Lunching the way to a brighter teaching profession

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Improving the professional status of teachers is a key issue in education. To this end, the Australian Council of Deans of Education are organising a forum and inviting education organisations to work collaboratively on the issue.

Well thank goodness for that!

There will be talks from politicians, journalists and even a session in which “Teacher education students, teachers and prospective students” will be allowed to speak.

Hoorah!

The whole thing will be moderated by some former journalist and is hosted at the iconic Melbourne Cricket Ground.

What a great venue!

But there’s a catch. It takes place on a Friday in term time, so most teachers will not be able to attend. Oh, and it costs $450.

Never mind, perhaps they can fix the status of the teaching profession without us.

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Mathematics for everyone?

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I remember a key moment early in my career. I had been receiving target grades that students were supposed to aim for in their exams in my subject. I knew these were based on a set of cognitive tests students completed when starting secondary school, but I wasn’t clear how. Now I was staring at a set of graphs, one for each child. They had bars at different grades representing the different percentage probabilities of obtaining each of those grades. None were greater than about 30% and every child had some non-negligible probability of obtaining any of the possible grades.

This made a nonsense of target grades which were simply based on the grade with the largest percentage plus a bit of ‘aspiration’. Yet if a child had a 10% chance of an A and their largest bar was at C, did B represent an aspiration? I realised that, although there was some powerful statistics sitting behind this data that could predict relative proportions of grades for large numbers of students, at the level of the individual student, they were pretty meaningless.

I’ve tried to stay out of the divination business ever since. Are some people just not cut out for maths? I don’t know. There’s a lot of interest in genetic factors in education in recent times, but I suspect the predictive power of genes at the individual level is even less than those cognitive tests. We can fool ourselves into making up narratives about our students and even ourselves, but I suspect they are just stories.

One issue with mathematics is that people tend to misunderstand it. It is a sequence of rigidly hierarchical knowledge, much of which becomes automatised and therefore feels like a skill. Yet if any steps in that sequence are missing, there will be trouble. If a student came to me and said they wanted to study Mathematical Methods at VCE, but they could not manipulate basic linear algebra, then I would be frank that success was unlikely. That’s not to write that student off as not a maths person. It is to state, quite logically, that first they would need to learn some linear algebra and see how that goes. In time, they could be as capable as anybody else of tackling Methods at VCE.

However, we all know the casualties – the kids who opt out of maths as soon as they can, convinced that it is not for them. And we know those who, despite years of maths lessons, don’t learn basic linear algebra. Is there a inevitability to this or are we, as maths teachers, contributing to the problem?

Jo Boaler, Professor of Mathematics Education at Stanford University, has written a blog post that attempts to address this question. Boaler is convinced that everyone can learn higher level mathematics and makes a number of suggestions about what might be going wrong.

Some of these are non-sequiturs that attempt to draw lessons from neuroscience. For instance:

“The brains of the “trailblazers” show more connections between different brain areas, and more flexibility in their thinking. Working through closed questions, repeating procedures, as we commonly do in math classes, is not an approach that leads to enhanced connection making.”

Is it not? How come? There’s no reference to turn to.

However, the major thrust is an argument Boaler has made before about the value of struggle. By struggling and making mistakes, we cause our brains to grow and change. Students therefore need to be presented with situations that make them struggle with maths, but in a supportive environment where they understand that it is okay to make mistakes.

For this to be a good plan, we need to accept two propositions. Firstly, we need to accept that struggle is an effective way of learning mathematics and, secondly, we need to accept that we can intervene effectively to frame that struggle in a positive way for students.

The second of these propositions involves what might be called a ‘growth mindset intervention’. Such interventions have been proposed based upon the work of Carol Dweck, a psychology professor also at Stanford who has researched different mindsets. Currently, the evidence for the value of such interventions is weak. Students may well have different mindsets but that does not necessarily mean that as teachers, we can tinker with and somehow improve them.

Without such a backstop, inducing struggle in the maths classroom represents a significant risk. It will increase cognitive load in a way which is likely to be demotivating for many students. Indeed, observational studies of teachers suggest that more effective teachers obtain a high success rate from their students, indicating that they carefully modulate the level of challenge and ensure it does not become too high.

