Deep learning (2): structuring and organising knowledge – responsive teaching update

What comes next?

James I, Charles, I, Charles II, James II, _________
2, 3, 5, 7, __
Je suis allé, je vais, j’irai; j’ai été, je suis, _________
A B A B C D C D E F E F _ _
Helium, Neon, Argon, Krypton, _______

Some of these clues may feel frustratingly cryptic: readers know A, 2, and perhaps ‘je suis’; they know about neon lights, and probably something about Charles I. Answering depends not just on what we know however, but on how it’s organised: the answer seems obvious once we recognise the structure (answers below). Deep learning means developing mental models – organised knowledge structures – which allow students to apply their knowledge flexibly: this post discusses the architecture of mental models; what structures and organisation make knowledge usable?

Mental models: organising knowledge usably

Flexible knowledge is an important step towards deep learning. If an item of knowledge is flexible, students can access it via a range of cues, not just the ones they originally learned. So – for example – flexible knowledge of Charles I would allow them to think about him when asked about the Stuarts, Ship Money, or the Divine Right of Kings (more on this here). This flexibility supports transfer of knowledge to new situations – a big achievement in itself – but, a sophisticated mental model is more than a plethora of knowledge: it’s organised.

A sophisticated mental model is a library, or an internet, which organises and connects ideas so they can be recalled and used. Understanding expertise means appreciating both the “quantity” of knowledge and “the form in which it is held in long-term memory”: to analogise, it’s not just “the book’s contents”, but also “the access routes to those contents, that is, its index (Larkin et al., 1980, p.1336).” Novice doctors learn anatomy and physiology: they develop expertise by experiencing clinical cases, which challenge them to access (and structure) their knowledge of the body as they will use it when treating patients (Schmidt and Rikers, 2007, p.1134). People develop expertise, first by learning more, then by structuring what they know usably.

The power of mental models

Mental models help students comprehend and retain new information. They provide a structure against which to test/through which to view this information: if students encounter a new letter for the first time, knowing what letters are and how they can vary (height, width) makes distinguishing the new letter’s defining features easier: a ‘t’ is like an ‘l’, but with a cross-stroke. Moreover, if thinking about the meaning of information is “the core principle in learning”, structure and organisation are critical to making new information meaningful: Charles I’s actions are more meaningful (and more interesting) when students understand his context and the constraints upon him; an unseen poem more meaningful if students understand the choices the poet has made.

Mental models also allow students to apply their knowledge to answer questions accurately and solve problems creatively. The first step in solving a problem is understanding it’s demands: when confronted with a physics problem, experts rapidly identify the underlying structure – ‘this is about friction’ – allowing them to solve it; novices focus on surface details: ‘this is about a block on a slope’ (Chi, Glaser and Rees, 1982). A mental model of poetic forms allows students to recognise that a poem is a sonnet, or to write a sonnet themselves. A mental model of the Seventeenth Century makes sense of Charles I’s actions by placing them in a political and religious context. A mental model of atomic structures explains the characteristics of helium and how it can be used. Mental models allow students to put their knowledge to work.

We recognise students effective use of mental models, but how we can help students’ develop them is less obvious. We need to teach the utility, use and creation of knowledge organisation (Reif, 2010), but it’s hard enough ensuring students recall the basics: this may be why teachers and textbooks “pay much more attention to the content of conveyed knowledge than to its organization (Reif, 2010, p.157).” If we are to develop students’ mental models, we need to know what a useful mental model looks like: to identify the structures and connections which help students make sense of and organise their learning.

Three ways to organise knowledge

Knowledge is best structured in the way in which it will be used: for doctors; the helpful knowledge structure links the distinctive features of a clinical case with its diagnosis (Schmidt and Rikers, 2007, p. 1134). We may organise knowledge by considering:

1) Underpinning structures

The most useful organising structures are likely to be intrinsic to the forms of thinking the discipline demands – how students will be asked to use the knowledge: chronology in history, linking literature to its contexts in English, connecting symbolic representations, atomic models and actual experiments in chemistry. There are likely to be no more than a handful that matter: our first step is to identify these underpinning structures. Often, we use them tacitly, without recognising their importance (or how tricky they are).

Question 1: What organisational structures are intrinsic to the discipline?

2) Hierarchies

Within these underpinning structures, we can place ideas into hierarchies. Why hierarchies? Reif (2018) suggests that, of four forms of knowledge organisation, a hierarchy is most useful (after random organisation, a list and a network), because it allows us to ‘view’ ideas at a range of scales: students can compare James I and Charles I (both Stuart monarchs), or can compare Stuart and Tudor monarchs. Students can compare helium with argon, or noble gases with metals. A memorable hierarchical structure is likely to have no more than three levels (Wright, 2007): poetry – sonnet – Petrarchan; gas – noble – helium; human geography – settlement – urbanisation.

Question 2: What hierarchies can be used to organise key ideas?

3) Links

Reif prefers hierarchies to networks, but Wright (2007) suggests that human history has seen ongoing competition between them, and that they can be used together. An early example in human history would be the categorisation of plants: hierarchical taxonomies are useful (tree – deciduous – oak) but so are crosscutting themes (edible plants). It’s helpful to place Charles I as a Stuart monarch (hierarchical); it’s also helpful to jump the Channel, and a century, to compare his situation with that facing Louis XVI before the French Revolution (network). The potential links and themes are infinite, so those we prioritise are likely to be specific to the curriculum: knowing students learn Oliver Twist in Year 7, I can connect this to their study of the Industrial Revolution in Year 8; knowing they study rivers in Year 4, I can connect this to natural disasters in Year 5. Claire Sealey suggests curricular links can be:

Horizontal – same year, different subjects
Vertical – same subject, different year, and
Diagonal – different subject, different year

Her students learn about tyranny with King John in Year 1 and revisit it with Hitler in Year 6 (vertical); read Holes in Year 6 with a tyrannical warden (horizontal) and meet the pharaoh in Exodus in Year 3 (diagonal).

Question 3: What links across hierarchies offer fresh insight?

Conclusion

There are (at least) three steps to expertise:

Learn the basic knowledge – students cannot organise what they do not know
Develop flexible knowledge, which students can access in response to many relevant cues
Organise and link ideas to create mental models which can be applied to solve problems/answer questions/whatever

If we are to organise and link ideas, we need to:

Identify disciplinary structures (perhaps 4-5 for a subject of which 1-2 will be relevant in a specific topic)
Place key ideas in hierarchies (2-3 for a topic)
Identify the most important links (no more than five for a topic)

Once we have chosen the most powerful organising structures we need to develop students’ knowledge of them. I’ll suggest ways to do this in a future post.

What comes next: 1) William and Mary (monarchs of Stuart England) or Cromwell/the Commonwealth (rulers of England in the 17th century); 2) je serai (future tense of être); 3) 11 (prime numbers); 4) G G (rhyme scheme in the English sonnet); 5) Xenon (Noble gases – Group 18 in the periodic table).

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