When creating a lesson, let’s think about where our content lands on the spectrum of abstraction.
I know, it sounds like a mouthful, but the idea is to ask students to think about both highly specific facts AND larger, more abstract concepts within a lesson. When we move back and forth along this spectrum of abstraction, it naturally unlocks opportunities for really interesting thinking.
The movement is key!
Moving from Specific to Abstract
Here’s a sample spectrum of abstraction starting with my very own car, a Kia Rondo from 2008. We start with this highly specific example and get increasingly abstract.
- My 2008 Kia Rondo (most specific)
- All Kia Rondos
- Cars made by Kia
- Cars
- Vehicles
- Transportation
- Systems (most abstract)
I went all the way to the very abstract idea of “Systems” (Hey! That’s a Universal Themes from the Depth and Complexity Framework!).
When students realize that a car is a system, they can then connect my junky ol’ hatchback to other systems, like governments, the human body, or ecosystems. That is powerful! Wouldn’t you love to hear your students notice that a car is related to Ancient Rome because both of them have interworking parts? “Gosh, class, what else has interworking parts that we’ve learned about this year?” Compound sentences! The solar system! Fractions!?
But I Don’t Teach Cars…
If you are reading a story, zoom out and connect to other stories, movies, myths, comics, folk tales, video games, etc. Notice how characters, themes, settings, and plots are all abstract ways that specific stories can connect. Hey, I have a whole series about this. And, hey, is a story another system since it’s made up of all of those interworking parts? How is a similar to a system like an engine?
Learning about your city? Make sure to also connect to Tokyo, London, and Rio de Janeiro. Connect across time to 1800s New York City or early Rome. Look at tiny villages. Look at aircraft carriers! Look at the International Space Station! How do all of these ideas connect? A city is a system. And so is a clock and a school and a laptop. How are cities like laptops?
Studying animals? Note how animals in one biome have a similar role to animals in another. Are sharks more like leopards or gorillas? Look across time for related animals serving the same role. Do plants serve similar roles? What job do people in cities have that is similar to this animal’s role? Do animals form a natural type of government? Which form of human government is this most like?
As we move towards abstraction, it becomes easier to connect to unexpected content areas and ask really interesting questions. But then we want to bring students back to specifics so they can explain their thinking.
Move Back and Forth (and Back Again)
Let’s say that your students have learned the steps of addition. Don’t stop there! Move them towards a more abstract idea. Well, addition is related to subtraction. They’re both operators. And yet. They’re opposites!
I might present my class with the interesting idea that 🏛️ “addition and subtraction are opposites but they are also closely related.“
And I’d give that idea to my class, asking:
Class, are there any other examples of things that are opposite,… yet also closely related? Feel free to go beyond math into any topic you like. Think about it tonight and let me know what you come up with.
You might hear ideas like:
- Carnivores and herbivores
- Darth Vader and Luke Skywalker
- Ice and vapor
- Anna and Elsa
- My little brother and me!
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.
Friends, this is interesting! When we move from specific to abstract and vice versa, we open up opportunities for new ideas, unexpected connections, and (in my opinion) lots of fun.
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. It repeats itself since it’s a cycle. 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 (visible light) and harmful (ultra-violet or x-rays) at the same time. What else within the electromagnetic spectrum is a paradox? How about within our earth science unit? What is similar to the electromagnetic spectrum in this way?
- Irregular plurals. This is an example of how rules can have exceptions. What other rules do we know that have exceptions? How does this relate to the American Revolution? Are their rules with exceptions in that unit?
- 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 anyway? Has this happened in our classroom? At your home?
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 get more specific and continue asking higher-level questions:
- 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.