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### Until I Know Better – Never Let Me Go

05 Jun 2017, Posted by admin in Michaela's Blog

# Never Let Me Go

At which stage in a topic do you stop modelling examples? I’m going to go out on a limb and suggest the answer is probably….too soon. I’m going to go further and suggest that the rationale you have for doing so is probably wrong.

Here are examples of conversations I’ve had, or resources I’ve seen shared, where what was suggested sounded superficially sensible until a moment’s reflection made me think they had it completely backwards.

1. (paraphrasing) I’ve prepared the lesson on multiplying proper fractions, and set them an extension homework on doing it with mixed numbers to really stretch them, since it’s set 1.
2. (paraphrasing) I’m going to model how to expand and simplify (a+2)(a+3) and (b+3)^2 and (a-5)(a-7). They need to be able to do it with coefficients in front of the variable as well, and when the order or variables are different, such as a (3+a)(5-b), or three terms in one of the brackets, but I don’t want to show them too much so I’ll put those ones in the worksheet.
3. This sequence of tasks in a lesson on TES (I’m not going to say the creator as it is obviously an act of generosity on their part to have shared and I am not seeking to ridicule them). First the example they planned for sharing with the class:

The tasks for the pupils to undertake following this example:

I don’t know the author for the TES resources, but I can certainly attest that the first two were intelligent colleagues who were making those judgements as a result of serious thought.

They are decisions I would have taken earlier in my career as they fit with not wanting to spoon-feed pupils and I wanting them to enjoy a few head-scratching moments. Both are laudable aims and are important considerations. It is boring for pupils if they never have to think, and it makes it less likely that they’ll remember what you teach them.

With the benefit of (some) experience, the examples above now strike me as badly misguided. They reflect a common problem in maths instruction: we model examples that are too easy, then leave pupils to ‘discover’ methods for the harder ones. I think this has several causes:

1. Modelling seems like a boring thing to do. They are just sitting and (hopefully) listening. Pupils will get bored and restless.
2. Modelling takes ages, especially if you’re checking they understand as you go and are asking questions to get them to tell you the next step, and so on. If you modelled every example, they’d never get any practice, surely!
3. We want to feel that they’re getting a chance to figure things out for themselves and really enjoy maths (i.e. feel like mathematicians, trying out strategies and reflecting on them).
4. It feels a bit cold and exam-factory-ish to explicitly model every form a procedure or problem can take. Where is the room for surprise?
5. They only need a basic grasp of it, they’ll get a chance to look at the harder ones again in Y9/10/11, right?
6. Homework should be interesting and new. Researching and learning about more advanced or complex versions of a problem or procedure is way more interesting than more practice of what they’ve already done.
7. (I suspect this is truer than we’d like to admit) The difficult examples are really difficult to model. We’re not sure how we know how to do them, they’re just….you just can see it, right?

Here are some counter-arguments:

1. Modelling isn’t thrilling, but it is the most efficient and effective way to get pupils to be able to do procedures. Procedural mimicry isn’t the goal of our instruction, but it is a crucial foundation. It is also the bulk of what we are doing in secondary. It is almost impossible to get a (typical) child to understand a concept when they have no procedural fluency with the topic.
2. Modelling wouldn’t take so long if you didn’t ask so many flipping questions during it. We do so much talking that isn’t simple, concise narration during an example that pupils – understandably – think procedures are much longer and more complex than they actually are. Think about how long it takes you to solve ‘4 + 5a = 17’ if you aren’t showing it to anyone. I assume 5-20 seconds (since you’re a teacher…), maybe 30 if you show every line of working. They should see this! Taking several minutes to model one example sets them up to think it is fine to think they can spend more than 2 minutes per question on questions that are, frankly, trivial.
3. Letting them have head-scratching moments is fine, but it should be in response to a question that synthesises what they have been taught, and doesn’t require them to invent new knowledge (well, new to them). Leaving the hardest content for them to try on their own is just crazy: it disadvantages the weakest pupils and those who haven’t had good teachers on this topic in the past, it makes ‘giving it a go’ seem incredibly hard and adds to the perception that teachers are just refusing to tell them how to do things to be annoying. They should try hard problems on their own, but you should have first equipped them with requisite techniques and knowledge.
4. You should still show them the elements of surprise in maths. When showing them how to form algebraic proofs, we first look at the propositions with real numbers and form conjectures (e.g. for four consecutive integers, what is the relationship between the product of the 1st and 3rd and the square of the 2nd? Does this always happen? How will we prove it?). They should get hooked in, and make conjectures, and experience the pleasing smugness of having applied what they already know…BUT YOU SHOULD ALSO SHOW THEM, REALLY CLEARLY. Ten may have figured it out before you finished modelling it, but twenty didn’t, and they’re relying on you. Well-designed questions in their independent work will still force them to think and synthesise what they know and test methods, but won’t ask them to stab in the dark with no sense of if they are right or wrong. We tend to overestimate how much pupils can tell if their work is correct or  not.
5. Lucky Y9/10/11 teacher. This increases the gap they need to bridge as they approach the end of Y11, and also means that they have simplistic ideas around a topic (and probably many misconceptions). They need to see the complex versions, and grapple with them, to really grasp a topic. Once you have taught them to reflect in the line y = x, reflecting a simple shape in a given line seems like a breeze. Often the fastest route to mastering the basics is tackling the tough stuff (at least, that seems to be true for my weaker classes!).
6. What a way to make homework seem annoying and pointless. If they struggled in class, there is no way they will be able to do the homework. If they got it in class, they MIGHT be able to do the homework…but probably only if there is an older person in the house who can help them, or a really good CorbettMaths video on exactly that procedure (so it will only work for procedural work anyway). I’m all for letting the most able fly ahead, but it shouldn’t be so cynical as this. I cannot see the logic of presenting the most challenging work at the point of lowest support (i.e. you’re not there, and they are tired and probably rushing it). It also makes you seem like a rubbish teacher: “I can’t do it because she didn’t teach it to me.” They wouldn’t be wrong for thinking this.
7.  Explaining how to enlarge a fiddly shape by a negative scale factor is annoying and difficult. Proving congruence with annoying parallel lines is really difficult to do, let alone explain in a clear way. I just ‘see’ the answer to those long locus questions and feel like if they just read the question more carefully then maybe…maybe they’d just kind of realise? If we struggle to explain it, and are relying on our instincts to know what to do, then goodness help them trying to do it with no guidance or instruction from us.

