I have always received good grades in maths. This made me feel special. I remember that day in year six when I, along with just two other students from my large-ish Primary school, sat the level 6 Maths SATs paper in a special room. Why was it just us three? Because we were special. There was only a level 6 paper for maths, not for English or science. Why? Because maths is special. Because maths can reach levels of difficulty that English and science cannot.
I remember the day in year seven when in the very first week we had a maths test. Because maths is about showing how much you know. I remember the day, a week later, when we were put into sets for maths. Not any other subject, just maths. Why? Because in maths, ability is important. In maths, the clever students need to be separated from the bad students so that they can learn hard maths unhindered.
I remember the day in year nine when I sat my SATs, and again, English and Science only went up to level 7, but maths went up to level 8. Only the top class got to do that paper. It was a paper for special people, for the chosen ones who were good at maths.
I remember the day in year eleven when I chose my A-Level subjects. I remember being told, "you're good at maths, so you should do maths". Other people were told, "you enjoy English, you should pick English," or "you enjoy design, you should pick design". Because maths is something you do because you're good at it, not because you enjoy it.
I remember the day in year thirteen when I chose the courses to apply for at university. I considered doing Psychology. I loved Psychology. But lots of people are good at Psychology. I was the best in my school at Maths. So I chose Maths. Not many people are good at Maths. I chose my university because it was the best non-Oxbridge, non-London university for Mathematics research. The cleverest mathematicians work there, so it must be the best place.
I found university maths very hard. I was not that good at it. So I stopped liking maths. Maths is not fun when you're falling behind. There was no help given at my university. The professors lectured but they did not teach. Because if you need help learning university maths, you're not good enough to be here.
Look at my bolded statements. These are the beliefs that I developed as a result of my education. These beliefs are shared by many whether they consider themselves good at maths or not. If you ask someone what maths was like for them at school, they almost always answer by commenting on their performance, e.g. "I was always good/bad at maths". If you ask someone what, say, Geography, was like for them at school, they almost always comment on their enjoyment of it, e.g. "I found it boring/interesting". This is because maths is seen to be a subject that is all about ability and performance.
I remember the day, not too long ago, when I was looking at year eleven students who had chosen to do maths A-Level next year.
I said, "She's in set four [out of nine], is she deluded? She can't do maths A-Level!"
I said, "Students shouldn't be encouraged to pick maths unless they're in set one"
I said, "Maths isn't like Psychology, not just anyone can do it!"
I said, "They need to realise maths is really hard, it's not like other A-Levels"
I said, "I'm sure she'll try really hard but she just doesn't have what it takes"
I cannot believe that I said these things just a week ago. Since reading Mathematical Mindsets by Jo Boaler, I have completely changed my beliefs about maths as a subject. No one is born good at maths. No one is born bad at maths. Maths is not about answering questions correctly. Maths is not about passing tests. Maths is about connections and communication. I almost want to petition to have maths re-named to that in my school. While I'm at it, maybe I should re-name my blog to "not just tests".
Here's what I think we should do to overcome this problem:
-Stop testing students in maths in the first week of year seven.
-Don't put students into sets in maths until you absolutely have to (do we ever have to? Finland doesn't).
-Stop praising students for getting answers right in maths lessons.
-Don't ever tell a student they are good at maths (I hope it goes without saying to never tell a student they're bad at maths).
-If your top set year eleven study Additional Maths or Further Maths GCSE, don't make it just for top set, make it an opt-in subject for any student who loves maths.
Let's eradicate this ridiculous notion that maths is different from every other subject. As maths teachers, it is up to us to end this.
Emma x x x
Thursday, 28 January 2016
Saturday, 23 January 2016
Is Homework Racist?
The other day I started reading Jo Boaler's new book Mathematical Mindsets and I think it is so far the book that that has had the biggest impact on my beliefs about teaching and learning in mathematics. When I have finished reading it I will give a full review and summary on this blog but for now I just want to talk about one of the things that really stood out to me as I was reading.
Homework is racist!
At the school where I teach, homework is given very high importance. We set a lot of it, especially in maths, where the policy is that homework is set after every lesson. We have a whole-school detention in place for students who do not complete homework. One quarter of every student's end of term report to parents is about homework quality and quantity. I tend to spend at least 25% of every lesson going through the previous day's homework. I used to say all of these things proudly. But now, knowing what I know now, I feel uneasy, and even slightly ashamed. And, well, racist.
So let me explain. Students from disadvantaged backgrounds and belonging to some ethnic minority groups are less likely to do their homework in the first place, are likely to spend less time on their homework, are less likely to have help on their homework from family members, are less likely to have the tools they need to do their homework at home (like a desk, a quiet place, stationery supplies), and are less likely to have the time to spend on homework, due to looking after younger family members, doing house work, or working a part-time job.
