When planning a lesson, it’s helpful to think about where your content lands on the spectrum of abstraction. On one end of the spectrum, we have highly specific facts. On the other end, very abstract concepts. When we move back and forth along this spectrum, it unlocks opportunities for really interesting thinking.
A Spectrum of Abstraction
Here’s a spectrum of abstraction starting with my own car. Each step becomes more abstract.
- My family’s 2008 Kia Rondo
- Kia Rondos
- Cars made by Kia
My car is an example of all of the more abstract concepts. It’s a car from Kia, it’s an example of transportation, and, yes, it’s an example of a system (which is one of the Universal Themes from the Depth and Complexity Framework).
And each level is an example of the more abstract concepts. “Vehicles” are examples of “transportation” and “systems.”
To get more abstract, we can ask ourselves (or our students):
- What is this idea an example of?
- What category or group does this belong to?
- What big idea or saying does this fit with?
We could also move back down and get more specific. We might break “vehicles” up into more specific categories: cars, trucks, boats, motorcycles, bikes (?), roller skates (?) (note that by getting more specific, I am thinking in new ways – what exactly is a “vehicle?” Heck, what exactly is a car?).
There is value in getting more abstract as well as getting more specific. It’s the movement that matters.
To get more specific, we can ask:
- What are some examples of this?
- What’s the definition of this?
- What might we find in a folder with this label?
Beware Staying At One Level
You’ve probably experienced teachers or presenters who focused too much on one end of this spectrum. Neither side is good by itself:
- Too many specifics: endless examples, graphs, anecdotes, without a clear message to guide it all
- Too much abstraction: big ideas that sound nice but leave you wondering “what would that actually look like?”
To really understand an idea, we have to understand its context within the spectrum of abstraction. We need specific examples, but we also need the broader, more abstract connections. We need to move students up and down the spectrum to activate thinking.
Yes, students need to know the steps to perform addition, but they also need to understand that the concept of addition is related to subtraction and multiplication and division. They’re all operators. You put two numbers in, something happens, and a new number pops out.
This leads to interesting ideas like “addition and subtraction are opposites… yet they are closely related.“
Then you can take that idea and abstract it further:
Class, are there any other examples of things that are opposite,… yet also closely related? Let’s go beyond math. Think about it tonight and let me know what you come up with.
You might hear ideas like:
- Ice and vapor
- Carnivores and herbivores
- Darth Vader and Luke Skywalker
- Anna and Elsa
- My little brother and me!
Friends, this is thinking! When we move from specific to abstract, we open up opportunities for new ideas, unexpected connections, and (in my opinion) lots of fun.
There’s so much we could do with this idea that “opposites can be related.”
- If Vader and Luke had to pick, which one would be addition and which would be subtraction? Why?
- Which is more like addition, carnivores or herbivores? Why?
- Is Anna or Elsa more like an herbivore? Why? Give me specifics.
To Get Started
So, to start, look at your next lesson. What’s the content? Is it abstract or specific (it’s probably pretty specific)? Can you move your lesson towards the other end of the spectrum?
Let’s say you have to teach:
- The water cycle. Well, this is a system that repeats. So, what other systems are there in nature that repeat? What about human-made systems?
- The electromagnetic spectrum. Oh! This is an example of a paradox! It is both helpful and deadly at the same time. What else do we know about that is a paradox?
- Irregular plurals. This is an example of how rules can have exceptions. What other rules do we know about that have exceptions?
- Solving for a variable in algebra. These steps are all about preserving balance. What other situations involve preserving balance?
- The causes of the War of 1812. This was a war where neither side was in a great position to fight a war. What other events have occurred where no one wanted it to happen, yet it happened?
When we move the content towards abstraction, it sets the stage for comparing and contrasting, categorizing, forming opinions, and even creating new ideas. We open up all of Bloom’s higher order thinking skills.
Now (based on those earlier examples) we could ask:
- Which repeating system is the most likely to fail?
- Which paradox is most paradoxical?
- Which rules’ exception most strongly violates the rule? Is it fair to have this exception?
- When is it ok to not preserve balance? When is it harmful to preserve balance?
- Rank your ideas based on how positive the outcome was for all of these events.
These all began with grade-level, specific content, but I’ve raised the ceiling, connected across disciplines, and given my advanced students something to really chew on.
What will they come up with? I don’t really know! And that’s how you know they really have an opportunity to think.
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