Keeping students on the maths bus

Mathematics is important. As teachers, we want to know the most effective methods are for maximising the maths performance of students. Ideally, we might create a virtuous cycle where increased maths achievement boosts students’ self concept, leading to greater motivation for the subject and further improvements in performance.

A new study sheds some light on how we might approach this. David Geary and colleagues analysed a rare longitudinal data set. 167 students were followed from Kindergarten through to Grade 8, undergoing a battery of assessments each year. Some of these were generic such as IQ and working memory tests, as well as reading assessments. Others were specific to mathematics and included tests of arithmetic and fraction knowledge.

The researchers found a correlation between all of these tests and maths performance. However, they found that the maths specific skills seemed to become more important as students aged. Fraction knowledge became particularly important in later grades.

This makes a lot of sense. Mathematics is not a general skill. You don’t improve at it by practising problem solving, you improve at it amassing knowledge specific to the subject.

There are some limitations to the study. The researchers had to decide what tests to run and so they picked factors they thought might be relevant. There could be other factors associated with mathematics performance – for instance, non-cognitive traits such as resilience – that the researchers did not test for.

However, I think that this demonstrates the importance of early maths teaching. If students do not learn basic maths skills and number facts at primary school then this will degrade their later ability in mathematics. The idea that we can then motivate these students into persisting with maths seems implausible.

Do teachers matter?

There has been uproar on Twitter following David Didau’s recent blog posts that question the effect that families and schools have on children. I suspect that many teachers go into teaching in order to make a difference. So are they misguided? I don’t think so.

Genetic fatalism

Didau argues that the effect of a person’s genes seems to matter more than their parents or schooling and he cites supporting data. I am not an expert in this area but it is worth pointing out that the studies used to draw such conclusions are correlational and, for obvious ethical reasons, cannot be experimentally replicated. Often these studies rely on twins or adopted children and so the subjects are not always representative of the wider population. For instance, many jurisdictions have quite stringent requirements on who can adopt. Another objection we might raise relates to the Flynn effect; the large rise in population scores on standardised IQ tests that has taken place over time. If it is genes that predominantly affect IQ then have our genes somehow improved?

The fact that variation in outcomes is predicted more by genes than schools can be explained if schools tend to have a relatively uniform effect. Schools could be contributing to outcomes but in a fairly homogeneous way. There might be variation within that, perhaps down to different teachers, but these would average out. We might also expect to see a few outliers where quality teaching is concentrated, or where a particularly effective set of policies are in place. And we do seem to see such outliers. This would imply that through the right kind of professional development, experimentation or by borrowing practices from others, we could potentially improve individual schools in the system. That would be a good thing.

We need to distinguish here between what is and what potentially could be.

It is also worth mentioning that effects that seem small at a population level can be huge for individuals. Lots of positive and negative individual effects would average out to zero but could be quite profound for the individuals concerned. This may be as a result of which teachers are assigned to which students or it could relate to other factors such as encouragement or opportunity.

Economic fatalism

Economic fatalism is the flip side of genetic fatalism and is promoted by a quite different section of the education community. This is the argument that poverty is far more important than teachers or curriculum and so teachers should focus on fixing poverty and inequality through political action.

I have some sympathy with this view and I vote for and support political parties that promise action on poverty and inequality. However, teachers have more direct influence on what happens in schools than they do on government policy. The fact that poverty matters to educational outcomes does not mean that schools don’t matter. Why can’t we work on both?

Interestingly, the argument is very similar to the genetic argument except that the cause is identified as nurture rather than nature. This is both contradictory to, and consistent with, genetic fatalism because correlational research simply cannot determine causes. What we know for sure is that kids from deprived backgrounds who have parents with poor educational outcomes don’t do as well as kids from wealthier backgrounds with more educationally successful parents. Despite what anyone claims, we don’t know exactly why.

