Inspiration for this post came from an unlikely source: a bottom set year seven class and a non-specialist maths teacher. He was teaching them factors, and was asked by a student, "is zero a factor of zero?"
This question would have just about made me explode with excitement. I think my colleague's reaction was a bit different. He is a humanities teacher by trade, so naturally he was very good at fobbing them off with an answer that sounded impressive without actually answering the question.
This colleague has obviously been working with me for too long now, because after this lesson he came and asked me the same question, because he was actually interested in the answer. I even caught him reading my post Is Zero a Square Number? at lunchtime. He's one of us now.
So, is zero a factor of zero? Well, as is often the case in maths, the answer is: it is if you want it to be.
It all depends on how you define a factor. Here are some possible ways.
For n and m natural numbers, n is a factor of m if:
1) n divides m with no remainder.
2) n x p = m, where p is a natural number.
[Side note: obviously natural numbers have negative factors too, and factors can be defined on integers rather than just the natural numbers, but negative factors aren't interesting, they're just the same as the positive ones but with a minus sign.]
Let's look at the two definitions:
1) From this definition, for zero to be a factor of zero, zero would have to divide zero with no remainder. What is zero divided by zero? That's my all-time favourite maths debate (and you all know I love to maths debate). Here are three possible answers:
-Anything divided by zero is infinity, therefore the answer is infinity.
-Zero divided by anything is zero, therefore the answer is zero.
-Anything divided by itself is one, therefore the answer is one.
In fact the answer could be anything you want it to be:
0 x pi = 0
Therefore 0/0 = pi.
So we say the question (and therefore the answer) is undefined. Or "MA ERROR" on your old Casio.
So by this definition, zero is not a factor of zero, in fact it can't be a factor of anything. However, every other number must be a factor of zero. Zero divided by anything other than zero is zero, which is a whole number with no remainder.
2) I think we'd all agree there exists a p such that 0 x p = 0. There are infinitely many such p! So by this definition, zero is a factor of zero.
So what is the answer? Well I'm going to solve this mathematical mystery the way mathematicians solve most of the really puzzling mathematical mysteries. I'm going to use the magic words: "by convention".
By convention, zero is not a factor of itself.
Done.
Emma x x x
Thursday, 4 July 2013
Tuesday, 2 July 2013
The Terrible Twos
This week marks my two year anniversary as a qualified teacher, and also the two year anniversary of NQTpi. Woo!
As a third-year teacher, I look forward to:
-A slight pay rise (the last automatic one I'll have. Cheers for that, government).
-The authority that comes with the phrase "I used to teach your brother" (of course this is far less impressive than "I used to teach your father", but I've got a good few years until that one I hope).
-Possibly having a TLR (teaching and learning responsibility). I am interviewing for this next week.
Now that the "terrible twos" are behind me and I enter my third year, I thought I'd talk about the terrible twos that appear in mathematics. That is, the things in maths that are always taught together, but perhaps shouldn't be.
Word association test (please join in at home):
Area and ...
HCF and ...
Differentiation and ...
Volume and....
Here's what I think you said: perimeter, LCM, integration, and surface area. Am I right? If you didn't, then I'm guessing you're not a maths teacher.
These things are always taught in pairs. And these are all things that get confused.
My year 9 class are not completely stupid. But every single time they are asked to find the area of a shape, most of them give me the perimeter instead. Why?! I think it is fairly obvious that the word "area" means the amount of space inside the shape. I don't see how this can be confused with the length of the border. But students always get these confused.
Area and perimeter are always taught at the same time. I have heard many maths teachers say that they shouldn't be. They are two entirely different concepts, after all. If we taught them separately, would this confusion be avoided?
Similarly with HCF and LCM. My top-set students always get these confused. I think it's because they think that the HCF must be higher than the LCM, because of the name.
