2.7. Why struggle and failure aren’t always good – Part 1

What I used to think

For many years, I have been a firm believer in the key role of mistakes in the learning process. In a video on her YouCubed.orgwebsite, Jo Boaler explains how ‘a research study found that when people make mistakes their brains grew more than when they got work right’, going on to explain that this finding is down to the dual-firing of synapses.

It was this sort of thinking – which was reinforced on pretty much every training course I went on in the 2000s – that led me to conclude that mistakes were the key to learning, and thus struggle and failure must be good.

Indeed, this thinking also prompted a school I once worked at to run a twilight session entitled ‘How to be a Bastard Teacher’. The idea was simple – we were to set students difficult challenges, and leave them to struggle, safe in the knowledge that their brains were growing so we were doing them good.

Hence, I would set my students ‘extreme challenges’ throughout my lessons. Here is an example I gave to my middle-set Year 10s, just in case you would like to play along at home:

Extreme Sequences Challenge

Here is a sequence:

2, 2√7, 14, 14√7

What is the value of the 21st term divided by the 17th term?

15 minutes.

Good luck!

I would then take a seat, be a bastard, and enjoy the struggle that followed. The strange thing was, many of my students didn’t seem to really enjoy this approach, and quite a few simply gave up on the problems I presented them with.

Sources of inspiration

My takeaway

I no longer believe that mistakes, struggle and failure are the key to learning, and indeed I think they can have quite the opposite effect. Let me try to explain what I mean.

A key element of motivation identified in Section 2.1 was some feeling of success, or belief that success was in reach. This seems logical – we tend to enjoy doing things we are either good at or believe we can become good at.

So, how would students’ expectations of their likely success be affected by the presentation of complex problems combined with my bastard teacher approach? Telling them that the problem is a difficult one, offering no hints, and making it very clear that I was not going to give them support is hardly the kind of recipe that is likely to raise their expectations.

In their comprehensive review of research related to motivation in mathematics, Middleton and Spanias (1999) reach a similar conclusion. They argue that ‘students’ perceptions of success in mathematics are highly influential in forming their motivational attitudes’. They explain that the effort a person is willing to expend on a task is determined by the expectation that participation in the task will result in a successful outcome, and in order to allow students to feel successful in mathematics without undermining either the value of success or a healthy attitude toward failure, teachers must structure tasks such that they present an appropriate level of challenge and difficulty for students. Cockcroft (1982) adds support to this view: ‘whatever their level of attainment, pupils should not be allowed to experience repeated failure. If this shows signs of occurring, it is an indication that the advance has continued too far and that a change of topic is needed’. Thus, mathematics activities must be difficult enough that students are not bored, yet must also allow for an experience of success given appropriate effort by the student.

So, my choice and presentation of task was clearly a poor one for many of my students. It was no surprise that so many of them lost motivation, gave up, and hence learned very little.

But I believe there is a bigger issue at play here. I think there is a widespread belief across education that we can somehow magically instil in our students that gritty determination to cope with anything that may come their way, and hence thrive in times of struggle and failure. I don’t think it is that simple.

Let’s take Dweck’s (2014) concept of a growth mindset – something that much of Boaler’s work is based on. Students with a growth mindset don’t give up. They take on challenges, work hard, and do not fear struggle, failure or mistakes because they view them as learning opportunities. Many schools across the UK have gone growth-mindset mad over the last few years, with posters adorning the walls and motivational assemblies ringing in students’ ears. Surely if we can instil a growth mindset into our students, then my concerns with the dangers of struggle and failure disappear into insignificance, because students with a growth mindset embrace such difficulties?

There are two problems with this.

First, several studies have been unable to replicate Dweck’s original findings. For example, Li and Bates (2017) cite three different attempts to replicate Dweck’s methods, all of which failed to produce results suggesting a significant effect of a growth mindset. Likewise, a study by Bahník and Vranka (2017) measured the mindset of university applicants taking a scholastic aptitude test. They found growth mindset was not positively associated with results of the test, did not predict change of the results for those who retook the test, did not predict participation in a future administration of the test, and did not predict the total number of tests taken.

