Struggling at mathematics 

It was a Saturday morning and I was stood in a field in the North of England, holding a shotgun. I had just missed five clay pigeons in a row while being gently mocked by the instructor. It was my friend’s stag weekend. The night before had been a late one and I was feeling a little depleted.

I gestured to a grassy bank and said that I was going to sit down. “I’ll just watch from now on,” I explained. The instructor, feeling a little guilty, tried to talk me around; he wanted me to get my money’s worth. But I was having none of it. Clay pigeon shooting and me were over.

This is how maths must feel to many students, except that we rarely let them sit it out – perhaps with the exception of some kinds of group work. Instead, we keep throwing them into the struggle and making them confront their own shortcomings. It can’t feel good. Maths is unforgiving in this regard. You can write a sentence full of spelling mistakes but, at the end of it, you’ve still written a sentence. If you’ve failed to solve a maths problem then you’ve achieved nothing.

Progressive maths educators recognise this issue. For them, it is even more prominent because of their view that learning maths should be mainly about problem solving. They valorise open-ended problems. They think these are motivating. But the motivation is fragile. It can be easily shot down. 

So their solution is to change the personalities of maths students. Instead of being bummed-out by failure, students should see this as a good thing. I don’t think it’s true to claim that every time you make a mistake, your brain grows, but this kind of statement might serve a useful purpose in shaping mindsets. We should teach students to value struggle. 

Such a strategy might even work for a short period of time. We might be able to psych our students up for the struggle so that they feel positive about it. But learning maths is a long term process. It will include times when our students are feeling depleted. It seems a stretch to think that we can change their attitudes in such a radical and persistent way.

There is an alternative, of course. Progressive educators want to take traditional maths teaching and revolutionise it. Explicit instruction, on the other hand, enhances traditional maths teaching with research-based practices. It works with the grain of how teachers naturally teach maths. 

One such enhancement is to tailor the teaching to obtain a high success rate of around 80% or more. This forms a key part of the gradual release of responsibility that starts with the teacher fully explaining and demonstrating and that ends with students independently solving complex problems. One tactic that I use to obtain success early in this process is the use of example-problem pairs: a fully worked example placed next to an almost identical problem for the students to solve.

This builds motivation because success builds motivation. Hitting four out of five clay pigeons is far more motivating than hitting none.

So you have a choice. Which option seems the best bet to you? Should you seek to cause a long-term change to your students’ personalities or should you enhance your teaching to ensure a higher success rate?

Proximal versus distal

It can be hard to cut through education research because there is such a great volume of it, most of which is not very helpful. So it’s useful to have some heuristics to fall back on. I have a few that I can recommend.

Firstly, I would ignore anything excessively jargon laden or that mentions French philosophers in its abstract. Such papers are unlikely to offer much to a practising teacher. I’ve picked my way through a number of them now and if there is a point to them, it tends to be quite trivial.

If the paper involves an experiment then take a look at the methods section. Surprisingly often this will have a great big hole in it. For instance, the control and experimental groups might be different.

However, I’m starting to think that there is something even more important to look for.  Any intervention should have a plausible mechanism. The writers of the paper need to be able to give a good account of how their intervention works. This is important for evaluating the results of any statistical tests because it relates to the ‘baseline’ probability: something that is never measured by the experiment itself.

Imagine, for instance, we randomised students into two groups and got a wizard to cast a spell on one of the groups before we gave both groups a test. Our null hypothesis would be that casting spells makes no difference to the test results. Imagine we then analyse the data and there is a difference. We do a statistical test and find that there is only a 1 in 20 chance of obtaining this difference if the spell had no effect. How would you interpret this result? I’d put it down to chance because I can see no plausible mechanism by which spells can affect test results.

One way you can roughly evaluate a proposed mechanism is to ask: How far removed is the intervention from the desired result? Is it proximal (close) or distal (far away)? It is much easier to understand the mechanism of a proximal intervention than a distal one. A distal intervention is likely to rely on a chain of influences, none of which correlate 100%, so by the time you pass through a few of the links in the chain, any effect may have washed out.

This distinction is made by Castles and McArthur in a fascinating new Nature paper about reading interventions. I met one of the authors, Anne Castles, at the recent Language, Literacy and Learning conference in Perth. 

Castles and McArthur suggest that proximal reading interventions such as phonics and vocabulary training have a much better evidence base than distal interventions such as fish oil, coloured lenses or, heaven forbid, chiropractic.

I wish that the Education Endowment Foundation in England would pay more attention to mechanisms. If so, they might pause before throwing even more money at Philosophy for Children, a distal intervention that is intended to improve English and maths.

