Soviet school education as summarised by my dad

I have enjoyed following many debates about education since I joined Twitter and begun reading blogs. To get a bit of perspective on some of the things being discussed, I’ll sometimes ask my parents for their perspective and about their experience. They both went to school in the USSR, my dad also completed his degree in Leningrad.

I asked my dad about his memories of the Soviet education system. What strikes me is the importance of subject disciplines within the programme of study, and yet the fact that maths wasn’t a subject per se. Also, the fact that the best elements came from the Prussian gymnasium system is telling. And there’s an interesting reflection on a very specific type of group-work. Here’s what he wrote as I translated it (original Russian from his email to me is at the bottom of the post):

The successes of the Soviet Education system in the post-war period (from 1945 to the end of the 70s) were predicated on the inevitable need to maintain the military-technological race with the West. A mass of literate engineers and technicians was needed, able to read technical drawings, make basic calculations, master some sort of machine or mechanism. And the Soviet regime did not spare resources and effort on this – which was not so difficult to achieve in a country where the average standard of living was indeed very low. And the teaching profession, despite the low wages, was very prestigious – as opposed to today.
Until the end of the 40s, the basic provision of secondary education was seven years of school – to 14 years old, after which the majority of teenagers went to work or to a specialised technical school (tekhnikumy), either daily or in the evenings. From the end of the 40s, the basic provision expanded to a ten year model to the age of 17 (in towns, not in the villages). From the fifth to the 10th classes the sciences (hard and natural sciences) were taught very thoroughly – in more detail than in the West – and this is something that the immigrants from Russia were convinced of when they found themselves in Israel or in the USA in the 70s – so their level of preparation in the hard sciences turned out to be, as a rule, higher than their peers.
For instance Soviet schools did not have a subject called ‘mathematics’. Until the fourth class you were taught arithmetic, and from the fifth to the tenth class you had separate lessons in algebra, geometry, to which were added trigonometry in the final two years as a separate subject. Further sciences were taught as distinct subjects – physics, chemistry, biology and human anatomy, and even astronomy in some schools. In the cities, nearly every school you had physics and chemistry lab equipment – separate spaces with necessary equipment, setup, instruments etc. In some schools you even had biology labs. Of course I’m talking here about European and Siberian parts of the USSR, In central Asia the situation was worse – there they had fewer ten-year school programmes.
The educational system was founded on principles developed in Germany in the 19th century and widely adopted in the Russian empire. The German approach to education is systematic (and regular). In each subject the emphasis is made on each subject’s place in the universal order of things. That is to say on the subject-specific theory and foundations that belong to it, and how it differs from other fields of knowledge. For example, what does physics concern itself with as opposed to chemistry, or chemistry from biology. Secondly, the curriculum [literally – programme of study] is detailed and cumulative, designed over a 3-4 year sequence. Thirdly, the responsibility for the fruits of his efforts lies with the individual efforts of each pupil – and in order to strengthen this responsibility exists a system of assessed work and exams – both oral and written.
In the 20s and 30s the Bolsheviks still experimented with school education. For example, a so-called ‘brigade method’ was introduced, when one or another aspect of knowledge had to be mastered not by the individual, but by a group of students, or a ‘brigade’. Classes were grouped into small groups of three to five students, each group was given a separate task, and the marks were given collectively, and not to any individual student. But what would you do with the lazy ones? After the war, this method was rejected. In an unofficial way (for the fifth – tenth classes), the Gymnasium system of pre-revolutionary Russia was restored. At its core: cramming, obligatory use of summaries of each subject, obligatory homework, random marking of homework during the lesson which was graded, written coursework every three or four weeks or at the end of every term (of which their were four not three), exams in certain subjects at the end of each school year – i.e. in June. What’s more, in algebra, geometry and physics the exams were written exams. If you failed your exams you had to resit them in September.
That’s about all that I can remember right now. Pose me questions and I’ll try to answer them in detail as much as possible.
 

Some context for The Brilliant Club Inaugural Conference

When we began our work at The Brilliant Club, it was part-project, part stab-in-the-dark. Jonny Sobczyk and Simon Coyle, who founded the organisation, ran the pilot at the school where I was teaching at the time and, taken by the idea and the possibility of setting up an actual organisation of our own, I decided to join them in the venture. We attained charity status in early 2012 and, just over 2 years on, are very proud of the scale and quality of the work we are doing across 4 regions of the UK (London & South East; Midlands; East of England; North East England).

