“No food without blood and sweat.”
“Farmers are busy; farmers are busy; if farmers weren’t busy, where would grain to get through the winter come from?”
“In winter, the lazy man freezes to death.”
“Don’t depend on heaven for food, but on your own two hands carrying the load.”
“Useless to ask about the crops, it all depends on hard work and fertilizer.”
“If a man works hard, the land will not be lazy.”
“No one who can rise before dawn three hundred sixty days a year fails to make his family rich.”
– Chinese proverbs quoted by rice paddy farmers, from Gladwell’s Outliers
This is part of a series offering my views on some problems with UK maths education. The first part looked at the state of affairs with regards to GCSE and PISA results, the second part looked at my attempt at a diagnosis, the third part looked at pre-existing maths education success stories, and the fourth part looked at how textbooks offer the largest potential to improve pedagogy across the nation. This post will look at the role of hard work.
Malcolm Gladwell’s Outliers is a great read. Chapter 8, on ‘Rice Paddies and Math Tests’ should be compulsory reading for maths teachers: Gladwell sets out to answer that perennial question: why are East Asians so good at maths? Even when they have grown up abroad? The following chart, from a UK Education Committee report is absolutely staggering (though it looks at educational attainment more generally, rather than just maths):
Take a look at the topmost teal line: that represents the average grade of Chinese students in the UK according to their wealth levels. As you’d expect, it has a similar trend to every other line – Chinese students who come from richer backgrounds tend to do better than those from poorer backgrounds. But now compare the lines: The most deprived 10% of Chinese students in the UK outperform the richest 10% of every single other ethnic group, save for Indians. That is staggering.
Gladwell quickly and rightly disputes the claim that Asians have higher IQs – instead, he even cites James Flynn’s research claiming that ‘Asians’ IQ… have historically been slightly lower than whites’ IQs, meaning that their dominance in math has been in spite of their IQ, not because of it‘. Yet the fact that East Asians transplant their educational success even outside of their native countries means that the answer isn’t totally located in specific education systems, either: since it isn’t genetic, it must be something cultural.
So what else can explain this dominance?
Amy Chua, in a quote from The Triple Package, both backs up Flynn’s viewand offers the key reason behind this success: ‘If Asian students were truly genetically superior to other students, they would not be spending twice as much time on homework each week as their peers in order to outperform them’. Gladwell’s chapter 8 concurs: the Chinese farming proverbs above show how an ethic of hard work has permeated East Asia/rice farming countries for millennia. (This is due to rice-farming’s particularly labour-intensive and labour-rewarding nature: the harder you work on your rice farm, the more and better your rice crop. In fascinating contrast, the sorts of crops grown in the West, such as wheat, are much more dependent on factors like weather – those outside of human control. Once they’ve been planted, such crops’ quality and quantity have very little to do with how much labour is expended on the farm. Note the Russian proverb: ‘If God does not bring it, the earth will not give it’.)
So, the answer’s obvious, but at the same time uncomfortable: hard work.
Hard work internationally
Alongside my arguments in favour of better textbooks in the previous post, one of the biggest factors for Shanghai and Singapore’s dominance, highlighted in part 3, is the fact that there is much more time given to maths both inside and outside of school hours:
This is true: in Singapore and Shanghai, daily maths lessons are the norm, compared to around 3 hours per week in the UK). Furthermore, both countries have a massive role for ‘shadow education systems‘ – what we call private tutoring, cram schools, extra classes. On top of even that, cultural work ethic (as exemplified in the Chinese proverbs above) means that even outside of tutor/teacher supervision, students keep on working by themselves. As Chua explains:
There’s a Chinese term, chi ku (吃苦), that a billion Chinese people know, that every Chinese immigrant knows, and that probably all their children are deeply familiar with too… chi ku means “eating bitterness” and refers to the capacity to endure hardship, which, along with perseverance and diligence, is a cardinal Confucian “learning virtue”. For a thousand years, these virtues… have been fundamental elements of child rearing and education in China and Confucian-influenced societies.
But it’s not just an East Asian story. In Jamie Escalante’s celebrated classroom, with a majority of Hispanic students, he emphasised the exact same message, making it absolutely clear that there were no shortcuts to success that bypassed hard work:
Students who enter the Escalante Math Program must sign a contract which binds them to participation in the summer programs held at ELAC, strict completion of daily homework, and attendance at Saturday morning and after-school study sessions. The students’ parents are also required to sign the contract…
The key to my success with minority youngsters is a very simple time-honored tradition: hard work, and lots of it, for teacher and student alike. To avoid merely stating a cliché and having its relation to my success overlooked, I will provide some examples.
