Our school system is designed for extroverts. Learning takes place in large groups, with participation and collaboration not just encouraged, but compulsory. Students who don't work well in groups, or who don't learn well as part of a collective, are at a disadvantage. Students who don't put up their hands are too often ignored. Quiet students are too often left to coast without being fully challenged.

Teaching extroverts is simple. They tend to respond quickly. They make fast decisions. They are comfortable with multi-tasking and risk-taking. They tell you when they don't understand something. They ask for help. They think out loud, so you can unpick their thinking and tackle misconceptions. They answer questions and contribute to class discussions. When you have students like this in your class, you will find yourself catering to their needs because they make their needs known. Extroverts dictate the pace of the lesson, because they are the ones giving you feedback.

In my year 11 class, for example, whenever the students are doing exercises from the textbook, there are certain students who will always call for me. Most of the time, they don't even need help. They ask me, "is this right?" (they could just look at the answer page in the back of the book) or they ask me questions they already know the answer to: "Am I supposed to differentiate it then substitute x = 2?" These are the extroverts. The introverts only call for me when they've already checked the answer in the back, seen that they've got it wrong, and tried to do it again and failed again. This could mean they end up working at a slower pace. That wouldn't be a problem at all, (in fact they will have gained a deeper understanding by doing this) except for the fact that the extroverts determine the pace of the lesson, and the class may move on before the introverts are really ready.

There's also the problem of teacher expectations. Studies have shown that people who talk more are viewed as more intelligent. Introverts may be labelled as slower, less confident, and weaker, and we all know that labelling students often has fatal consequences. Students also compare themselves to each other, and introverts may see extroverts as being more intelligent than them. This may make them feel inferior and this could lead to lower self-expectations, and hence lower achievement.

So what can we do to remedy this?

Encourage introverted students to email you when they are stuck on something. Emailing is a much easier method of communication for introverts because it does not involve physically being around people. It also allows them to read and absorb your reply at their own pace and internalise it (which is an awkward process when you're face to face with someone).

Similarly, ask students to write you questions or comments in their exercise books. When you take in their books to mark them, you can read and reply to these comments.

Using mini whiteboards with quickfire questions is a very effective method of gauging a class's understanding, and picking up on and dealing with misconceptions quickly. However, it is not well-suited to introverts. Introverts prefer to work at their own pace, without external pressure. They may panic at the idea of working something out so quickly and having to show the teacher immediately. In this panic, they may end up simply copying someone else's answer. Allow these students to complete questions in their book instead, and after that section of the lesson, go to those students and check their answers, and address misconceptions if necessary.

Provide hint cards for students to use when doing an activity. If they get stuck, introverts can look at the hint card and use this to get themselves unstuck. Or provide them with a website they can look at on their phone, or a page reference for their textbook.

When making seating plans, it's probably very tempting to put louder students next to quieter students in an attempt to make the louder students quieter, and keep the overall volume down. It may achieve this goal, but I'd argue it's detrimental to both types of student. Extroverts need to give and receive external stimulation (thinking out loud, talking through their reasoning) and introverts need to have as little external stimulation as possible. Therefore it makes most sense to sit introverts with introverts and extroverts with extroverts. You might say, "---- is so quiet, I should make ------ sit next to her to try and bring her out of her shell a bit". If you're thinking that, you don't understand introverts. If someone feels most comfortable inside their shell, that's where they should stay, because that's where they will learn most effectively.

Introverts are not necessarily shy, but many of them are, and many of them hate being made to answer questions in front of the class. If they haven't put their hand up to answer any questions, sometimes you may call on them just to check their understanding and to check they're actually listening. Do you have to do this? Could you wait until the class are busy with an activity, and approach these students individually and check their understanding one-to-one? If you really want them to participate in a class discussion, give them some advance warning that you are going to ask them to contribute, so that they have time to prepare what they're going to say. Extroverts are good at thinking out loud, so they can talk and think at the same time. Introverts find this really difficult, so they have to fully form their thoughts before they open their mouth.

Every so often, you'll have what you consider a "fun" lesson. This might involve a team competition, an active lesson like a relay, or something a bit different like role playing or drama. This sort of thing might be considered fun by extroverts, but not necessarily by introverts. For introverts, a fun lesson might be one where everyone is working very quietly, maybe listening to music through headphones (so that no one can talk to you), working on an individual task that involves no collaboration at all. It might involve not having to sit in their usual seats at desks, but being able to sit on the floor in the corner, or using the window sill as a desk so they can stare out of the window as they think. If you're going to have fun lessons for extroverts sometimes, you should also have fun lessons for introverts. Otherwise, you're not being fair.