The problem that we exist to solve is a very specific one within the broader debates and activity around social mobility: at highly selective universities the number of students from non-selective state schools, and in particular from the poorest backgrounds, is disproportionately low. The Sutton Trust provides a swathe of research on the issues, slicing through the data in a number of different ways – here is one particularly pertinent example about uni progression rates by individual school – and also making recommendations. The Higher Education Funding Council for England also analyses students’ secondary to HE progression rates. In 2010, when setting up The Brilliant Club, we looked at their report on trends in youth HE participation. A few key trends and findings stick out for me personally:

  • In 2010, at the 25 most academically selective universities in England, only 2% (approximately 1,300 pupils each year) of the student intake was made up of Free School Meal pupils, compared with 72.2% of other state school pupils, and just over a quarter of the intake (25.8%) from independent schools. This proportion may be changing, but only slowly and with huge regional variation.
  • 80% of disadvantaged young people – those from low HE participation neighbourhoods – live in the vicinity of a highly-selective university, but only 1 in 25 of these disadvantaged young people attends such a university (compared to 1 in 4 from the highest HE participation neighbourhoods). (Link here, page 5)

Within these two research findings, we had a defined problem and a potential solution: given the proximity of schools serving low participation communities and universities, there would surely be a way of building good links between them. What was needed was a scalable way of doing so that focused on meaningful academic experience to develop realistic aspirations and improve attainment, giving timely and accurate advice, and creating a precedent for progression to highly selective HE courses for pupils from low-participation backgrounds. Of course there is a huge amount of widening participation and fair access activity already ongoing – it is a growing part of what universities do (look at the latest WP budgets for next year here). We wanted to add to the effort as the problem is big enough to warrant multiple solutions and collaborations.

We have found that the PhD and post-doctoral research community is perfectly placed to be this link. Our PhD tutors – selected at an assessment centre that looks for their ability to communicate and their motivation for working with young people – have a wealth of subject expertise, a passion for their area of study, extensive experience of universities (and in many cases the world of work). They design courses for small groups of pupils that the school will select to take part in the programme. The pupils are selected using a mixture of contextual factors (such as eligibility for FSM and parental history of HE) and teacher discretion. The courses are based on an aspect of the PhD tutor’s research and will be categorised as ‘Arts & Humanities’, ‘STEM’ or ‘Social Science’. From the pupils’ point of view, it is like being taught a university module with a final assignment at the end that will be graded in a university-style (1st, 2.1 etc.). All courses include trips to our partner universities. We work with Year 5s upwards because we believe that starting the conversation with pupils when they are younger helps give them time to inform themselves about progression to university before it becomes necessary for them to make any decisions. At crucial transition points between key stages, starting young helps equip pupils with some very important perspectives on where their education can take them.

I want it to be normal for academics to be seen in schools and for pupils from all backgrounds to think of university – including the most highly-selective courses and institutions – to be their right and entitlement. It is rewarding, therefore, when the conversation with the pupils we work with moves on from “what is university?” to “which course would I enjoy the most?” to “I wonder whether I would want to do a PhD myself?”. And at the same time, it is incredibly rewarding to see what our PhD tutors get from it. As a lapsed teacher, I didn’t quite realise initially how exciting it is for an academic to teach their particular area of research as opposed to a general ‘introduction to…’ undergraduate course. Moreover, the Research Councils of the UK have a strategy of Public Engagement that encourages researchers to take their specialisms to non-expert audiences. Some of our PhD tutors have gone on to become teachers (including through http://www.researchersinschools.org – the new ITT partnership launching in September). Others have remained as teachers and researchers in academia or moved to industry. We hope their professions are enriched by a more detailed understanding and experience of the state education sector.

The Brilliant Club Inaugural Conference will be taking place at King’s College London on Thursday 24th July, bringing together academics, teachers, widening participation professionals and third-sector organisations like our own. It is fully booked, but we have a livestream from the main lecture theatre which will capture the panel debates and keynotes. At this conference we hope to begin to answer the question:

How can universities and schools help pupils from low-HE participation backgrounds secure places and succeed at highly-selective universities?