What we should be doing instead:

1. Think of all the variations a problem or procedure can have, and plan examples that cover all these eventualities.
2. Pair every modelled example with a highly similar one for pupils to do. This holds them accountable for listening to, and thinking about, what you are showing. It also gives you feedback on if that small segment of instruction made sense to them.
3. Make examples challenging. Yes, start with (a+4)(a+6) to help them see the simplicity of a grid. Unless you haven’t secured the basics with multiplying and simplifying, you should be able to then show (2a+5)(4+3b) and then an example with three terms in one of the brackets. I was struck by this in a talk at MathsConf last year, where teachers who had visited Shanghai were showing the kind of examples that teachers there used with pupils. They were doing LOADS of examples, but briskly and covering a wide range of applications, which meant that pupils were in a better position to see the common threads and critical differences, and not jump to incorrect conclusions. I shudder to think how many pupils in the UK think that the terms in ‘the diagonal’ in a grid for double brackets must be the ones ‘that go together’, having only seen examples in the form (x+a)(x+b).
4. Just model it! Make it quick, make it concise. Something that works well for my weakest pupils is to have a silent model (i.e. they see the physical motions to enlarge a shape, or expand two brackets, or do the same to both sides), then one which I narrate (no questions or clarifications), then one where I check that they can mimic (i.e. they do a very similar one on whiteboards so I can see if they can recall and follow the steps – this is much more important than them being able to articulate the steps…at least at the early stage).
5. Start at the basics, but move as fast as you can to the harder content, and you will reap rewards. They will also ask much more interesting questions and feel smart. You’re also not saddling their future teacher with too much to get through.
6. Just use homework to practise and consolidate things they already know how to do. Set homework where you can expect 100% of pupils can get close to 100% (provided they are putting effort in). Otherwise you are setting up a grey area where you can’t tell if non-compliance is your fault or theirs, and you have lost the homework battle. You also save class time by not practising things where they need your help less.
7. The harder it is to explain, the greater the imperative that we spend time together planning and refining (and ideally practising) those explanations. The return on planning and rehearsing complex examples is huge: it will illuminate the key features for simpler cases, help you see the crucial things they must do from the start, and also streamline your language for easier questions. Pupils always rate highly a maths teacher who can explain well, and lose faith in those who can’t. If you can’t explain it well, they’ll think the problem is that they are stupid. That is a tragedy.

### Aien Aristeuein – Year 7 History at Michaela

15 May 2017, Posted by admin in Michaela's Blog

# Year 7 History at Michaela

One of the great things about working at Michaela is watching the rapid transformation of our Year 7 pupils. From their baptism of fire induction in the first week, through to the end of the summer term, our youngest cohort improves hugely in terms of habits, behaviour and confidence.

The same is true when teaching them history. I was really impressed by their latest essays, particularly from the lowest ability groups, that I thought it would be useful for me to blog about how we got there.

We are so lucky in our department, in that we are given the space and time to talk about what to teach and how to make sure it sticks. Unlike the monstrous regimes of data meetings, school wide marking policies, or discussing the latest diktat from on high induced by ineffectual accountability regimes, we are actually given the space to talk about what to teach our Year 7s.

That process of constantly thinking has led us to where we are now. We have lots to learn, and we are by no means there yet. My colleague Jonny has outlined some of this thinking in his blog, in particular the focus we have on the ‘horizontal’ or ‘domain’ specific vocabulary needed to make sense of a historical era or epoch and the ‘vertical’ vocabulary which is needed to analyse a specific historical debate, issue or question. Some might call the latter ‘conceptual’ vocabulary – tools which enable pupils to discern change and continuity, causation, significance or interpretative elements of the past. I think that can be quite limiting. While ‘concepts’ are vital components of the historian’s tool kit, it is important to remember that any historical question is rooted in a specific domain of knowledge, even if there are conceptual similarities across time. The causes of the enlightenment will need a radically different conceptual toolkit to the causes of the First World War, despite both questions being causation focused, for example. We would therefore expand ‘vertical’ vocabulary to include all of the thematic and conceptual terms needed to answer a specific question and to understand a particular period.  We try to choose questions which allow pupils to master a broad domain of history, without the tapered and conceptual enquiry questions which often mean pupils only remember knowledge which is needed for that specific enquiry. Our Year 7s answer the following questions: ‘What led to the development of Egyptian/Greek/ Roman civilisation?’ ‘What led to the development of the English nation by 1066?’  & ‘What were the main challenges to the king’s power in late medieval England?’

How do we get Year 7 writing analytically?

