The problem:
- Students can answer questions, but only if they are posed in familiar ways: if we say “Cuban Missile Crisis”, they remember “1962”, but if we ask for “major events in the 1960s” they draw a blank.
- Students know the basics, but they can’t use them flexibly: they can tell you that 4 x 3 is 12, but they can’t tell you the factors of 12.
- Students can answer simple questions, but can’t use the same knowledge in more complicated questions: they know that Romeo is rash and Othello is jealous, but they struggle to contrast Romeo with Othello.
- Students don’t know when to apply their knowledge: when they examine a problem, they don’t recognise that they could use algebra to solve it.
In each case, students have some knowledge, but they struggle to transfer it; in each case, students’ learning has proved less deep and less flexible than we would hope.
Deep learning, flexible knowledge and transfer sound desirable – but what do they mean? It’s easy to critique rote learning and memorisation; we know deep learning when we see it: when students have a flash of insight connecting two ideas, for example. But I’ve always found it harder to offer viable, evidenced ways to achieve deeper learning. This update to Responsive Teaching considers ways to promote flexible knowledge and transfer, as a basis for deep learning:
- Flexible knowledge – helping students to use what they know in different ways: for example, knowing that 4 x 3 is 12 and that this means that 3 and 4 are factors of 12;
- Transfer – helping students to apply existing knowledge in new situations: for example, using knowledge of Romeo’s character flaws to evaluate Othello;
- Deep learning – supporting students to develop mental models which allow them to use their knowledge flexibly: understanding the Cuban Missile Crisis by reference to the Cold War, events in Cuba and US politics.
Inflexible knowledge: benefits and limitations
Inflexible knowledge is tied to the context in which it is learned. For example, we might introduce the concept of diffusion by describing the spread of deodorant within a room: students’ knowledge is inflexible if they can only recall diffusion by reference to deodorant, and don’t recognise that sugar dissolving is another example of diffusion. Inflexible knowledge is unavoidable: new information enters long-term memory tied to the context in which it was learned: it’s “a natural step on the way to the deeper knowledge that we want our students to have (Willingham, 2002).”
Inflexible knowledge is a prerequisite to flexible knowledge: students can only transfer what they already know; they can only contrast Romeo and Othello if they can describe their characters already. But how do we go beyond inflexible knowledge? Daniel Willingham suggests that “What turns the inflexible knowledge of a beginning student into the flexible knowledge of an expert seems to be a lot more knowledge, more examples, and more practice (2002).”
Which knowledge, which examples and what kind of practice? Our choices matter: if we practise factual-recall questions, this helps students answer further factual-recall questions; if we practise higher-order questions, this helps students answer higher-order questions (Agarwal, 2019). This post explores the pursuit of deeper learning through creating semantic memories: flexible, transferable knowledge which can be accessed without reference to the context in which it was learned and applied whenever needed. A future post will examine ways to help students organise and connect what they know.
Deeper learning: From episodic to semantic memory
I want my teaching to be memorable, but to achieve deep learning, I need students to forget about it. Imagine I’m introducing Galen, the Ancient Greek physician, and trying to make him vivid and memorable: I could use a story, or a video, but let’s imagine I dress up, describe his career, wave about different liquids to represent the Four Humours he believed influenced health, and draw how I think the body works. (We’ll assume, for these purposes, that this successfully helps students to think meaningfully about what I want them to learn). If students recall my efforts, they have formed an episodic memory, a memory of – and tied to – a specific event. Students recall their knowledge by reference to this specific episode: I may ask them to “Remember when I dressed up and chose between four different liquids… I was being Galen.”
An episodic memory is a good start, but I want students to be able to use their knowledge whenever it’s needed. If students need to use their knowledge for an exam question about Ancient medicine, I want them to be able to remember Galen without having to think back ‘Now who did sir dress up as again…?’ I want them to think about Galen when they hear a range of cues: dissection, Greek doctor, Rome. This is a semantic memory: memory divorced from it’s original context; stuff we just know. For example, I know 7 x 5 is 35: I can call this to mind without having to recall the episodic memory of when I first encountered this idea; it would be a huge barrier to arithmetic if I had to call on episodic memory whenever I needed to do a sum.
How to create semantic memories from episodic memories
Once we’ve introduced an important idea in a meaningful and memorable way, we want to help students access it without reference to how they learned it, to make the knowledge more flexible. Naturally, we’ll be asking students to retrieve key ideas we’ve introduced previously, since this increases retention, but – crucially – we can ask them to retrieve it in different contexts. Many aspects of context get bound up in episodic memories (Smith, Glenberg and Bjork, 1978): students may connect something they remember with the weather that day, or what they had for lunch; we could promote retention by asking students to retrieve ideas in in different classrooms (or with different teachers) – but this is not particularly practical.
Simpler, and more powerful, is to vary the question stimuli which trigger recall. Asking a variety of questions targeting the same idea, and giving feedback which encourages students to think about the idea in relation to different cues, significantly increases the chances students will transfer knowledge to new situations (Pan and Rickard, 2018). Having introduced Galen, I might ask:
- Who did I dress up as last week?
- What was Galen’s theory of medicine?
- Whose theory of medicine was the Four Humours?
- Name a famous Greek doctor. Outline their theories.
- Name an influential Ancient doctor and their theories.
- How did Ancient ideas influence medieval medicine?
How could I use such questions? I would space them out: this might be a term’s worth of questions. I could ask them in almost any way: as extra questions on exit tickets, reframed as hinge questions, at the start of a lesson, or as part of a weekly quiz.
More important than how students encounter the questions is the way they are designed. Each question is slightly harder than the preceding one; each offers slightly less contextual information. This makes it harder for students: it forces them to try to recall the key ideas without all the clues they had originally. This helps students practise accessing their knowledge by reference to a range of cues: Greece, Ancient medicine, medieval influences and so on. Eventually, I want them to be able to think of Galen without any clues: answering the final question would satisfy me that they could do so. Equally, any time they struggle, I might ask an easier question again: if students don’t think of Galen when I ask them ‘name a lasting influence on medieval medicine’, I can hint “someone from Ancient Greece… I dressed up…”
Conclusion
We want students to be able to use their knowledge flexibly; we want them to form semantic memories of key ideas. We can help them by making recall progressively harder, asking questions which challenge students to think about what they know using a wide range of stimuli. The key question to ask ourselves is What are all the cues I might want students to use to access this memory? In teaching that 5 x 7 is 35, this might include:
- What’s 5 x 7?
- What’s 7 x 5?
- _ x 5 = 35?
- Name two numbers I could multiply to get 35?
Whenever the chance arises to recall or reintroduce key ideas, we can use this idea of varying cues to strengthen students’ memories of the idea and create more flexible knowledge. The greater the range of stimuli, the more different ways students access key ideas and the more likely they are to be able to transfer it to new situations.
In a future post, I’ll examine ways to help students structure and organise their knowledge to access and apply these ideas.
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Detailed discussion and exemplification of various aspects of feedback in Responsive Teaching: Cognitive Science and Formative Assessment in Practice, alongside discussion of five other endemic problems in teaching.
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The key idea in planning: of what will it make them think
References
Agarwal, P. K. (2019). Retrieval practice & Bloom’s taxonomy: Do students need fact knowledge before higher order learning? Journal of Educational Psychology, 111(2), 189-209. (Helpful summary here)
Willingham, D. (2002). Inflexible Knowledge: The First Step to Expertise. American Educator. Winter.