Have a read of the programme and take a look at our livestream here. If you’re on Twitter then please get involved @BrilliantClub and on #BrillWP14

Finally, can you find your school on this POLAR 3 dataset? How likely young people are to participate in HE varies across the UK mapped out by small local area.

Open invitation to University Learning in Schools: A research project for London

Two recent trends within secondary education in England have led us at The Brilliant Club to join in collaboration with Achievement for All and the GLA to run a research project exploring ways to enhance KS3 teachers’ subject knowledge and pedagogical skills. These two trends are:

  1. GCSE reform which aims to assess pupils across more challenging content.
  2. Efforts to engage further with research across the profession, as epitomised by initiatives such as ResearchED.

We asked ourselves a question: would a partnership between researchers (who possess exceptional subject knowledge) and teachers (who possess the pedagogical experience), help improve student outcomes?

Over the last term, five teacher-researcher pairs have created academic units of work to enhance teacher knowledge and teach aspects of their research to KS3 pupils. The units of work have been taught, and will be disseminated at a free CPD event for KS3 teachers on Friday 4th July. The day will have three parts – a keynote presentation from Sam Freedman, Director of Impact and Research at Teach First, an academic lecture by the researcher which will teach the subject-knowledge to the delegates, and an afternoon workshop by the teachers that taught the module to disseminate the resources.  Teacher delegates will be able to attend an English/Humanities/Science stream for the day.

We are finding that the teachers involved saw the benefit of this approach in preparing KS3 pupils for the new GCSE qualifications, and their reflections will form part of the workshop that they will give in the afternoon when presenting the free materials. The researchers are from King’s College London, UCL, CERN and Warwick University. A (brief) summary of each module can be found in the table below:

English Language

How we use talk and writing to develop understanding 

Explores the importance of talk and the ways in which we talk as we learn, considering the use of technology in providing a means for a form of ‘talk’ through text-based communication.
English Literature

Travel Writing

Introduces pupils to travel writing extracts from the nineteenth and twentieth centuries. From Byron to Patrick Leigh Fermor, via Mary Kingsley, this module will further pupils’ knowledge and understanding of life-writing, descriptions of place, and recounting exploration, adventure and discovery.
Geography

Global Childhoods

Explores concepts of children in society and introduces learners to a global perspective of what it is like for children living around the world. This module will introduce the theoretical underpinnings of ‘childhood’ from a biological and sociological perspective, and apply them to children in the home, at work, in school, and at war.
Biology

Antibodies:Weapons of Microbe Destruction

Focuses on antibodies starting with their function in tackling pathogens, in the immune system to application in medicine and in the research laboratory.
Physics

LASERs: Cutting Edge Science

Explores the diverse applications of laser technology and the crossover with physics, using Quantum Theory, Electromagnetic Waves, Optics and Thermodynamics.

 

From attending educational research conferences over the last couple of years, it has become clear that, provided it is structured in a manageable way, many teachers are keen to be part of an educational research project. Should it still be of interest, we are offering further opportunities for delegate who attend to get involved in the research project:

  • Teach the resources that you receive in your school and let us know what impact this unit of work has on your pupils.

and/or

  • Register your interest in being partnered with a PhD Researcher next academic year to design a KS3 unit of work of your own.

More information and free signup is here: http://bit.ly/freecpd. I hope this is of interest to:

  • School leaders/teachers responsible for curriculum design, teaching & learning, and preparation for GCSE reform
  • KS3 subject teachers looking to improve their subject knowledge
  • Non-specialist teachers in English, Humanities (Geography) and Science (Biology/Physics).

Could we crowd source concept maps for what we teach? #ResearchED #Touchpaper

At ResearchED Birmingham last weekend, Alex Weatherall and I used our presentation to sound out the delegates on an idea that stemmed from our previous discussions on Touchpaper Problem 4: determining the complexity of a concept. Many thanks to everyone who attended and listened to us. Even more thanks to those who have since been in touch with reviews, comments, questions and suggestions.

Physics concept map

I have blogged previously about why a concept map is a useful thing:

  • … it makes you think about the order you do things in as a teacher.
  • … it helps you pitch work at the right level for your students.
  • … you can become more confident in sequencing units of work.
  • … it identifies gaps in your own subject knowledge.
  • … it provides you with a diagnostic for correctly identifying your students’ misconceptions.
  • … it can help you pre-empt difficulties.
  • … it involves identifying threshold concepts that probably take more time to teach.
  • … it could help you work out an assessment structure.