Writing analytically is, of course, not a generic skill, but an ability to bring relevant horizontal and vertical (conceptual) vocabulary to bear on a specific question, which draws upon the wider context of the relevant domain. Many make the mistake of assuming this ‘analysis’ is divorced from the wider domain of knowledge. This wider domain and the vocabulary to make sense of it needs to be explicitly instructed. In essence, we do the following:

1. Use of Knowledge Organisers to embed key dates, people and events as well as analytical vocabulary needed to analyse a specific question.
2. Lesson content which challenges all pupils, with extra content used to enable the high ability pupils to draw upon more examples in their essays.
3. Pre-empting common misconceptions and more practice for the weaker pupils.
4. Constant repetition and drilling of the key horizontal and vertical vocabulary within lessons.

Pupils need to be constantly exposed to good historical writing. We are doing them a disservice by assuming that even with enough knowledge, pupils will be able to conjure up a well written and historically sound essay. It is fair to say, that most of the main historical ‘points of clash’ in a debate have already been discerned. A pupil in Year 7 is not going to break any new ground in terms of historical scholarship. We, the experts, need to guide our pupils onto the right path of analysis (for that specific topic). Critics may say that this is too prescriptive, or that we should just teach them how to ‘think critically’, and analysis will follow naturally.

I think we need to be teaching them the main arguments for an essay as explicitly as we teach the dates, people, and events needed to construct the essay.

Patently, as the pupils acquire more knowledge and with our guidance they will come to realise that there is not necessarily a clear cut answer to historical questions. Our latest Year 7 essay was “What led to the development of the English nation by 1066?” This is clearly a question about causation. In most history classrooms, teachers will be getting the pupils to sift through card sorts, evaluating and synthesising the relative impact of different factors. There is nothing disingenuous about getting kids to evaluate the relative impact of causes on an event. However, the questions we need to ask are:

1. Is this how historians really conduct their analysis? Do they approach every question with the same critical toolkit, or does each question require specific domain knowledge in order to answer that question and formulate that critical toolkit?
2. Can our time in the classroom be better spent embedding knowledge and the structure of analytical writing, or getting them to discover the answers themselves – particularly in Year 7?

By the end of year 7, some of our pupils are able to prioritise causes and sequence them both chronologically and in order or importance. By Year 9, given the strong foundation they already have, we are able to develop their vertical vocabulary to include the ‘weight’ of different causes (latent causes, triggers, underlying causes, accelerators and pre-conditions).

Every time pupils write a paragraph, we give short and sharp feedback which the pupils then act upon immediately. Because the behaviour is so good, it also gives us time to go around and give verbal feedback to each pupil in the lesson itself. Their paragraph structure has remained the same since their first unit, with more examples and complex conclusions built in as time goes on. In the future we can flex and adapt this structure to meet the complex demands of historical questions later at KS3. In their final year 7 unit, we try and flex this foundational structure even more by looking at a question which incorporates change and continuity as well as causation. Below are some examples of the final essays they wrote for their Anglo-Saxon history unit. All essays were completed in 50 minutes entirely from memory. These are a selection from our high, middle and low ability groups.

Essay 1 – High Ability

Strengths: Excellent sense of period. She clearly understands the ideas of peace and conflict as pre-conditions for nation-building in the English context. It is also really pleasing to see clear references to her knowledge of religion, which is taught alongside history as a Humanities subject (see use of ‘monotheistic’ and her knowledge of the ‘Ten Commandments’. She also makes a link between King Alfred and King Hammarubi, from when she studied Ancient Mesopotamia.

Essay 2 – Middle Ability

Strengths: Correct chronological sequencing.  Huge amounts of specific details recalled to strengthen her analysis. Eg. Correct dates of the Synod of Whitby, Bede’s Ecclesiastical History of the English people. This pupil has an excellent sense of period, with the essay drawing upon ideas from 597AD-1066, and with clear references to the development of the ‘heptarchy’ through comments about the development of a nascent identity through religion and clarity on the role of translation from Latin to West Saxon English as a vehicle for unification. She also makes links between her bigger concepts, by linking Alfred the Great’s penchant for translating great works and his leadership of Wessex during the Viking invasions.

Room for improvement: There is an implication that conflict was the key factor, but it is not explicit. As I suggested earlier, this is not necessarily a problem at this stage – particularly for such a broad question. These analytical structures will be taught in the subsequent late medieval unit.

Essay 3 (two paragraphs) – Middle Ability

Strengths: The strengths of a knowledge-rich curriculum are really highlighted with this pupil’s paragraph on conflict. Here the pupil makes reference to the Great Heathen Army, the Battle of Brunanburgh and even the campaigns of Edward the Elder and Aethelflaed. He also remembers the historical significance of Aethelflaed as one of the key women in English history. He also uses the correct Old English diphthong: Æ.

Room for improvement: He is evidently thinking in a thematic, rather than chronological way. It would have been much better had he had prioritised and ordered the disparate elements of warfare in a logical way.

Essay 4 (three paragraphs)- Low Ability

Strengths: Excellent clarity and prose. Use of various synonyms to highlight ‘importance’. Good links made to his religion lessons (monotheistic, Ten Commandments).

Room for improvement: Clearer explanation of why Offa’s coinage enabled him to project his authority and create a shared sense of loyalty, rather than just focusing on the economic element.

### Conception of the Good – Arithmetic Average 2

15 May 2017, Posted by admin in Michaela's Blog

In my last post, I discussed whether an instructional programme could be created to teach a deeper concept of mean. I mentioned five different properties.

After a conversation with Kris Boulton about the blog post, he spotted something interesting about property 5.

Property 5: The average is only influenced by values other than the average.

