Surface v. Deep Learning

This is my first public blog... ever... and as such I thought it most appropriate to simply dive in and ramble my way through a few thoughts and ideas which are in my mind.

Today's topic is 'learning and assessment' in the context of a UK secondary school. Learning must surely be what a school is all about, although perhaps the scope of learning should be clarified.  I am not talking simply about the internalisation of facts such as "two times three is six"... (and let's leave aside the debate as to whether anyone truly knows mathematical facts of whether they are believed)... I am of the opinion that we should include many other aspects of learning too:

• Learning facts (or at least what we believe at the current time to be facts)
• Practising and mastering skills and processes
• Applying skills and processes to facts (or hypothetical situations) and refining that application in light of feedback
• Developing understanding of self and society (and figuring out how the two best interact)
• Constructing paradigms encompassing those items listed above

Where learning implies the uptake or development of a piece of knowledge or a skill, assessment suggests the necessity to appreciate how much of that knowledge been retained or how deeply the skill has been internalised.  Perhaps this last sentence is the beginning of a definition, i.e. knowledge is an accumulated breadth of subject matter whereas skills are processes or actions which may be first replicated at a superficial level but then mastered upon deeper understanding of the facets and applications of that skill.

Such discussion of knowing v. mastering meanders into the domain of 'surface learning' as compared to 'deep learning'.  These titles are effective in suggesting their own definitions, with surface learning implying a rudimentary understanding of a wide breadth of topics (and topic areas) and deep learning suggesting mastery and the ability to interpret and apply irrespective of context.

It is probably easy (and logical) to have a predisposition to the assumption that deep learning is somehow better; that the two types of learning are at opposing ends of a continuum.  I would argue that such opinion is a reflex response and that both stages on a learning journey.  Consider the metaphor of a learning journey as described by a passenger train.  Individuals are independent travellers: the point of embarkation is a given in terms of their prior learning... the point at which they alight will be decided by the individual by reference to where they want to go along the particular train line.  The terminating station might be considered the pinnacle of deep learning, but not everyone will want to go there nor have the appropriate fare (where the fare is considered the propensity to learn / master the subject matter).  Different train lines exist and their final destinations and calling points might be likened to subjects and disciplines within the school environment.  It might be possible to extend this notion to include express trains v. stopping trains (in terms of how quickly the destination of 'deep learning' is reached), but perhaps that would be to over-egg the pudding.

Regardless, my contention is that the two types of learning are not necessarily better or worse than each other, but perhaps serve different purposes.  Framing the context in my own subject specialism of Mathematics, I would argue that it is difficult for everyone to achieve a deep learning of the subject given that it is a collection of axioms, definitions, lemmas and theorems which are hardly ever of practical application on a standalone basis (if at all).  Being absolutely honest about things, I am a fully qualified teacher of Mathematics with enough certificates of qualification and prowess to wallpaper my study, but I still do not class myself has having a deep understanding of Mathematics.  I am at the 'application' stage, which could perhaps be compared to a parkway station using the metaphor of the rail journey above (yes, I am milking it now), i.e. close to the destination, but still not quite there.  Even degree level Mathematics is still a case of recall, regurgitate and apply in a familiar context, which is not dissimilar from what we do at GCSE level in school.

That's perhaps a long winded way of making a point which I believe is seldom acknowledged: that different subjects have different thresholds at which surface learning stops and at which deep learning begins.  With this in mind (contentious statement alert) I pose the following question - with subject specificity in mind, why do we strive for a one size fits all approach to a teaching and learning paradigm if such thresholds of mastery exist?

Let's introduce a new category on the surface-deep learning continuum... "superficial deep learning", where the illusion of deep learning is given but the actual reality is simply a surface approach dressed up for the benefit of an observer.  To exemplify this, a colleague being observed wanted to take an approach to teaching the topic of simultaneous equations which would allow for an outstanding judgement to be given.  Their instinctive approach was to turn a simple,though time-tested and robust, textbook exercise into a jigsaw puzzle where a pair of equations were matched to another piece of the jigsaw containing the answer.  At first glance this might seem an excellent idea, but what had actually been achieved was to turn an advanced topic, which in its original textbook form could be argued to require a deep understanding of algebra, into a much simpler task of substitution.  The former skill requires high level thinking in terms of deciding how to rearrange, factorise, expand, etc. (grade B or above) whereas the latter approach, although seemingly encouraging deeper learning, actually encourage pupils to work at a simpler level (grade E or D).  We must therefore be careful when making judgements as to what is surface learning and what is deep learning - appearances can be very deceptive.

Time to climb off my high-horse, I think.  While the distinction between surface and deep learning might not be immediately clear across differing subjects, the notion of fight or flight is very, very real... and Mathematics is perhaps one of the most common subjects in which this emotional dichotomy exists.  Only a few days ago the cosmetics giant L'Oreal was accused of exploiting this very emotion in the context of Mathematics.

L'Oreal agrees to change 'bad at maths' boast advert

On a daily basis I see pupils puzzled by various aspects of Mathematics to the point at which the fight or flight mentality is drawn out.  I suggest that it is not the actual Mathematics which is at fault, but more-so the manner in which it is presented.  Show even the most intelligent and committed pupil a second order differential equation and I suspect they would struggle to understand it, engage with it or solve it.  But, scaffolded in the right way many of those pupils who would initially opt for flight should be able to make some headway.  My opinion is not simply that it needs to be dressed up and made to look pretty, but that the problem is split into bite size chunks, each of which may be digested in succession and ultimately allow solution of the original problem.  Getting pupils to 'discover' the solution is very much not the way forward - it took mankind thousands of years to do so - but scaffolding in a way which initially allows supported repetition, followed by independent repetition, followed by application should surely allow for competent use that Mathematical skill both in examinations and in the wider environment as and when an opportunity exists.

The manner in which scaffolded activities may take place can be many and varied.  For example, despite extolling the virtue of the Mathematics textbook, I recently decided to appeal to pupils' more creative sides when beginning a topic on circles.  Cliché as it is we attempted to discover 'pi'.  An unscaffolded,  approach would likely have yielded little progress in the fifty minutes available to this lower ability set.  Indeed we struggled in the first ten minutes to effectively use a tape measure - I predicted some might start measuring from "1" rather than zero, but I was not prepared for the random placement of the tape measure and then, with gusto, pupils proclaiming measurements which were, to all intents and purposes, random.  Perhaps some concrete learning experiences would have eventually led pupils to the correct use of a tape measure... for example measuring one's waist, buying a suitably sized pair of trousers and then wondering why they didn't fit properly... but we don't have that kind of time.  I much prefer a learning approach that makes use of the 'More Knowledgeable Other' (Vygotsky) from the Social Development Theory approach.  This quite simply makes sense to me.  Why let other people make mistakes already made and learned from by humanity at large when placing that person in Vygotsky's Zone of Proximal Development allows the mistake to be pre-empted and instructed against.

Anyway, back to the point of my lesson on discovering pi.  In the end, pupils did take the necessary measurements, entered them into a spreadsheet on the teacher's computer and then as a group explored what happened if we added, subtracted, multiplied or divided the measurements of the circumference and diameter of a circle.  At this point we could have made notes in books or solved problems requiring application of this skill, but instead we made instructional videos showing others how to similarly discover pi.  Whether anyone will ever learn FROM these videos or not is irrelevant... the main learning of the lesson took place DURING THE MAKING of the videos - this activity appealed to the various learning styles and Multiple Intelligences identified by Gardner.