The question then becomes about what is the best way of putting together a concept map for school subjects that is

  1. comprehensive enough to serve these uses.
  2. tailored for teachers.
  3. accurate.

Our inspiration is two-fold: Galaxy Zoo (and the Zooniverse) that crowd sources the classification of galaxies, and Wikipedia which invites contributions from all, but has an editing policy to ensure accuracy (click here to have a look at the different levels of editor you can get to!). We would like to see if it is possible to create an interactive software that over time would help display and categorise the key concepts in the subjects that we all teach.

We do not think this work would need to be done from scratch. Although it may seem like a daunting task, the plethora of curricula, schemes of work and concept maps already in existence means that many teachers are already doing this. We need to find the best way that this can be shared and coordinated.

In our research to date we have encountered several key thoughts around complexity that have influenced our approach:

1) Complexity is not the same as difficulty

When something is complex it is because it is made up of many parts. This can be objectively determined by identifying them. When something is difficult, the pupil finds it strenuous, requiring more effort. This might depend on prior knowledge and is subjectively determined. However (and this is where it becomes a little confusing), there is usually a correlation between something that is more complex also being more difficult. This is because if something requires more prior conceptual understanding, it will be more cognitively demanding.

2) Some concepts are more important than others

There is a lot of research, spearheaded by Jan Meyer and Ray Land, into Threshold Concepts. I highly recommend that people read a short introduction to the idea here, from which I pull the following definition:

A threshold concept can be considered as akin to a portal, opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something without which the learner cannot progress. As a consequence of comprehending a threshold concept there may thus be a transformed internal view of subject matter, subject landscape, or even world view. This transformation may be sudden or it may be protracted over a considerable period of time, with the transition to understanding proving troublesome. Such a transformed view or landscape may represent how people ‘think’ in a particular discipline, or how they perceive, apprehend, or experience particular phenomena within that discipline (or more generally).

 Alex and I propose that if it is possible to map concepts and how they link to each other, it is possible to identify which are the key threshold concepts as they will probably have the most links, bringing together a varied, and perhaps unexpected, range of subject concepts. This is a hypothesis that will need testing, but might provide an answer to the Touchpaper problem as it might determine the complexity of concepts.

3) Linguistic complexity is important

In many of our discussions, Alex and I felt that some concepts were more difficult because they were not easy to explain in words. We also know from teaching that homonyms and homophones can cause pupils difficulty because they confuse meaning. What we propose, is that a concept map may include a linguistic dimension. This might take the form of a glossary or links to the etymology of key conceptual terms and provide teachers with a tool that both improves the definitions that they can give of each concept, and helps identify potential misconceptions before they happen.

Is this not just remapping a national curriculum?

No – a curriculum includes detailed content as well as concepts, but is prescriptive. It does not give you a complete map of the subject area as it has already selected what must be taught. This is not to say it is wrong, but it does mean that as a teacher you might be unaware of the full complexity of a concept and how it links to other areas of the curriculum. This is a particular problem when teaching non specialist subjects as happens frequently at primary level, and between subjects such as mathematics and physics at secondary. A particularly pertinent example might be the new computing curriculum which requires an understanding of binary, which is not included in the mathematics curriculum (as far as we are aware!). From a brief survey of the teachers at our ResearchED session, most agreed that a large, accurate and detailed concept map would be a useful tool to improve the planning of units of work.

Practicalities

There is still a long way to go with this project and many questions to resolve. At the end of the presentation we proposed a timeline for anyone who is interested to get involved in the project. If you don’t think we’re completely bat crazy – do complete the form below and we’ll be in touch.

Why should we study complexity? Reflection 1 on #Touchpaper problem party

For a context for this reflection, please read the previous two posts.

In this blog I have compiled a short list of the reasons why determining the complexity of a concept is so important for teachers. In subsequent blog posts I will unpick some of the discussions that we had when trying to solve this knotty, philosophical question.

Determining the complexity of a concept is important because…

1) … it makes you think about the order you do things in as a teacher.

In our discussions on Saturday we identified three broad stages each teacher needs to go through to help their students understand difficult concepts:

a) Map out their topic area into linked and ordered concepts.

b) Consider what barriers and difficulties students might experience in trying to understand a given concept…outside of the inherent difficulty of the concept.

c) Check for their students’ conceptual understanding…preempting and engaging with misconceptions.