For me, the really interesting one is integration and differentiation. Obviously these are opposites. They're inverse operations, according to the Fundamental Theorem of Calculus. But when you think about what they actually do, they don't seem to be that linked at all. Finding the gradient and finding the area don't seem that similar. I think what many maths teachers do is teach differenriation, then teach un-differentiation, and announce that this is called integration, and then teach the application of integration to finding areas. I believe it should be the other way round: teach integration in its own right, and then discover that, holy sh*t, it's the opposite of differentiating! By the way, if your students swear in maths lessons it's a sign that you're doing something right.
Where do you stand on the area/perimeter: together or apart debate?
And congrats to all PGCE/GTP/PGDE teachers that have just qualified! Enjoy your NQT year!
And also congrats to all NQTs who have just passed their probation year! Enjoy your terrible twos!
Emma x x x
As a third-year teacher, I look forward to:
-A slight pay rise (the last automatic one I'll have. Cheers for that, government).
-The authority that comes with the phrase "I used to teach your brother" (of course this is far less impressive than "I used to teach your father", but I've got a good few years until that one I hope).
-Possibly having a TLR (teaching and learning responsibility). I am interviewing for this next week.
Now that the "terrible twos" are behind me and I enter my third year, I thought I'd talk about the terrible twos that appear in mathematics. That is, the things in maths that are always taught together, but perhaps shouldn't be.
Word association test (please join in at home):
Area and ...
HCF and ...
Differentiation and ...
Volume and....
Here's what I think you said: perimeter, LCM, integration, and surface area. Am I right? If you didn't, then I'm guessing you're not a maths teacher.
These things are always taught in pairs. And these are all things that get confused.
My year 9 class are not completely stupid. But every single time they are asked to find the area of a shape, most of them give me the perimeter instead. Why?! I think it is fairly obvious that the word "area" means the amount of space inside the shape. I don't see how this can be confused with the length of the border. But students always get these confused.
Area and perimeter are always taught at the same time. I have heard many maths teachers say that they shouldn't be. They are two entirely different concepts, after all. If we taught them separately, would this confusion be avoided?
Similarly with HCF and LCM. My top-set students always get these confused. I think it's because they think that the HCF must be higher than the LCM, because of the name.
For me, the really interesting one is integration and differentiation. Obviously these are opposites. They're inverse operations, according to the Fundamental Theorem of Calculus. But when you think about what they actually do, they don't seem to be that linked at all. Finding the gradient and finding the area don't seem that similar. I think what many maths teachers do is teach differenriation, then teach un-differentiation, and announce that this is called integration, and then teach the application of integration to finding areas. I believe it should be the other way round: teach integration in its own right, and then discover that, holy sh*t, it's the opposite of differentiating! By the way, if your students swear in maths lessons it's a sign that you're doing something right.
Where do you stand on the area/perimeter: together or apart debate?
And congrats to all PGCE/GTP/PGDE teachers that have just qualified! Enjoy your NQT year!
And also congrats to all NQTs who have just passed their probation year! Enjoy your terrible twos!
Emma x x x
Friday, 28 June 2013
Introduction to Mechanics: Lesson Plan and a Speed Riddle
First, the riddle:
The first answer I got from the class was 90mph. Is that what you think the answer is? If you do, you're wrong. Sorry.
(30+90)/2 = 60, but this is not the average. You would spend longer driving at 30mph than at 90mph, and this average does not take that into account.
Hint Number One:
What is the definition of "average speed"? Total distance covered divided by total time taken.
At this point the calculators started to come out. Pens and paper had yet to make an appearance. I then started to get some bizarre answers like 2mph. This is an example of why a calculator without pen and paper is a dangerous thing.
Hint Number Two:
To average 60mph, how long should the entire journey take?
Speed = distance/time. So 60 = 2/t. So t = 2/60 hours. This would be 2 minutes. Have you worked out the answer yet?
Hint Number Three:
How long have they been travelling so far?
Speed = distance/time. So 30 = 1/t. So t = 1/30 hours which is... 2 minutes.