The latest craze seems to be Walking, Talking Mocks. This is where the teacher talks through an exam paper and models answering every question, which the students then copy down. Doing it this way favours extroverts, who like to talk through problems and like to have teachers talking at them, as this is external. However, introverts find it difficult to think about things that are external. The teacher's model solution is external, and the introvert needs a few minutes to read it to themselves and internalise it. So an adaptation that is a good compromise is getting the students to spend a few minutes answering a question by themselves, then go through the model solution, then provide a few minutes for reflection, then repeat. Alternatively, record yourself doing an exam paper, and talk through your thought processes as you do it. Give this to the students to watch, either in a lesson (with individual devices and headphones) or at home. Introverts can pause the video whenever they need to stop and contemplate.

Please let me know if you have any other ideas. Also let me know if you agree or disagree with anything I've said here. I'd love to know your thoughts.

Emma x x x

## Wednesday, 29 March 2017

## Tuesday, 28 March 2017

### Being an Introvert in an Education System Built for Extroverts

I recently read Susan Cain's book Quiet: the Power of Introverts in a World that Can't Stop Talking and felt like I finally understood myself. I had always thought that I was an extrovert. I love public speaking. I'm always the first on the dance floor. I'm not at all shy in front of a camera and will happily post videos of myself on the internet. Clearly an extrovert, right? Well it turns out I was wrong. Let me explain why.

Introversion and extroversion are not about being shy and being outgoing. They are about where you get your energy from. An introvert recharges their batteries by spending time alone, in an environment with little external stimulation. Their batteries get drained by being around lots of people, with lots of external stimulation. For extroverts, it's the other way round.

I love public speaking, but that's because I'm standing by myself on a stage, not interacting with people. I'm always the first on the dance floor, because that's when it's at its emptiest and I can dance as a means of escaping social interactions. I always leave the dance floor when it becomes too crowded. I'm not shy in front of a camera, because I'm alone, and I'm sort of just talking to myself. Posting it on the internet doesn't bother me, because I don't have to be around people in real life. I don't mind attention (in fact I love it), I just don't like being physically surrounded by lots of people in a loud, stimulating environment.

Realising I was an introvert made me understand myself a lot better. It made me realise that I need a certain amount of alone time everyday in order to recharge my batteries. My job is not particularly well-suited to introverts; I spend most of my working day surrounded by 30 hyperactive children. That's why I walk to and from school everyday: that 40 minutes of quiet reflection helps me recharge my depleted energy stores.

Unfortunately for me, the way our society is built favours extroverts. That's because those in positions of power are quite obviously more likely to be extroverts. Managers and leaders are more likely to be extroverts, but that's not because extroverts make better managers, they're just more likely to apply for the job, perform well in the interview, and enjoy many of the aspects of the job.

But this is a blog about teaching and learning, not office politics, so let me get to the point. Our education system favours extroverted students. Here's why:

- Students are taught in groups, usually between 10 and 35 students in each group. Thus students spend the majority of their day surrounded by a crowd.
- Group work is encouraged, and is seen as good pedagogy. Students get told off for not contributing.
- Students who put their hands up to answer questions are the ones who receive the most teacher attention. They also receive the most praise.
- Classrooms are designed to be visually stimulating, with brightly coloured, busy wall displays and fluorescent lights.
- At lunchtime and break time, students do not generally have the option of seeking out a quiet spot they can call their own. In most schools, they either have to sit in the canteen or go out to the playground. Both of which are crowded and noisy.
- The new "thing" in education is using technology to make every aspect of the lesson "interactive". Some of us don't like interacting.
- Most of the new teaching techniques I've been introduced to during teaching and learning meetings at my school seem to cater to extroverts: speed dating, relays, walking talking mocks, hot seating, role playing... Maybe teaching and learning leaders in schools are more likely to be extroverts themselves?

In my next post, I will talk about how we can redress the balance a little by using techniques that can support introverted students.

Are you an introvert or an extrovert and do you think it affected your education at all? Do you disagree that our school system favours extroverts? Let me know in the comments.

Emma x x x

## Sunday, 12 March 2017

### Bad Exam Advice

I was marking mock exam papers this weekend (in fact that's pretty much the only thing I did this weekend - whose idea was it to introduce a third paper? And whose idea was it to put 31 students in my class?) when during a moment of extreme boredom I read the front of the exam paper.

I was going to blur out the student's name to protect his privacy, and then I realised he had (very considerately) already made his name unreadable. Unfortunately for me, he also made all of his working out illegible too.

In the section that says "instructions to candidates", it says:

When trying to solve a maths problem, you will very rarely know what you have to do before you start answering it. For example, take the last question of this paper:

When I look at this question, I don't know exactly what the steps are and what the proof looks like. I know it will involve some angle rules, but which ones and in which order, I don't know. It would be completely stupid to sit there looking at the question for fifteen minutes trying to work out exactly what I need to do before starting my answer. The sensible thing to do would be to write down something you do know. For example, you know that OQ and OR are both radii and hence equal in length. After that, you might be a bit stuck, so you start trying things. Eventually, you might realise that drawing in the line PO would be helpful. At this point, you still don't know how you're going to complete the proof. You give some angles some letters, so that you can write some relationships more easily. You could let PQO=x, and therefore QPO=x too. Let ORP = y, so OPR =y. Then you might decide to work out QOP and ROP, not because you know that it's going to help, but because you know how to do it so you may as well. QOP= 180-2x, ROP = 180-2y. Then you work out QOR, because, well, it's there. QOR = 360-(180-2x)-(180-2y) = 2x+2y. Then you realise that QPR= x+y which means that you have proved it. Then you do a happy dance and probably write your maths teacher a note like "circle theorems is bae" (yes one of my students actually wrote that).

