The Core Assumption

When I was still teaching in the traditional way (by which I mean pre digital media network technology based way), the scope of what I imagined the effects of my teaching might be on the world was largely constrained by the operational principles of the educational system in which I worked. One teacher in one place can be assumed to make no real difference to the way that the world goes. The inspirational teacher story, based on real events (I am not sure how closely), of Freedom Writers is a pretty striking counterexample to this fatalism, but this story very starkly highlights just how much a teacher who wants to really redress the failures of the system they work in must be prepared to sacrifice to do so, and for a victory that may be tremendous in terms of the lives affected by it first hand, but which is in the end a drop in the ocean. I chose to work in EdTech because of the possibility of building functionally superior education systems that could offer people hopeful possibilities that the world’s failing educational systems and institutions increasingly could not.

In vastly more concrete and functional terms, I had ideas about how technology could help make learning mathematics and related subjects much more accessible, so that learning such subjects successfully could be a realistic aim for a majority rather than merely for a minority. This goal, and how it might be achieved, has two appealing qualities; firstly, it is tremendously rich and deep, and secondly, it seems obvious that it is a worthwhile endeavour. So obvious in fact does the worthiness of the undertaking seem that until recently it had never occurred to me in any properly conscious way to even wonder if it actually was as important as I supposed. What reasons do I have then for thinking it good that mathematical understanding become much more widespread?

Giving some conscious deliberation to this question fairly rapidly made it clear to me that I was considering mathematical understanding as a proxy for the better use of a more general kind intelligence, something like Khaneman’s System Two thinking. A world of people in the grip of System One thinking is a world where everyone makes only unreflective decisions based on being convinced that what they know is by definition the only thing that they need to know. This is a world in which people only learn things the hard way, and anything too hard to learn is never learned. A pessimist might say that this is the world we actually live in, and there is some truth to that, but it is hardly the whole truth.

Accepting a healthy dose of pessimism, I must concede that learning mathematics (and physics, statistics, logic, etc…) does not ultimately drive out the demons of System One thinking even a little distance beyond the context in which these things are learned. As learning is detached from life in general, so are the fruits of that learning. One of the enduring themes in (some) EdTech dreaming is the notion of embedding learning in the broader pattern of living. Quite recently, this was a fairly prominent theme. M-Learning (both mobile and micro), lifelong learning, and learning on demand were popular buzz-terms. More recently, educational institutions (and the funds that they represent) have become more EdTech enthusiastic. Project based learning, based around hubs that map conveniently to existing educational infrastructure, has taken more of a foreground position since then. PBL could be a way of merging the world of work with the world of education; schools becoming makerspaces promoting design thinking and STEM skills.

When I was teaching, I would stress to my tutees preparing for higher education or employment, that they needed to be giving major consideration to what they could learn to do that would not be easily automatable in the near future. Jack Ma took this idea to something of an extreme in the speech where he argued that students should not be learning anything that a machine could do, because machines will outsmart them soon enough. Ma’s extreme statement does not perhaps go very much farther than Ken Robinson’s ideas on individuality and creativity. Robinson is critiqued rather well in this blog post, and I concur that Ma and Robinson are wrong to say that we can avoid being outsmarted by machines purely by doing different things than they do, because if we do not understand what machines do, then how do we know what would be different to that? I should have said to my tutees (not that they believed my warnings) that they should anticipate that in their future they would be competing for jobs with a computer, and that like in any other competition, they should want to know anything about their competitor that they could find out in case something in that would help them to win the contest.

The question that bubbles up from these insights (hopefully) is the question of what kind of skill and/or intelligence is really going to be helpful for most people, now and looking ahead. In the twentieth century there was almost no question that what basically mattered was IQ. The dominance of the importance of IQ has been such that it has become uncontroversial for people to see IQ as a synonym for intelligence. I would argue that IQ is more properly a particular kind of intelligence, but the only kind that can effectively be systematically measured, and the kind that generally mattered most in a world overwhelmingly organised along systematic approaches to solving problems. Human evolution, and the ways of learning that come most easily to most humans, are not particularly systematic, they’re far more heuristic. Heuristics can be very effective in many situations, but they don’t tend to travel well or to scale well. The effectiveness of heuristics in the particular niches in which they apply can easily act as a disincentive to painstakingly learning systematic alternatives to the heuristics, as the heuristics so often work better (up until the point where they don’t).