If I set homework and a student does not do it, that 25% of the lesson I spend going through the homework has little benefit to that student. If that student never does their homework, they are effectively only receiving 75% as much teaching as the other students (and that's assuming the homework itself was of no educational value). You might say it's the student's fault they didn't do their homework, or it was the student's choice. However, when you consider on a national scale that some ethnic groups are less likely to do their homework, we are actually indirectly discriminating against those ethnic groups.
In America, some students take an Algebra course in eighth grade (year 9) then if they pass it they can move on to Geometry in the first year of high school (year 10). However, whether they are put into Geometry or back into Algebra in high school is at the teacher's discretion. In 2012, the Noyce Foundation studied student placement in nine school districts in San Francisco and found that 60% of students who should have moved onto Geometry were actually placed into Algebra. This is damaging for those students because it means they would not be able to do AP Calculus in their final year, and hence may not get into college to study a STEM course. When the Noyce Foundation looked more closely at the data, they found that of the 53% of African American students who passed Algebra in eighth grade, only 18% were put into Geometry, and of the 50% of Latino/a students who passed Algebra in eighth, only 16% took Geometry in ninth. (For Asian students, 52% became 52%, for white students, 59% became 33%). Given these facts alone, you would conclude that the teachers who were deciding which classes to put students in were racist. The Silicon Valley Community Foundation hired lawyers who found that the schools were actually acting illegally. But the teachers did not see themselves as racist, nor did they realise they were discriminating. They had simply been choosing which students to advance by looking at test scores and homework completion. What they did not take into account was that the homework completion criteria disproportionately impacts minority students, and is hence still illegal discrimination.
Something similar may be happening at your school. Have you ever seen a student move down a set for not completing their homework or for having poor behaviour? As some ethnic groups are less likely to do their homework and more likely to have poor behaviour, this may be a case of illegal racial discrimination.
PISA, the organisation which compares mathematics achievement of students around the world, did a study in 2015 into homework and achievement. They had data from 13 million students, and found that homework perpetuates inequities in education.
Interestingly, Finland and Korea, two of the highest achieving countries in terms of maths, set the least amount of maths homework.
You might be tempted to say that instead of reducing the achievement gap by eliminating homework, we should instead focus on getting ethnic minority or Pupil Premium students to do their homework. After school homework clubs, often made compulsory for certain students, could work to address this. However, after reading around the topic, I am starting to doubt whether there is actually any point in maths homework at all.
Here are a list of studies that have started to convince me to ditch homework:
Baker and LeTendre (2005) found no positive link between amount of maths homework and maths achievement.
Mikki (2006) found that the countries that set the most homework have the lowest achievement.
Kistantas, Cheema and Ware (2011) found that the more time students spent on homework, the lower their maths achievement across all ethnic groups.
Author Alfie Kohn has written extensively on the subject.
So setting maths homework might not have much of a positive effect on the students that do it, but it does have a negative effect on the students who don't do it. This is almost contradictory, but if it's true, it makes setting homework a completely ridiculous thing to do.
I am going to do some more research before throwing out homework altogether (not that my school would let me, anyway). In the meantime, I am going to change the type of homeworks I set so that they are more in line with my new beliefs about growth mindset and mathematics learning, which I will talk about more in future posts.
Emma x x x
Homework is racist!
At the school where I teach, homework is given very high importance. We set a lot of it, especially in maths, where the policy is that homework is set after every lesson. We have a whole-school detention in place for students who do not complete homework. One quarter of every student's end of term report to parents is about homework quality and quantity. I tend to spend at least 25% of every lesson going through the previous day's homework. I used to say all of these things proudly. But now, knowing what I know now, I feel uneasy, and even slightly ashamed. And, well, racist.
So let me explain. Students from disadvantaged backgrounds and belonging to some ethnic minority groups are less likely to do their homework in the first place, are likely to spend less time on their homework, are less likely to have help on their homework from family members, are less likely to have the tools they need to do their homework at home (like a desk, a quiet place, stationery supplies), and are less likely to have the time to spend on homework, due to looking after younger family members, doing house work, or working a part-time job.
If I set homework and a student does not do it, that 25% of the lesson I spend going through the homework has little benefit to that student. If that student never does their homework, they are effectively only receiving 75% as much teaching as the other students (and that's assuming the homework itself was of no educational value). You might say it's the student's fault they didn't do their homework, or it was the student's choice. However, when you consider on a national scale that some ethnic groups are less likely to do their homework, we are actually indirectly discriminating against those ethnic groups.
