nanny Pat, and she will always be in my heart.

Thankfully, both Grandad and Nanny Pat were able to make it to my wedding, and were both healthy for it. When my wife and I married in August 2013, they were both there in St Andrews with us, and the wedding photos are one of my final memories of them both.

One of the saddest parts of their passing when they did though is that they didn't get to meet their great-grandchild who was born in 2017.

The Miscarriages

I have written before about The Hardest Time of My Life. Briefly, before the birth of our son, my wife and I went through 4 miscarriages. It was not a good time. Nanny Pat was one of the few family members who knew. We were not at a point to be able to share that with others at the time (something that, looking back, was a mistake).

But those four babies were losses for me as much as any other family member who has passed. They taught me to be more human, and treasure the human connections we make. They taught me to be more resilient, to keep trying, to push through it. They taught me that life is not always roses, that we all have to go through difficult times. They taught me that family is more important than work.

And they taught me to be more open about how I feel. I am not a particularly open person when it comes to my feelings and what I am thinking, but going through that time made me realise that I have to be open with the people I love, and particularly my wife. I am not perfect at it, and I still find it hard to share my feelings. But I try. I want to be more comfortable doing it.

Nanny Pop

My feeling is that it is not common for people to have a great-grandmother into adulthood. I did. Nanny Pop (or just Nan) was my great-grandmother. I remember sitting with her in her house having rich tea biscuits with butter. I remember playing buses with her on the stairs. I remember playing Beggar My Neighbour in her sitting room.

I remember her being at my wedding at the age of 91. I remember her face when she first talked to me via Skype when we were in Peru. I remember her face when she met my son, her great-great-grandson.

I don't think many families can boast having 5 generations alive at the same time.

Nanny Pop died this year after a couple of years battling old age. She made it to 98.

She was always the person in the background, listening and learning about people. She didn't do anything with the information, she just knew that being there for people was important. She was the embodiment of trust. Anything you said to her was safe. I do my best to be somebody that people can trust. I am trying harder to not engage in gossip. I want people to know me as somebody they can talk to, without fear of that information being repeated.

Dora Farman (nee Neil) was my great-grandmother, and she will always be in my heart.

]]><![CDATA[The Teaching Delusion - Some Reflections]]>Sun, 19 Jul 2020 23:22:35 GMThttps://www.interactive-maths.com/blog/the-teaching-delusion-some-reflectionsI have just finished reading The Teaching Delusion by Bruce Robertson, and it hit all the right notes for me. I found myself nodding along, lapping up what Robertson says, constantly thinking "This is exactly what I think, but said so much more eloquently." In fact, I am thinking of copying a few extracts to give to people when I can't put into words my own thoughts!

I jest, of course. There were plenty of insights in the book that I had not thought about before, and a couple of things I disagreed with.

The main premise is that no matter how good teaching is, it can always be better. This has been a point I have made at the start of each new school year since getting the job of T&L Coordinator, and my most recent phrasing has been "It is both our right and our duty to continue to improve our teaching". I use this wording carefully, to instil the idea that it is our right to want to continue to improve ourselves, get better at our jobs, and become better teachers. This aligns with Robertson's idea of a Professional Learning Culture. On the other hand, we serve a community of children and their parents (who, in my case, pay a fair amount of money for our services), and it is also our duty to them to do the best job we can, which includes continually improving our teaching. Our duty to the parents who pay, yes, but mainly our duty to the young people we have the pleasure of working with, whose future depends so much on what we say and do, how we make them feel, and what they learn from us.

Robertson asserts that The Teaching Delusion is made up of three factors:

Most teachers and school leaders think they know what makes great teaching, but they don't;
Most teachers and school leaders think they know what it takes to improve teaching, but they don't;
Most teachers and school leaders think that teaching in their classroom/department/school is good enough, but it isn't.

On that last point, Robertson (and I) are very clear that there is poor teaching in schools, but this is not due to a lack of effort on the part of teachers, but rather a consequence of the first two parts of The Teaching Delusion. A lack of knowledge about what makes great teaching, and a lack of knowledge about how to improve teaching have left many teachers doing a good job, when they could be doing a great job, and a smaller minority doing a poor job when they could be doing a good (or great) job. This book is not an attack on teachers or school leaders. It is a realistic look at what happens in many schools, and more importantly, a road map to addressing the three issues it identifies.

"Hard work and effective teaching are not the same thing. Neither are hard work and effective leadership."