The curious case of explicit writing instruction

This weekend, I was honoured to give a talk at the Language, Literacy and Learning Conference organised by the Dyslexia-SPELD Foundation in Perth. Regular readers of this blog will not be surprised to learn that the subject of my talk was explicit instruction. Specifically, I discussed evidence that explicit instruction is more equitable than implicit methods (You can find my PowerPoint slides here although they won’t make much sense if you weren’t at the talk).

One point that I really wanted to stress was that explicit instruction has been tested many times and in many different settings. It’s simply not true that it has only been shown to be effective for teaching basic skills. In Project Follow Through, students in the Direct Instruction condition showed greater gains in higher order outcomes such as reading comprehension and mathematical problem solving. Barak Rosenshine makes the case that explicit ‘strategy instruction’ for reading comprehension and writing have also been shown to be highly effective, even if there is some criticism that reading comprehension strategies provide a one-off boost and don’t need to be practised to the extent that they often are.

It is the evidence for explicit writing instruction that I have been thinking about. I have been doing some work with my school’s English teachers, trying to find and filter evidence to support their teaching. So I went along to a session at the Language, Literacy and Learning Conference by Dr Lillian Fawcett. Fawcett works one-on-one with students to improve their written work and the session was about explicitly teaching creative writing. She had a number of scaffolds and suggested that it was important to ask students to do specific tasks rather than simply getting them to write any old thing. For instance, after setting a scene with a prompt and some teacher-student discussion, one of the scaffolds on her handout starts with, “1. Begin with your key character speaking (Make sure you include his/her name and the setting.” The next scaffold reads, “Begin with a prepositional phrase (In front… Behind… All around… Over the… Next to… Under…).

I can imagine some progressive educators feeling uncomfortable about this. They might suggest it stifle’s creativity. I am happy to have that argument because I believe that this kind of explicit teaching broadens the strategies and abilities of students and ultimately leads to them being better able to express themselves creatively.

Fawcett’s approach reminded me of a passage I read in “Explicit Direct Instruction” by Hollingsworth and Ybarra; a book I picked up at the conference. The authors distinguish between ‘talent discovery’ classrooms and ‘talent development’ classrooms:

“In talent development classrooms… we see evidence of instruction in every essay. Students are successfully practicing something they were taught, not just relying on their innate writing ability. Depending on the grade level and genre, we should see sensory details, consistent point of view, use of transition works, and so forth.”

So now to the really curious thing.

Where do you think that writing strategy instruction might feature in the Education Endowment Foundation’s (EEF) toolkit? It doesn’t have its own category and there is no category for explicit instruction. Instead, the evidence for explicit writing instruction is part of the evidence base for, “Meta-cognition and self-regulation.” This category has a single pound-sign icon, four padlocks and delivers eight additional months of progress, or so we are led to believe.

I have remarked before that, “Meta-cognition and self-regulation,” seems to be an extremely broad category of approaches. If you look through the technical report you see that it includes writing interventions alongside critical thinking interventions, philosophy for children, interventions that seem to target executive function, cognitive acceleration based on the old CASE materials, reading comprehension and more. Such a category is incoherent and useless for school leaders. Should they being explicitly teaching writing or messing about with philosophy for children? Assigning a figure of 8 months additional progress to it seems spurious and daft.

Yet rather than reviewing these categories, the folks at the EEF seems quite keen to promote this particular one. I’m not sure why.

Edugenic Academic Failure #dsfconf

To Perth for the Language, Literacy and Learning conference organised by the Dyslexia-SPELD Foundation. I am suspicious of many education conferences because there is a tendency for the sessions to be dominated by sociological theories rather than scientific evidence. But this is not a standard education conference. It is an event where speech pathologists, researchers, policy wonks and teachers all mingle and where the common touchstone is evidence.

The morning keynote was delivered by Professor Kate Nation from Oxford in the U.K. The topic was poor comprehenders. These are the students who show a strong ability to decode – turning written words on a page into the correct sounds – but who struggle to comprehend what they have read. Nation does not set decoding in opposition to comprehension as some whole-language advocates might. She stresses the need for explicit and systematic phonics instruction. Yet she also made the point that nobody thinks this is all there is to reading. She referred to the ‘simple view of reading’ that sees reading as the sum of decoding skills and oral comprehension. With a few caveats – reading is not simple – this model provides a good guide.

So what should we do with the poor comprehenders? Nation discussed an RCT from the U.K. that I had not heard about before. It had a cunning design: Students with poor comprehension were assigned to one of three groups. The first group was a waiting-list control. The other three groups had withdrawal lessons in text comprehension, oral language or a combination of the two. All groups benefited but the greatest, sustained benefits came from oral language training, with this improvement seemingly related to an improvement in oral vocabulary.

