February  2014     Edition 99
Teaching Abstract Thinking

There's a huge quantity of written information about Abstract Thinking

. A Google search on it yields over 18 million results, so the definition, explanation and opinions about Abstract Thinking are plentiful. Here are mine:

First, let's define Abstract Thinking

and then a little about how to teach it.

Abstract Thinking

- The ability to:
•    Understand and separate context from content.
•    Generalize from a set of specific circumstances
•    Compare different situations and recognize common elements
•    Connect the dots, i.e. understand the relationships between events
•    Understand the meaning behind words, events, and situations

Concrete Thinking

- Usually defined as the antonym of Abstract. It is the here and now, what is at face value, the literal translation.

An example of Concrete vs Abstract thinking might look like this;

Two people observe a train go by. One person sees a locomotive with smoke billowing from the engine, followed by 82 train cars full of coal, crossing the tracks in front of him. He comments; "Look at that train pulling all those train cars" The other person nods, and says, "That coal might eventually result in supplying thousands of homes with electricity". Both kinds of thinking have their place, and are valuable.

We all have the ability to use both concrete and abstract thought

. Some are more adept then others at one or the other. When it comes to solving new problems, one of the key strengths you want people to exhibit is abstract thinking. You need this so they can apply a disparate knowledge base to a new problem and solve it

Abstract thinking is a learned process.

When you were four years of age, someone may have said that you'll be going to school in about a year. The concept of "a year" was very new. You just got used to what "tomorrow" meant. The "day after tomorrow" was still tough, but a "year", oh my! Perhaps that's why little kids keep asking "are we there yet?". The abstract concept behind time, while trivial to you today, was very confusing when you were four. If you think you've got time mastered, think about this. Scientists believe the age of the universe, is about 13.8 plus billion years old. Hard to imagine. Harder still is the concept that before that time, there may have been no time, that is, time itself did not exist. Now that's abstract.

There's a lot more to say about abstract thinking, but let's just hone in on one particular aspect of it, which is how do you teach someone an abstract idea?

Take counting

. When you first learn to count, you might do so my counting your fingers. One day, as you're sitting on your high-chair with a plate of peas, you're parent says, "Hey let's count the peas". You probably had a hard time. Peas are not fingers. You know how to count fingers, but counting peas ... who does that? You eat peas, you don't count them. You count fingers, you don't eat them. Very different. But you watch and you listen. You watch others count. You listen to them think. They count fingers, toes, peas, pennies. They count all the time. Eventually, you get it. Counting isn't about fingers, it's about "how many". You just transitioned from Concrete to Abstract thinking (at least for counting).

We are all capable of learning many abstract notions

the first time we are introduced to them, but we all have difficulty and need help in some areas. For example; You might be really good at abstracting ideas related to projects and planning and time dependencies, but not be as versed in abstraction related to financing, accounting, balance sheets and ROI strategies.

One of the things I've learned in teaching critical thinking

is that in order to get someone to understand the abstract, it really helps to give them a bunch of concrete examples. Then you introduce the generalization (the abstract) of the concepts that you are trying to get them to understand. But you're not done. If you want them to remember the abstract, you have to go back to the concrete examples again, and show them how those concrete examples fit into the generalization.

Here's an example;

Algebra is one of the first mathematical abstractions you learn as a student, and one of the basic steps to get there is to learn to add. Teaching a child the abstraction of adding might look like this.

Give three concrete examples about adding:

•   Concrete Example 1: If you have 3 apples and I give you another apple how many apples do you have? (Four)
•   Concrete Example 2: If you have 6 apples and I give you another apple how many apples do you have? (Seven)
•   Concrete Example 3: If you have 10 apples and I give you another apple, how many do you have? (Eleven)

Introduce the Abstract

Abstract: If you have 3 or 9 or 25 apples, or any amount, and I give you another apple, you'll always end up with one more than you had. So if we use the letter "n" to just be a symbol that stands for how many apples you have, then after I give you one apple, you now have n+1 apples.

Going back to the examples ...

•   If you have 3 apples to start, we'll say "n" means 3, then if I give you an apple you now have n+1 or 3+1 apples, a total of four.
•   If you have 6 apples to start, we'll say "n" means 6, then if I give you an apple, you have n+1 or 6+1 apples, a total of seven.
•   If you have 10 apples to start, we'll say "n" means 10, then if I give you and apple, you have n+1 or 10+1 apples, a total of eleven.

Repeat the Abstract:

So "n" just stands for the number of apples you have, and n+1 is the number of apples you have after I give you one."

It's a lot of words, and a lot of time. But next you learn n+2, and n+3, and n+m, and then n-m, and then 2n+m, etc.

Here are the rules

I found successful to help others understand and abstract idea.
(a) give at least 3 examples that are concrete
(b) introduce the abstract connection
(c) show how the very examples you used in (a) fit the abstract connection
(d) repeat the abstract connection

Here's a business example that taught me a great lesson many years ago.

I was developing computer graphics software that created pie, bar and line charts. I was invited to show the software to very senior executives at a very large energy company. The software was very powerful and easy to use. You could just plug in a few numbers and out came a chart. (This was all before Powerpoint was even a thought !). Anyway, I thought I would demonstrate a Pie chart, so I created one called "Boxed Pizza, kinds of pizza consumed" and one "slice" was labeled Pepperoni, and "slice" was labeled "cheese" and a third "slice" was labeled "Mushroom". I thought it was clever (at the time).

The executive from this very large company said, "Pretty chart, but we don't do pizza here". I quickly brought up the entry screen and changed "Boxed Pizza .. " to "Oil consumed", and changed "Pepperoni" to "Texas Crude", change "Cheese" to "North Sea Crude", and changed "Mushroom" to "Alaskan Crude". Eyes lit up, and they asked, "what about these products", and I quickly created another chart. Then they gave me one other to do. Then I said, "you could create a pie chart (or bar chart) for any of your products". They purchased three copies on the spot.

The lesson I learned here and never forgot

is to be very careful not to begin with the abstract, but begin with concrete examples, and then, once understood, introduce the abstract.

There are many ideas and techniques to help those understand the abstract.

I found an interesting article related to this subject written by Mark Ylvisaker, Ph.D. While it was published by an organization related to brain injuries, he has a section that is applicable for teaching abstract thinking, titled Facilitating the Development of Abstract Thinking. I thought it was a good read. Here's the link. http://www.projectlearnet.org/tutorials/concrete_vs_abstract_thinking.html

The Takeaway
: Teaching someone an abstract idea takes patience. Start with concrete examples. Introduce the abstract and then tie it back to examples. Repeat so the learning sticks.

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