My schema of schemas

I really like using journeys and travelling as analogies about learning – I’ve written about them before when I wrote “Let’s go for a walk”. I love thinking of topics and ideas through the lens of schemas. I’ve read lots on schemas (and other bits too) and whilst writing about “the kernel of truth”, I realised that slowly an analogy has been developing in my head for schemas that encapsulates some other ideas from cognitive science.

Efrat Furst has some amazing diagrams of schemas, showing them as dots and lines. They clearly show the interconnected network of knowledge that we want to form in the minds of learners about our topics. The individual dots or nodes of network are often thought of as the individual ideas or objects, and the lines are the links between them. Over time we want to add new ideas (new nodes) to the network and increase the number of connections to old ideas too (the lines).

My analogy

As an expert (in physics), I can pluck stuff out of “thin air” because my schema is very linked together and one idea leads to another. This means that I can quickly whiz around my network of knowledge and I don’t get lost. My network is well travelled so the roads are wide and well maintained so I can travel from one idea to the next quickly and I can still get to even the oldest of ideas rapidly. The network is well signposted so I know exactly where I’m going and it’s hard to get lost.

The width of the road gives me the ability to travel faster.

The signposting of my network means I know where I am within it.

An expert has a mental network akin to a complicated motorway system — wide roads, well-signposted. You can move from A to B to C very quickly and know where else you could have gone.

Novices are different. We are explicitly trying to build their schema (often from scratch). To begin with, they are much slower to travel around their own network and it’s easy for them to lose their way as they travel. They need to spot the footpaths they’ve only travelled once or twice but there are no signposts (so it’s easy to not get to where you intended). The roads are narrow and overgrown so it takes a long time to get around.

A novice has a mental network akin to some newly formed paths in the woods — narrow and not signposted. You take ages moving from A to B to C, possibly getting lost and not knowing alternative routes.

The only way to get from novice to expert is to continue to travel around the network and make more sense of it as you go. Not just creating new paths and new locations (expanding the network/your knowledge), but continually traversing the old paths, widening them and signposting them.

How to help develop a novice’s developing network

This is a blog for another day but one thing I’m looking into this year is Advanced Organisers - a simple depiction of the ways in which ideas are connected. They look a little like mind maps, but the links between topics are labelled (much in the way that we discussed schemas earlier). This is a work in progress but I’ve seen ideas from multiple places (Theory of Instruction by Engelmann and Carmine as well as Sarah Cottingham’s book about Ausubel’s work and Christian Moore Anderson’s book on biology teaching) that, in a “kernel of truth” sense, make me think there’s definitely something here to delve into.

I’ve looked at these before and my temptation is to get sucked in and make a HUGE one detailing all of the links and thoughts an expert might have. But on reading Engelmann and certain parts of Sarah’s book on Ausubel, I think I see a huge utility in more focussed, smaller ones to begin with to help students explicitly see the links.

As I say, this is a blog for another day as I start to develop them.

How to test a novice’s developing network

The temptation I have is to sample students’ schema randomly looking for specific nodes or specific links. And this might strengthen one link or help to ensure that students don’t forget a specific link. But I’d like to develop my own practice significantly in this area:

This year, I’m going to be looking more at elaborative interrogation – I’m going to ask students to explain more widely what they have understand about an idea or topic. More open-ended questions that get them to more explicitly interrogate their own understanding and write it down. I think this will take some scaffolding to achieve which is where the advanced organisers will play an important role.

Anyway, back to the analogy…

Links to retrieval strength and storage strength

If you’re unsure of the distinction, the Learning Scientists have a great guest blog on the topic

The Learning Scientists Blog

My takeaway is that:

• Retrieval strength is how quickly you can bring things to mind. When retrieval strength is high, you bring it to mind quickly. When retrieval strength is low, you bring it to mind still but it takes a while.
• Storage strength is how well-embedded an idea is. When storage strength is high the information is stuck forever. When storage strength is low, it won’t be remembered long into the future.
• You can think of them as being on different axes so an idea being easy to retrieve doesn’t mean that it’s got high storage strength.

In my road based analogy each of the two ideas appear as:

• Retrieval strength is the width of the road and how permanent the road has become (dirt track, gravel path, tarmac path, tarmac road, giant motorwar)– how quickly can I get to the idea?
• Storage strength is how well signposted the turnings are – can I get back to the idea at all? If an gets to a point that it’s signposted so clearly (high storage strength) that you don’t need to travel there frequently, you know it’s there and you can always get back to it (because it’s clearly signposted). The roads might deteriorate slightly and it might take longer to get there (low retrieval strength), but you will always make it back.

You can imagine roads that are wide and empty but terribly signposted. These are ideas with high retrieval strength (I can feasibly get to them quickly) but low storage strength (it’s hard to get to them again later on). This applies to new content that we’ve learned and is a state we often find our students in.

You can equally imagine the opposite, a well-signposted network but of roads that are not maintained well and have deteriorated with obstacles abounding (think of any major road network in some dystopian future where virus/zombies/war has broken out). Here, you can still get around the network (as it’s well signposted) but it’s no longer quick as the network is not well-travelled. These are the ideas that you hold onto for ages but may take a while to bring to mind. This is the state we’d actually like our students to be in when they leave us — some ideas or ways of thinking about the world that are stored so deeply that they’re always accessible. Considering what these ideas are for each subject is a really interesting way to spend/waste an hour or twelve!

I’d like to explore this idea more over a few more posts. I’d love to hear any feedback! I’m @tchillimamp on Twitter/X or @drchillimamp on Threads.