Again, the fact that school effects are fairly uniform does not mean that they have to be. If an entire education system adopts balanced literacy then we would expect the effect of that to be fairly uniform. However, this does not mean that adopting the more effective systematic synthetic phonics (SSP) approach would fail to improve matters. SSP has the potential to reduce the number of kids with reading difficulties and so this might be a real and significant improvement for the most vulnerable students. Arguing that we shouldn’t consider SSP until we fix poverty is an abrogation of responsibility.


I am not a fatalist. I choose to be an optimist. I am optimistic about human potential and the possibility of progress. I am politically progressive even as I recognise educational progressivism as misconceived. We each have just a short time to try and make a positive difference and I am not going to spend it worrying about whether I can.


What Australian parents need to know about the reading wars

Let me tell you a story.

Many years ago, there were two great armies. One army consisted of starry-eyed dreamers who believed in a whole language approach to teaching reading. The other army was made up of drill-em-and-kill-em phonics obsessives who mostly had a commercial interest in selling phonics programmes. These armies battled and skirmished until, one day, academics and bureaucrats negotiated a settlement. “Best practice involves a balance of approaches,” they proclaimed. And thus the sensible, pragmatic, utterly reasonable and measured ‘balanced literacy’ was born. And this is how we teach reading in Australia.

It’s a good story. It’s an uplifting story. But it’s a story nonetheless. And it is a story that has been manufactured quite deliberately.

Systematic synthetic phonics (SSP), the approach championed by those phonics obsessives, is supported by the best scientific evidence available. Despite the alternatives to SSP grabbing hold of words like ‘whole’ and ‘balance’, SSP is a complete approach to teaching early reading and not a dry worksheet shuffling exercise. Three English speaking governments have commissioned expert panels to review the evidence and SSP was broadly found to be the most effective by all of them (here, here and here).

Balanced literacy achieves its balance by adding in less effective whole language practices such as the three-cuing system (searchlights), asking students to memorise large numbers of sight words and incidental rather than systematic phonics teaching.

Typically, children’s readers are not chosen on the basis of which grapheme-phoneme correspondences they have learnt but on the basis of various approaches to ‘levelling’ books, often based on factors such as sentence length. This can lead to a frustrating early reading experience. Given that much early reading instruction is outsourced to parents, this frustration will play out in the family home.

Balanced literacy appears to have been influenced by Reading Recovery. This is a one-to-one intervention originally designed to mitigate the worse effects of whole language teaching. Latterly, it has added elements of phonics. I have written a number of posts about the relative ineffectiveness of Reading Recovery (e.g. here and here) and it seems to have influenced the current New South Wales L3 programme.

I believe that the story about balanced literacy has been constructed by those who are committed to alternatives to SSP, whether these are proponents of whole language or Marxism-inspired critical literacy. By muddying the waters, the methods that sit at the foundation of many careers can persist in the face of overwhelming evidence.

There is evidence of a deliberate attempt to paint a negative view of SSP in the minds of politicians. In 2009, there was a proposal to run a trial in Australia of Multi-Lit, an SSP programme. One whole language advocate suggested flooding the relevant minister’s office with emails making use of ‘framing theory’. The idea was to associate Multi-Lit with ‘failure’ in the minister’s mind and to coin the term ‘readicide’ to describe it.

So don’t accept the stories you are told at face value. Evidence supports SSP. ‘Balancing’ it with ineffective whole language practices serves only to weaken the teaching of reading and increase the number of children with reading difficulties.

Half a million hits – my top five posts

As the hit counter on this blog ticks past 500,000, I thought it would be worth sharing my top five posts of all time:

5. PISA shows you can’t always get what you want

In this post, I demonstrate that the Programme for International Student Assessment (PISA) keeps finding out things that are the opposite of what it probably hoped for.

4. No best way

Is there really no best way to teach? Maybe. But, if so, why do those who mount this argument write reports that advise schools to adopt specific teaching methods?

3. Four ways cognitive load theory has changed my teaching

Cognitive Load Theory (CLT) is the subject of my PhD research and has been described by none other than Dylan Wiliam as the ‘single most important thing for teachers to know’. In this post, I explain how it has changed my teaching practice.