In America, some students take an Algebra course in eighth grade (year 9) then if they pass it they can move on to Geometry in the first year of high school (year 10). However, whether they are put into Geometry or back into Algebra in high school is at the teacher's discretion. In 2012, the Noyce Foundation studied student placement in nine school districts in San Francisco and found that 60% of students who should have moved onto Geometry were actually placed into Algebra. This is damaging for those students because it means they would not be able to do AP Calculus in their final year, and hence may not get into college to study a STEM course. When the Noyce Foundation looked more closely at the data, they found that of the 53% of African American students who passed Algebra in eighth grade, only 18% were put into Geometry, and of the 50% of Latino/a students who passed Algebra in eighth, only 16% took Geometry in ninth. (For Asian students, 52% became 52%, for white students, 59% became 33%). Given these facts alone, you would conclude that the teachers who were deciding which classes to put students in were racist. The Silicon Valley Community Foundation hired lawyers who found that the schools were actually acting illegally. But the teachers did not see themselves as racist, nor did they realise they were discriminating. They had simply been choosing which students to advance by looking at test scores and homework completion. What they did not take into account was that the homework completion criteria disproportionately impacts minority students, and is hence still illegal discrimination.
Something similar may be happening at your school. Have you ever seen a student move down a set for not completing their homework or for having poor behaviour? As some ethnic groups are less likely to do their homework and more likely to have poor behaviour, this may be a case of illegal racial discrimination.
PISA, the organisation which compares mathematics achievement of students around the world, did a study in 2015 into homework and achievement. They had data from 13 million students, and found that homework perpetuates inequities in education.
"Homework may then have the unintended consequence of widening the performance gap between students from different socio-economic backgrounds". (PISA, 2015)Read the full paper here: Does Homework Perpetuate Inequities in Education?
Interestingly, Finland and Korea, two of the highest achieving countries in terms of maths, set the least amount of maths homework.
You might be tempted to say that instead of reducing the achievement gap by eliminating homework, we should instead focus on getting ethnic minority or Pupil Premium students to do their homework. After school homework clubs, often made compulsory for certain students, could work to address this. However, after reading around the topic, I am starting to doubt whether there is actually any point in maths homework at all.
Here are a list of studies that have started to convince me to ditch homework:
Baker and LeTendre (2005) found no positive link between amount of maths homework and maths achievement.
Mikki (2006) found that the countries that set the most homework have the lowest achievement.
Kistantas, Cheema and Ware (2011) found that the more time students spent on homework, the lower their maths achievement across all ethnic groups.
Author Alfie Kohn has written extensively on the subject.
So setting maths homework might not have much of a positive effect on the students that do it, but it does have a negative effect on the students who don't do it. This is almost contradictory, but if it's true, it makes setting homework a completely ridiculous thing to do.
I am going to do some more research before throwing out homework altogether (not that my school would let me, anyway). In the meantime, I am going to change the type of homeworks I set so that they are more in line with my new beliefs about growth mindset and mathematics learning, which I will talk about more in future posts.
Emma x x x
Thursday, 14 May 2015
A Maths Game with a Psychological Twist
Today I'm going to tell you about one of my favourite ways to kill a spare fifteen minutes in a maths lesson. It's great because it requires absolutely no preparation, no prior knowledge, and no differentiation. All you need is a class set of mini whiteboards and pens.
Tell students that you're going to ask them to write down a number. It must be a whole number (no decimals, fractions or surds) and it must be zero or greater. They have to write this secretly and not show anyone their number. Tell them you are going to count down from 5. At 2, everyone's pens need to be down. At 1, everyone needs to show their boards. The winner, and this is the important bit, is the person who has the smallest number that no one else has.
This should be simple enough to understand, and if a student doesn't quite get it, they can at least write down a number and participate until it clicks.
When students hold up their boards, first look for zeros. If there's just one, the zero wins. If there's more than one, tell all the zeros to put their boards down and then look for ones. Repeat until you have found a number that only one person has written. They are the winner. This doesn't take very long at all, even with 32 students like my year 7 class.
I have found that this game intrigues students immediately. They have to try to predict what everyone else is thinking. I have found that I can usually predict who in the class will write zero. Zero rarely wins, and I've never seen it win in the first round. I've found that the winning numbers vary massively from class to class. The results are also very different when I've played this with adults. I'm sure there's a lot that can be explored here in terms of psychology (and economics, actually) but I'll leave that for you to think about.
I like to try to encourage strategic thinking and annoying my students at the same time by saying things like "oh, so three won that time. That means you are probably thinking about choosing three this time. But if other people think that too, you won't win, so you'd better choose four instead. But now that I've said that, you can't choose four, it's too obvious, so..." The students usually interrupt me at this point and beg me to shut up because I'm ruining their strategy.
The beauty of this game is it can be done with year 7s, year 13s, and even the Maths faculty as a pre-meeting warm-up. I have never met a class (or group of adults even) that doesn't enjoy this game.
A more mathematical version of this game is to have the same rules but this time the winner is the student whose number is the closest to the mean of all of the numbers. This is too difficult to do as a whole class, so I do this in table groups. The four students each choose a number, they calculate the mean, then the winner is whoever's closest. They keep a tally of how many times each person wins so they can declare a winner at the end of the fifteen minutes.