At the end of my previous post, I explained property 5. It is because when we add the average value to the data set then the resulting sum is divisible by the mean. When we add a value that is not the previous average, the resulting sum is not divisible by the new denominator. However, the second sentence is incorrect.

If I do not add the average value of the original data set, I can still have a resulting sum which is divisible by the new denominator. The third example shows this.

Example 1: Original data set with a mean of 5.

Example 2: Add the average value to the new data set – resulting sum is divisible by the new denominator. The mean has not changed.

Example 3: Not adding the average value to the new data set – resulting sum isstill divisible by the new denominator. The mean has changed.

Is there another way to communicate this property?

This is an idea from Kris which he discussed as a potential second attempt to communicate property 5. It communicates property 5 nicely. It also has non examples too. If I do not add the average value then the mean is not 5.  Below is another example that can go along with the example above because the average value (19) is not a number in the original data set. Pupils are then seeing an example where the average value can be present in the data set, and where the average value will not be a number in the data set.

I have added the average value to the original data set.

The mean has not changed.

I added the average value twice to the original data set.

The mean has not changed.

I have not added the average value to the original data set.

The mean has changed.

I think both examples are important to use because they communicate the same property. The second example communicates the message in a more explicit fashion. The first example should be included because it is a nuanced example compared to the second. This may or may not be that important, but telling a pupil that the average value can be a number in the original data set is knowledge a pupil should know.

I wanted to convey an example where the procedure of dividing by the number of values was visible to pupils. However, at the same time, what is the most important aspect is pupils seeing that we have added the average value and the new average hasn’t changed. The division isn’t adding the value that I initially thought it was. The new examples communicate a quality of sameness that can clearly communicate the property effectively. Also, showing the features of the new data set which are permissible to be a positive example, and the non examples show the features of the data set which are not present to be an example for property 5.

### Edu Dyertribe – Our Mistakes in Science

10 May 2017, Posted by admin in Latest News

# OUR MISTAKES IN SCIENCE

As is the case in every school, the Michaela Science department has made its fair share of mistakes. After a few years of experimentation, trial and error, we have learned many lessons about what to do – and what not to do – in the science laboratory. Like all teachers, we want to provide our pupils with the best possible experience, and enable them to learn as much about the subject as possible. We also want to instil a lifelong love of science, and support lots of our pupils to use science in their future careers.

Fundamentally, our belief is that the best way to support pupils’ curiosity in science is through knowledge. By giving them the building blocks of scientific knowledge, and by supporting them to remember it throughout their time in school not only ensures they will have secure understanding of the world around them, but will provide them with the foundation for greater creativity in science.

But whilst our fundamental philosophy hasn’t changed over the last three years, we have of course reshaped and adjusted where necessary.

Booklet Annotation

Rather than using traditional textbooks or piecemeal worksheets as we did early on, we print each pupil a copy of our co-planned department textbook. Textbooks contain recap questions, explanations, diagrams and questions, and pupils can annotate examples with any further clarification given to them by the teacher.

Standard Lesson Format

In the first year, with only one year group, I was the only science teacher in the school. This had lots of benefits: I was able to spend my time focusing on the pupils and getting the curriculum ready for future year groups. In terms of lessons, I relished the flexibility. I was able to spend longer on certain topics, often blending from one lesson into the next. But as new staff joined the department, I realised that wasn’t helping them. To support them better, I had to decide on what to cover in each lesson, and make that clear to them in the textbooks.

Regular Exam Practice

It doesn’t matter how well taught pupils are in the fundamentals; if they don’t practice exam technique frequently enough, they will struggle in assessments. I have dedicated more time to this over the years, and now all of our pupils answer a 25 mark exam paper every week.

Practicals

Untangling practical skills from ‘Bloom’s Taxonomy’ skills took a while. Now, before every practice, pupils are explicitly taught practical skills such as identifying variables, plotting graphs, choosing graph scales, completing risk assessments, writing conclusions and evaluations.

Drilling

We’ve switched from verbal to written drills over the last year, and I wouldn’t go back. This has really helped to increase the amount of practice each pupil gets, and gives me clear, instant feedback that I can focus on immediately as well as in subsequent lessons.

Quizzes

In the first year, we spent hours each week planning multiple choice quizzes. At one point, I was even differentiating these for each class, which was extremely time consuming, and didn’t seem to have much impact on learning. Now, we simply test content taught that week in a simple format. The quizzes increase in complexity each week, meaning that there is enough stretch built into the unit for the most able pupils.

We haven’t perfected it yet, but learning from our mistakes has helped to department to grow, supporting pupils and staff to achieve their very best.

### Conception of the Good – Arithmetic Average

08 May 2017, Posted by admin in Michaela's Blog

Many pupils are taught how to calculate the arithmetic average (the mean.)  They are also taught a shallow understanding of the concept: it goes along the lines of “the mean is a calculated ‘central’ value of a set of numbers.” Or pupils have a very loose understanding of ‘average’ as colloquially referred to as ‘on average’. This is a start, but can an instructional programme be created to teach a deeper concept of the mean, accessible even to young pupils (8-14)?

I believe it can.

If so, it will aid future understanding of the weighted average at GCSE level.

Furthermore, it will lay the groundwork to understand how the trapezium rule approximates the area beneath a curve, at A Level.

I’m going to cover:

1. Properties of the mean
2. Selecting which properties to teach
3. How to teach them
4. Why it’s important

Fundamental properties of the mean

In Strauss and Efraim (1988) seven properties of average are outlined and these properties were chosen to be discussed because “they are fundamental, and tap into three aspects of the concept”.

I’m going to discuss what I think are the five most important.