This is a variant of an ABC design that pits one intervention against another and I believe that this is the best way forward for large-scale RCTs such as those conducted by the Education Endowment Foundation in the U.K. and Evidence for Learning in Australia.

It is no surprise to me that improved comprehension comes with improved vocabulary growth. It is a relative lack of knowledge that differentiates low achieving students from their peers and our current instructional methods only serve to enhance this gap.

This was a point that came up in the symposium that I contributed to as part of the second session of the day. First, Dr. Jen Buckingham of the Five From Five literacy project showed us domestic and international data to demonstrate the stagnation of Australia’s literacy performance over time, particularly in terms of the long tail of low performance.  Then Professor Pamela Snow took to the stage to look at the issue from the perspective of the school-to-prison pipeline. There were a number of issues to reflect on from Snow’s talk but chief amongst these was her coining of the term ‘edugenic academic failure’. This is academic failure caused by education.

This happens, for instance, when schools defy the evidence and use ‘balanced’ approaches to teaching decoding skills rather than explicit synthetic phonics teaching. Almost all of the students in the school-to-prison pipeline have academically underperformed and one of the greatest protective factors against entering the criminal justice system in strong academic performance. Reading is a basis for all academic performance and so literacy is a key ‘bridge’ for students to cross.

Mandy Nayton then placed the discussion in the perspective of school practice and how we might be able to diagnose a learning disability, again making it clear that schools have an impact in the teaching methods they choose.

I spoke about the reasons why explicit instruction leads to more equitable outcomes. Explicit instruction does not require students to bring prior knowledge from home. It doesn’t assume what students know. Instead, it teaches all of the components. I suggested that this is the key difference between explicit teaching and implicit methods. Explicit teaching takes a standard level of explanation – the sort of explanation we might give in everyday life for how to operate a dishwasher or how to make a casserole – and adds to it. For instance, explicit programmes might use non-examples. There is a good discussion of this in a book that I bought at the conference: When teaching the concept of an equilateral triangle, we might show equilateral triangles of different sizes and rotated in different ways but we might also show an isosceles triangle and explain why that is not equilateral.

Implicit approaches generally give less guidance than an everyday explanation because they prioritise students figuring things out for themselves. This then becomes dependent upon the child’s prior knowledge and home experiences and this leads to the growing gap between the haves and the have-nots.

And so we have a potential mechanism for edugenic academic failure which made me think about a few other implications.

Firstly, Kate Nation’s possible solutions to oral language comprehension issues involved explicit teaching. The oral language component of the RCT that she mentioned combined a number of processes but they were all explicitly taught and, as Nation pointed out, they were proximal to the issue: You don’t fix an oral language problem by running a philosophy for children programme, you fix it by explicitly teaching oral language content.

Secondly, as Barak Rosenshine describes in this piece, explicit teaching has been shown to be the most effective way of teaching pretty much anything. Sometimes, there is quite a heated debate about the behaviour problem in Australian schools. There are a number of ways to tackle this, including tackling root causes such as poor literacy. Yet one other obvious way to tackle it – explicitly teaching the behaviours that are socially normative – is attacked on the basis that this is authoritarian or coercive. Instead, we do little other than contain behaviour problems until they escalate to a stage where students are excluded.

Thirdly, it may seem obvious that children need individual, differentiated, small-group intervention. I certainly think we should follow this logic wherever we can, provided that our interventions are based on sound, scientific principles. However, the bulk of the school day will continue to involve teachers interacting with relatively large groups of students. Whole-class, explicit instruction offers a way of organising this teaching that does not disadvantage the struggling students in the class.

Can a critical thinking course stop people believing in daft ideas?

A number of people have pointed me towards an article about study on the teaching of critical thinking. The study took place at North Carolina State University and the subjects were undergraduates students.

The test subject were given pre-tests on their knowledge of science and belief in pseudoscience, pseudo-history or pseudo-archaeology. These areas basically encompasses those ideas popular in best-sellers of the 1970s such as that Atlantis really existed or Stonehenge was built by aliens.

Students in the experimental condition were then taught a humanities course in, “Frauds and Mysteries in History”. There were two texts to support the course. The first was a ‘positivist’ text which seems to have dissected fraudulent claims on the basis of evidence and plausibility. The second text was groovier, with a, “post-modern approach to understanding interests in the past in popular culture and the ways people connect with the past in the present.”

The students who participated in the course saw a decrease in their beliefs both in those ideas that had been studied as part of the course as well as in similar ideas. This is taken to suggest that the course taught them critical thinking skills.