The clash between the short-term gains versus the long-term opportunity costs of relying on heuristics is something that I think could be ameliorated in two main ways.

The first way would be to teach the heuristic and systematic approaches to learning things in parallel, only making connections when learners are interested in making them. There exists a qualification called “Use of Maths”. The name is misleading, the course content is barely any different from applied maths, but what if “Use of Maths” did exactly what it said on the tin? What if it was a subject that taught people heuristics that would be helpful in their lives, things that were mathematically derived but didn’t need to be understood systematically. People do not need to know how to calculate compound interest to be taught and to remember that a 25% APR on a loan is not a particularly good thing to be offered. The collection of useful facts that people can know about dealing with money, and more generally with risk, as well as how to better recognise manipulation and deception relating to quantifiable events, are things that can be learned pretty much in isolation from their systematic underpinnings, by whatever heuristic methods people find helps them to remember the key facts.

The second way of aligning heuristic learning with the painstaking effort of systematic learning would be to make systematic learning less painstaking. One way of doing this would be through interacting with artificial environments in which heuristics applied that taught things which corresponded rather than clashed with what systematic approaches to learning would teach, such as games that were constructed to teach mathematical procedures while also being enjoyably playable; your brain would like them even if you didn’t.

What I’ve more and more come to realise is that no one really knows with much surety what the important things are for people to learn to prepare them for the future. I do still think though that whatever approaches reduce the insight lag between people’s System Two and System One thinking ought to be worth trying.



It has been quite a while since I last posted. I have had a lot less time to post since I returned to full time work. I am now wholeheartedly working in EdTech, and hope to continue to do so. It is sometimes strange to think that I am perhaps unlikely to teach in a classroom again, but life can be strange. 

Working in Edtech has turned out somewhat differently than I imagined it would. Rather than the kind of technical role I thought I would find, I am working as a Subject Matter Expert. My work is primarily concerned with writing, and I mean writing subject content rather than writing code.

When I was teaching for a living, it was very obvious how little most of the learners I encountered were willing to read even a very tiny amount, and the reading that these learners were willing to do was not what I recognised as reading so much as it was copying (in the sense of the action that immediately precedes pasting). Learners would hold what they read (or thought that they had read) in their mental copy buffers just long enough to transcribe it (often severely mangled) to some repository external to their biological memory. Communication of information in such a reading (or more accurately, such an anti-reading) culture as this necessarily had the attributes that I think can be aptly characterised as ‘high noise, high redundancy’. The assumption had to be made that what was communicated would not be understood until it was repeated several times (if then) and that the content being communicated would not be stably retained, or even received, and so the forms suitable for communication had to be those which were as robust and self-correcting as could be achieved. This requirement meant that broad, general principles of the subjects being communicated were far more amenable to reception than precise details; this shift of focus over a number of years led me to think about such principles in ways that I might not have otherwise considered. The inevitable variability in communication approaches necessitated by ubiquitous noise and need for repetition naturally led to the formation of multiple representations of subject content. Broadly speaking, these conditions promoted the development of a meta-cognitive approach to the communication of subject content. The approaches necessary for dealing with non-intrinsically motivated learners seemed to me to be potentially highly cross-applicable to much more engaged learners, a small number of which I was fortunate enough to teach and who seemed to enjoy not just learning the content that I was charged with teaching them but reflecting on how it was that they were or were not succeeding in understanding the content. 