Property 1: The average is always located between the extreme values

The average value of a set of data cannot be smaller than the minimum value or larger than the maximum value of the said data set.

This seems like common sense to an adult but expertise induced blindness underestimates the difficulty for pupils to understand this property of the mean.

How can this be communicated to pupils?

By example, show that the average value is never smaller than the minimum value or larger than the maximum value.

Then, test pupils’ understanding of the property using the following type of question:

For each question the average value could be true or definitely false, state whether the average value is true or false for the corresponding data set:

The following true or false questions are testing a pupil’s understanding of the property rather than their procedural knowledge of calculating the mean.

Property 2: The average is representative of the values that were averaged.

More technically: “the average is the value that is closest to all of the others in the set of values that are being averaged.”

Therefore, the average value represents all the values within the data set.

This property ties in nicely with the third property.

Property 3: The sum of the deviations from the average is 0.

Each value in the data set is a certain distance away from the average value which is clearly understood from a visual example. If we total the distances between each value and the average value, that total will equal to 0. This helps pupils to visualise that the average value is central to all the values. This highlights that the concept of the average value is again the central value to values within the data set. Furthermore, this highlights that the average value represents all the values that were averaged (property 2).

How do we communicate this to pupils?

1. Outline how to find the distance between each value and the average value.
2. Emphasise that I do (value – average value) and that the distance can be negative, if the value is smaller than the average value. However, the pupils need to picture the distances.
3. Total the distances, also tell pupils that we call this sum the sum of deviations

There are two questions that can be asked to develop understanding around property 3:

1. Show for each data set that the sum of the deviations from the average is 0 (Qs 1 – 3 only)
2. For each set of data, the average value is either true or false. Determine which of the following average values for the corresponding data set are true or false using your knowledge of the following property:

The sum of the deviations from the average is 0.

The first question is asking pupils to apply their knowledge of finding the sum of the deviations for the average value. The second question is asking pupils to apply this knowledge but then decide which of the following data sets has the correct average value.

Property 4: When one calculates the average, a value of 0, if it appears, must be taken into account.

Dylan Wiliam has an excellent hinge question that deals with this property very well.

Pupils often think they don’t have to include a 0 value when calculating the mean.

A good way to overcome this is to simply include it in one of your examples.

Seeing this in a concrete context also allows pupils to see why 0 must be included as a value in the data set.

Concrete context:

Sarah collected some money from her three siblings to raise money for charity. Hannah donated £5. Adam donated £7. Clare donated £9. Sarah did not donate any money. What was the average amount of money each of her siblings and Sarah donated?

Property 5: The average is only influenced by values other than the average.

This is a really nice point to make about arithmetic average:

Adding a value to a data set which is equal to the average value of the current data set does not influence the new average.

Why not?

Because when we add a value that is the previous average, the resulting sum is divisible by the new denominator. How can we communicate this to pupils?

The worked examples above show how the mean does not change when you add the average value of the previous data set (going from example 1 – 2 and 2 – 3). The last example shows that the mean does change when a value which is not the average of the previous data set is added.

To communicate this I would ask pupils to determine if the number added would change the average value. For example, the question series is designed for pupils to do the following

1. calculate the average for each data set
2. Decide if the mean has changed by adding a value.
3. Explain that we have added a value which is equal to the average value. Adding the average value does not influence the values being averaged.

At the end, I would explain how when we add the average value to the data set (5), we get a sum which is divisible by the denominator (20/4 = 5). When we add a value that is not the previous average, the resulting sum is not divisible by the new denominator.

In summary, these properties of arithmetic average can be taught effectively with the correct worked examples and problem exercises which communicate each property at one time. It gives pupils a spatial understanding of the mean which is above and beyond the procedural calculation of calculating the mean. I think it is highly powerful knowledge that can lend itself for more complex understanding of the mean when learning about the difference between simple mean and weighted average mean.

### Reading all the Books – Warm Strict

08 May 2017, Posted by admin in Michaela's Blog

# Warm – strict

I have written previously about Teach Like a Champion, a book I feel to be the most important contribution to pedagogy advice I have read. Although it is nearly impossible to pick which of the important techniques are the most vital, ‘warm strict’ is definitely up there: in fact, it may even be the foundation of a successful education.

The thinking behind ‘warm strict’ is that you should not be either the warm, friendly, kind teacher or the strict teacher: you need to be both. And not one after the other – it’s not Jekyll and Hyde – but both, at the precise same time.

So ‘warm’ and ‘strict’ are not mutually exclusive. In fact, at Michaela, we have found that the more strict we want to be, the more warm we have to be.

Anyone who has visited Michaela is immediately struck by the behaviour of the pupils. It is unusual, they say, to find classroom after classroom where 100% of pupils are focused for 100% of the time. Row upon row of eyes are fixed on their teacher, or on their exercise books. There is no staring out the window, no fiddling with a pen, no hanging back on their chairs.

But this does not happen by magic. Watch any Michaela lesson, and teachers areconstantly issuing corrections to pupils. These can take the form of reminders or demerits, and are swift and public. ‘Kevon, remember to keep those eyes glued to your page,’ might be issued to a year 7 who is still in terrible habits from primary school, who desperatelywants to focus on his work but just isn’t quite in the habit of it. ‘Shyma, that’s a demerit: if you focus 100% on your paragraph you know it will be the best you can do,’ might address a year 9 who is knowingly letting their eyes wander because they are seeking to distract others or themselves. It’s a judgement call, and one we don’t all always get right, but in general Michaela teachers are incredibly consistent in the messages they give the children. (We achieve that consistency through frequent observations – the topic of a future post.)