So it is impossible.
Surprised? I was. It still don't really see how it can be impossible. Surely if you go fast enough you can catch up? It seems wrong somehow.
Now, onto the rest of the lesson.
I borrowed from the science prep room a mechanical weighing scale. The kind you have in your bathroom. Side note: what is it about science prep room technicians that makes them so formidable? I have never returned a borrowed item so promptly!
Anyway, I put the scales on the floor and stood on them. I asked the class to look at the number displayed. I then pointed out I was wearing heavy clothes and block heels and a big watch and I'd just eaten lunch. Then I asked the class what would happen to the number if I put my hands on the back of the chair in front whilst standing on them. They correctly told me the scales would say I've lost weight. Then I asked if there was a way for me to make the scales think I've gained weight. That's a more interesting question. I'll leave you to think about that.
Then I asked them to consider a person weighing themself whilst in a lift. What would happen to your weight when the lift is going up? The class was split almost exactly in half on this. Some thought you would gain weight because the lift is pushing the scales into your feet. Some said you would lose weight because the lift is pushing your feet off the scales. They were also divided over what happens when the lift is going down.
Mechanics is a very sciency bit of maths, and when there's a debate in science there's only one way to settle it: an experiment! So I simply declared, "To the lift!" The students were surprised and I think a little bit excited. We all went to the lift and took it in turns to go in groups of four up to the third floor then down to the ground floor, then back.
We returned to the classroom and discussed our findings and tried to explain them.I won't tell you the result of our experiment, but if you ever get the opportunity to try it out, please do!
Next I held up a tennis ball and a basket ball (borrowed from the PE department, who are a lot less scary than the lab techs) and told them we were going to do another experiment. I asked them which ball they thought would hit the floor first if we dropped them at the same time from the same height.
Again, the class was divided. We discussed mass, surface area, rigidness, air resistance... It was a good discussion. And then we gleefully left the classroom to do our experiment. Half of us went to the top floor (the third floor, or the fourth floor if you're American), and the rest went down to the bottom. Our school is kind of open so that from the top floor you can see all the way to the bottom if you lean over the balcony on the inside. This made it ideal. (The building won an award recently for its awesome architecture).
There were a few students in the corridor working on the computers or printing stuff so we drew a bit of an audience. And when the two balls hit the ground (at the same time? Well, that would be telling...) we definitely drew some attention to ourselves! It was loud.
So we went back to the classroom and discussed our findings. We talked about how the experiment was kind of rubbish because there were too many variables. So I told them we were going to watch a better experiment where these variables were controlled. That's when I showed them this clip from Brainiac. Sorry about the Arabic subtitles.
That concluded the lesson. I think it was a great way to introduce the mechanics module and give them a bit of a taster. Hopefully it has made them excited to start their A level maths in September!
Emma x x x
You are driving along a 2-mile long bridge. You drive the first mile at an average speed of 30mph. You want your average speed for the whole bridge to be 60mph. What speed do you need to drive at for the second mile?This is how I began my mechanics taster session with next year's AS students. Have you worked it out yet?
The first answer I got from the class was 90mph. Is that what you think the answer is? If you do, you're wrong. Sorry.
(30+90)/2 = 60, but this is not the average. You would spend longer driving at 30mph than at 90mph, and this average does not take that into account.
Hint Number One:
What is the definition of "average speed"? Total distance covered divided by total time taken.
At this point the calculators started to come out. Pens and paper had yet to make an appearance. I then started to get some bizarre answers like 2mph. This is an example of why a calculator without pen and paper is a dangerous thing.
Hint Number Two:
To average 60mph, how long should the entire journey take?
Speed = distance/time. So 60 = 2/t. So t = 2/60 hours. This would be 2 minutes. Have you worked out the answer yet?
Hint Number Three:
How long have they been travelling so far?