I cannot stress enough how great was the gulf between the intrinsic motivation of some learners I taught and what was implied by the expectations implicit in the official documentation of the qualifications that these learners were nominally engaged with. I recall one particular learner, a tutee of mine, who was really extraordinarily, staggeringly unmotivated. This person seemed to me to have something of the same feeling for apathy that Schopenhauer had for pessimism. Schopenhauer maintained that we would be objectively better off if we had never existed, and equivalently this learner seemed to regard any sort of deliberate intention to do anything that was not a route towards ever further disengagement as the most futile kind of masochism. In a tutorial that involved applying mental imagery to the recall of surprisingly long lists of items, this person caught me off guard by extremely uncharacteristically asking an unprompted question. He apparently found it so disconcertingly bizarre and counter-intuitive that anyone would go to the bother of generating their own mental imagery when an effectively inexhaustible supply of imagery could be obtained online that he could not help actually being curious enough to ask me why I would want to waste my time auto-generating images when (as he put it) someone else could do that for me. When I told him that compared to what I could imagine, the input from YouTube etc… was generally cloying and numbing, he appeared to interpret this as my outrageous bragging, at which point he went back to his usual not caring.

This anecdote may or may not have anything useful to say about education, but I have come to think that I have explicitly said plenty up till now about educational theory and suchlike. Colleagues of mine in my new job have suggested that I should explore writing more narrative (and less theory presumably), maybe to see what ideas develop from that, or maybe just to practice better writing. Writing is now my job after all.         


Starting with something new

In a previous post I wrote about what I called Open Content Learning Webs (OCLW). These are hypothetical community run (and ideally community owned) trans-disciplinary knowledge sharing websites that assess the ability of their users based on the community’s responses to content contributions that users make to the OCLW. 

It might be supposed requiring learners to contribute new content for them to be assessed would be a serious limitation in terms of assessment; how can inexperienced new learners be expected to generate new content? Educational taxonomies tend to rank creation as a very high level mode of learning activity appropriate for learners who have achieved fluency in various precursory activities (like remembering and applying).

What this apparent difficulty is missing I believe is that new learners’ contributions need not be content that is in any sense involved in the foundations of the subjects to which they contribute content but rather represents novel applications of existing content; not necessarily remarkable or ingenious new applications, but simply applications not already specified. New learners need not contribute new knowledge but only new uses for knowledge. Actually, a contribution need not even be a new use for knowledge. A contribution could be concerned with already specified applications if the contribution provides information to the community that facilitates community members’ location of and/or recognition of uses of existing knowledge. A vast amount of knowledge exists today that could have a multitude of transformative effects on the lives of a multitude of people if only those people were aware that this knowledge existed and how this knowledge could benefit them.

This kind of novel application and consolidation of knowledge has started to impinge on mass awareness, such as in the form of the phenomenon of ‘life hacks‘. Life hacks however are so far not generally seen by educators as being much at all to do with education or learning. Education as a formal process tends to characterise life hacks (if it acknowledges them at all) more as laziness-inducing distractions from learning that insinuate to learners that many of the problems that they perceive as relevant to them can be satisfactorily addressed without very much recourse to the formal process of education. The possibility that life hack curious learners might in fact be correct regarding the efficacy of life hacks to their concerns rather than the educators who deride the usefulness of such life hacks is indicative of the implicit necessity for education as a formal process to be given the exclusive right to determine what is and what is not useful for a learner.

Open Content Learning Webs would be communities where those who did not have specialist subject knowledge to contribute would acquire merit within their community by devising and sharing life hacks and by recognising how the knowledge existing in these learning webs could be used to make more and better life hacks.         

Disclaimer: This post has nothing to do with Audrey Watter’s Hack Education blog.

Keep stirring the concrete

To have learned something implies that one remembers it; a person must have ready access to their learning for it to be learning worthy of the name. The most direct forms of assessment are essentially concerned with what learners can recall when prompted to do so. By calling these forms of assessment direct, I mean to say that they are most directly concerned with what a learner has supposedly learned. The concern is primarily on the content- how stably it has been stored and replicated. The question of what that content may or may not mean to a given learner is of lesser consideration. If the learner can produce the content when prompted, they are assessed as successful (and as not if they could not).