So perhaps struggle is effective but potentially demotivating? Not so, the same approaches that manage cognitive load appear to be both more effective and more motivating. This is not a surprise because we can intuitively grasp that it is motivating to improve at something.

I’m not sure what brain scans can really tell us about that.

However, I like Boaler’s optimism. Whether everyone can manage higher level maths or not, we should do our best to give students a strong grounding, using the evidence as our guide. They may then make their own decisions about what to pursue.

Back to basics

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In 1993, John Major, the British Prime Minister, stood up at the Conservative Party conference in Blackpool and announced his ‘back to basics’ campaign. It was meant to be a call for a return to ‘neighbourliness, decency and courtesy’ and a focus on education and the economy, but it became conflated in the media and popular imagination with social conservatism and family values.

Inevitably, there followed a string of tawdry sex scandals involving senior figures in the Conservative government before finally, long after Major’s political demise, we all unwillingly learnt about his own affair with Edwina Currie – an affair that had fizzled out long before he ever stepped onto that Blackpool stage.

Rank hypocrisy? I’m not sure. I’m of the old-fashioned opinion that what politicians do to improve public services is far more important than whether they have consensual affairs and I’m not certain Major ever launched the kind of moral campaign that justifies accusations of cant.

But phrases like this morph in meaning and cause trouble in the process.

Take ‘no excuses’ charter schools in the U.S. The term used to mean that educators would not use a child’s deprived background as an excuse for academic failure, but it has been shifted and misinterpreted into something quite different. Say ‘no excuses’ now and people think of a ‘zero tolerance’ behaviour policy. I think neither term – ‘no excuses’ or ‘zero tolerance’ – is an adequate or fair description of a complex school environment and so I’d now like to put them both in the bin, please.

And while we are on, let’s do the same with ‘back to basics’ when referring to Australian education. There are two reasons.

The first is personal and perhaps parochially British. The term makes me think of 1990s politicians getting their jollies and so reminds me of something I wish I never knew about in the first place. Think of the wincing, squirming discomfort that is causes me. Think of my embarrassment.

No? That’s not enough?

Alright then. How about this: There is nothing basic about good teaching.

Just take reading. English has a deep orthography that means that different phonemes can be represented by a number of different graphemes, with the same grapheme sometimes representing different phonemes. If you are taken through the planned learning sequence of a systematic synthetic programme such as Sounds Write, as I have been, then you will undoubtedly marvel at the structured way it introduces grapheme-phoneme-correspondences and how it cycles back to reinforce and embed that knowledge. It also becomes clear just how well-trained and knowledgeable the teachers need to be.

‘Back to basics’ is not just a trite three-word slogan, it is a falsehood that devalues the complex work of teachers.

The state of the Australian education debate

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Jonathan Simons has written a piece for Schools Week, a UK trade newspaper, in which he argues that, whatever the shortcomings of the education debate, at least England is having one. It is a great piece to provoke reflection from 17,000 km away. What is the state of the debate in Australia and what can we do about it?

First, it is important to agree with Simons. It is easy to underestimate the value of open and frank discussion. There are individuals on social media who suggest the debate is all a confection, or perhaps even a conspiracy. However, when you look at the unthinking guff pumped-out worldwide about education and the groupthink that bodies such as the Organisation for Economic Cooperation and Development all sign-up to, uncritically, this position is untenable. I think the OECD folks are wrong, but even if they are right, we all benefit from a bit of critical thinking. Analysis and criticism can only strengthen a solid set of ideas.

So what is the state of play in Australia? We certainly do not have the kind of debate that is taking place in England, but there are some encouraging signs.

The phonics debate

The end of July saw a debate between Australian proponents of phonics and the cloistered establishment. Team phonics wiped the floor with their opponents who could only really make vague appeals about ‘meaning’. This felt like a step change. I think team whole-language agreed to the debate, assuming they would easily win and were witness to the ground shifting under their feet.

A lot of time in education, people do not know the opposing arguments and this became apparent when team whole-language failed to anticipate much of what team phonics had to say. Nothing makes the need for open debate clearer.

The newspapers

I have been pleasantly surprised throughout 2018 at the quality of Australian education journalism and a reinvigorated willingness to be investigative. It may be just my perception, but I have seen fewer stories in the serious papers that are essentially puff-pieces uncritically promoting a given school’s new initiative.

Phonics is still the vanguard issue, but every movement needs a vanguard and phonics is pretty important.