2) … it helps you pitch work at the right level for your students.

If you work out how complicated a concept is, then you can work out how quickly your students might grasp it, what prior stage in their understanding they might need filling in, what they might need reminding of or, alternatively, what they might already find too easy.

3) … you can become more confident in sequencing units of work.

How do you order the concepts in your subject? Historically (as they were discovered), chronologically (as they ‘happened’), empirically (by working out what most people know vs what most people don’t know), in order of complexity (simple to complex) or spiralling (to repeat the most difficult of concepts several time)? Or a mixture of some/all of them?

4) … it identifies gaps in your own subject knowledge.

I remember being told at teacher training that if you can’t teach something to someone else, you probably don’t have mastery of it. Now while this might not be true in the completely literal sense, there is a grain of truth behind it at least: if you cannot break down complexity in your subject area in order to explain it to someone else, you probably need to do some more work getting to know the subject area! Mapping out your subject concepts is very useful for identifying these areas.

5) … it provides you with a diagnostic for correctly identifying your students’ misconceptions.

If a student doesn’t ‘get’ something, you can use your understanding of how the concepts within your subject area link together to identify dependent concepts that need to be taught prior to the student being able to ‘get’ the thing you were trying to teach them in the first place.

6) … it can help you pre-empt difficulties.

Mapping out complexity and considering why students might find something difficult means that you may be more likely to choose a more appropriate range of teaching techniques to suit the teaching of that topic. When you stop to ask yourself if a concept is counter-intuitive, or if it requires a lot of prior knowledge, or whether you have prepared sufficient examples to explain it, then you are more likely to have identified a difficulty that you can plan for.

7) … it involves identifying threshold concepts that probably take more time to teach.

Subject disciplines have paradigms particular to themselves. Some of these are counter-intuitive, others can be considered ‘troublesome’ because in understanding them, you subvert a preconceived notion or previously held knowledge. The idea that light can be considered a wave or a particle in physics. The idea that a reader constructs meaning in literature. The idea that cooking is all about energy transfer. These have been termed threshold concepts and may need more time devoted to them as they are so crucial. Once you grasp a threshold concept, it’s very difficult to forget; it shapes your understanding of the whole discipline. In future blogs I will look at some examples to see how this applies across the subject disciplines.

8) … it could help you work out an assessment structure.

In order to write an assignment with a metric of some sort, teachers encounter the need to devise a mark scheme or set of success criteria. Within each subject these are different depending on the stage that the pupil is learning at. This forces the teacher to determine the complexity of a concept because they have to find out at what point they can award a top mark, at what point they differentiate for complexity and how much of the complexity the students need to grasp at the given stage in their learning. By way of example: a top mark for an 11 year old’s essay about a piece of literature, would be less difficult objectively speaking than the top mark for an undergraduate analysing the same text.

These are some of the justifications for why this #touchpaper problem is worth deliberating further.

Party Planning: My thoughts on #Touchpaper problem 4 – what determines the complexity of a concept?

On Saturday I will be facilitating the #Touchpaper Party organised by Dr Becky Allen and Laura McInerney at the IOE. Here are some brief thoughts on the problem that my group will be tackling. Read a background to this here.

Problem #4: What determines the complexity of a concept?

Laura McInerney has put this problem into a teacher’s context for us here. If you haven’t already, please read it first. For most references to Wittgenstein I am deeply grateful to Dr John Taylor for sending me his excellent lectures on the philosopher which distilled some very complex concepts indeed!

Proposed definitions:

  • Complex: made up of more than one. (Not to be confused with difficult).
  • Concept: an essence; an idea; a process; a category of real or imagined existence.
  • Difficult: finding something not easy, often requiring more knowledge resulting from a cognitive overload.

Here are some “givens” – both premises, observations and assumptions.

1. It’s personal, and therefore relative.

“There is a temptation for me to say that only my own experience is real: ‘I know that see, hear, feel pains, etc., but not that anyone else does. I can’t know this, because I am I and they are they.” (Wittgenstein, Blue and Brown Books, p. 109)

We are all so complex ourselves that there are several reasons why we might understand things in different ways: our brains are wired differently, we perceive things differently, we make different assumptions and so on.