At no point during this proof had you worked out what you needed to do to answer the question. You tried some stuff, and some stuff led to other stuff, and eventually the problem was solved. This is how maths problems should be solved. If you know exactly how to answer the question before you start answering it, it's probably not a very interesting question.

I'm wondering whether the creator of this exam question intended for the students to know what they have to do before answering it. That would mean they were expecting students to have memorised by heart proofs to all of the circle theorems. What a depressing thought that is. How is regurgitating a bunch of proofs a sign of good mathematical thinking?

My head of department has a speech he likes to give students on this topic. (Actually, he has lots of speeches he likes to give, as his (and my) students know all too well). He says that it's like untangling your earphones. Earphones, as we know, automatically tangle themselves as soon as you stop using them. And when you want to use them, you have to spend a good five minutes untangling them. When you do this, do you look at the ball of entwined wires in your hand and think, "right, first I'll move that bit under that bit, then I'll pull this end through there, then I'll twist that bit round..."? Of course you don't, that would be silly. Instead, you get stuck in trying to untangle them. You pull bits and you twist bits and you play around with it. And eventually, no matter how bad the tangling was, you always succeed in getting them straightened out. This is exactly how you should tackle a maths problem.

So my advice would be to ignore the advice on the front of the exam paper. Well, except the bit that says "read each question carefully". Oh and also the bit that says "You are reminded of the need for clear presentation in your answers" (which several of my students definitely ignored).

Emma x x x

I was going to blur out the student's name to protect his privacy, and then I realised he had (very considerately) already made his name unreadable. Unfortunately for me, he also made all of his working out illegible too.

In the section that says "instructions to candidates", it says:

"Make sure you know what you have to do before starting your answer."Does anyone else disagree completely with this advice?

When trying to solve a maths problem, you will very rarely know what you have to do before you start answering it. For example, take the last question of this paper:

When I look at this question, I don't know exactly what the steps are and what the proof looks like. I know it will involve some angle rules, but which ones and in which order, I don't know. It would be completely stupid to sit there looking at the question for fifteen minutes trying to work out exactly what I need to do before starting my answer. The sensible thing to do would be to write down something you do know. For example, you know that OQ and OR are both radii and hence equal in length. After that, you might be a bit stuck, so you start trying things. Eventually, you might realise that drawing in the line PO would be helpful. At this point, you still don't know how you're going to complete the proof. You give some angles some letters, so that you can write some relationships more easily. You could let PQO=x, and therefore QPO=x too. Let ORP = y, so OPR =y. Then you might decide to work out QOP and ROP, not because you know that it's going to help, but because you know how to do it so you may as well. QOP= 180-2x, ROP = 180-2y. Then you work out QOR, because, well, it's there. QOR = 360-(180-2x)-(180-2y) = 2x+2y. Then you realise that QPR= x+y which means that you have proved it. Then you do a happy dance and probably write your maths teacher a note like "circle theorems is bae" (yes one of my students actually wrote that).

At no point during this proof had you worked out what you needed to do to answer the question. You tried some stuff, and some stuff led to other stuff, and eventually the problem was solved. This is how maths problems should be solved. If you know exactly how to answer the question before you start answering it, it's probably not a very interesting question.

I'm wondering whether the creator of this exam question intended for the students to know what they have to do before answering it. That would mean they were expecting students to have memorised by heart proofs to all of the circle theorems. What a depressing thought that is. How is regurgitating a bunch of proofs a sign of good mathematical thinking?

My head of department has a speech he likes to give students on this topic. (Actually, he has lots of speeches he likes to give, as his (and my) students know all too well). He says that it's like untangling your earphones. Earphones, as we know, automatically tangle themselves as soon as you stop using them. And when you want to use them, you have to spend a good five minutes untangling them. When you do this, do you look at the ball of entwined wires in your hand and think, "right, first I'll move that bit under that bit, then I'll pull this end through there, then I'll twist that bit round..."? Of course you don't, that would be silly. Instead, you get stuck in trying to untangle them. You pull bits and you twist bits and you play around with it. And eventually, no matter how bad the tangling was, you always succeed in getting them straightened out. This is exactly how you should tackle a maths problem.

So my advice would be to ignore the advice on the front of the exam paper. Well, except the bit that says "read each question carefully". Oh and also the bit that says "You are reminded of the need for clear presentation in your answers" (which several of my students definitely ignored).

Emma x x x

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