In my previous schools, I was also issuing constant corrections; the difference was my stress level. With a tough class, counting up those three warnings before issuing a sanction would lead to me delivering corrections with an emotional tone, conveying the stress I was feeling. Because the bar for behaviour is set so ludicrously high at Michaela, and pupils are never doing anything worse in lessons than turning around, whispering or fiddling with a pen, we can all take the time to explain every correction we give throughout the lesson. And we give corrections, reminders, demerits and even detentions with care and love: ‘that’s your second demerit, which is a detention – this will help you to remember to keep your focus so you will achieve your full potential.’

Not only within lessons, but also between lessons, Michaela teachers are seeking out opportunities for warm interactions with pupils. At break time, tutors circulate the hall their year group is based in, shaking hands, chatting about their weekend or their interests; we even have footage of pupils teaching their tutors how to dance. At lunchtime, we eat with our pupils; teachers will seek out kids they have had to sanction or have a difficult conversation with, and use that friendly interaction to reset the relationship in a more positive tone.

Because we are so strict, it is vital that every teacher greets every child with a smile and happy ‘good morning!’ prior to each lesson. Because we are so strict, we must smile and chat with the pupils on the playground, in the lunch hall, and even at the bus stop. Because we are so strict, we need to let our love show.

All truly excellent teachers love their pupils – that seems obvious to me. But if you want to be really, really strict you need to show them that love in every smiling interaction.

### Cheng Reaction – Lesson Observations at Michaela

08 May 2017, Posted by admin in Michaela's Blog

# Lesson Observations at Michaela

At Michaela, lessons are not graded. Like many schools, we have moved away from the old paradigm of observing teachers once per half term in a high stakes, pre-planned, pay-determining observation, towards a new one.

We have a truly open door policy in which all staff are encouraged to observe each other regularly. We also have a number of visitors each day, so I regularly have people observing from the back of the room. Rather than feeling a bit unnerved by the presence of an observer, I now feel pretty relaxed, like it’s the norm. I don’t feel like I have to perform or change what I’m doing just because someone has walked in. Even when one of the school’s SLT pop in, I don’t feel the pressure to show off.

The other great thing about having an open door policy is that there’s no pressure to spend hours the night before planning the lesson or creating silly bits of paper that only benefit the observer (endless data sheets, colour-coded seating plans, 3 page lesson plan pro formas, and so on).

My most frequent classroom visitor, of course, is Olivia Dyer, my Head of Department. She pops in perhaps three or four times a week- perhaps for 10 minutes, perhaps for the whole lesson- and fires through a quick feedback email straight away.

The main purpose of lesson feedback at Michaela is twofold: first, it needs to be immediately actionable. I should be able to read the email in a couple of minutes over break, perhaps, and then implement it straight away in the next lesson. If I can’t get to the email until the end of the day, I want to improve quickly, I do try to read it as soon as possible. Secondly, lesson feedback aims to help all teachers hone their practice, and most importantly, becomemore ‘Michaela’.

At Michaela, we believe in ‘rowing together’. We value consistency and want all our pupils to get a similar experience across the board. Critics might argue that such an approach is too rigid, that it prevents teachers’ individualities from coming across in lessons. This is a misconception, I think. Teachers’ personalities are still able to shine through. When I go to see Mike Taylor or Hin-Tai Ting teach, I see many of the same features (kids encouraged to put their hands up, books given out in 10 seconds, teacher saying ‘321 SLANT’, etc.), but their respective personalities are different, and their relationships with the kids can flourish as a result. In many ways, the fact that we get teachers to align on the things the mechanics of the lesson means that teachers are free to be themselves and build relationships.

We also accept that there may be differences between departments. So Science lesson feedback will probably have different emphases to that of a History lesson for example. The differences might be quite small, such as ‘when explaining the experiment, hold the beaker higher up so the kids can see it at the back’- clearly, that sort of thing won’t come up in History, but tailored feedback on the teaching of historical paragraph writing will at some point. But because the general principles are the same across the board, subject-specific differences don’t undermine the overarching philosophy of consistency.

Observers provide helpful, concise, immediately actionable feedback that supports teachers to improve.

Here is an example of a lesson feedback email:

Hi Cassie

Thanks for having me in again today.

A couple of tiny, quick fix things!

• Only ever write on the board in black, other colours are really hard to read
• It’s always ‘3, 2, 1, SLANT’, not ‘3, 2, SLANT’

Some bits of feedback to think about:

1) Pace.  You need to ensure absolutely no downtime in the lesson.  You should aim for the kids to always be actively listening, tracking, thinking and working.  Figure out ways of logging merits, etc. quickly so it doesn’t interrupt the pace of the lesson.  I like to give the kids a piece of paper and get them to write down merits and demerits – that means you can just get on with teaching.

2)  Sharpen the timing of sanctions, and always frame them positively.  “Sammy*, we SLANT perfectly so that we’re 100% focused at all times, so I’m giving you a demerit to remind you to SLANT really well at all times, thank you.”  You don’t always need to seek understanding from the kids, but if they have any kind of negative reaction, give them a second DM.  They’ll get the message!  Make sure if you’re giving a second DM that you tell the kids it’s a detention – I think you gave Sammy 2 DMs but didn’t say ‘that’s a detention’. Also, pre-empt further demerits by saying something like “remember guys, a demerit is half-way to a detention, and it’d be a real shame for you to miss your lunchbreak or go home later than your friends.”

3) Radar. Your use of silent reminders and getting them to practise routines is great; now, you need to practise having your eyes on every child every minute.   This will take time to develop, but when you’re delivering from the front, try and scan the room as much as possible to pick up distractions. Stand up on your tiptoes and look round the room like a meerkat so the kids know you’re watching them.