Obviously, very little can realistically be learned about any subject without access to a set of referents that are foundational to that subject. It is very reasonable for a teacher to want learners to have ready access to various facts that act as highly efficient short-cuts in solving problems in a subject. If learner’s understanding of a subject is in a state of perpetual, unpredictable, turbulent flux then they may easily forget or unlearn what they had learned, or learn some alternative incompatible concepts that preclude the attainment of the understanding that their teacher hoped to bring them towards. This is a very obvious problem.

Another problem which seems to be less readily recognised is that a learner’s path towards understanding may become impassable not because a learner loses sight of that path, but rather because their view of it gets blocked by their existing knowledge; possibly the very knowledge that they were taught in order to keep them on their path.

I saw a striking example of this kind of phenomenon illustrated in Skemp’s Psychology of Learning Mathematics, in which a fatally flawed understanding of the Pythagorean theorem is illustrated.


Seemingly, the mathematics learners who produced diagrams such as these had a acquired the belief that the orientation of a square relative to a page it was displayed on was part of the definition of a square. Making one side of a square parallel to the diagonal hypotenuse of a right triangle apparently disqualified it from being considered a square. I suspect that learners who had made this error would probably also not recognise the shape below as a hexagon; they would assume that hexagon exclusively meant regular hexagon.


It is not hard to imagine (for me anyway) the well-intentioned efforts of teachers to inculcate stable knowledge of certain common shapes having the effect of making those shapes only recognisable as the shapes that they in fact were when they appeared in ways that were substantially similar to the ways in which they were shown when the recognition of them was taught. The effect of this would be that concepts that were taught to learners became not only concepts but examples of fixations

I chanced across a nice example of the opposite of such a fixation based misunderstanding in this online puzzle.


One popular solution to this was to change 4 + 9 = 1 to 4 + 3 = 7, but I preferred a different solution that one person had suggested.


 I liked the solution -4 + 5 = 1 more than 4 + 3 = 7 because of the inventiveness of recognising that the 4 has an implicit sign, which can be changed just as well as the explicitly shown sign can.

The learning of physics has a particular susceptibility to being made more difficult by learners’ reification of nonessential, circumstantial aspects of how physical concepts are presented to them during their learning. I strongly suspect that this susceptibility has at least some of its origins in the method of attempting to explain physical phenomena through exposure to various models that aim to represent successive stages of  approximation of said physical phenomena. 

The problematic aspect of making use of initially highly oversimplified models for explaining physical phenomena is that the oversimplifications of those models can become sufficiently familiar to learners to be perceived as the final explanations of these phenomena, not mere stepping stones to more subtle understanding. 

Take for example a model of the molecular structure of a solid that might be used in teaching atomic theory of matter.


Presenting a model like this can reinforce a naïve concept of an atomic solid as consisting of stacked atoms that remain in position because nothing pulls or pushes them in directions perpendicular to gravity, while gravity holds them down. That is indeed what would be happening to a macroscopic model made in this form, which is what a naïve learner is primarily aware of. Crucially, such a learner would probably have only a vague intuitive concept that there are attractive (or repulsive) forces between the atoms. The ability of the atoms in the model to stay in their positions when the model was manipulated would need to be understood in some way or another. The learner would look at the model rotated, and ask themselves…


The naïve answer is probably that some sort of friction wedges the atoms together, so that The atoms collectively inhibit each other’s motion.

This misconception could lead to the further misconception that if single lines of atoms were removed from the atomic lattice them friction would not hold them together, and they would fall apart into individual atoms.


A learner might conceive of this as a phenomenon that explained the characteristics of powdery materials, and then go on to conflate this with the change of matter from solid to gas phase; influenced by the recognition that some powders can when disturbed form clouds- clouds that superficially resemble diagrams they would have been shown of atomic models of gasses as freely moving particles.

The overall point is that learners have abundant motivation and opportunity to interpret models that they are shown in terms of what is already something that for them is concrete in an experiential sense.