However, in theory, the teacher has control over one variable which unlocks this dilemma: teaching a whole group the same thing to bring them to the same level of knowledge and understanding.

Except in practice, that doesn’t always happen because pupils’ prior knowledge is so varied and mastered to such different degrees. And knowledge cannot be abstracted and isolated from context.

This is why difficulty of understanding is relative: because what might be considered easy for one pupil is difficult for another.

Equally, the complexity of any given concept is relative: as Laura suggested, a 7 year old and an 18 year old can all understand ‘appeasement’, but to different levels.

2. Context is crucial to understanding.

“If the development of vocabulary knowledge substantially facilitates reading comprehension, and if reading itself is a major mechanism leading to vocabulary growth which in turn will enable more efficient reading-then we truly have a reciprocal relationship that should continue to drive further growth in reading throughout a person’s development.” (Keith Stanovich, Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. 1986)

If the concept is presented in a context where little related fact is known, it becomes more difficult. If it is presented in a context which is familiar it becomes easier.

The more you know, the easier it is to learn more, as Stanovich demonstrated in his seminal paper on the Matthew Effect in reading. 

The analogy of the Matthew Effect can be applied to our acquisition of knowledge through a range of metaphors. It could be said that knowledge is a net in your mind whose mesh becomes finer and finer the more you know, and makes it easier to trap and hold on to new knowledge that falls through your mind. It could also be said that knowledge has mass – the more you know, the larger the mass and the larger the gravitational pull, making it easier to attract new knowledge and ensuring it attach itself.

Context can also change meaning, however. Depending on how the concept is used, it will mean different things.

3. Language is crucial to understanding.

“It seems that there are certain definite mental processes bound up with the working of language, processes through which alone language can function. I mean the processes of understanding and meaning.” (Wittgenstein, Blue and Brown Books, p. 3)

 So if we delve into each student’s mind to work out what they know, how they understand and at what level of complexity they engage with a concept, we bump up against the transmission of knowledge through language. 

Language is tied up with meaning and understanding. And conceptualisation.

This leads us to suggest that the conduit metaphor for language might have its limitations. Could it be said that the language is the knowledge or this is an oversimplification?

4. Clarity of language is clarity of thought.

“[The English language] becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts. The point is that the process is reversible. Modern English, especially written English, is full of bad habits which spread by imitation and which can be avoided if one is willing to take the necessary trouble. If one gets rid of these habits one can think more clearly.” (George Orwell, Politics and the English Language)

Whether it is an oversimplification or not, the language that someone uses provides us with plenty of clues as to how well they understand something. The more clearly they write or speak, the more clearly they probably understand the concept.

Here is a suggested flow diagram of the expression you make of conceptual understanding:

A. what a concept means in a given context > B. what you understand the concept to mean > C. what you intend to say > D. the language you use > E. what is understood.

Let’s assume that A is objectively true. At every other stage there is scope for misunderstanding and a lack of clarity: you could be guilty of mis-conceptualising in the first place, you could be guilty of meaning something illogical or untrue, you could be guilty of choosing the wrong language to express yourself, you could, in turn, be misunderstood.

5. Language can be a barrier.

“Texts in social sciences and humanities tend to be loaded with grammatical metaphor, as they construct and evaluate abstract concepts about social life.” (David Rose and J.R. Martin, Learning to Write, Reading to Learn, p. 195)

Language can obfuscate (as George Orwell suggests above) or it can just be difficult for a student, especially if the concept is complex or abstract enough so as to be beyond their current level of knowledge.

Therefore we need to unpack the complexity of the concept. This often means ‘de-nominalising’ abstractions – “by turning them back into activities that involve people and concrete things, and making logical relations between activities explicit with conjunctions” (Rose and Martin, p. 196).

Denominalising means unpacking the noun form. For an abstract concept, a noun is a proxy for the abstraction – a noun is not a name or an object.

Not all nouns are names. Concepts are often nominalised (i.e. turned into nouns). In order to unpack them we need to denominalise them. Grammar can be misleading here. If I ask “what is the sun?” that is not the same as asking “what is time?” The sun is an object. Time is something more problematic, and intangible in comparison.

Metaphor can also be misleading, especially when it is embedded in what we think of as ‘correct’ language.

