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)
- 2008 Kia Rondos
- Kia Rondos
- Cars made by Kia
- 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? “That’s amazing, Joanne. Gosh, class, what else has interworking parts that we’ve learned about this year?”
Compound sentences! The solar system! Fractions!?
How To Move Students Towards Abstraction
If you plan your lessons around models of instruction like Concept Attainment or Concept Formation, you’ll naturally move towards abstract thinking. It’s built into the models. They purposefully move beyond specifics and ask students to consider groups or categories.
Class, looking at all of these examples of transportation (or stories or fractions or animals), could you form three or four or five different categories?
That’s part of the Concept Formation model. Students note similarities and differences within a set of related examples and create categories out of those examples. Different students will come up with different categories. You’ll be surprised by their thinking every year.
Or, I could have said:
Class, I’ve put these examples of vehicles (or stories or fractions or animals) into two groups. I’d like you to figure out why they are in these groups.
This is along the lines Concept Attainment. The teacher creates two groups, and it’s up to the students to analyze the examples, find the similarities and differences, and name the reason for the groups.
You could also ask students to make a huge brainstorm of possible categories:
What are all of the categories that my 2008 Kia Rondo (or this story or this fraction or this animal) could be a part of?
Well, my car belongs to the categories of “hatchbacks” and “automobiles from 2008” and “vehicles.” But also “transportation”, “systems”, “paradoxes”, “technology”, and so on.
If you use Universal Themes, you can always end with a question like: which of our generalizations does this lesson make you think of? Maybe “Systems have interworking parts?” or “A system can be part of a larger system.”
Go The Other Way: Abstract to Specific
Now, we could also move from abstract to specific. Let’s break the abstract concept of “vehicles” into more specific categories.
Vehicles could include cars, trains, aircraft, boats, motorcycles, bikes (?), roller skates (???). Note that, by getting more specific, I am thinking in new ways. It forces me to consider, well, what exactly is a “vehicle?” Is a bike a vehicle? Heck, what exactly is a car? Is a truck also a car? What’s the actual definition of a truck vs. a car? This is interesting thinking, spurred by moving from abstract to specific.
To get more specific, we can ask:
What are all of the examples of this idea that we can think of?
If you’ve ever used Concept Formation, you’ll note that this is that model’s first step: students brainstorm lots and lots of examples of an abstract idea.
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.“
(Notice that I’d give that idea to my class. As teachers, we need to raise the ceiling with ideas that our kids won’t necessarily come up with independently. Too often, I’d just ask kids to come up with their own big ideas. But it’s important to do both throughout a week: offer advanced, teacher-generated ideas AND let kids think up their own.)
So, then, you can take this “opposites yet related” idea further:
Class, are there any other examples of things that are opposite,… yet also closely related? You can go beyond math. 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 thinking! Students are pondering things that are opposites, yet very similar in some way.
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.
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