Thursday 28 January 2016

The Elitist Nature of Mathematics

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

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.

 "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