2. Learning lessons from the failure of Scotland’s “Curriculum for Excellence”

Scotland’s revolutionary new curriculum has been a failure. Why? What can we learn from this?

1. Can teaching be given a score?

My top post asks whether we can measure the effectiveness of teaching and give it a score. It is also the home of one of my post popular diagrams; ‘How rubrics fail’.

Two trends and some advice

I’ve notice two trends since I started blogging. The first is that I am gaining proportionally more hits from Australia than when I began. The U.K. still tops my hits but my home country now comes a close second. The second trend is that fewer people pop up to disagree with me, rebut my posts or criticise them on Twitter. I can only guess why this is the case but, coupled with my own more selective approach to responding, the effect has been for me to be able to focus on my message a little more and expend less effort dealing with criticism.

My hit count is not as high as the top education bloggers but it is much higher than I ever imagined when I started out. If you want to grow your own blog from scratch then my only advice is to simply keep going. Too often, promising and provocative blogs spring up, post four or five times and then stop. I just didn’t stop.

Five ways to damage a good school

As teachers in the northern hemisphere reflect on the past school year and consider the new one to come, it falls to me to channel my inner Cassandra.

Imagine you are in charge of a good school; a school that is recognised as doing a decent job by the local community but also a school with aspirations to reach ever greater heights. This is a time of vulnerability; a time when bad ideas are as likely as good ideas to take hold of the imagination. Doing something is not always an improvement. Here are my top five howlers.

5. Focus on the furniture

Focusing on furniture and walls is a distraction from the real work that needs to be done. However, the effects are greater than simply those of wasting time and effort. The most efficient physical arrangement is to have individual classrooms with tables that are laid out, or at least can be laid out, in rows, yet you will struggle to find a consultant or architect who will recommend this.

Instead, the enthusiasm will be for knocking down walls and installing pods and break-out or open-plan spaces. Teachers will have to waste time and energy trying to mitigate the noise and distraction these arrangements cause before, three years down the track, someone finally decides to put up partition walls. Even then, those tables will still be arranged, immovably, in strange patterns that prevent students from seeing the board or the teacher.

4. Lock yourself into the latest novelty

It is almost impossible for schools to filter out all of the bad ideas. Often, senior managers will have a pet project or enthusiasm that seems pretty reasonable at the time. And this is where the idea of a pilot project comes in handy. My advice is to initially commit to something that is fully reversible. This way, you can cut your losses when the expected transformative gains fail to materialise.

About ten years ago, I remember discussing a ‘vertical tutoring’ notion that was all the rage at the time. This would have meant rearranging all of our students’ tutor groups so that they were a mix of ages. The idea was that sensible and mature older students would be a good influence on younger students. I asked what we expected the effect of silly and immature older students to be on younger students but this was never really answered. In the end, we dodged that one and it was probably for the best.

In a different school, we went all out for something called ‘Building Learning Power’. We had training and placed it on all of our materials, lesson plan templates and schemes of work. We wrote it into the criteria for performance management reviews. After a couple of years, nobody except for one assistant principal still believed in it but we all had to keep going through the motions.

3. Listen to the GOGS

Here is a fact about the OECD’s PISA programme: PISA define good teaching as having a student-oriented classroom climate and yet, using PISA’s own measures, a greater amount of student-orientation is associated with worse PISA maths results. Similarly, more ‘enquiry-based’ science teaching is associated with lower PISA science scores.

Yet you won’t hear this from PISA. Instead, they make odd claims about memorisation and seem determined to develop new measures of supposedly generic skills such as creativity or critical thinking or collaborative problem solving. It is as if they think that they might eventually find a measure that correlates positively with the kind of teaching they approve of.

This is a fool’s errand. These skills are not generic and any measures PISA develop are likely to end up testing cognitive skills very closely related to the academic ones already assessed by PISA. The same countries will dominate except that the tests will be less reliable and more gameable.