Robertson uses the first chapter to draw attention to what he sees as the issue in most schools, and put together the case for there being a Teaching Delusion. He takes time throughout the book to clearly set out his thoughts on what would improve the situation, which I will go into further below.

In chapter 2, he starts by talking about the purpose of schools (a dangerous topic, but one in which he and I agree), stating that the main purpose of schools is "supporting, challenging and inspiring our young people to learn". Then he gives an overview of some ideas from the research and reading he has done over the last few years, that will be building blocks for later in the book. In this section he attacks some 'myths' such as interpretations of Blooms Taxonomy and student-led learning, before making the assertion that great teaching is made up of a mixture Specific Teaching (explicit instruction, if you will) and Non-Specific Teaching (student led activities, Mode B as Tom Sherrington calls them), but that the balance of these is important. For Robertson, 80-90% Specific Teaching is the optimum, as "Specific Teaching can be thought about as the cake; Non-specific Teaching is the icing".

"As a reaction to their experience of poor teaching, their solution is to minimise the role of the teacher in teaching and learning processes and maximise the role of students. Accordingly, they advocate the importance of students leading their own learning."

Chapter 3 is an exploration of "The science of how we learn", and Robertson works through 7 keys ideas:

Knowledge - everything is built upon this
Memory - how working and long term memory work
Thinking - "Thinking is the interaction of knowledge, from our environment and our long term memory"
Learning - a change in long term memory
Retrieval - retrieving memories strengthens the memories
Understanding - see quote below
Schema - complex knowledge constructs

I am not going to review each of these, as Robertson himself has reviewed a range of ideas in this chapter, and most of these ideas are familiar to many now, but I did particularly like this quote:

"Understanding happens when knowledge takes on meaning. When we experience new knowledge, whether or not it has meaning to us will depend on the knowledge we already have. In other words, the more knowledge we have, the more likely we are to understand something new."

In chapter 4, Robertson starts to build toward implications for actual teaching. This chapter acts as a brief summary of ideas from a variety of sources in this field, including:

What Makes Great Teaching, Robert Coe et al
Formative Assessment, Dylan Wiliam
Effect Sizes, John Hattie
Principles of Instruction, Barak Rosenshine
Why Don't Students Like School, Daniel Willingham

At this point, we get the first glimpse of Robertson big picture: a description of great teaching.

"I suggest that great teaching is that which typically focuses on teaching knowledge, using pedagogies which are best for teaching knowledge (direct-interactive instruction and formative assessment), by teachers who have a strong knowledge of what they are teaching and how students typically think about this, and who develop strong relationships with their students."

Robertson then splits the remaining chapters into two broad categories, though they are interweaved so do not appear consecutively. For the purpose of this summary, I have put them into the broader categories. These address parts 1 and 2 of The Teaching Delusion that Robertson described in chapter 1.

Great Teaching

We start with the assertion that high-quality student learning has two main factors:

Great teaching
Hard work on the part of the student

Whilst there are things we can do to push students to work hard, ultimately that is not in our control, so Robertson focuses on the former.

"Great teaching requires deep knowledge and skills in relation to pedagogy."

After some discussion of what great teachers have in common (their attributes), we get to what will form the meat of this section, a list of 12 components of high-quality lessons, which are "the delivery units of great teaching". In brief, these 12 components are:

Activities that require students to recall knowledge from previous lessons, which may or may not be relevant to this lesson, but which needs to be learned as part of the course;
Clear communication and use of learning intentions and success criteria;
Activities that allow the teacher to find out what students know or can do already (in relation to what is being taught in this lesson);
Clear teacher explanations and demonstrations which hold student attention;
Activities that allow students to put into practice what they are being taught;
Appropriate levels of support and challenge;
Use of questions to make students think and to check for understanding;
Activities that get students to discuss and learn with other students;
Clear feedback to individual students and to the class about their learning;
Activities that evaluate the impact of lessons;
Strong teacher-student relationships;
High expectations and standards for student behaviour and quality of work.

I do have a minor disagreement with Robertson here. Whilst I accept that lessons are the practical time we spend teaching things, I am not sure it is useful to think about teaching in terms of lessons. I subscribe more to Mark McCourt's idea of a learning episode which will take as long as it takes. That is, I will prepare resources, but if they spill over into the next lesson, then that is fine. Similarly, if we get through them quicker than expected, I have more available to move on to the next piece of the puzzle. So whilst I agree with the elements, I am not sure I agree in the wording of talking about great lessons.