What's really nice about this variation is that students will be calculating means with much more enthusiasm and motivation than if they were meaningless numbers on a worksheet. Also, by playing this game and trying out different strategies, students begin to appreciate the nature of the mean. There will always be a student who will write down a million, thinking it will skew the mean towards them. However, if the other three numbers are low they still won't win.
You can also play this game with the median instead of the mean. It doesn't quite work with mode! Actually, maybe one of my amazing readers could come up with a way of making a mode variation. Comment below!
Try one of these games out when you have ten minutes to spare. Let me know how it goes by commenting below.
Emma x x x
Tell students that you're going to ask them to write down a number. It must be a whole number (no decimals, fractions or surds) and it must be zero or greater. They have to write this secretly and not show anyone their number. Tell them you are going to count down from 5. At 2, everyone's pens need to be down. At 1, everyone needs to show their boards. The winner, and this is the important bit, is the person who has the smallest number that no one else has.
This should be simple enough to understand, and if a student doesn't quite get it, they can at least write down a number and participate until it clicks.
When students hold up their boards, first look for zeros. If there's just one, the zero wins. If there's more than one, tell all the zeros to put their boards down and then look for ones. Repeat until you have found a number that only one person has written. They are the winner. This doesn't take very long at all, even with 32 students like my year 7 class.
I have found that this game intrigues students immediately. They have to try to predict what everyone else is thinking. I have found that I can usually predict who in the class will write zero. Zero rarely wins, and I've never seen it win in the first round. I've found that the winning numbers vary massively from class to class. The results are also very different when I've played this with adults. I'm sure there's a lot that can be explored here in terms of psychology (and economics, actually) but I'll leave that for you to think about.
I like to try to encourage strategic thinking and annoying my students at the same time by saying things like "oh, so three won that time. That means you are probably thinking about choosing three this time. But if other people think that too, you won't win, so you'd better choose four instead. But now that I've said that, you can't choose four, it's too obvious, so..." The students usually interrupt me at this point and beg me to shut up because I'm ruining their strategy.
The beauty of this game is it can be done with year 7s, year 13s, and even the Maths faculty as a pre-meeting warm-up. I have never met a class (or group of adults even) that doesn't enjoy this game.
A more mathematical version of this game is to have the same rules but this time the winner is the student whose number is the closest to the mean of all of the numbers. This is too difficult to do as a whole class, so I do this in table groups. The four students each choose a number, they calculate the mean, then the winner is whoever's closest. They keep a tally of how many times each person wins so they can declare a winner at the end of the fifteen minutes.
What's really nice about this variation is that students will be calculating means with much more enthusiasm and motivation than if they were meaningless numbers on a worksheet. Also, by playing this game and trying out different strategies, students begin to appreciate the nature of the mean. There will always be a student who will write down a million, thinking it will skew the mean towards them. However, if the other three numbers are low they still won't win.
You can also play this game with the median instead of the mean. It doesn't quite work with mode! Actually, maybe one of my amazing readers could come up with a way of making a mode variation. Comment below!
Try one of these games out when you have ten minutes to spare. Let me know how it goes by commenting below.
Emma x x x
Thursday, 7 May 2015
The Mathematics of Voting
I'm going to do something completely out of character and write a TOPICAL post! Yes, I may live underneath a proverbial rock (what, there was an earthquake recently?) but even I am aware that there is a General Election today in the UK. In fact, I was the first person at my polling station to vote this morning!
I've
mentioned in a previous post that I love Lewis Carroll. He combines two of my
favourite things: books and maths (Lewis Carroll is the pen name of
mathematician Charles Dodgson. Please keep up!)
Dodgson
became involved in college elections in the early 1870s at Oxford university
where he was a professor. He became interested in the theory of voting, of the
accuracy and fairness of different voting systems.
First Past The Post
Dodgson
was not a fan of this voting system. He claimed "the extraordinary
injustice of this Method may be very easily demonstrated". He then gives
an example to show how stupid it is:
Suppose
there are 11 electors and 4 candidates a, b, c and d. Each elector ranks the
four candidates in order of preference. The 11 columns here show their choices:
a
|
a
|
a
|
b
|
b
|
b
|
b
|
c
|
c
|
c
|
d
|
c
|
c
|
c
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
d
|
d
|
d
|
c
|
c
|
c
|
c
|
d
|
d
|
d
|
c
|
b
|
b
|
b
|
d
|
d
|
d
|
d
|
b
|
b
|
b
|
b
|
It's easy
to see that a is considered best by three of the electors and second best by
the rest. But in actual fact, it is b who ends up winning, even though he/she
was considered the worst by seven voters.
I don't
think Dodgson looked at "Alternative Vote", although he did write
about lots of other systems.