One can find many of my students still working in my classroom (a converted music hall) at 4:00, 5:00, or even 6:00 p.m. each weekday and as early as 7:00 a.m. in the morning. No student with a question or a confusion is allowed to go home with it unresolved. [keep reading it here, in the section entitled ‘Hard Work’].
The benefits of hard work
It’s worth asking why hard work is so helpful, just to be clear. A recent review on how we learn best revealed the two indisputable ‘Gold Star’ study techniques: self-testing, and distributed practice. Self-testing is simply trying to do a question (or remember a fact), noting your answer, and then checking whether you got it right. Distributed practice is going over material (e.g. self-testing how to add fractions) over a mid/long period of time (e.g. every 1-4 weeks), instead of blocking practice all at once.
Note that these two study techniques are pretty much what it means to work hard at maths. In my experience, from year 7 students are aware / quickly made aware that doing better at maths (whether independently, or through tuition) is straightforward: constantly go over old material by testing yourself with lots of questions – in other words, distribute self-testing over time. Through such hard work, old material is committed to long-term memory, key skills are mastered over time, leading to immediate success and also providing a solid foundation for harder topics. This leads to further success in maths – and then hopefully one is upon a virtuous circle of motivated success. (Caveat: none of this doesn’t apply if students are taught poorly in the first place, whereupon they’ll practise unsuccessfully – and again, that’s why I think textbooks are necessary.) Indeed, this is part of the focus of Gladwell’s Outliers: hard work through successful practise (if you have access to it) is the bedrock, not just for successful maths performance, but for most arenas of professional achievement.
Work ethic among UK students
Given the importance of hard work, how does the situation in the UK compare? Hard work – or rather, the lack of it – is undoubtedly a problem with low-attaining students. In my diagnosis, I flagged up perennial issues with homework among bottom sets & struggling students, not to mention their lack of motivation to work hard even in lessons. A perennial complaint in staffrooms each year is in how teachers feel like they’re working harder than some of their own targeted students, even (especially?) in intervention sessions that go above and beyond. It’s thus absolutely no surprise that such students don’t attain as highly as they could. Furthermore, external tuition is becoming increasingly common – but mainly among aspirational students/families whose attainment is fine; it doesn’t seem particularly prevalent among lower-attaining students. But why are they like this?
It seems to me that a big reason in their lack of motivation lies in repeated failure in maths assessments. Part of this failure is pedagogical – when I try to teach something but they just don’t understand it – hence the need for better textbooks. But it seems to me that the main failure is related to memory: students got it in the lesson, but 4 weeks later they got the same question wrong on an assessment. I remember many all-too-similar, all-too-depressing conversations I’ve had with students in bottom sets. We were going through a test; there’ll be a simple question, on fraction operations, or on simplifying basic algebra, and there’d be a howler like adding denominators or 2a + 3a = 5a², on the kind of question that we all knew they could do in class. ‘Didn’t you read the test topic list/do all of the revision homework? Adding fractions was on it!’ And of course, they hadn’t read the topic list or properly attempted the homework. Of course they had forgotten.
We’re thankful if every student has attempted the homework (with zero copying); it was practically unheard of for a student to come to me, before the homework was due, asking about how to do a particular question. I’m sure I’m not alone in this. On the flipside, too, on the part of teachers, UK students are lucky if they receive a weekly hour long maths homework, every week of the year (which seems to be a common amount). A quick glance at most homework available TES show they can mostly be done in around 15 minutes, up to 30 minutes at most.
In contrast, I asked a number of Singaporeans their recollections of maths lessons at school; contrast their attitudes with those mentioned attitudes above:
‘For primary school, there was a lot of focus on practice… Secondary school… focus was always on practice makes perfect.’
‘I can’t recall much of my primary/secondary education in terms of pedagogy now – my clearest memory of doing well in math in primary and secondary education was tons and tons of practice!’
‘Going over the material daily is expected regardless of whether it was done with a tutor or independently.’
‘Math lessons depended greatly on us doing homework… Homework was issued after almost every class’
‘Tonnes of homework. Boring drills. But once you finished, you would get this set of juicy interesting questions to try out as a prize.’
‘homework was thrice a week. The homework was manageable.’
Of all the students who have gone through maths education in the UK, how many do you think would say anything like this, if asked for their memories of maths lessons? Similarly, how many students in the UK are like Escalante’s students: willing to come into school at 7am and stay til 5pm/6pm/7pm, to work on their weaknesses?
There are several possibilities in which students work harder: we could increase maths lesson time; we could increase demand and supply of the shadow education system; or we could increase independent studying and homework.