Yet this idea of generic skills is everywhere. Andreas Scheicher and his staff seem to have watched a Ken Robinson TED talk and become True Believers. Their conviction is so strong that no quantity of their own data will dislodge them from it. So with a passing nod to Pasi Sahlberg, let’s call this the Global Orthodoxy on Generic Skills (GOGS).

Schools that pursue this agenda of focusing on, and attempting to measure, these (non) generic skills will waste a lot of time and money.

2. Introduce project-based or inquiry learning

This is a specific case of a fashionable novelty that is highly likely to go wrong. First, there is little evidence that these forms of teaching are effective. Explicit teaching has a much stronger evidence base. Inquiry and project-based learning tend to be justified on the basis of delivering generic skills and yet there is little evidence that they succeed at doing this.

More importantly, introducing such teaching methods will involved months and years of asking teachers to focus on teaching and learning processes rather than the content of the curriculum. Maths teachers should be thinking about maths and how to make complex abstractions accessible to students. They should not be thinking about how to wring a bit of incidental maths out of a cross-curricular project or how to manufacture a group-based inquiry.

1. Start blaming teachers for poor behaviour

In my experience, schools that go downhill often start by gradually losing grip on student behaviour. This may be as a result of a general malaise or the adoption of a specific anti-authoritarian ideology. Whatever the cause, if the view starts to take hold among senior managers that teachers are to blame for poor behaviour then you enter something of a death spiral.

Yes, there are strategies that teachers can learn to prevent poor behaviour or to close it down quickly and with minimal fuss. And teachers should follow the school policy. However, I have seen teachers criticised for following the school policy. In these schools, poor behaviour is seen as a sign of poor teaching and so it is now in teachers’ interests to hide it away and not report it. From this point, the school will only ever lose.

A quick introduction to the education debate

There is a great debate going on in education about what and how we teach. A lot of teachers are unaware of this discussion, even if they notice the specific effects of it. Oddly, this lack of knowledge is used by some to dismiss the debate as unimportant. And yet how can something as fundamental as what and how we teach be unimportant to teachers?

It’s time to address this. If teachers really don’t know about this debate then I think we have a duty to inform them about it. Please share this post. Perhaps you might print it out and pin it to a notice board in your staffroom.

What we teach

The dominant view in education is that curriculum content is functional; it serves a wider purpose. We don’t read literature or study science in order to know literature and know science. Instead, these are contexts for developing higher order skills such as critical thinking or scientific literacy.

In this view, content becomes interchangeable. Why read Macbeth if you can read Holes? You can, after all, develop these generic skills whatever the context. This argument has frequently been supported by appeals to the future: we don’t know what knowledge will be needed in the future and so it is better to develop generic skills that can be applied to a wide range of situations.

The alternative view is that skills like critical thinking are not generic. Instead, they depend upon strong knowledge of a particular area. For instance, if you want to think critically about the ethnic make-up of Roman Britain then you need to know a lot about Roman Britain. And yet knowing about Roman Britain won’t help you think critically about genetically modified foods.

How can we then prepare students for an unpredictable future? By teaching them knowledge that has endured. The logic is that knowledge that had proved valuable and enriching over time is likely to be valuable and enriching in the future. Whereas knowledge of a specific word-processing package may become obsolete quickly, quadratic equations or the structure of English grammar are likely to continue to matter. Academic subjects encapsulate ways of thinking that have endured and so they should be the basis on which the curriculum is organised.

So the choice is between content as a context for developing valuable skills and content as a valuable end in itself.

How we teach

The dominant view is that we need to engage students in their learning and that this looks like some kind of physical activity. Group work is valued because it involves students talking to each other. Children dressing up as vikings is better than children listening to a teacher talk about vikings.

This view has its roots in naturalism; the idea that learning in schools should be natural, joyful and relatively effortless like it is for learning to speak or walk. If students appear demotivated by a lesson then this is a sign that the content or delivery is developmentally inappropriate. Teachers should not need to use their authority to coerce students to work because, if the lesson is right, they won’t need such external carrots and sticks.