The Method of Elimination
In this
method, each voter chooses their favourite, and then the one who gets the
fewest votes is eliminated, and the process is repeated (a bit like Big
Brother? The TV show, not the Orwellian thing). This method at first seems
pretty flawless. However, consider the following situation:
b
|
b
|
b
|
c
|
c
|
c
|
d
|
d
|
d
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
b
|
c
|
d
|
c
|
d
|
b
|
b
|
b
|
c
|
c
|
b
|
d
|
d
|
c
|
d
|
c
|
d
|
d
|
d
|
b
|
b
|
c
|
c
|
b
|
Notice
that a is everybody's first or second choice, and hence appears to be the best
candidate. However, he/she will be eliminated first. c will be elected instead.
The Method of Marks
In this
method, each voter is given a specified number of marks that they can divide
between the candidates. Then the candidate who gets the most marks wins.
Dodgson said that this method would be perfect as long as the voters divided
their marks fairly: giving most to their favourite but some to the candidates
that they wouldn't mind electing. But Dodgson commented that "since we are
not sufficiently unselfish and would assign all our votes to our favourite
candidate, the method is liable in practice to conicide with that of the simple
majority [first past the post] which has already been shown to be
unsound".
I hope you voted today! Let's get rid of the current education-ruining idiots!
Emma x x
x
All
quotes are from Robin Wilson's "Lewis Carroll in Numberland", a book
I highly recommend.
Tuesday, 28 April 2015
Are Our Students Thinking Too Much?
"It is a profoundly erroneous truism that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilisation advances by extending the number of operations we can perform without thinking about them."
-Alfred North Whitehead, An Introduction to Mathematics
How many times in your life as a maths teacher have you said to your students, "think about what you're doing!"?
And how many times in your life as a maths teacher have you thought to yourself, "how do you still need to use your fingers to know 4 times 5 is 20?"
I know that I have these two conflicting belief systems. I believe that knowing times table facts, number bonds, the values of sine, cosine and tangent for common angles, the quadratic formula, and probably loads more things are very very useful. I would go so far as to say important. Maybe even so far as to say, your exam success depends on it.
But at the same time, I believe that rather than relying on memory, we should have a solid understanding of maths and think about what we are doing and why at each stage of a process. This is why I am conflicted.
A good example is long division. Students in UK Primary schools are generally taught chunking as their primary method of long division. On the one hand, I'm in favour of this. Chunking is my preferred mental method, and I have even started doing it as my main written method. However, students (especially those who do not know their times tables very well) are slow with chunking. It also takes up a lot of space. In secondary schools, I think most teachers teach the traditional bus stop method of long division. Students find this difficult at first but after much practice they can use it efficiently and accurately. But when they are used to this method, they do it without thinking about it. Is this a good thing or a bad thing?
Does it make sense to "save your brain" for the more challenging bits and rely on your subconscious to do the easy bits? Or should we be mindful at all times?
Should we memorise the quadratic formula or derive it by completing the square every time we want to use it? Should we memorise that cos(30) is root three over two, or draw a 30/60/90 triangle every time? Does it free up space in our memory if we don't memorise these? Do we free up space in our working memory or unburdon our central executive if we do memorise them? Which is more beneficial?
I think that in the UK, we place much much less emphasis on arithmetic fluency compared to other countries. I'm frequently told by friends and colleagues who went to school in Asia or Europe that you simply did not move on to the next grade or year group until you had mastered addition, subtraction, multiplication and division. And mastered means you can do these things efficiently and accurately. Over here, we move on to algebra before students know their number bonds. We teach fractions and percentages before they know their times tables. We say, it's OK if you're no good at arithmetic, you might be really good at shape and space. Is it the lack of arithmetic fluency that is holding UK students back? When it comes to maths, are our students thinking too much?
[Is it just me, or is that last sentence totally Carrie Bradshaw-esque?]
The GCSE for maths now has a much larger emphasis on functional problem solving. Teachers say this will be a challenge because our students are bad at problem solving. I think they're wrong. I think our students are brilliant at problem solving. But they do badly on these questions because the arithmetic involved in these problems poses a much bigger problem to our students than, say, Korean students. If you know how to do arithmetic automatically, without thinking, you only have the problem to think about. If you also have to think long and hard about the arithmetic, it interrupts your thinking process and tackling the problem becomes much harder. It also means you won't as easily spot neat tricks or patterns that simplify the problem.
For example, there is a Foundation GCSE question with a rectangular patio 3m by 3.6m. Henry has 32 square paving slabs with side length 60cm. Does he have enough slabs to cover his patio? If you are good at arithmetic you may spot that 60cm goes into 3m and 3.6m nicely. If you don't know your six times table, you won't notice this. That means you may choose a longer, more complicated method, like finding the area of the patio and the area of the slab and doing a division. This was a non-calculator paper so now students will be having to calculate 3 x 3.6 and 0.6 x 0.6, then use long division. It is much, much simpler to see that you need 5 rows of 6 slabs, which makes 30.