Robertson then uses the remaining part of chapter 5, along with chapters 9 and 13 to delve into each of these in detail. I am not going to comment on all of them here, but I am going to give some personal reflections on my own teaching.

1. Recalling knowledge - I have become quite systematic in how I approach this. I discussed how I am tracking and Spacing Key Facts, Skills and Concepts, and I will be starting to do this with all my classes next year. Prior to that I used the Last Lesson, Last Week, Last Unit, Further Back approach which also worked well, but I found that I missed out some ideas, especially in the Further Back section. I need to figure out how I am going to build this in to the spreadsheet (content covered in previous years when I haven't taught them). Since going on lockdown I have also dropped the weekly quizzes I used to do, simply because of time pressure. I am planning to build in some more smaller quizzes, perhaps only 3 questions a lesson, which should also have the benefit of breaking up a long lesson on Zoom.

2. Learning intentions and success criteria - this is an interesting one, and one of the few things where I disagree with Robertson. I do not believe that students need to be shown the learning intention, but I certainly agree that they should be at the forefront of teacher planning. My use of Booklets and Lesson Sheets have really helped me to do this, both in the curriculum planning when putting them together, and in individual lessons.

However, I can see the benefit to having these explicitly stated, and I think I will add them to my booklets and sheets, following the advice that Robertson gives, using the phrases "Will know", "Will be able to" and "Will understand". But then I will have them all available, and refer to them as we get to them, rather than at the start of a given lesson. Referring back to learning intentions reminds me of the Learning Map that Jim Knight discusses in High-Impact Instruction that I have been playing around with. I could adapt this to map the learning intentions perhaps, but I need to think more carefully about how I will go about this.

Success criteria is more interesting, and whilst I once again disagree that they need to be made explicit to students (in my subject anyway), having a clear question that can be asked to evidence their performance against would be useful. Again, this is something I can easily build into the booklets and sheets, having 1 or 2 questions at the end of each section which all students do before moving on. This would be a little like an exit ticket, but they would not appear at the end of a lesson, but rather when we get to them.

4. I have been thinking a lot more carefully about the questions I use as examples in recent years, ensuring that I show students the full breadth of a concept, including non-examples and boundary examples. But I have not focused as much on explanations. There is an argument that giving a good explanation is what separates a teacher from a subject expert: they both know their stuff, but not every expert can explain this to others, especially kids.

"It is often quite striking to me just how many teachers are reluctant to actually 'teach'."

I want to keep developing my example sequences, in line with some of the ideas from Engelmann's Theory of Instruction (Summary by Alex Blanksby here), and delve deeper into that text to explore the order of examples and non-examples in different contexts.

5. Practice is so vitally important, and in Maths especially so. Students need to practice methods to gain fluency, but also different types of problems to develop flexibility in their thinking around an idea. But this is always the first thing to get cut from my teaching when the time pressure hits. The pressures of "covering the curriculum" can get to us all, and I know that when they get to me, this is where I cut corners. Unfortunately we have lost time with all year groups in the last couple of years, so this is even more of an issue now. I need to make more use of homework tasks to get students practicing their new knowledge and skills.

8. I am not a fan of group work. It rarely works for me, and even when it does, there are always some who just sit to one side and get nothing from it. For this reason I have swayed too far away from it. I need to give students structured ways to work together, and Think-Pair-Share seems to be the most appropriate way to do this. I ask a question for students to do on their mini-whiteboards, give them time to complete it themselves, then share with their partner. In Reflect, Expect, Check, Explain Craig Barton gives some examples of prompts he used to get students following the structure he has developed, and something similar for Think-Pair-Share could be useful, until it becomes habit for students and me!

Improving Teaching

"Teachers are unlikely to improve a particular element of their teaching practice unless attention is drawn to the fact that they could be improved or need to improve."

The other main part of the book is about improving teaching, and creating a "learning school". It is based around the idea discussed at the start of this post, that all teachers can improve their practice, and so should be doing so.

"learning should be the core business for everyone involved in the life of a school - students, teachers, school leaders and support staff"

There are two interesting scales that schools need to think about when thinking about improving teaching:

Professional autonomy
Consistency

These are clearly linked, though they are separate (high levels of professional autonomy may result in low levels of consistency, though depending on how it is managed, this is not necessarily true). There is no correct place on these scales, but having the discussions as a school is important. Are there things we want to be consistent about? Behaviour is one area where most agree that consistency is important, but what about pedagogical choices. My personal view is that a certain amount of consistency amongst teachers would make everybody's life easier: students would need to spend less mental effort thinking about what each teacher wants; teachers do not have to come up with their own systems, and students develop the habits more widely so can apply them better in every class.