Personally, I greatly favour finding ways to base conceptual learning on concrete operations, through manipulative methods like interactive simulations and the designing and making of models. I have a very strong interest in the representation of numbers and mathematical operations in concrete forms in ways that continue their use drastically beyond the pedagogical stage at which symbolic representations of numbers and number manipulations usually replace concrete representations (this is a splendid example of what I mean). While a learner still has access to concrete versions of what they are learning, they retain a degree of ability to use them as they see fit; to play with them. Exchanging concrete representations for symbolic versions is for many learners effectively an act of faith, or at least of compliance. The symbolic operations are a code that they are assured is how things really work. Learners may be reassured that this code will come to be meaningful to them, but ultimately this change in them may mean abandoning what they once meant by meaning and understanding for something that is basically aspirational; meaningfulness as an ever unfulfilled promise, and a void where once imminent understanding resided as a condition that one simply learns to live with- understanding conceived of as becoming resigned to not really understanding but carrying on regardless.





The (In)Visible College

I posted a while ago about the possibility that people’s knowledge is at least partially generated by the process of asking them questions about their knowledge, perhaps even to the extent that such knowledge may not even exist in any well defined sense before the questioning process occurs (this post). The first book I read that seriously and persuasively proposed the notion that how knowledge actually forms in learners’ minds is an essentially opaque and impenetrable phenomenon was The Learning Spy, by David Didau (which I discussed in this post). Didau didn’t seem at all concerned with ontology, just with epistemology. Fair enough I suppose; it probably doesn’t make any difference whether knowledge actually exists before it is measured in some way if the only way to show that knowledge exists is by measuring the interactions of knowledge possessors with the world. Perhaps ways to infer the results of interactions between different items of unmeasured knowledge could be devised, but presumably with great difficulty.

If knowledge is in some sense created by the attempts made to apply it, then I think what kinds of attempts to apply knowledge are involved in learners’ education would potentially make a great deal of difference to the character of the resulting knowledge. 

Two particular, contemporary educational approaches have names that explicitly refer to the premise that the nature of learning involves something not directly observable; Visible Learning and Invisible Learning. 

John Hattie has made the term Visible Learning (somewhat) famous. To be succinct, Hattie’s approach has been to consistently and (as much as possible) comprehensively replace anecdotal, heuristic, and superstition based theories of effective teaching practice with effect-size measurements found from multitudes of studies. Hattie has gone on to use the results obtained to justify the argument that there ought to be greater emphasis on modelling metacognition to learners that builds on learner fluency with subject matter acquired through directed instruction. The dependence of effective learner metacognition on effective learner motivation and an analysis of the factors that most affect learner motivation is another key area that Hattie has stressed. Visible Learning is so named not because learning is intrinsically visible, but precisely because it is not so, and must be made visible to learners (and teachers) for it to occur effectively. Hattie’s body of research is certainly impressive. I cannot help but wonder though to what extent the results of studies from which he obtains effect-sizes are measuring learning in the sense in which he uses the term rather than in the sense of learners learning how to give the right answers to the right questions at the right time without them necessarily being able to shed much inner light on how they themselves were able to do that.   

Invisible Learning is associated with the Education Futures organisation. Unlike Visible Learning, Invisible Learning is not much concerned with educational studies and their effect-sizes but rather with the importance of informal learning, that is not measured by education systems (although what data Google et al may be mining is another question). According to Invisible Learning, informal and serendipitous learning is argued to be the dominant factor in determining learners’ overall motivational proclivities and metacognitive abilities. Learners whose experience of schooling does not result in the successful elicitation of motivation to engage with and achieve mastery of academics may well be effective learners in various other areas of their lives which unfortunately go unrecognised and unrewarded. John Moravec has as one of the principal drivers of Invisible Learning has published Manifesto15a guide for educators to a future of education that he sees as increasingly based on invisible, informal learning that is becoming ever further separated from what is measured by educational institutions. Manifesto15 states that

The best innovations are often killed the moment we start worrying about measurement. We need to put an end to compulsory testing and reinvest these resources into educational initiatives that create authentic value and opportunities for growth…Black boards have been replaced by whiteboards and SMART Boards. Books have been replaced by iPads. This is like building a nuclear plant to power a horse cart. Yet, nothing has changed, and we still focus tremendous resources on these tools, and squander our opportunities to exploit their potential to transform what we learn and how we do it. By recreating practices of the past with technologies, schools focus more on managing hardware and software rather than developing students’ mindware and the purposive use of these tools. 