Given that content is interchangeable, one solution for demotivated students is to simply change the content for something more appealing. Similarly, students might be given choices so that they may choose contexts that appeal to them. Another solution is to make the mode of learning more naturalistic; more authentic. What do real mathematicians or scientists or historians or writers do? Let’s ask students to do that. This leads to a preference for inquiry learning and other broadly constructivist approaches where students find things out for themselves. What is more, these approaches are thought to help develop generic skills such as hypothesising or collaborating.

The alternative view is that academic learning is fundamentally different to learning to speak or walk. It is necessarily effortful and frequently difficult. By working through these difficulties, students may or may not develop a love for the subject. It is a teacher’s responsibility to help students through this struggle, drawing on their authority and sometimes with the help of external motivators.

In this view, explicit teaching is efficient and effective. People have been using it for centuries and it gets the job done. There is no naturalistic preference for alternatives to explicit teaching and no reason for them based on the objective of developing generic skills because these skills don’t really exist.

Why does this matter?

None of our education systems are aligned completely with either the dominant view or the alternative view. There is usually a kind of tension between educationalists who promote the dominant view and teach it to new teachers, and politicians who generally don’t understand the debate but seek to appease voting parents by imposing testing and national curricula.

It is also not at all obvious whether one view is right or whether the truth lies in a mix of these perspectives or maybe somewhere else entirely. And that is why the debate is so healthy. I have avoided references here but there is a range of evidence and theory that proponents of either position draw upon when they construct their arguments, much of it is interesting and some I find compelling.

In any given school it may be true that the teachers use a mix of approaches and are unaware of this debate. But what if the particular mix of approaches they are using is not delivering the best possible education to their students? That should matter to teachers. If it doesn’t then they either lack the capacity to imagine they may be wrong or they are complacent. I believe in teachers and I believe that we are better than that.

Ignorance is strength

In 2011, I read an academic paper that changed the course of my career. Until this point, I had taught fairly explicitly but this was a guilty secret. I knew that it was superior for students to find things out for themselves and so I viewed my own explicit teaching as a cheat; a dodge. This meant that I could not work at improving it. In 2011, this changed.

And once you realise the possibilities of explicit teaching and you abandon the pursuit of generic skills, you start to see value in a much richer academic curriculum. I have some sympathy for those who argue that curriculum is more important than teaching methods but I believe the two are strongly linked by ideas about what education can achieve.

Yet there are those who would deny me my experience. The story goes that most real teachers who aren’t on Twitter don’t care about some vitriolic debate about teaching methods or curriculum. They just get on with the job like proper little troopers. Perhaps this is how you feel?

If so, it is worth noting that this narrative has been constructed. It is seductive because it spares us the work of finding out what the debate is about. Teachers can think of themselves as pragmatic types who just get the job done. Ignorance is strength.

As with all constructed narratives, it is worth looking at who is constructing it and why. Education academics should be in favour of critical thinking and open discussion. And yet it is they who seem to push this barrow. “There’s nothing to see here,” they claim. “It’s just some funny foreigners on Twitter,” they suggest on Twitter. 

This narrative has been constructed because it is highly effective. By denying the grounds for any debate, there is no need to support a position with arguments or evidence. It’s just those silly obsessives mouthing off again. Yet the same people take plenty of positions themselves that are worthy of scrutiny: For example on direct instruction or teacher preparation.

The reading ‘wars’ help explain what this is about. By writing off the debate as something only of interest to obsessives, constructivists were extremely effective at marketing a version of whole language known as ‘balanced literacy‘. Who could possibly object to balance, right? So it works.

And the vitriol? From my perspective, a lot to of it seems to be aimed at me. I write reasoned posts about the evidence as I see it, accepting that I might be wrong. In return, I get compared to Tommy Robinson by Twitter trolls and receive threats to complain to my school or university. I’ve even had threats of legal action. Yet the narrative is constructed so that bloggers like me are to blame for any unpleasantness. It’s our fault. We bring it on ourselves by disagreeing with important people and asking for evidence.

It’s up to you how you read the debate. You are free to dismiss it if you wish. But before you do, ask yourself whose interests this serves.