Speed = distance/time. So 30 = 1/t. So t = 1/30 hours which is... 2 minutes.
So it is impossible.
Surprised? I was. It still don't really see how it can be impossible. Surely if you go fast enough you can catch up? It seems wrong somehow.
Now, onto the rest of the lesson.
I borrowed from the science prep room a mechanical weighing scale. The kind you have in your bathroom. Side note: what is it about science prep room technicians that makes them so formidable? I have never returned a borrowed item so promptly!
Anyway, I put the scales on the floor and stood on them. I asked the class to look at the number displayed. I then pointed out I was wearing heavy clothes and block heels and a big watch and I'd just eaten lunch. Then I asked the class what would happen to the number if I put my hands on the back of the chair in front whilst standing on them. They correctly told me the scales would say I've lost weight. Then I asked if there was a way for me to make the scales think I've gained weight. That's a more interesting question. I'll leave you to think about that.
Then I asked them to consider a person weighing themself whilst in a lift. What would happen to your weight when the lift is going up? The class was split almost exactly in half on this. Some thought you would gain weight because the lift is pushing the scales into your feet. Some said you would lose weight because the lift is pushing your feet off the scales. They were also divided over what happens when the lift is going down.
Mechanics is a very sciency bit of maths, and when there's a debate in science there's only one way to settle it: an experiment! So I simply declared, "To the lift!" The students were surprised and I think a little bit excited. We all went to the lift and took it in turns to go in groups of four up to the third floor then down to the ground floor, then back.
We returned to the classroom and discussed our findings and tried to explain them.I won't tell you the result of our experiment, but if you ever get the opportunity to try it out, please do!
Next I held up a tennis ball and a basket ball (borrowed from the PE department, who are a lot less scary than the lab techs) and told them we were going to do another experiment. I asked them which ball they thought would hit the floor first if we dropped them at the same time from the same height.
Again, the class was divided. We discussed mass, surface area, rigidness, air resistance... It was a good discussion. And then we gleefully left the classroom to do our experiment. Half of us went to the top floor (the third floor, or the fourth floor if you're American), and the rest went down to the bottom. Our school is kind of open so that from the top floor you can see all the way to the bottom if you lean over the balcony on the inside. This made it ideal. (The building won an award recently for its awesome architecture).
There were a few students in the corridor working on the computers or printing stuff so we drew a bit of an audience. And when the two balls hit the ground (at the same time? Well, that would be telling...) we definitely drew some attention to ourselves! It was loud.
So we went back to the classroom and discussed our findings. We talked about how the experiment was kind of rubbish because there were too many variables. So I told them we were going to watch a better experiment where these variables were controlled. That's when I showed them this clip from Brainiac. Sorry about the Arabic subtitles.
That concluded the lesson. I think it was a great way to introduce the mechanics module and give them a bit of a taster. Hopefully it has made them excited to start their A level maths in September!
Emma x x x
Monday, 24 June 2013
Thursday, 20 June 2013
A New Way to Teach Dividing Fractions
How do you divide a fraction by another fraction?
For example, how would you do something like this:
My guess is you would flip the second fraction upside down and then multiply like so:
If you are a maths teacher, is this how you teach students?
Do you think your students understand why this method works? And, be honest, do you understand why it works?
Well today in the maths office at my academy one of my colleagues showed us a new method he'd thought of.
It works like this:
I think this is a little bit more intuitive.
My colleague got the idea from one of his year sevens who had answered this question without showing any working out:
The answer is quite obviously three. How many quarters are there in three quarters? Three, duh. But I am quite certain most of my A* students would perform the technique of flipping and timesing without even thinking. My colleague was impressed that this student had used some common sense. He wondered whether the same idea could be applied to fractions with different denominators. It is a little bit less obvious that 21/28 divided by 20/28 is 21/20, but it's not entirely unbelievable. Whereas the "trick" of flipping and timesing can look a little bit like magic to some students.