So although I'm a big fan of exploring, discovering, reasoning, and understanding, I'm starting to think that a bit of rote learning of efficient, accurate methods, and drilling of times tables (and their related quotients) would actually improve students' ability to solve problems a lot more than simply getting students to practise problem solving.
What do you think?
Emma x x x
Wednesday, 22 April 2015
Show Me Your Knowledge - An Alternative to Tests
I had become fed up of marking my year 10s' fortnightly assessments. They are aiming for a grade C, and following the Higher syllabus, which means the assessments are quite challenging for them. Marking takes a lot longer when the student has got almost everything wrong.
One day I decided to do something different. I offered my class the choice. They could either do the assessment as normal, or they could Show Me Their Knowledge (Patent Pending). I explained what I meant by this. I wanted them to pour out the contents of their brains on that particular topic (it was averages) onto an A3 sheet of paper. I told them they needed to make up their own examples to demonstrate all of the skills. I gave them a list of skills so they wouldn't forget anything: mean, mode and median from a list, mmm from a frequency table, mmm from a grouped frequency table.
What was quite interesting was all of the boys chose to take the normal test, whereas all of the girls chose to Show Me Their Knowledge. And the girls loved it, they were begging me to do this every assessment. This gender difference is worth exploring in more detail, so I will save that for a separate post.
The pages that were created were impressive. Most girls did an example for each of the three sections, and heavily annotated the solution with explanations. For example, "You find the midpoint here because you don't know the actual number" then an arrow from this led to, "To get the midpoint add them together and half it or just work it out by looking at it".
Some girls put up their hands at various points and said they didn't know how to explain a certain bit. I told them that means they maybe didn't understand that bit. I told them to leave a bubble or box where they wanted to write the explanation, so that they could see there was a gap in their understanding. I told them I would help them fill that gap in the follow-up lesson.
When it came to marking, I read through the explanations and tweaked some of the wording if it wasn't quite right. I did this very neatly because girls don't like you defacing their work (male teachers please take note of this). If I thought some bits needed further explanations, I drew bubbles or boxes (copying their style) but left them blank, or started the sentence for them. For example, I might have written, "If there are two numbers in the middle..." or "The question will usually tell you to r____ your answer...".
When I gave these back, they filled in the bits they could by themselves, then I talked to them on each table to explain any bits they didn't understand. They also talked to each other to fill in the gaps. By the end, they all had a poster explaining the whole chapter. That is now a very useful resource for their revision. The best looking one I could have copied and had laminated for future classes to use.
I will continue to use this method of assessment, although I will still do some normal tests too, as at the end of the day, they will have to sit a traditional exam, and they need to be prepared for this. I can't help but think the fact that girls prefer this method suggests that maybe they are disadvantaged by our exam system and that girls could do much better if we changed this. But again, that's a post for another day.
Emma x x x
One day I decided to do something different. I offered my class the choice. They could either do the assessment as normal, or they could Show Me Their Knowledge (Patent Pending). I explained what I meant by this. I wanted them to pour out the contents of their brains on that particular topic (it was averages) onto an A3 sheet of paper. I told them they needed to make up their own examples to demonstrate all of the skills. I gave them a list of skills so they wouldn't forget anything: mean, mode and median from a list, mmm from a frequency table, mmm from a grouped frequency table.
What was quite interesting was all of the boys chose to take the normal test, whereas all of the girls chose to Show Me Their Knowledge. And the girls loved it, they were begging me to do this every assessment. This gender difference is worth exploring in more detail, so I will save that for a separate post.
The pages that were created were impressive. Most girls did an example for each of the three sections, and heavily annotated the solution with explanations. For example, "You find the midpoint here because you don't know the actual number" then an arrow from this led to, "To get the midpoint add them together and half it or just work it out by looking at it".
Some girls put up their hands at various points and said they didn't know how to explain a certain bit. I told them that means they maybe didn't understand that bit. I told them to leave a bubble or box where they wanted to write the explanation, so that they could see there was a gap in their understanding. I told them I would help them fill that gap in the follow-up lesson.
When it came to marking, I read through the explanations and tweaked some of the wording if it wasn't quite right. I did this very neatly because girls don't like you defacing their work (male teachers please take note of this). If I thought some bits needed further explanations, I drew bubbles or boxes (copying their style) but left them blank, or started the sentence for them. For example, I might have written, "If there are two numbers in the middle..." or "The question will usually tell you to r____ your answer...".
When I gave these back, they filled in the bits they could by themselves, then I talked to them on each table to explain any bits they didn't understand. They also talked to each other to fill in the gaps. By the end, they all had a poster explaining the whole chapter. That is now a very useful resource for their revision. The best looking one I could have copied and had laminated for future classes to use.