As to Professional autonomy, I believe that this should be high: teachers should be in control of what happens in their classrooms and in their professional learning. But I do not believe that "teachers should be left to get on with the teaching" in a vacuum. The role of school leaders is to oversee the productive learning of teachers, just as it is a teacher's role to oversee the productive learning of students. How these are approached differs in the fact that students are (relative) novices, whereas teachers are (relative) experts as professionals. And Robertson goes on to describe what he calls a "Professional Learning Culture", which basically means that a school (leaders, teachers, administrators) sees professional learning as important.

In such a culture all teachers are working to improve, and they do so in a collaborative way. When somebody learns something new from reading, it is shared amongst other members of staff. Teachers observe each other and give each other effective feedback. Teachers feel confident to try new things, without fear of repercussions should they go wrong (within reason, obviously). Teachers participate in discussions, reading groups and collaborative planning as ways to learn from each other.

In building a Professional Learning Culture, Robertson argues for a group of teachers to lead it. This is something we do not have. I act alone in leading the T&L Programme in our Upper School, in semi-regular communication with my counterparts in other sections. One thing I want to do soon is set up such a group within the Upper School. This would be a group of keen teachers to help plan the T&L Calendar, run activities, and possibly most importantly, act as ambassadors for the benefits of getting involved. Ideally there is a mix of leaders and teachers in this group, and my plan is to open it up next term.

This sits alongside the Professional Learning Evaluation survey that Robertson supplies. I have copied this off to give to our Management Team for them to reflect and evaluate how they feel we meet against these ideas. I will then be passing this survey to all teachers next term, and it will be interesting to see the different viewpoints from staff at the different levels. My suspicion is they will be quite different, but we will wait and see.

And now to what I found to be the most interesting and useful part of the whole book: the Lesson Evaluation Toolkit. Robertson sells this as a key part to developing a culture of improving teaching, as it can be used in many ways:

Building a common understanding of great teaching
Self-evaluation of lessons
Planning of lessons
Focusing feedback in observations
Peer observations
Focusing INSET sessions

It is basically a list of the elements of great lessons as identified by the school, with examples of their use and a space for teachers to take notes. I go into further detail about where I am going with this idea below, linking the idea to The Principles of Great Teaching.

"Use of the Lesson Evaluation Toolkit in lesson planning is not about making all lessons look the same - it is about getting all teachers to think about the same pedagogy as part of their planning."

The main way to deliver good and improving lessons is through careful planning, delivery and then evaluation of the lesson afterwards. The Lesson Evaluation Toolkit can be used in both planning and evaluations. In planning teachers could have a copy to hand whilst planning, so they can refer to it. Or they could go further and plan on the document itself. After a lesson teachers can ask themselves evaluation questions, and give themselves a rating (red/amber/green) against the elements of the toolkit, along with some brief notes. This process of evaluation is what is important, rather than the finished sheet (which could be thrown in the bin). By sitting down and focusing on evaluating a lesson, a teacher thinks about what went well and could be repeated again, and what didn't and they need to work on for next time.

Another key part of improving teaching is to make use of lesson observations. There are two broad types of lesson observations:

By a leader (to provide useful feedback to the teacher, to provide feedback to the leader about areas of development, and NOT as a way to make judgements)
By a peer (to inspire the observer, to provide feedback to the teacher, to share good practice)

"I actually believe that giving feedback to teachers about teaching practice is one of the most important things that school leaders can do with their time."

In either case, lesson observations must focus on professional learning. And even if they do, there are still reasons they may not have much of an impact on improving teaching practice, usually related to the issue of feedback. Robertson suggests 4 reasons why feedback from lesson observations does not lead to improving teaching:

No feedback is given to teachers;
The feedback is poor;
The person giving feedback isn't confident about delivering it (that is, it is delivered poorly);
Nothing is done with the feedback.

"Use of your school Lesson Evaluation Toolkit can help to create a degree of consistency in the feedback given to teachers following an observed lesson."

