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.

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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.

local_optimum

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.

chaos3

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. 

grids

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.