But not all concepts are abstract concepts.

6. Concepts that can be understood scientifically are actually processes and can be sequenced in order of complexity.

“You can’t understand electrolysis unless you know what an aqueous solution is.” Juan Casasbuenas, in the staff kitchen, yesterday.

First you explain what an ion is, then solutions, then electrolysis…

There is a sequence to teaching concepts that are actually processes. The best sequence is subject-specific and determined by the learner’s prior knowledge.

The teacher: identifies the end-point concept that must be understood, ‘reverse engineers’ the concept to its constituent parts, sequences the constituent parts into the most logical order drawing on their own subject expertise to do so, identifies at which point along the sequenced conceptual continuum the learner currently finds him or herself and begins teaching from that point. This is scaffolding and sequencing and planning as we know it.

The learner: relates to the material that is first being taught because they recognise it. They then build new knowledge onto this, constructing their own understanding with the help of the teacher. 

We can also see that for certain complex concepts it is possible to break them down into their constituent parts. This would be a scientific approach. 

7. We need different ways of thinking: scientific and philosophical.

“Wittgenstein claimed that this obsession with generality was a result of our obsession with science. Science seeks to reduce the variety of the natural world to a few, primitive natural laws. It seeks to explain the world’s diversity in terms of laws which are framed using natural kinds of property, such as mass, force, temperature, charge, etc. The scientific method is tremendously powerful, and it is tempting for philosophers to emulate it – to try to reduce the diversity of language to simple, generally applicable definitions. But this tendancy to copy science, in Wittgenstein’s opinion, leads into ‘complete darkness’.” Dr John Taylor, lecture on Wittgenstein.

What Wittgenstein refers to as generality is the tendency to believe that a concept can have a single, simple, definition. This goes against what I have suggested in point 2.

This summary of Wittgenstein’s thought in the quotation above demonstrates why a philosophical approach is necessary to answering this question; when it comes to understanding and meaning (both complex concepts in their own way), we risk running around in circles if we’re looking for generality, when meaning can change depending on the context of the concept.

That said, there is clearly a scientific approach that is relevant in certain contexts.

So what next?

Suggestion for how to tackle Touchpaper problem #4.

Behind the problem as it is currently phrased are the following ‘sub questions’ which can be addressed in turn:

1) What is ‘meaning’?

This will address some of the problematic philosophical questions that arise and will therefore require a philosophical approach, drawing on subject specialisms. Some suggested topics could include:

    • how language is used to create meaning
    • how the essence of an idea remains separate from the language that we use for it

2) How can I tell if my students really understand?

This will address the issue of understanding being personal to each student and of ascertaining the prior knowledge of each student, as well as working out how much they understand along the way to conceptual mastery. Some lines of inquiry could include:

    • how does what students say and what students write help us gauge their understanding on a scale from novice > expert?
    • what range of techniques is required in order for a true assessment of learning to take place and which techniques assess for which type of learning?

3) How does one best scaffold and sequence content for mastery?

This will address the issues of building complexity, especially for those concepts which are also processes. Suggested approaches could include the following:

    • What is the best way to scaffold the introduction of new knowledge for linear or scientific complexity (that deals with cause>effect)? This would have to be addressed by subject experts, perhaps with reference to threshold concepts.
    • Is it possible to teach conceptual mastery through teaching language and grammar? This could draw on the advances of genre theory (a defence of this approach by Frances Christie, addressed to Michael Rosen, complete with reading list) and language-based pedagogy (a link to what this looks like in practice, with thanks to Lee Donaghy).

Please do have a read and let me know what you think, folks.

TouchPaper Problem #4 – What determines the complexity of a concept?

Laura McInerney

This is the fourth blogpost expanding on the TouchPaper Problems first discussed at #Researched2013 and due to be tackled at the first TouchPaper Problem Party.

Question #4 – What determines the complexity of a concept?

In my estimation, this is the hardest of all the problems, but it’s also really important.

As a teacher I was constantly trying to figure out “how difficult is this material?” and gauging whether I needed to edge it up or scale it down depending on the students I was teaching. But: how do we know if something is complex?

I remember working with a history revision class who were learning about the appeasement. I didn’t think appeasement would be a difficult concept. I mean, kids appease each other all the time in the playground when they, say, allow an older bullying set of kids to play football with them, even if they don’t…

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