Such inflammatory words would not I suspect really be Hattie’s style, yet Hattie would surely agree that educational systems are on the whole set up so as to focus efforts on obtaining favourable knowledge measures more than they are on ensuring that those knowledge measures are compatible with what the world beyond the educational system considers to be useful knowledge.

Visible Learning strikes me as being more focused on the epistemology of learning. It looks in detail at formal methodologies. It extensively uses quantitative measures. It does not actively question the continued viability of the contemporary educational paradigm. Invisible Learning seems to be more interested in redefining learning, and to that extent is asking what learning is and whether it is even possible to distinguish learning from the ways in which learners determine what they do or do not know, implying that such determinations are perhaps inherently relative- what does a learner know compared to another learner? Who or what can a given learner learn from? Knowledge is supposed to arise from information exchanges that flow unpredictably. Learning Chaos, by Mac Bogert, very clearly argues for the embracing of unpredictability as a way to revitalise education. Chaos theory may be actually be more useful than quantum mechanics as a basis for comparison in understanding the learning process.  




Yes, and…

A great deal of what I understand about learning I know because I practised improvisation for many years and with a great deal of personal commitment. One of the principles of improvisation is to accept whatever is happening and build on it. That principle is often explained in theatrical/dramatic improvisation as the ‘Yes, and’ principle. Applying this principle in practice means that when creating a scene, if an actor makes a statement, a gesture, an expression- does anything really (the generic term used is to ‘make an offer’), other actors in the scene agree with that offer and then express something else which in some way references the offer. This principle can be applied in teaching (not easily!) and some teachers are actively promoting this.  

What makes using  ‘Yes, and’ difficult in teaching is firstly that the learners need to be prepared to use it just as much (if not more so) than teachers. The other big obstacle is the extent to which various subjects are based around the idea of correct and incorrect statements. Mathematics is probably the most polarising subject in terms of correct vs incorrect. If ‘Yes, and’ can work in mathematics it can work in anything. So, how can that polarisation be circumvented in mathematics teaching?

To sincerely attempt to apply ‘Yes, and’ in mathematics, a teacher would have to be prepared to accept the challenging of the most axiomatic aspects of the mathematical content that they were trying to teach. For example-

Learner: Does 5 + 1 = 7?

Teacher (For who saying ‘No’ is not option) : It can do, yes- and 5 + 2 can equal 7 as well. Why do you think most people choose that 5 + 2 = 7 instead 5 + 1 = 7? 

Learner (Being deliberately awkward): I don’t accept that 5 + 2 = 7, only 5 + 1 = 7.

Teacher: Yes, and you can define numbers to mean whatever you want them to mean. Everyone who has done mathematics so far uses meanings that make different mathematical statements consistent with each other.

Learner (Seeing how far they can push being awkward- maybe even thinking about it):  5 + 2 = 7 is consistent with 5 + 1 = 7  

Teacher: Yes, and it could be, depending on what ‘=’ means. Can you explain what ‘=’ means?

Two obvious difficulties with this are that some learners are likely to decide to use up a lot of teacher time on this sort of dialogue as a proxy for some kind of status jostling with teachers (and/or with each other), and that while ‘Yes, and’ may be suitable for discussing learning content it may not be suitable for managing conduct. If a learner asks if they are allowed to hit another learner and if a teacher says ‘Yes, and there will be disciplinary consequences’, then the learner may just respond impulsively to the ‘Yes’, and hit someone and say that the teacher said that they could; there is no neat and practical way to completely separate discussion of conduct from discussion of learning content. What this implies is that the learning of one thing is at a deep level inseparable from the learning many other things (which is one of the main insights that I gained from practising improvisation).