Instantly it’s obvious that homework is the most practical way forward we can help students work harder. contact time is nearly impossible to increase significantly; we have no control over getting parents to pay for extra tuition; and while Escalante’s example is indeed inspiring, it’s impractical and non-scaleable to expect teachers and schools to go above and beyond their normal (large) workloads at school. If hard work is effective (which it is), increasing homework seems the best way forward.
On this subject, I find it interesting how little most UK schools require their students to work, particularly with regard to homework. Part of this scepticism towards homework seems to be directed at its perceived educational value – for example, see the extensive studies & newspaper articles & books on whether it’s any use whatsoever. Part of the scepticism comes from the administrative burden upon teachers: homework can so easily be a ‘hornet‘: it takes considerable time and effort to produce, set, keep track of, remind, check, collect, mark, record, chase up, sanction, glue into books, chase up… and all of that is multiplied per class, per week. As a result, weekly homework seems to be the norm that teachers can just about keep up with, and it’s worth acknowledging that Shanghai & Singapore teachers more time to plan and mark homework due to lighter teaching loads. (It’s also worth pointing out that their standardized textbooks make homework setting much easier, too.)
Yet when all that is said and done, I have never heard anecdotes about low attaining students who are ‘working too hard’ and ‘worrying too much about their exams’ or ‘spending all their evenings staying up late doing homework’. Those complaints usually concern students at high performing schools, or able students who we know will be fine (e.g. the extremely selective and high-attaining Tiffin Boys’ School is quoted here as planning to reduce its homework). Indeed, the opposite is true for low attainers: every frustration I’ve had or heard about them is directed to their poor work ethic, their low quality homework, their neglect of independent study. These frustrations are magnified when we know that such students’ poor attainment, if reflected in their real exams, means nothing else but significant barriers to their future life chances – and yet they don’t try very hard to do anything about it themselves.
Now as I write this, I have to admit to a certain bewilderment at these counterarguments I’m having to make. It’s staggering to me (especially as a Chinese) that there even exists this debate over homework – to return to Gladwell and Chua’s research, alongside the EEF reviews of the research, alongside Jaime Escalante’s own practise quoted above – these success stories all involve hard graft in independent study. We know hard work is necessary.
Granted, homework is often a big workload burden upon teachers, even when all students hand it on time. When that isn’t the case, when teachers have to follow up, chase up, track, sanction, cajole, and all that – it’s easy to give up, or view it as low priority. What’s more, it’s particularly students who are failing and/or from difficult backgrounds – i.e. those who need it most – who will put up the most problems in doing and handing in homework. This is a perfect storm: if homework isn’t benefiting those who would benefit from it, then it’s very easy to think: what’s the point? Indeed, Dan Meyer gave up setting homework (for a temporary period) for this very reason:
The kids who need [homework] most (D and F students), won’t, or else they’ll do it halfassedly, gaining as much credit with the least effort possible. This goes double for high-poverty students, where I performed a Master’s thesis study that concluded as much.
In such a context, it seems laughable to suggest Singapore-style daily homework.
To this fatalism, Escalante’s point of view is a good rebuke:
When students of any race, ethnicity or economic status are expected to work hard, they will usually rise to the occasion, devote themselves to the task and do the work. If we expect kids to be losers they will be losers; if we expect them to be winners they will be winners. They rise, or fall, to the level of the expectations of those around them, especially their parents and their teachers.
Hard work works; so, it’s unjust not to demand it, encourage it and support it from those who need it the most.
Summary so far:
- Hard work is a huge factor in determining maths attainment.
- Homework is the most practical way for maths departments to increase the amount of hard work that students put in.
- Homework is nonetheless particularly difficult to implement for the low-attaining, struggling students who need it the most.
When comparing UK education with other systems in this regard, crafting a better way to implement maths homework, then, seems to me to be an area with huge potential to improve attainment. How can we solve this trilemma?
Towards a better homework policy
Any viable and successful homework policy should to take these things in account:
- Make homework effective, in line with the research.
- Minimize as far as possible the administrative burden of homework, comprising everything from creating/setting/distributing/helping/checking/marking/feeding back – so that homework can be done as frequently as necessary
- Minimize the chances of students simply copying work
- Minimize the administrative burden of following up on students who do not complete it
If you did have such a system, nothing would stop you from setting daily homework, a la Singapore and Shanghai. Does such a solution exist? Well, it seems to me that we’re living in something of a golden age, with a recent explosion of online homework options in the last few years.