Poor behaviour

The elephant in many classrooms is poor student behaviour. Where the recent PISA survey data should have caused a major round of introspection, it was all explained away with little fuss.

Discussion of behaviour is Australia mainly proceeds via slogans such as ‘all behaviour is communication’ or ‘we don’t want a punitive approach’ and very little of this is examined. And criticism tends to see the critic pointed to an (ir)relevant piece of government legislation. This is turf firmly occupied by educational progressivism and would take something akin to England’s free school programme to disrupt it, so perhaps there is less hope of movement here.

Gonski 2.0

The defining issue of 2018 was perhaps the publication of Gonski’s platitudinous report, reheating many of the familiar OECD and world education conference circuit cliches.

But Gonski 2.0 received a drubbing from critics and only a luke-warm response from fans. Perhaps future reviews may spend more time reading through the public submissions before signing up to a programme very like everything that has gone before.

And so to 2019…

What will the next year hold? Watch this space and, if it is safe for you to do so, add you own voice to the debate. We need you.

Doing it like a scientist

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One of the implications of Cognitive Load Theory is that inquiry-based learning is ineffective. When I make this point, I often provoke a response similar to Mike Ollerton’s response here:

The second point perhaps has some validity. No matter how many instances I can point to where it doesn’t work, I cannot rule out that there is a context where it does. However, it is the first point that has caused me to reflect.

There are two reasons why my own PhD research is different to a school student learning basic maths or science. I am further along the novice-expert continuum and so less guided forms of learning become more effective – this is the ‘expertise reversal effect’ from Cognitive Load Theory. I am also trying to answer a question which has not been fully answered before. If it had, it may be more efficient for me to obtain the answer from someone else.

Which strikes me as something of a key point.

I am currently working on my thesis and part of this is a lengthy literature review that attempts to summarise every major development that precedes and is relevant to my experimental work. It is interesting to note that those who advocate for inquiry-based learning on the basis that it is the way that real scientists, mathematicians, historians or whoever work, rarely seem keen to replicate the literature review component. There would be a major problem if they tried – the answers to inquiry questions posed at school are already known and so students would stumble upon them as part of any literature review process (if they are able to understand the literature, that is). I suspect it is also the case that although literature reviews are absolutely central to any genuine scientific investigation, there is a disjoint here between practice and philosophy.

Inquiry-based learning is essentially a modern incarnation of educational progressivism with its emphasis on natural learning through exploration and play. Insofar as the work of professional scientists matches this ideal, their example is useful to the cause. However, the highly artificial process of literature review is not something children do when they play or learn to talk.

I need to write about 80,000 words for my thesis, so you may be forgiven for thinking I must have found out a lot about the world, but this is not the case. Most of that is a literature review and a discussion of the methods I have used.

My main findings could be communicated relatively quickly and simply. I have tested the effect of the order of problem solving and explicit teaching under certain conditions. The theory of productive failure predicts problem solving prior to explicit teaching is a more effective order because problem solving primes students in some way for the explicit teaching (there are various suggested mechanisms). Cognitive load theory predicts the reverse order, at least for relative novices dealing with reasonably complex materials. So that’s what I have tested and I think I’ve designed a pretty good way of doing this. I will not communicate the results on this blog until they are published in a peer-reviewed journal, but, when I do, the overall findings will be pretty easy to communicate. You will be able to ‘learn’ them from a short blog post.

In contrast, arriving at these findings myself has been a nearly four-year project so far. That perhaps gives us an extreme example of the efficiency of learning from others when contrasted with discovering something for yourself. In some cases, where the required knowledge does not exist, discovery is the only option, but it seems perverse to insist on it in other circumstances.


If you want to read more on the difference between learning science and behaving like a scientist then I recommend this piece by Paul Kirschner.

Cognitive Load Theory and the bit in the middle

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I have written before that, as a young teacher, I thought I should be using inquiry-learning-style teaching strategies, that I could not make these work very well and so I guiltily resorted to explicit teaching. However, this explicit teaching was far from optimal. It was never a focus of my training and so I had to work out my own approach through a combination of trial-and-error and observing more experienced teachers. You could describe the style I developed as ‘I-do-you-do’. I would demonstrate a procedure and then ask students to do the same or I would explain a concept and then ask them to answer comprehension questions. If students could not complete the procedure or answer the comprehension questions then my strategy was to repeat the process.