I haven't tried teaching this method so I can't comment on its effectiveness yet. But as a mathematician it appeals to me. It's quite neat. And in case you were wondering, yes this works with algebraic fractions too.
If you're going to be teaching fractions soon, why not try this out? If you do, please let me know how it goes.
Do you think this is a good method?
Emma x x x
For example, how would you do something like this:
My guess is you would flip the second fraction upside down and then multiply like so:
If you are a maths teacher, is this how you teach students?
Do you think your students understand why this method works? And, be honest, do you understand why it works?
Well today in the maths office at my academy one of my colleagues showed us a new method he'd thought of.
It works like this:
I think this is a little bit more intuitive.
My colleague got the idea from one of his year sevens who had answered this question without showing any working out:
The answer is quite obviously three. How many quarters are there in three quarters? Three, duh. But I am quite certain most of my A* students would perform the technique of flipping and timesing without even thinking. My colleague was impressed that this student had used some common sense. He wondered whether the same idea could be applied to fractions with different denominators. It is a little bit less obvious that 21/28 divided by 20/28 is 21/20, but it's not entirely unbelievable. Whereas the "trick" of flipping and timesing can look a little bit like magic to some students.
I haven't tried teaching this method so I can't comment on its effectiveness yet. But as a mathematician it appeals to me. It's quite neat. And in case you were wondering, yes this works with algebraic fractions too.
If you're going to be teaching fractions soon, why not try this out? If you do, please let me know how it goes.
Do you think this is a good method?
Emma x x x
Wednesday, 19 June 2013
A Mathematician's Lament
Sorry it has been so long since I last wrote. Exam season is a very busy and stressful time for teachers as well as students! (Perhaps even more so). Now that the wonder of "release time" is upon us, I should be able to write more.
I stumbled upon a piece of writing called A Mathematician's Lament. I think it is one of the most beautiful pieces of writing I have ever read. As I was reading it, I found myself screaming (inside my head, I don't want to make a scene - I'm British remember) "that's exactly what I think!". It's like Paul Lockhart looked inside my head, stole my thoughts, and wrote them down but in a nicer order and with better punctuation.
I urge you to read it if you can spare the time. At least read page one. For those of you who really can't be bothered, here is a TL;DR summary for you:
*Mathematics is an art.
*Mathematics should be taught the same way that music and art are taught.
*Maths is not about acquiring skills that you might apply "one day".
*Much like music lovers have certain types of music they like and certain types they dislike, mathematicians can dislike some types of maths. It is a matter of taste.
*Maths is about imagination, you do not deal with real things because real things are inaccurate and messy; maths is simple and beautiful.
My favourite quote:
I have shared this with my department and I am considering sharing it with my students as well. I think it is especially important to share with year 11s who are looking to take A Level maths. Those students who have thought they were good at maths all these years because they got all the answers right might not realise that rote learning won't get them very far in A level.
Read the whole thing and then tell me what you think in the comments below.
Emma x x x
I stumbled upon a piece of writing called A Mathematician's Lament. I think it is one of the most beautiful pieces of writing I have ever read. As I was reading it, I found myself screaming (inside my head, I don't want to make a scene - I'm British remember) "that's exactly what I think!". It's like Paul Lockhart looked inside my head, stole my thoughts, and wrote them down but in a nicer order and with better punctuation.
I urge you to read it if you can spare the time. At least read page one. For those of you who really can't be bothered, here is a TL;DR summary for you:
*Mathematics is an art.
*Mathematics should be taught the same way that music and art are taught.
*Maths is not about acquiring skills that you might apply "one day".
*Much like music lovers have certain types of music they like and certain types they dislike, mathematicians can dislike some types of maths. It is a matter of taste.
*Maths is about imagination, you do not deal with real things because real things are inaccurate and messy; maths is simple and beautiful.
My favourite quote:
"there is nothing as dreamy and poetic, nothing as radical,
subversive, and psychedelic, as mathematics."