The first three can all be addressed by using a lesson evaluation toolkit as this provides a structure to giving feedback. With a defined toolkit, all feedback should be given in relation to these, and it also allows for feedback meetings to be more of a discussion as the teacher can also reflect on the lesson in terms of the toolkit. In particular, when feedback is specific and related to an agreed area of focus, the teacher is more likely to act on the feedback. This is where coaching can fit in as well, as coaches can work with teachers to implement the feedback. We are currently implementing a coaching programme at Markham College (…) and I can see the place of the Growth Coaching model following a lesson observation to help a teacher work through how to make the feedback impactful on their teaching.

Robertson also goes into the details of how to run effective lesson observations, and what the observer needs to do to make it useful. In particular, he suggests that an observation should be as much work for the observer as it is for the teacher, as they should be thinking hard about what they are seeing, and whether it matches up to the lesson evaluation toolkit.

"If you try to improve too many things at any one time, the likelihood is that you won't improve anything, certainly not to any significant extent. "

Next Robertson moves on to think about planning schoolwide improvement, and the quote above is given in that context. However, it is also true of individual teachers improving their teaching. It is important that when feedback is given to teachers following a lesson observation, only one or two target areas are highlighted. The observer should sit down and go through their notes before giving feedback in order to clarify what feedback they are going to give, and what areas of improvement they are going to suggest. If the observation was done as a pair (something Robertson suggests is useful), then the observers should discuss their notes together and come up with an agreed set of feedback.

Back to schoolwide improvement, of particular interest to me was the idea of collecting data about the areas on which to focus improvement. Without data, school leaders are focusing improvement planning on what they think are the biggest needs, but they may be very wrong. Data allows us to be more sure that what we are doing is a) needed and b) making a difference. Robertson gives an example of a simple spreadsheet which can be used to record data from lesson observations. The idea is that leaders observe lessons (ideally in pairs), then after the feedback they record a simple Red, Amber, Green in the spreadsheet against each element of the lesson evaluation toolkit. Over time this gives leaders data on two things:

Areas of weakness across the whole school, which should then inform further improvement planning;
Areas of strength of particular teachers, who can be used as examples for other teachers to learn from.

"the overall quality of lessons is not being evaluated. Instead, it is specific pedagogical elements of lessons that are being thought about, as identified in the school's Lesson Evaluation Toolkit."

This process could be used at a whole-school level, or within departments. I would say there is an argument that the latter is a better way to approach it, because elements of a lesson evaluation toolkit will probably look quite different in different subjects. This data could also be collated on a whole school level to focus whole school CPD.

The other main type of data that can be used to inform improvement planning is student feedback. This is probably best if given straight to the teacher and not via leaders to make sure that teachers don't feel like they are being "checked up on" by students.

"it is important that the focus is on improving the 'right' things. Without a focus on the right things, teachers and school leaders will be working hard but their efforts are likely to be in vain."

Robertson offers the acronym PACE to help maintain focus on the 'right things'. The acronym stands for:

Pedagogy
Attainment
Curriculum
Ethos

Finally, Robertson turns towards leadership in school, and he argues that school leaders should take a teaching-centred approach to leadership. The vital importance of knowing where you are going and communicating this to teachers is explored with the analogy of a driver in a car with passengers where the driver either will not tell the passengers where they are going, or does not know and is just out for the drive. Whilst the passengers might initially go with it in both cases, they will eventually get fed up and probably start to mutter in the background.

The teaching-centred leadership approach puts improving teaching at the heart of what a leader does, with the intended outcome of this being improved student learning and outcomes. Robertson identifies 5 reasons why many leaders are not teaching-focused:

Too much time is spent on other priorities
Too much time is spent on 'dealing with things' which could be dealt with by others
They don't know how to improve teaching quality
They believe that teaching is good enough
They believe that teachers will take care of their own improvement and that leaders don't have a role in this

So what should teaching-centred leaders be doing?

Make improvement of teaching the number 1 priority
Develop a shared understanding of great teaching
Focus professional learning on pedagogy
Lead by example
Read a lot
Observe lessons a lot
Support and challenge teachers to improve
Make time for people
Take different approached with different colleagues
Recognise strengths and good practice
Have difficult conversations when necessary
Talk about teaching and learning
Invest time and resources in collaborative professional learning
Plan for improvement taking into account data

And this is the message that Robertson finishes with. A focus on improving teaching being the main job of school leaders.