In learning about Cognitive Load Theory, I have come to realise the importance of a middle stage, particularly when dealing with concepts that are high in element interactivity, as I frequently do when teaching maths and physics. We might characterise this as ‘I-do-we-do-you-do’ teaching, where there is a more structured and gradual release of responsibility to the students. This is roughly mirrored in the ‘Guide student practice’ phase of Rosenshine’s Principles of Instruction. This is no coincidence. Rosenshine’s principles are derived from studies investigating the practices of the most effective teachers and I see Cognitive Load Theory as providing a theoretical explanation for why many of these behaviours are effective.

But how do we gradually release control? What specific strategies can we use? John Sweller, Jeroen van Merriënboer and Fred Paas have authored a new paper looking back on developments over the last 20 years of Cognitive Load Theory. The paper is open-access and worth reading for a number of reasons, even if it is quite technical in the way that it is written. However, it also goes some way to helping address what this guided practice or we-do stage might look like.

A key strategy is pretty simple. Rather than provide a full worked example or ask students to solve a problem completely on their own, provide a partially worked example. This may seem like a trivial and perhaps over-literal way of fading guidance, but it has extraordinary versatility and power. An obvious application would be to provide a maths problems with a few steps left undone. However, a strategy that I have seen English teachers develop relies on the same principle. Instead of modelling a body paragraph, teachers can provide a body paragraph without a topic sentence and ask students to write that topic sentence. Alternatively, they could omit some other sub-component of the paragraph. Given that writing is a highly complex activity for novices, such a strategy may also be an example of the ‘isolated element effect’ where students are instructed in different components of a more complex task prior to integrating these components.

It is interesting to contrast this with an alternative approach that manages the we-do stage in a different way. Instead of breaking complex tasks down into discrete components, four component instructional design (4C/ID) focuses on whole tasks from the start of learning (see van Merriënboer and Kirschner). However, the tasks are structured so that more simple ones are tackled first and guidance is gradually reduced during each task focus, moving from very highly guided examples to ones that students complete largely by themselves. It is a complex approach that I have oversimplified here and I would need to learn more about if I were to use it as a guide to answering the we-do question.

Another intermediate effect that teachers may be able to use is the ‘imagination effect’. It seems particularly well-suited to the intermediate stage of learning and reminds me of retrieval practice. Instead of studying a worked-example, a student may imagine themselves running through the different steps. Clearly, a novice cannot do this, but it would also probably be a pointless task for a relative expert.

My experience in schools suggests that the we-do stage is the one that perhaps needs the most attention in any attempt to develop a more effective explicit teaching approach. Cognitive Load Theory may offer some useful pointers.

Mapping element interactivity


I recently wrote about the idea of element interactivity and the fact that it does not depend upon the learning materials alone, despite how some people interpret the concept.

I have now created a graphic that perhaps better illustrates the way that element interactivity depends on both the task and the level of expertise of the person completing the task.

Briefly, tasks can involve the processing or recall of discrete elements, or they can involve the processing of increasing numbers of interdependent elements. For instance, learning the capital cities of the different states and territories of Australia would be an example of the former. You can learn each in isolation from the other. The capital city of Victoria does not depend on or interact with the capital city of New South Wales.

However, if you are learning a process for solving mathematical problems, each element you might manipulate depends on other elements. If you rearrange an equation by subtracting an item from one side of then you must also subtract it from the other side. Similarly, when writing a paragraph, each sentence has a relationship to the next. For instance, in some forms of academic writing the first sentence may introduce a topic and the next two may provide supporting evidence relating to that topic. Crucially, as we build ever more sophisticated mental schemas for these processes, we can begin to retrieve these schemas from long-term memory and utilise them with little effort. This then has the reverse effect of reducing the number of elements we have to consciously process.

Understanding the progression from relative novice to relative expert and the way this links to task materials is useful to teachers because it can help us select appropriate tasks. Early in instruction, we need to explicitly introduce a few elements at a time. Later in instruction, we need to bring these together to solve more complex problems or create more sophisticated products. Element interactivity generates intrinsic cognitive load and so it is something that, as teachers, we may seek to manipulate by reducing element interactivity for relative novices and increasing it for relative experts.