‘Yes, and’ based teaching appears to have numerous underlying similarities to Socratic teaching, which I discussed in this post and in doing so alluded to the idea of a Socratic chatbot (which would address the time-wasting and conduct management issues associated with human teaching). Unfortunately, some sort of ‘Yes, and’ chatbot would presumably be incredibly difficult to program. It might well be fun to try and program it though. Seeing a team of machine learning experts attempt to make some algorithms  based on observations of improvisation groups in action could be bizarrely joyful.

Riser run wiser

After decades of bludgeoning British schools for not meeting various standards, OFSTED (the schools inspectorate) has rather suddenly changed tack; The new chief inspector of OFSTED (Amanda Spielman) is now seriously unhappy that schools are preoccupied with teaching to the test. Spielman is concerned about schools that are gaming the system (the very same system that OFSTED has done so much to help maintain) and about the lack of a broad curriculum in schools (see this article). 

This change of heart by OFSTED is epically belated and it shows a staggering insensitivity in its failure to acknowledge that what OFSTED is saying now is an echoing of what the voice of the teaching profession has been saying for decades (speaking out against the tone of the inspectorate throughout that time). What ought to have been an apology to educators by OFSTED has been expressed as a fresh criticism of them. 

The inspectorate’s admission of failure is to be welcomed regardless of its dismally poor handling however. The important question is how educational institutions can now best address the recognised atrophy of broad based curriculum and erosion of defining purposes beyond the merely bureaucratic. Readers of this blog will likely know that I have a generally skeptical outlook on educational institutions and might not expect me to muster much enthusiasm for their potential renewal. In all fairness, what I have written in this blog is critical not of educational institutions across the board but specifically of educational institutions that are designed to operate along lines that are significantly based on Taylorist ‘scientific’ management principles (which the great majority of educational institutions unfortunately are).  

If there is a way to breath life back into educational institutions as they predominantly exist currently (rather than as the decentralised, spontaneously self-ordering, scale-free, complex networks that EdTech can potentially transform them into) then I am inclined to believe that the way that this could be done would be if the curriculum of such institutions took to its heart the study and practice of philosophy.

Why philosophy?

For a start, it appears to be effective. A study conducted by Durham University found that (as reported by The Independent)-

Teaching philosophy to primary school children can improve their English and maths skills, according to a pilot study highlighting the value of training pupils to have inquiring minds.

Children from deprived backgrounds benefited the most from philosophical debates about topics such as truth, fairness and knowledge, researchers from Durham University found.

The 3,159 primary school pupils from 48 schools who took part in the trial saw their maths and reading scores improve by an average of two months. But the benefits were even more pronounced for pupils from disadvantaged backgrounds, whose reading skills improved by four months, their maths results by three months and their writing ability by two months.

The Durham study was one of a number of international studies showing similar results. The costs associated with introducing a few hours a week of philosophy teaching are pretty low by the standards of educational interventions in general. Good philosophy teachers are probably not going to be easy to come by in large numbers any time soon though so this approach would not be as easy to rapidly scale as technology based interventions, unless… It occurred to me a while ago (and not only to me, although to few others it would seem) that there was a particular nugget of philosophical practice which seemed to overlap rather neatly with a current EdTech trend.

Imagine the philosopher Socrates as a chatbot. Someone already has (and I am not referring to the ‘Socrative’ app). The Socratic method of teaching can be (very) simplistically explained as teaching which offers no instructions to learners other than that they attempt to supply an answer to an initial question and thereafter for each answer that a learner supplies they must additionally answer the question ‘How do you know that (answer) is true?’ 