### JLMFL – The Summer Project (#French)

03 May 2017, Posted by admin in Michaela's Blog

# The Summer Project (#French)

In the past, my hands-down-favourite thing about teaching was being in the classroom, with the kids, bouncing off their energy and enthusiasm and teaching them French, and seeing them grow in knowledge and confidence and ability. That feeling only increased when I started at Michaela. The exceptional behaviour standards meant that we could have a real giggle, that my pupils would learn LOADS in an hour and their energy and enthusiasm would stem, in the main, from feeling clever.

But a new thing threatens to knock the act of teaching off its perch as my favourite thing about… well, teaching. And that is: resourcing.

We teach French very differently at Michaela, and in order to do that we make our own resources. Those resources are very dense – you can get loads out of a single text, or a single practice activity, and our emphasis on repetition and spaced practice means they get reused again and again. I have shared a couple of our knowledge organisers – one of those, along with other practice activities, normally lasts six weeks. We are constantly refining and developing the materials we use, but they are built on a solid foundation of the written word, lots of reading, lots of transparency and lots of beautiful language.

This Summer, from Monday 24th July to Friday 4th August, we are running a Summer Project to design and produce even more resources, with a particular emphasis on Key Stage 4. We – my colleagues and I – will be working for two weeks to design and produce the texts, activities, practice drills etc. that we will use with our pupils week in, week out, for years. I’m ridiculously excited!

Evangelical as we are about how we teach French, we want to share this experience with others, and give you the opportunity to come and work with us. We’ll be based at Michaela, and you will get an insight into the thought process behind our resources, a chance to work with Michaela staff to create them, and a chance to discuss the fun parts of pedagogy, like “what little story can we tell about the word ‘quelqu’un’ to help pupils remember it?” and “which idiom sounds more authentic here?”.

It would be ideal if you could do the full two weeks, so that you get the most out of it, but we will consider those interested in doing one of the two weeks. Expect it to challenge everything you previously thought about language teaching! If you’re interested in taking part, please send a brief email explaining why you’d like to be part of the project to me at jlund@mcsbrent.co.uk.

### Pragmatic Education – Staying Stoical in School

02 May 2017, Posted by admin in Michaela's Blog

## Staying stoical in school

Some two thousand years ago, a teacher, a playwright and an emperor asked:

What is the best way to live?

How can we deal with the difficult situations we face?

What does it take to improve our minds?

Their answers are the heart of Stoic philosophy. We in schools can use their insights on themind, on adversity and on practice to help our pupils shape their thought patterns.

Here is a rough overview of what we teach our pupils about staying stoical at Michaela:

1. Mind

“Some things are under our control, some are not. We are responsible for what is in our power to control: our mind and its perceptions. The chief task in life is simply this: to identify which externals are not under our control, and which are the choices we actually control. We control our opinion, choice, attachment, aversion. It is learning to separate the things that lie within our power from those that don’t.

“Whoever can be irritated – that person is a slave. No one can frustrate you without your cooperation; you are only hurt the moment you believe yourself to be. So when we are frustrated, angry or unhappy, never hold anyone except ourselves responsible. We forever compound our problems because we make them out to be worse than they actually are.”

Epictetus

“Life itself is only what you deem it. Your mind will take the shape of what you frequently hold in thought. Such as are your habitual thoughts, such will also be the character of your mind. Your anxieties are creatures of your own imagination, and you can rid yourself of them. Observe how disquiet is all of our own making. Troubles never come from another’s hand, but are creatures of our own creation.”

Marcus Aurelius

“Difficulties show a person’s character. So when trouble comes, think of it as training, strengthening, toughening. When a challenge confronts you, remember you are being matched with a stronger sparring partner, as would a physical trainerA boxer derives the greatest advantage from his sparring partner, training his patience and even temper. In adversity, be happy that what you have learned is being tested by real events. Philosophy is preparing ourselves for what may come. So, what should we say to every trial we face? This is what I’ve trained for, for this is my discipline!”

Epictetus

“Like a boxer with a sparring partner – no protest or suspicion – act this way with all things in life. Instead of: “How unlucky I am, that this should have happened to me!” Say rather: “how lucky I am, that it has left me with no bitterness, undismayed: to endure this is not misfortune but good fortune.” The obstacle on the path becomes the way.”

Marcus Aurelius

“Seize your adversities head on. To bear trials with a calm mind robs misfortune of its strength and burden. Complain little: no condition is so bitter that a stable mind cannot find some consolation in it. Think your way through difficulties: harsh conditions weigh less on those who know how to bear them.”

Seneca

1. Practice

“Study, practice and train if you want to be free: for as time passes we forget what we learned. The secret of happiness of the human mind is gratitude. Discipline yourself with thinking, exercises and reading: that’s the path to human freedom. If you’re succeeding, you see any moment as an opportunity to practise.”

Epictetus

“Train your mind through regular practice. Persevere in your efforts to acquire a sound understanding. One needs constant, daily practice … the pursuit of wisdom sets us free.”Seneca

“Make a habit of studying the maxims. Practise even when success looks hopeless.Discipline brings peace of mind.”

Marcus Aurelius

Stoicism in school

Children at school are learning how to deal with difficult emotions: frustration, worry, fear, cravings, temper, arguments, gossip, jealousy, squabbles, hurt, bitterness and more. Stoicism offers fortifying ways to think about these difficulties.