But failure to replicate findings is common in research, and does not, on its own, falsify a theory. Indeed, Dweck herself responded (see Chivers, 2017) to the findings of the first study by saying: ‘Not anyone can do a replication. We put so much thought into creating an environment; we spend hours and days on each question, on creating a context in which the phenomenon could plausibly emerge’. But if researchers cannot replicate the ideal conditions to foster growth mindsets, what hope is there that schools and teachers can do so? A few posters and assemblies at the start of the year are hardly likely to do the trick. Indeed, in a 2017 interview with John Hattie, Dweck herself concedes that much of her work on mindsets has been misinterpreted and misapplied in schools. And in an interview with TES later that year, Dweck explained: ‘some educators have seen [growth mindset] as reducing to effort. They are just telling kids to try hard. Far from a growth mindset, that’s called nagging … If you just go in there and explain growth mindset you can’t expect to create it … there are many complexities and subtleties that need to be transmitted’. So the problem may not be the concept of a growth mindset itself, but the difficulty of instilling it in our students, especially in the short-term. It is a long-term belief from teachers that every child can improve that is reinforced to students every day. It is not enough to put posters up or have a few motivational assemblies, nor is it a case of simply saying try harder. In the same TES interview, Dweck explained that a growth mindset is ‘developed over time through learning, mentoring, hard work, good strategies’. And I fear many schools have failed to realise this.

But there is a bigger problem. I feel that a key component of a growth mindset that is often overlooked is the importance of success. Past success is where the belief that students will succeed again comes from. As one of my Year 9s, having sat through an assembly on mindsets, so eloquently put it: ‘it’s kind of hard to have a growth mindset when I keep doing shit on tests, sir’.

All of this is not to say that students should never be allowed to struggle, fail, or make mistakes. Far from it. Struggling, failing, making mistakes and learning from the experience is clearly a key part of mathematical development. If students down tools at the first sign of difficulty, how will they ever learn? No one is born with fully formed schemas, everyone holds misconceptions, and even the most carefully planned-out explanations are prone to misinterpretation. Furthermore, without the kind of classroom atmosphere where students are not afraid to try things, make mistakes, and admit to those mistakes, we as teachers are blind to their weaknesses and powerless to help them. When mistakes do occur they should be embraced and treated as the learning opportunities that they truly are. Lemov (2015) calls this a Culture of Error, emphasising the need to ‘create an environment where your students feel safe making and discussing mistakes, so you can spend less time hunting for errors and more time fixing them’. This is 100% true, and I will dig deeper into how to identify and resolve errors in Chapter 11.

But my fear is that in the past I have gone too far. I have prioritised struggle over success. Students cannot struggle and fail all the time. Without the belief that they may succeed that only comes with the experience of past success, it will take a special kind of student to keep going, and going, and going.

What I do now

For Coe (2013), learning happens when students think hard. But I now realise that students may only be willing to think hard if they believe that effort will pay off. Too much experience of past struggle and failure will only dampen that belief.

The work of Boaler (eg Boaler, 2015) and Dweck (eg Dweck, 2014) certainly does not say students should struggle and fail all the time. But I believe this is how it has been interpreted in many schools. By emphasising the importance of mistakes in the mistaken belief that we can magically produce gritty, determined students with growth mindsets, we are in danger of overlooking the importance of success. Success is the foundation upon which grit and a growth mindset must be built.

Indeed, I don’t think mistakes are the key to learning – if repeated mistakes, struggle and failure lead to students putting in less effort, and eventually giving up, how can they be? I think identifying, understanding and resolving mistakes is one of the most important things we as teachers can do, but I believe success is the key to learning. It is success that motivates students to try harder, and helps them cope and thrive when things get tough.

So, how can I help my students avoid too much struggle and failure, whilst still ensuring they are thinking hard?

I can start by improving the tasks I give my students. The sequences challenge in the form I presented it above may be suitable for some students – those with strong domain-specific knowledge and experience of past success who will revel in the challenge – but for many other students it caused them to down tools. Hence, it can be restructured as:

Sequences Challenge

Here is a sequence:

2, 2√7, 14, 14√7

a) What do you multiply by to get from one term to the next?

b) What is the next term?

c) What is the nth term rule?

d) What is the 17th term?

e) What is the value of the 21st term divided by the 17th term? Try on your own, and ask your partner if you are stuck.

This is better, but still not great. The choice of activities we give our students is crucial. Ideally we should give them a taste of immediate success (within 20 seconds as a general rule), but with enough challenge to keep them thinking hard. In Chapter 10 we will look at a collection of tasks that I feel do exactly this, aiding the development of both procedural fluency and conceptual understanding.

I can also be more aware of the language that I use. Being told something is really difficult may well motivate some students, but for others it will only reduce their expectancy of success, and hence have the opposite effect on motivation than what we intend. Of course, this all comes down to our knowledge of the students we teach – there is no black-and-white rule that works for everyone. But I certainly have toned down the adjectives I use to describe the tasks I give my students. And following the advice of Dylan Wiliam in a 2017 podcast interview for TES, when a student says they can’t do something, I correct them by saying: ‘you can’t do it yet’.

But this alone is not enough to help students feel they can be successful. Fortunately we have a whole book to try to figure out how to do it better.