Obviously there is more to the Socratic method than that. What I have stated above is merely how a software developer might sketch out the basic idea of how to start making a chatbot designed to emulate Socrates. A human teacher using the Socratic method to instruct learners would have in mind certain conclusions that they would hope that learners might arrive at (although they would not acknowledge this to their learners) and would embellish their responses to learners’ answers beyond ‘How do you know that (answer) is true?’ so as to more effectively guide learners towards approaching those conclusions. A simple Socratic chatbot that knew no more than its learners did about what conclusions to reach (much less probably- which might though be useful in helping it to avoid false positive conclusions) would be much less likely to direct its learners to discovering anything significantly true than it would be towards directing them to discover their own fixations. This can be understood visually.


A learner’s fixation corresponds to some local optimum in a conceptual landscape of understanding where the higher up one is the more one understands. The peak of a local optimum is a point from which it is not possible to rise any higher without first descending some distance in order to move closer to a bigger optimum (or even the biggest optimum- the global). Someone trying to at all times increase their understanding would be trapped on a local optimum as to move away from it they would have to decrease their understanding. A human Socratic teacher understands what makes the global optimum different from local optima and so steers learners away from local optima that block progress towards the global optimum. A simple Socratic chatbot that just asks ‘How do you know?’ is not equipped to steer learners away from local optima other than by the brute force approach of repeating ‘How do you know?’ until a learner becomes frustrated enough to admit ‘I don’t know!’- assuming that such frustration has not long since disengaged the learner entirely. 

An appealing feature of the conceptual landscape of understanding model of learning is that recognises the importance of paths taken rather than just points occupied. Understanding something need not mean occupying a particular point in the understanding landscape so much as recognising the influence of that point on other points around it. Such a point might in fact be a local (even a global) minimum rather than a maximum of understanding. This puts me in mind of strange attractors in the phase diagrams of chaotic systems in which the phase space path of a system irregularly orbits a point which represents a state that the system never actually visits.


Such are the places that thinking on philosophy (and mathematics) can take us. In my opinion it is in a large part this sense of mental freedom engendered by philosophy that schools ought to be incorporating in their new broad based curricula. Mental freedom is not the entire basis of curriculum of course. Mental freedom which remains entirely mental remains basically inconsequential. Curriculum needs to engage with the issues around how mental freedom can be maintained in a social context where actions have consequences that place restrictions on free actions. Social and political and ethical philosophy are as key to curricula as the parts of philosophy more concerned with the worlds that a mind partaking of an isolated freedom can explore. Philosophy does not necessarily have a great track record in this department.

Postmodern philosophy is loved by some and hated by others. I see both good and bad things in it. Conveniently, the conceptual landscape of understanding model of learning can illustrate this. 


Defining optima depends on the existence of an agreed definition of a flat grid representing some baseline of understanding. For much of its history, philosophy can be thought of as representing a set of discussions about the characteristics and qualities of the features of a landscape and speculations about what features might exist that had not been observed (perhaps because they were too small, changed too quickly, or were too distant). The onset of postmodern philosophy represents the beginning of discussions about the assumptions made regarding the definition of a flat grid which was necessary to make all other discussions possible. Postmodern philosophical arguments led to situations whereby any point in the landscape could be defined as the global optimum just by redefining what a flat grid is. While these arguments were very clever and indicative of a great deal of mental freedom, accepting these arguments fatally undermines the motivation for actually leaving any particular occupied point and exploring the landscape around it. Any point in the landscape can be at any height if ‘height’ can be redefined arbitrarily. Why go looking for greater heights? Why learn when anything can be correct just by appropriately defining it so (perhaps by critically analyzing the perspective of the teacher who argues that learners are supposed to supply correct answers)? 

I have admittedly rather heavily ‘put the boot in’ to postmodern philosophy here. I do acknowledge that there are good aspects of it despite the problems I’ve described but I really don’t think that it can form a very good basis for a broader curriculum for learners other than those who have already been fairly extensively educated. Postmodernism is very much a critical-analytical set of (loose) methods that can be useful in overturning limiting assumptions that have somehow or other remained under-scrutinized. This is something like an antidote to false knowledge rather than a means of approaching true knowledge. Those who have not yet gone very far on their life’s learning path are more in need of what might inspire them to continued exploration than what could make them question what the point of exploring is at all.