Teachers can …

• show pupils what is always within their control: their thoughts, responses and reactions.
• preemptively teach pupils how to anticipate and cope with adversity.
• guide pupils to change their perceptions so that they complain, blame and resent less, and instead keep perspective, stay grateful, and are happy.

Pupils can learn how to…

• let go of frustration: by realising that it is in the mind, so within our control, and by remembering that irritation is counter-productive and should be released and not dwelt on.
• let go of worry: by remembering that the more we worry about things we can’t control, the worse we feel; the less we worry, the calmer and happier we feel.
• cope with arguments: by avoiding criticising, complaining, blaming or resenting others, and instead feeling cheerful and grateful for what we have.

School leaders can convey the lives of the thinkers, and their thinking …

Epictetus was a Greco-Roman slave who earned his freedom and became a teacher.

Marcus Aurelius was a Roman emperor taught by philosophers who wrote personal diaries.

Lucius Seneca was a tutor and advisor to the emperor of Rome, who wrote letters and plays.

All three thinkers used analogies, mantras and writing: notebooks, diaries, letters or plays.

Three Analogies

Slavery: irritation enslaves us; wisdom frees us.

Illusions: anxieties are creatures of our own creation; we can get rid of them.

Boxing: we must train hard so we don’t get beaten!

Interactions

At Michaela, we continually return to stoicism in our interactions with pupils. From their first week at Michaela, we teach them about its approach to life: that everyone experiences difficulties, but that we can overcome them. We have assemblies on it, we spend an hour lesson on it, we discuss it over family lunch, and we revisit it in form time. We teach them to anticipate the frustrations of life, and the mantra: ‘stay stoical!’

Here are six ways we see it come in handy: in detentions, in exams, in arguments, inpain, in sport and with their families.

1. In detention … stay stoical!

Sometimes, pupils feel upset or resentful about being given a detention. In conversations with them, we remind them to stay calm, stay stoical, keep perspective, let go of anger, work out what they control, think about how they can build trust in future, and decide what they can do differently next time.

1. Before, in and after exams … stay stoical!

Tests can be seen as stressful by children. We help them see that preparation, revision and overcoming procrastination is within their control. If they fail an exam, or get a poor result, staying stoical and not agitating about it, but instead focusing on what they can do differently, helps them for the next assessment ahead.

1. In arguments … stay stoical!

When children get into arguments with their friends or fellow pupils, stoicism can help remind them to practise keeping a calm mind, ignoring gossip, vicious rumours, or insults, and staying positive rather than exacerbating mistrust and anger.

1. When ill or struggling… stay stoical!

It is sometimes a struggle to come in to school if children have a cold or feel a little ill; persisting rather than giving up makes them feel proud and strong. One Year 7 pupil we teach lost a tooth in assembly, put it in his pocket and carried on listening. One was stung by a wasp at sport, and overcame the pain by keeping stoicism in mind. Another gets regular nosebleeds but proudly endures. After she broke her wrist just before exams, another taught herself to write with her left hand, and is now ambidextrous. The stoic mindset reduces our fragility: the volatility of the world can’t destabilise us. With stoicism, problems become opportunities to train our resilience.

5. At sport … stay stoical!

Sport, by its competitive nature, is a time when tempers can run high. Stoicism reminds pupils not to overcelebrate and jeer at others when scoring a goal or winning a match; and not to despair or blame team-mates (or the ref!) having conceded a goal or losing a match. It prevents yellow cards turning into red cards and prevents fights breaking out. At Michaela, we call our football team The Stoics as a symbol of this mindset. If it’s cold and raining, we say: ‘great! character-building stuff: a chance to train our willpower!’

6. With your families … stay stoical!

Children experience difficult times growing up with parents, siblings and cousins. If they are taught how to stay stoical at school, it helps them to overcome arguments, illness and adversity in their family. It can help them keep perspective, stay grateful and not take their brothers, sisters, mums and dads for granted, but appreciate them.

Teaching children to stay stoical when times are tough gives them a powerful perspective that helps them improve their resilience, their relationships, and ultimately, their lives. It even improves teachers’ lives, too!

### Aien Aristeuein – Changing my mind on grammar schools

21 Apr 2017, Posted by admin in Michaela's Blog

# Changing my mind on grammar schools

When I was 16, after having completed my GCSE examinations, myself and a few friends travelled to London for a few days of sightseeing. We visited the Palace of Westminster on our last day and out of the corner of my eye, I spotted our local MP. As any group of precocious and politically aware grammar school boys would, some of us decided to go over and greet our Member of Parliament.

At the time, our MP was Graham Brady, who had just resigned from his position as Shadow Spokesperson for Europe in light of David Cameron’s pronounced objection to any further expansion of grammar schools in England. Myself, and one other friend of mine congratulated him on his principled stand. My constituency at the time was in the heart of Trafford – one of fifteen selective local education authorities still left in England. Our school was one of the remaining 164 grammar schools in England after the Crosland scythe in the 1970s (As he so eloquently put it:“If it’s the last thing I do, I’m going to destroy every f****** grammar school in England. And Wales and Northern Ireland”). At the time, we thought Brady was absolutely right to defend grammar schools, particularly as our school and many others in Trafford were so oversubscribed and successful in the national league tables. Our school was also a Catholic grammar, which meant that it selected on religious grounds, as well as academic. This made it somewhat more interesting, as catchment selection was much further down the pecking order than most grammar schools where they are often stuffed full of middle class kids whose parents didn’t want to stump up the private school subs but were willing to move into the school’s catchment area – selection by stealth, and wealth if you will. As a result, our kids had a real mix of middle class and less affluent pupils, many of whom went on to Russell Group and ancient universities.