I think online maths homework is a really good thing. The massive benefits they all have in common:
- homework creation/distribution/checking/marking/tracking is all done in nearly-negligible time, and in perfect detail
- homework accountability is higher – it’s much harder simply to copy.
- students get instant feedback as to how they have done, and can retake homeworks themselves before waiting for the usual marking cycle
- many homework solutions come with online tutorials, often of a seriously high quality – so if students struggle (which they’ll know instantly), they have instant access to feedback as to how to get it right
- motivated students are able to learn independently as much as they wish.
In themselves, I think online homework instantly sorts out requirements 2 and 3 above. To streamline it further, heads of Key Stages could be responsible for assigning homework tasks to each year group/set (assuming they are following the same scheme of work across the year/set).
How about my fondness for daily homework? Many will balk at this idea e.g. Meyer: ‘if my kids evaluate and graph forty points over a class period, as they did yesterday, why would I send them home with any more?’ Meyer’s got a point. But this is exactly where requirement 1 is important: homework needs to be in line with the research. Here, the research on distributed practice is very helpful: it states that timing and frequency are of paramount frequency. Meyer’s example makes sense: his students don’t need to go home to do any more graph plotting that same night. However, fast forward two weeks or so, and suddenly all those students will benefit hugely from refreshing their graph plotting skills – especially in the UK, where spiral curricula reign supreme, where those same students are likely to have moved onto probability or Pythagoras or percentages. I’m sure every maths teacher can see that such daily, spaced, practise homework would be undeniably effective – much more effective than 45 minutes of homework on a particular topic, and much more effective than expecting/leaving it to students to ‘revise’ nebulously.
Such homework needs not be long, either: if students practised solving 100s of equations in class time, the skill would be well refreshed in 2 weeks by solving another 5-10 a day, in about 15 minutes (I know that Hegarty Maths tasks are usually limited to around 10 question, fitting this quota). Such daily practise would undeniably improve the attainment of low-attaining students. Remember the sorts of questions needed to secure a grade C – they require very little beyond question recognition and method recall. Yet so many leave secondary school unable to do even that.
Finally, there remains the all important question of those difficult students who don’t do their homework. Firstly, it’s worth noting again that online homework is harder to copy, and much easier to check and track. Secondly, I think unmotivated students are no match for a well-planned, well-coordinated policy, that might involve something like:
- a rota of teachers checking online homework completion each morning and compiling the names of those who haven’t done it, to be read in form time
- a clear expectation for these students to make their way at lunchtime/after school to a specified IT room to log on and complete their homework (where there’ll be a register and supervision and potentially a rota of teachers to help those who struggle).
- a rota of other teachers/SLT to roam the school to pick up those who haven’t shown/regularly don’t show
None of this is original, but based on various school policies that seem to work – but I’m aware that many schools don’t have such policies. Given that daily homework should only take 15-20 minutes to complete, too, the lunchtime burden shouldn’t be too great on supervising teachers either. After a while, I’m sure students would quickly learn to do their homework at home, or there would emerge a core of students who prefer to get through their daily homework in school time/after school. Furthermore, the regularity of daily homework would also make it easier for students to remember, since there is no ambiguity as to when it’s due.
Putting it all together: such a policy would increase (or maybe redistribute) the amount of hard work students put in, it would decrease workload for teachers, and all towards research-backed best practice. Unlike my previous suggestion of textbooks, it’s eminently possible for September, too: such a policy can be implemented by a head of maths and a well-coordinated department. Arguably, such a daily online homework strategy would not only be more beneficial, but also easier administratively for teachers – it could be the rare Pareto-improving/‘butterfly’ policy that lighten teachers’ workload while massively improving outcomes. Just compare it to the usual policy of ‘each teacher must produce/find, set, collect, mark, track, check, feedback their own homeworks for their own class every week, and follow up those who don’t do it’. I can’t see what’s not to like – but then again, most schools don’t seem to have such an expectation upon their students. Is this the best we can do, in terms of expecting our students to work hard? Clearly not; but better possibilities are there and waiting.
In some ways, this post can be viewed as an overlong read on doing homework better – something that most maths teachers would be interested in. However, I wanted to set it into the context of this series, as I think the potential of homework is far greater than we usually realise in our day-to-day teaching. A post on better homework policies can come across as ‘take it or leave it’, slash ‘thanks but we’re happy with those weekly homework booklets that I collated 3 years ago’ – but I just don’t think such strategies are enough to address the problems that low-attaining students face in the UK. The amount and way in which we set homework reflects the priority we give to hard work, and ultimately, the priority we give to creating independent hard workers. Judging from our perennial existential debates on homework itself, it seems that in the UK we just don’t prioritise hard work enough.