I am quite happy to accept that a course like this might have an impact. Far from teaching critical thinking as a set of skills such as “think about why the author might be making this claim”, it teaches relevant content. This is precisely the mechanism by which an increased knowledge of the world leads to better critical thinking; we can reason by analogy. We can say, “this reminds of that idea about Atlantis that we debunked in history class.” This is one key advantage of studying standard subject disciplines in depth.

However, there are a number of pretty fundamental caveats.

Firstly, the students were low in dodgy beliefs to start with. So these are students who are already well along the path of critical thinking. Further, this was not a randomised controlled trial. There were three groups of students. The first group had opted to study psychology. They were the control group and did not receive the humanities course. The two experimental groups both volunteered for the humanities course and one of these groups consisted of many more science students. The three groups differed in other ways such as their gender profile. So we can’t be sure whether any effect was actually due to the different make-up of the groups.

Finally, we have demonstrated only near transfer here. Students can apply what they have learnt about one pseudo-archaeological claim and apply it to another. I think this is worth having and I don’t expect much more from education. That’s why students have to learn so much stuff to be able to function as educated citizens. However, claims about critical thinking tends to be more general than this. We have no evidence, for instance, that this kind of training might make students more sceptical about political claims or the claims of those opposed to vaccination.

Influencing Australian Education

Despite being based in Australia, this blog has tended to attract more readers from the U.K. This is perhaps not surprising. I am from the U.K. originally and it is England that has made the greatest efforts to move away from the worldwide educational consensus typified by the views of Andreas Scheicher (21st century skills, critical thinking and so on). It is no coincidence that it was the British minister, Nick Gibb and the London-based education writer and thinker, Daisy Christodoulou who took on Schleicher in a recent debate.

The trend of gaining the most hits from the U.K. continues. However, I have just pushed past my previous record for the number of views in a month. This record is from way back in November 2015 and a comparison between the two months is instructive.

In November 2015, I had 13,317 hits from the U.K., 3,258 from the U.S. and only 2,282 from Australia. So far this month, I have had 11,461 hits from the U.K., 5,136 from Australia and 2,756 from the U.S. So it is Australia that has increased its share and I would like to thank all my Australian readers, as well as my readers more generally, for taking the time to engage with what I have to say.

This trend is important to me. I am an Australian citizen and, more than anything, I would like to have some small influence over education policy in my home country. It is great to be quoted in a speech by a minister from overseas but I would also like to have some impact at home.

I’ve noticed an additional trend. Australians used to rebut my posts a lot more than they do now. Some of this was a little clumsy but it was often present either in blog posts or on Twitter. These days there is not so much rebuttal. Perhaps people have decided to ignore me in an effort to deny me oxygen or perhaps they have run out of arguments.

It is important to note that it is much harder to influence Australian education policy than U.K. policy because of our federal system. I have heard proponents of federalism make the case that having different education systems in different states provides useful variation: States can innovate and we can all learn from the successes and failures. Yet it just doesn’t seem to work like that. It tends to lead to a system where the only real policy discussion is an argument between the states and the federal government about funding. The actual details of what is enacted seems to be left to state level bureaucrats with the result that the same tropes about creativity and critical thinking get replicated in almost identical ways.

I don’t think this is just an Australian issue. I was surprised to find that Wales is embarking on replicating all the aspects of Scotland’s curriculum that seem to have led Scotland into its recent decline.

I think this is because state-level or country-level variation is the wrong level of variation. It incentivises states to copy each other and play it safe. This is why we need more school-level variation. A starting point for Australia would be to allow some schools to opt out of the flabby Australian curriculum with its ‘expanding horizons’ humanities stream, its inquiry orientated science stream and its woolly ‘general capabilities’ in order to focus on teaching academic subjects properly. We could then see whether the students from these schools fared better or worse and whether these schools were more or less popular with parents.

Despite my growing readership, I have become less optimistic about using facts and evidence to convince whole education systems to stop doing silly things. People are just too invested in the status quo and far too few of them think critically about it. It is only through a diversity of provision that we can break the death-grip of bureaucracy and address the problems with Australian education that are so obvious when you look at NAPLAN, PISA or TIMSS data.

Competing visions

“‘You can go out this morning, my dears, with Mr. Spencer,’ said the governess to her pupils, after listening with pursed-up lips to one of the philosopher’s breakfast tirades against discipline… the philosopher found himself presently in a neighbouring beech wood pinned down in a leaf-filled hollow by little demons, all legs, arms, grins and dancing dark eyes, whilst the elder and more discreet tormentors pelted him with decaying beech leaves.” Beatrice Webb reflecting on the philosopher Herbert Spencer in her memoir, ‘My Apprenticeship’.