I have shared this with my department and I am considering sharing it with my students as well. I think it is especially important to share with year 11s who are looking to take A Level maths. Those students who have thought they were good at maths all these years because they got all the answers right might not realise that rote learning won't get them very far in A level.
Read the whole thing and then tell me what you think in the comments below.
Emma x x x
Thursday, 25 April 2013
The Top Ten Stupidest Teaching Tips
There is a lot of advice out there for teachers. As an NQT, every experienced teacher you meet will probably start their first conversation with you by imparting some "words of wisdom". Often this begins with, "I don't know what they've taught you on your PGCE, but in my experience [insert gratuitous advice here]".
I have been given a lot of bad advice is my short time as a teacher. Some of it was from my PGCE course, some from books, and some from the soapbox in the corner of the staff room.
So, here is my list of the top ten stupidest teaching tips (in no particular order):
"Don't smile until Christmas"
This is probably the most oft-quoted teaching tip. But does anyone actually do this? I think it's terrible advice!
I love maths. I want my students to love maths. Can you share your enthusiasm for a subject without smiling? If I explain a topic in maths completely straight-faced, doesn't that imply to my students that I don't find that topic interesting/exciting/inspiring? And they'll be thinking, even Miss finds this boring and maths is her favourite subject!
Also, the first term of teaching a new class is when you're trying to make relationships. Is it possible to make a relationship with someone without smiling?
Of course you want to lay down the law and show them who's boss, but without coming across as cold, boring, and unrelatable.
"As your students leave the room, stand by the door and tell each of them you love them".
You probably think I've made this one up. But no, I read this in Rocket up Your Class! which I actually thought was a great book until I read this particular titbit.
However, being the diligent student that I am, after reading this advice, I decided to try it out. I don't think I can really call it a success. The first student out the room was definitely uncomfortable, the last person out the room only got a very lacklustre "Uvyoo" (you try saying "I love you" thirty times in thirty seconds!) The students didn't even find it funny, they just thought I was weird.
The main problem I have with this is that to be quite honest, I don't "love" my students. They're perfectly nice people (some of them) and all, but my love is reserved for immediate family, pets past and present, and chocolate-covered popcorn. Sorry kids.
"Positives and negatives should be given out in the ratio of 4:1"
I've already written about my scepticism of this. I know teachers who are highly effective and have excellent relationships with students who very rarely use praise, and never use rewards.
I hate over-praising. It just devalues the whole currency. I'd rather be praised meaningfully once in my whole seven years with a teacher, than shallowly every lesson.
"Never take work home with you"
If it were possible to not mentally take work home with you, I might have thought this was good advice.
In terms of physical work: marking, lesson planning, reports, various admin (far too much of it, considering teachers aren't technically supposed to have to do admin)... the way I see it there are two choices.
Go home lugging your books on your back (or in the boot, if, unlike me, you have a car), get home at 4:30, make yourself a cup of tea by filling the kettle from the kitchen sink, not from the communal toilet's sink (the closest water source to the maths office), using milk that's not perpetually "on the turn", in your favourite mug, not whatever vessel you can find that hasn't been appropriated by the faculty slob. You can immediately change into your jammies, put on your guilty-pleasure music (a certain adorable quintuple springs to mind), and mark/plan/do stuff whilst stuffing your face with roasted chickpeas (too smelly to eat in the office).
Or...
Stay at school, do your work, get home at 7pm, and smugly say to your spouse/kids/tamagotchi: "I don't take work home with me. Check out my work-life balance!"
"Don't do more than one of the same type of question"
This advice was actually given to me by an OfSTED inspector. Despite my new-found respect for HMIs, after they showed excellent judgement in awarding me the coveted title of "outstanding teacher", I still feel I have to disagree with this particular tip.
I talked at length about this in this post. I won't bother repeating myself.