The Lesson Evaluation Toolkit and The Principles of Great Teaching

As I read about the Lesson Evaluation Toolkit, the first thing that came to my mind was that we have one of those. A couple of years ago I led a team in putting together what we have called the Principles of Great Teaching, and the purpose of this was to create a shared language around great teaching, focus our T&L programme, and make it easier to share great practice and expertise. But so far we have not been super successful in this goal, and there were several parts of this book that has helped me realise why.

The first thing I did on reading about this was to turn our Principles policy document into a toolkit like document, that is hopefully more usable by teachers. I have largely followed the structure recommended in the book to do this.

What must be made clear is that this is not a tick-list of things that are expected to be included in every lesson. In fact, we talk about these being Principles of Great Teaching rather than Lessons for that very reason. Over a period of time, we would expect that these Principles will appear, but certainly not in any single lesson. The more a teacher uses this to self-evaluate, the better the picture they will get of how well they meet these Principles. The exception is the first four which we call the Core Principles, which are expected to be in every lesson.

"A push for a shared understanding of what great teaching is and what typical features of high-quality lessons are is not the same thing as a push for every teacher to teach in exactly the same way."

The second point is that these are Principles and not specified activities. We expect teachers to challenge students, but we do not specify how they should do this. This is the idea of "freedom within form", and the balance of Professional autonomy with consistency I referred to before. Again, there are 3 exceptions, the Standards at the end, which are more specific things we want to be consistent throughout the school. There is still room for teachers to make this suit their own classes, and one error that we originally made was having the second Standard worded as "use a no hands up policy" where that is really a specific example of the idea we wanted to promote.

I said above that we have had some issues with rolling the Principles out successfully, and partly that is because our teachers still do not have a shared understanding of what each of these things means. My hope is that by turning it into the Evaluation Toolkit we can get it into teachers hands and get them using it more regularly. As teachers use it to reflect on their lessons, as teachers meet with coaches to discuss their teaching in relation to the Principles, as leaders start to use it to reflect on the practice within their department, teachers will become more aware of the different Principles, and they will be forced to engage with what they mean. Carefully planned whole school and department sessions will then allow us to see what different people think, and slowly build towards a shared understanding. This is not going to be a quick process. As an international school, we have teachers who have been trained in various different countries and so have very different ideas about education, and so all these ideas need to brought together.

But it will be worth it in the end. I have to keep reminding myself of that. In the end, this will lead to better teaching and thus better learning, and that is what is important.

How do I see this being used moving forward?

The first thing I am planning to do is to sit down with some departments and ask them to reflect on the department as a whole using the Evaluation Toolkit. This will hopefully spark some discussions, and through a coaching process, I hope to get them to move towards a departmental goal within the framework of the Principles, and how they can work towards this. Working with a few departments, especially some of the bigger ones, will get the language of the Principles in discussion with a large number of staff.

Following this I will be talking with the coaches we have trained over the last year, and asking them to guide teachers to this document where appropriate. Especially within the framework of instructional coaching, this will give teacher and coach a framework to identify the current reality, which is a vital part in identifying a goal.

Then I am hoping to start doing more observations of teachers. In the last couple of years I have focused more on Learning Walks, but I think seeing whole lessons will be helpful. This will give us a structure to base feedback upon, and if I can get Heads of Department to use it when observing their teachers it should lead to more productive feedback meetings following the observations. This will then hopefully lead to teachers engaging in Peer Observations, making use of the Principles Evaluation Toolkit to structure feedback.

We put our collaborative projects on hold for a couple of years because there were some policy items that took up a lot of time (the introduction of the IMPACT course, which is a skills based curriculum, and then the new national curriculum and assessment regulations introduced in Peru this year), but I am looking to bring them back next year, with a focus on the Principles, where teachers will choose to work in a group that focuses on one of them.

Within INSET sessions (we have one every Wednesday 3:00 - 3:40), I will plan sessions which are dedicated to reflecting on our teaching practice, and for these sessions I will provide all staff with a copy of the toolkit to make notes on.

All this will hopefully (fingers crossed) lead to staff seeing the toolkit as a useful document to scaffold their thinking when it comes to planning lessons and reflecting on them.

The end goal is that teachers are using it to reflect on their teaching regularly, but how it is used in those individual cases will not be dictated. It is, after all, a toolkit, and teachers need to decide how to use it that is best for them. But, by having lots of exposure to it through a variety of linked ways, I am hoping that teachers will start to develop the shared understanding of what makes great teaching, and the document will evolve with that understanding.

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