I will continue to use this method of assessment, although I will still do some normal tests too, as at the end of the day, they will have to sit a traditional exam, and they need to be prepared for this. I can't help but think the fact that girls prefer this method suggests that maybe they are disadvantaged by our exam system and that girls could do much better if we changed this. But again, that's a post for another day.
Emma x x x
Sunday, 19 April 2015
Run a Reverse Pilot
It's the start of a brand-new term, and lots of us teachers will be returning to work with more energy and a renewed sense of purpose. It is when we are in this frame of mind that we are eager to read about new teaching techniques and "tweaks" and we are thinking about adding a few new things to our lessons.
Well, here's a new idea for you. Instead of starting to do something new this half term, do the opposite. Stop doing something old.
You will have all heard of the idea of a "pilot", where you trial something on a small scale to see if it will add value and if it does, you run with it.
Daniel Shapero, a director at LinkedIn, coined the term "reverse pilot" to refer to the exact opposite: removing an activity or initiative to see whether there will be any negative impact.
Is there anything you are currently doing that is taking up a lot of your time but you suspect is not actually adding any value? For example, maybe you have developed an elaborate points system with prizes and a "star of the week" award. This might have been effective at the start of the year, but maybe it is no longer doing anything. Try getting rid of it for a trial period, and see if it has a negative impact. If it doesn't, you have just saved yourself the time it used to take you.
Does your faculty have a weekly lunchtime meeting (sorry, not "meeting", calling it that would make the unions unhappy, so let's call it a "gathering") that takes up 15 people-hours and accomplishes very little? Try scrapping it, and see if anything bad happens.
Do you make sure to write "next steps" or similar after marking your students' books? Stop writing these, save yourself 3 minutes per book (an hour and a half per class per fortnight) and see if your students' progress starts to decelerate.
Are you currently running a weekly after-school revision class for your exam class? Have you done this every year since you can remember? Don't do it this year. See if the results are worse than normal. If they're not, then you've just saved yourself an hour a week for the rest of your life. You are welcome.
Of course, it could be that everything you do at the moment does make a positive impact on learning. But we shouldn't just assume that they do. To do so would be wasting precious resources. I flippantly said in the above paragraph that you could stop doing that revision class to save yourself time. Well think about redirecting that time towards something else - better quality feedback, or one-to-one tuition. These might have a bigger overall impact. That lunchtime meeting (sorry, gathering) could be spent producing the world's best corridor display. Or it could be spent, I don't know, eating?!
There are several cognitive explanations for why we are probably wasting a lot of time on activities that might be adding little or no value. These are loss-aversion, the sunk-cost fallacy, and the status-quo bias.
It has been shown that human beings are naturally loss-averse. We think that losing something will have a bigger negative impact on us than gaining something of the same value will have a positive impact. So it seems to you that stopping sending out your weekly teaching and learning newsletter (which takes three hours to write) would have a big negative effect, but gaining three hours of extra time per week would have a smaller positive effect, not enough to balance it out. When you write it down like this, it might seem that the choice is obvious, but most of us don't write it out like this, and hence we don't question whether carrying on doing the things we're doing is the best use of resources.
You spent hours setting up your praise and reward spreadsheet, with built-in mail merge facility and automatic colour coding. So spending an hour a week filling it in for all of your classes is definitely worth it, right? After all, you spent so long on building it, it would be a waste not to use it, right? This is the sunk-cost fallacy in action. The time you spent making the spreadsheet is just that, spent. You cannot unspend it. Therefore whether you use it or not makes absolutely no difference. Do you still have a dress in your wardrobe you've never worn, but you can't get rid of because it cost a bomb? Whether you keep it or not, you have already wasted the money. Let it go. Spent forty minutes waiting for a bus so there's no way you're paying for a taxi now? That forty minutes has been lost either way, do what you want. The only time the sunk-cost fallacy is your friend is with your gym membership. "I've paid all that money, I really have to use it!" this is a fallacy, but a healthy one. Don't fight it.
The "status quo bias" is where we have a tendency to keep doing something simply because we have always done it. Why do we write the learning objective on the board at the start of the lesson? Because we've always done it (and in my case, because my own teachers did it). Why do we begin each lesson with a starter activity? You can probably think of lots of examples.
I challenge you this half term to stop doing one thing. I suggest at first you don't replace it with anything else, just stop doing it. Feel the relief of having one fewer thing to do. If you observe no impact, then keep not doing it. If you observe a negative impact, instead of going straight back to doing the same as before, tackle the problem from scratch. You might find there is a better solution.
To read more about the cognitive biases I have mentioned in this post, I recommend The Art of Thinking Clearly by Rolf Dobelli.