"Never touch a student"
Way too many teachers are terrified of being called the P word. A gentle hand on the arm isn't going to cause any trouble! A pat on the back isn't going to put you in jail! (Obviously if the student in question has ASD or is a CP case then exercise caution).
On January results day just gone, one of my year 12s asked me for a hug. I am ashamed to say I almost said no. But then I thought, screw it, this girl was so nervous this morning and now she's overcome with relief, of course I should give her a hug! She shouldn't have had to have asked, I should have offered her a hug! It's a one-off ting, it's not a big deal. Stop being scared.
"Show students the insides of your wrists to show them you trust them"
This wee gem was imparted on me by someone at university when I was doing my PGCE. Not only is this advice bizarre, it is also incredibly hard to do. I challenge you all to attempt this in one of your lessons this week. Unless you have a curiously-shaped mole on your wrist you can somehow incorporate into your starter activity, I don't think you'll manage it.
"Keep your hands above waist height to demonstrate power"
Another PGCE one. I should point out these were external speakers, not my actual teachers, who were all brilliant.
My question is this: where can you put your hands above your waist? On your shoulders? Under your armpits, in the manner of a gorilla? Stroking your chin with your left and scratching your head with your right? Or arms spread wide, as if welcoming in your students' ideas and basking in their insights. Hmm.
Oh dear, a quick google has revealed to me that this advice is not only given to teachers but to business people who have to make important presentations and speeches. Listen up guys, here's my public-speaking advice: if you need to resort to body-language tricks to get people to agree with you, the content of your speech is probably rubbish.
"Do vocal exercises in the shower every morning"
We had quite a few sessions on looking after your voice during my PGCE. Teachers talk a lot compared to people in other jobs, and voice strain is definitely something that could be an issue. I know that the first day back after a holiday my voice always hurts by the end of the day.
But do any teachers ever actually do vocal exercises? Every morning? In the shower? Don't get me wrong, I enjoy my sessions with the loofah-microphone as much as the next person, but certainly not at 5:45am, and anyway, my performances are limited to actual songs, not odd bird-like squawks and exaggerated vowel sounds. I can't believe I attended those lectures.
"Get a gun"
No, I've not gone crazy. Read this article. I'm not even going to pass comment. Except perhaps to say: oh dear, America.
Got any stupid teaching tips for me? Post them in the comments!
Emma x x x
I have been given a lot of bad advice is my short time as a teacher. Some of it was from my PGCE course, some from books, and some from the soapbox in the corner of the staff room.
So, here is my list of the top ten stupidest teaching tips (in no particular order):
"Don't smile until Christmas"
This is probably the most oft-quoted teaching tip. But does anyone actually do this? I think it's terrible advice!
I love maths. I want my students to love maths. Can you share your enthusiasm for a subject without smiling? If I explain a topic in maths completely straight-faced, doesn't that imply to my students that I don't find that topic interesting/exciting/inspiring? And they'll be thinking, even Miss finds this boring and maths is her favourite subject!
Also, the first term of teaching a new class is when you're trying to make relationships. Is it possible to make a relationship with someone without smiling?
Of course you want to lay down the law and show them who's boss, but without coming across as cold, boring, and unrelatable.
"As your students leave the room, stand by the door and tell each of them you love them".
You probably think I've made this one up. But no, I read this in Rocket up Your Class! which I actually thought was a great book until I read this particular titbit.
However, being the diligent student that I am, after reading this advice, I decided to try it out. I don't think I can really call it a success. The first student out the room was definitely uncomfortable, the last person out the room only got a very lacklustre "Uvyoo" (you try saying "I love you" thirty times in thirty seconds!) The students didn't even find it funny, they just thought I was weird.
The main problem I have with this is that to be quite honest, I don't "love" my students. They're perfectly nice people (some of them) and all, but my love is reserved for immediate family, pets past and present, and chocolate-covered popcorn. Sorry kids.