In a recent blog post, literacy expert and Professor Emeritus, Tim Shanahan, expressed surprise at the popularity of a teaching approach known as ‘Reading Workshop’. Reading Workshop seems to involve students selecting books to read themselves with the teacher largely getting out of the way. Shanahan notes that this idea has been around for a long time and there is very little evidence to suggest that it leads to either improved reading ability or a greater love of reading. Perhaps students enjoy these sessions in comparison to the other subjects they study but Shanahan is sceptical that this will translate into a love of literature.

I recognise this pattern from science teaching. Practical activity is the great panacea of science teaching because it too is thought to be motivating. Children genuinely do love lighting bunsen burners and placing various items in the flames – who wouldn’t? However, this does not seem to translate into a love of balancing chemical equations. It’s actually pretty easy to motivate students. Every teacher knows that asking a class to make a poster will lead to an easy, conflict-free lesson. The difficulty is in motivating students about academic content; motivating them about the thing you actually want them to learn. Academic content is hard. By its very nature, it requires effort. If it didn’t, we wouldn’t need schools.

It is on this issue of motivation, rather than teaching methods, that educational progressives and traditionalists fundamentally divide. Progressives want learning to be natural and joyful. They want students to learn skills in the same way that they learn to walk or talk. They take a lack of motivation on the part of students as a sign that the teaching is not engaging enough or the curriculum is inappropriate. This is because they come from the romantic tradition that sees truth and beauty in all that is natural; that views children as fundamentally good beings who are corrupted by the world of adults.

Left to their own devices, high school students will choose young adult literature over classic works. This is why educational progressives fight hard to argue that young adult fiction is as worthy of attention as Charlotte Bronte, Virginia Woolf or Zadie Smith. The students’ motivations cannot be wrong. Content must therefore be seen as interchangeable. Yet this creates a problem. If there is no specific content worth learning, what is education for? The solution is to insist that the purpose of education is to teach the nebulous ‘skills’ that are characteristic of modern curricula.

In Reading Workshop, students are practicing the skill of reading. It therefore does not matter what they are reading. If someone presents evidence that Reading Workshop is less effective at developing reading than more traditional methods there are two obvious responses: Firstly, it must not have been done properly. Secondly, who cares if a method is slightly more effective if it puts children off reading for life?

By following children’s interests, we can define a number of such generic skills. Have you noticed that children like using the internet? Right, so let’s define a skill called ‘digital literacy’ and prioritise that over content. Have you noticed that children prefer working on a drama project to learning grammar? That’s fine, we can define a skill called ‘learning to learn’ that children can develop in any context. We’re all good here.

Except that we are not. There are a number of threats to this vision. Hardworking teachers inevitably have to be pragmatists and so, guiltily perhaps, they will subvert the theory. And the biggest threat of all lies in puncturing the foundational myth; that we must motivate students and give them veto over what and how they learn.

You can see this in the reaction to Tom Bennett’s behaviour report. Overwhelmingly welcomed by classroom teachers (see the retweets here, for instance), a number of commentators have taken exception on Twitter. Often, this does not take the form of directly criticising actual points made in the report because that is hard to do. So, instead, we have questions about the use of the word, ‘muscular,’ and so on. Why does this report represent such a threat? Because students must be able to maintain their veto in order to advance the progressive agenda. Teaching techniques that help students engage with traditional academic content call the foundational myth into question. It is meant to be impossible for teachers to have good relationships with students whilst pushing them through content that the students would not have chosen to engage with by themselves.

This is also why you see such a visceral reaction to Michaela Community School in London. It unashamedly uses ‘behaviourist’ techniques to manage student behaviour. The latest spate of outrage comes from the seemingly innocuous idea that Michaela requires students to read only those books that are in the school library when they are in school and not bring in other books from home. This kind of academic quality control is anathema, with one earnest critic wondering whether it was even legal.

I think Michaela gives us a hint at the way forward. There is an unhappy marriage at present between Utopian progressive theorists and a pragmatic teaching profession. The theorists don’t get what they want because the pesky teachers keep subverting the vision. The teachers don’t get what they need because the theorists are in charge, writing generic skills into curricula and generally pushing that agenda by any means possible. And this is why I think Australia needs mechanisms through which the equivalent of a Michaela Community School could open. This is why we need our own Free School model. Rather than continuing to talk past each other, traditionalists could open schools and progressives could open schools. Parents could then choose which vision they prefer.

Of course, progressives would need to find and retain teachers who are prepared to work in their schools. That might be tricky. Perhaps they could follow the lead of Herbert Spencer and try a bit of teaching themselves.