To read more about the idea of doing less to achieve better results, I recommend Essentialism: the Disciplined Pursuit of Less by Greg Mckeown.
Emma
x x x
And by the way the weekly lunchtime meeting referred to in this post is a work of fiction and bears no resemblance to any real weekly lunchtime meeting, living or dead. Any resemblance to the weekly lunchtime meeting my own faculty has on a Thursday is purely coincidental.
Well, here's a new idea for you. Instead of starting to do something new this half term, do the opposite. Stop doing something old.
You will have all heard of the idea of a "pilot", where you trial something on a small scale to see if it will add value and if it does, you run with it.
Daniel Shapero, a director at LinkedIn, coined the term "reverse pilot" to refer to the exact opposite: removing an activity or initiative to see whether there will be any negative impact.
Is there anything you are currently doing that is taking up a lot of your time but you suspect is not actually adding any value? For example, maybe you have developed an elaborate points system with prizes and a "star of the week" award. This might have been effective at the start of the year, but maybe it is no longer doing anything. Try getting rid of it for a trial period, and see if it has a negative impact. If it doesn't, you have just saved yourself the time it used to take you.
Does your faculty have a weekly lunchtime meeting (sorry, not "meeting", calling it that would make the unions unhappy, so let's call it a "gathering") that takes up 15 people-hours and accomplishes very little? Try scrapping it, and see if anything bad happens.
Do you make sure to write "next steps" or similar after marking your students' books? Stop writing these, save yourself 3 minutes per book (an hour and a half per class per fortnight) and see if your students' progress starts to decelerate.
Are you currently running a weekly after-school revision class for your exam class? Have you done this every year since you can remember? Don't do it this year. See if the results are worse than normal. If they're not, then you've just saved yourself an hour a week for the rest of your life. You are welcome.
Of course, it could be that everything you do at the moment does make a positive impact on learning. But we shouldn't just assume that they do. To do so would be wasting precious resources. I flippantly said in the above paragraph that you could stop doing that revision class to save yourself time. Well think about redirecting that time towards something else - better quality feedback, or one-to-one tuition. These might have a bigger overall impact. That lunchtime meeting (sorry, gathering) could be spent producing the world's best corridor display. Or it could be spent, I don't know, eating?!
There are several cognitive explanations for why we are probably wasting a lot of time on activities that might be adding little or no value. These are loss-aversion, the sunk-cost fallacy, and the status-quo bias.
It has been shown that human beings are naturally loss-averse. We think that losing something will have a bigger negative impact on us than gaining something of the same value will have a positive impact. So it seems to you that stopping sending out your weekly teaching and learning newsletter (which takes three hours to write) would have a big negative effect, but gaining three hours of extra time per week would have a smaller positive effect, not enough to balance it out. When you write it down like this, it might seem that the choice is obvious, but most of us don't write it out like this, and hence we don't question whether carrying on doing the things we're doing is the best use of resources.
You spent hours setting up your praise and reward spreadsheet, with built-in mail merge facility and automatic colour coding. So spending an hour a week filling it in for all of your classes is definitely worth it, right? After all, you spent so long on building it, it would be a waste not to use it, right? This is the sunk-cost fallacy in action. The time you spent making the spreadsheet is just that, spent. You cannot unspend it. Therefore whether you use it or not makes absolutely no difference. Do you still have a dress in your wardrobe you've never worn, but you can't get rid of because it cost a bomb? Whether you keep it or not, you have already wasted the money. Let it go. Spent forty minutes waiting for a bus so there's no way you're paying for a taxi now? That forty minutes has been lost either way, do what you want. The only time the sunk-cost fallacy is your friend is with your gym membership. "I've paid all that money, I really have to use it!" this is a fallacy, but a healthy one. Don't fight it.
The "status quo bias" is where we have a tendency to keep doing something simply because we have always done it. Why do we write the learning objective on the board at the start of the lesson? Because we've always done it (and in my case, because my own teachers did it). Why do we begin each lesson with a starter activity? You can probably think of lots of examples.
I challenge you this half term to stop doing one thing. I suggest at first you don't replace it with anything else, just stop doing it. Feel the relief of having one fewer thing to do. If you observe no impact, then keep not doing it. If you observe a negative impact, instead of going straight back to doing the same as before, tackle the problem from scratch. You might find there is a better solution.
To read more about the cognitive biases I have mentioned in this post, I recommend The Art of Thinking Clearly by Rolf Dobelli.
To read more about the idea of doing less to achieve better results, I recommend Essentialism: the Disciplined Pursuit of Less by Greg Mckeown.
Emma
x x x
And by the way the weekly lunchtime meeting referred to in this post is a work of fiction and bears no resemblance to any real weekly lunchtime meeting, living or dead. Any resemblance to the weekly lunchtime meeting my own faculty has on a Thursday is purely coincidental.
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