"Positives and negatives should be given out in the ratio of 4:1"
I've already written about my scepticism of this. I know teachers who are highly effective and have excellent relationships with students who very rarely use praise, and never use rewards.
I hate over-praising. It just devalues the whole currency. I'd rather be praised meaningfully once in my whole seven years with a teacher, than shallowly every lesson.
"Never take work home with you"
If it were possible to not mentally take work home with you, I might have thought this was good advice.
In terms of physical work: marking, lesson planning, reports, various admin (far too much of it, considering teachers aren't technically supposed to have to do admin)... the way I see it there are two choices.
Go home lugging your books on your back (or in the boot, if, unlike me, you have a car), get home at 4:30, make yourself a cup of tea by filling the kettle from the kitchen sink, not from the communal toilet's sink (the closest water source to the maths office), using milk that's not perpetually "on the turn", in your favourite mug, not whatever vessel you can find that hasn't been appropriated by the faculty slob. You can immediately change into your jammies, put on your guilty-pleasure music (a certain adorable quintuple springs to mind), and mark/plan/do stuff whilst stuffing your face with roasted chickpeas (too smelly to eat in the office).
Or...
Stay at school, do your work, get home at 7pm, and smugly say to your spouse/kids/tamagotchi: "I don't take work home with me. Check out my work-life balance!"
"Don't do more than one of the same type of question"
This advice was actually given to me by an OfSTED inspector. Despite my new-found respect for HMIs, after they showed excellent judgement in awarding me the coveted title of "outstanding teacher", I still feel I have to disagree with this particular tip.
I talked at length about this in this post. I won't bother repeating myself.
"Never touch a student"
Way too many teachers are terrified of being called the P word. A gentle hand on the arm isn't going to cause any trouble! A pat on the back isn't going to put you in jail! (Obviously if the student in question has ASD or is a CP case then exercise caution).
On January results day just gone, one of my year 12s asked me for a hug. I am ashamed to say I almost said no. But then I thought, screw it, this girl was so nervous this morning and now she's overcome with relief, of course I should give her a hug! She shouldn't have had to have asked, I should have offered her a hug! It's a one-off ting, it's not a big deal. Stop being scared.
"Show students the insides of your wrists to show them you trust them"
This wee gem was imparted on me by someone at university when I was doing my PGCE. Not only is this advice bizarre, it is also incredibly hard to do. I challenge you all to attempt this in one of your lessons this week. Unless you have a curiously-shaped mole on your wrist you can somehow incorporate into your starter activity, I don't think you'll manage it.
"Keep your hands above waist height to demonstrate power"
Another PGCE one. I should point out these were external speakers, not my actual teachers, who were all brilliant.
My question is this: where can you put your hands above your waist? On your shoulders? Under your armpits, in the manner of a gorilla? Stroking your chin with your left and scratching your head with your right? Or arms spread wide, as if welcoming in your students' ideas and basking in their insights. Hmm.
Oh dear, a quick google has revealed to me that this advice is not only given to teachers but to business people who have to make important presentations and speeches. Listen up guys, here's my public-speaking advice: if you need to resort to body-language tricks to get people to agree with you, the content of your speech is probably rubbish.
"Do vocal exercises in the shower every morning"
We had quite a few sessions on looking after your voice during my PGCE. Teachers talk a lot compared to people in other jobs, and voice strain is definitely something that could be an issue. I know that the first day back after a holiday my voice always hurts by the end of the day.
But do any teachers ever actually do vocal exercises? Every morning? In the shower? Don't get me wrong, I enjoy my sessions with the loofah-microphone as much as the next person, but certainly not at 5:45am, and anyway, my performances are limited to actual songs, not odd bird-like squawks and exaggerated vowel sounds. I can't believe I attended those lectures.
"Get a gun"
No, I've not gone crazy. Read this article. I'm not even going to pass comment. Except perhaps to say: oh dear, America.
Got any stupid teaching tips for me? Post them in the comments!
Emma x x x
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