How to Teach Abstract Or Higher-Order Concept Knowledge

How to Teach Abstract or Higher-order Concept Knowledge

Martin Kozloff
2012

We’re going to teach kids abstract or higher-order concepts. A procedure that’s effective (that is, most kids learn from it) and efficient (that is, most kids learn fast and with hardly any mistakes) is pretty simple. But to design an effective and efficient procedure, you have to know the following.
What We Need to Know
1. What an abstract or higher-order concept is. (Kame’enui and Simmons, 1990).
2. How teaching the identified abstract concept fits in your curriculum.
3. What lessons look like.
4. We are working on the first phase of learning and teaching---the acquisition of knowledge—using explicit instruction. After acquisition, we will work on generalization to new examples, fluency, and integration of knowledge elements (e.g., concepts) into larger wholes, such as essays.
5. We must decide when to teach a concept with a synonym and examples, and when to teach a concept with a verbal definition and examples.

1. What an abstract or higher-order concept is.
There are two kinds of concepts: basic or sensory concepts and abstract or higher-order concepts (Kame’enui and Simmons, 1990). The thing about sensory concepts is that:
a. Their defining features (the sameness in certain features in all examples) are tangible; you can see, hear, smell, feel, or taste the features; and
b. Any example shows all of the defining features; the features are all right there in front of your face or ears or nose.
So, you can teach basic concepts just by showing and naming examples. “This is a triangle.” Or, “This is red.” Or, “This is straight.” And then you show contrasting examples (“This is red.”) with nonexamples (This is NOT red) that are the same in NONdefining features, but are DIFFERENT in the DEFINING features.

“This is red.” “This is not red.”
(1) Same in nondefining features: size, shape. (2) Named differently (red, not red). (3) So, the way they are the same logically CAN’T be why they are named differently. (4) Different in defining feature (color). (5) So, logically, the way they are different (color) MAKES the difference in how they are named.
However, with abstract concepts,
a. Some defining features are NOT tangible; they are themselves abstract; you can’t directly see, hear, smell, or feel then.
b. Each example may not show all of the defining features. For instance, any example of red (a basic concept) will show THE defining feature---redness. But every example of democracy (an abstract concept) may not show all the defining features at once.

For example, voting is a defining feature of democratic political systems (the concept). You might show an example of Athens in the fifth century BC (a democracy), but Athenians were NOT having a vote at the time. Maybe they were at war. So, basically, you can’t bring an example of an abstract concept into class and say, “Here’s (a democracy, a forest, a galaxy, plate tectonics, volcano).

Instead, to teach an abstract concept you have to either:
a. Give a synonym (a more common word) that means the same thing as the
new concept.
b. Give a verbal definition that TELLS the defining features. And then show examples that ALL
have the defining features (and call them the same thing---“This is a democracy.”) and
contrasting NONexamples that do NOT have the defining features (and call them
something different from the examples---“This is NOT a democracy”).

2. How teaching the identified abstract concept fits in your curriculum.
Your state’s and district’s standard course of study, scientific research, expert opinion, and your own expertise will help you to establish objectives (what students will DO) for a whole year or course. For instance, among many other objectives in a science curriculum,
“Students will:
a. Define ecosystem, desert, rainforest, ocean, and salt marsh.
b. Correctly identify examples and nonexamples of ecosystems, deserts, rainforests, ocean
and salt marshes.
c. Make a diagram of a model, with verbal explanation, of threats to salt marsh
ecosystems, and how salt marsh ecosystems deteriorate.
These final objectives will help you establish objectives for units, and unit objectives will help you establish objectives for each lesson. For instance, given the final science curriculum objectives, the UNIT on ecosystems, and therefore LESSONS in the unit, will have to teach the concepts identified above. It will also have to teach concepts such as convection cells, equilibrium, feedback loop, and acceleration.
3. What lessons look like. A lesson is a sequence of tasks.
a. Review and firm what was taught earlier; e.g., system, natural system, elements and
wholes, boundaries.
b. Teach new item; e.g., the concept, ecosystem. Modelà lead à testà correct errors or
verify correct answers.
c. Teach more.
d. Review and firm it all.
e. Integrate earlier and new knowledge into something larger, if possible; e.g., a diagram
of a model of ecosystem.
4. We are working on the first phase of learning and teaching---the acquisition of knowledge. We will use explicit instruction to ensure that most kids “get it” quickly and with few errors.
After acquisition, we will work on generalization to new examples and integration of knowledge elements into larger wholes. For examples, students might use earlier and new concepts and rules to diagram and describe relationships among parts of a salt marsh ecosystem.
5. When to teach a concept with a synonym and examples, and when to teach a concept with
a verbal definition and examples.

a. Use synonyms to teach concepts that are defined by FEW features, and so you can give the synonym definition quickly. For example, huge (very big), unalienable right (part of being human, can’t be taken away), monarchy (rule by one person).

b. Use verbal definitions plus examples and nonexamples to teach concepts that are defined by many features, and when these features are themselves NOT tangible objects. Political system, economics, galaxy, nebula, justice, democracy. These have so many features that you can’t find a synonym (one or two words) that means the same thing. You’d have to give a verbal definition that TELLS the features, followed by examples that SHOW the features.
Let’s see when she could use synonyms and when we should use verbal definitions plus examples. Here’s an introduction to solar systems from a science for kids website. Some words (concepts) can be defined with synonyms WHILE you and/or students read it. Other concepts are more complex, and are so important, that you would PRE-TEACH these with verbal definitions and examples. I’ve added synonyms, [in italicized brackets] below, as if I we reading the document to students for the first time. I’ve put in bold face concepts that I would pre-teach.

How did the solar system form? This is an important question, and one that is difficult for scientists to understand. After all, the creation of our Solar System took place billions of years before there were any people around to witness it. Our own evolution [changes over time in our species] is tied closely to the evolution of the Solar System. Thus, without understanding from where the Solar System came from, it is difficult to comprehend [understand] how mankind came to be. Scientists believe that the Solar System evolved [develop] from a giant cloud of dust and gas. They believe that this dust and gas began to collapse [parts got closer and closer, like squeezing a piece of paper into a small ball] under the weight of its own gravity. As it did so, the matter contained within this could begin moving in a giant circle, much like the water in a drain moves around the center of the drain in a circle.
At the center of this spinning cloud, a small star began to form. This star grew larger and larger as it collected more and more of the dust and gas that collapsed into it.
Further away from the center of this mass where the star was forming, there were smaller clumps of dust and gas that were also collapsing. The star in the center eventually ignited [caught flame] forming our Sun, while the smaller clumps became the planets, minor planets, moons, comets, and asteroids.
Once ignited, the Sun's powerful solar winds began to blow. These winds, which are made up of atomic particles being blown outward from the Sun, slowly pushed the remaining gas and dust out of the Solar System. sastronomy.com/solar_system.htm

So, before we start reading or teaching from the document, we would teach the concepts: solar system, billions of years, gravity, matter, star, planets, minor planets, moons, comets, asteroids.
solar winds, atomic particles.
1. We would teach some of these concepts (atomic particle, billions, gravity, matter) much earlier, perhaps near the beginning of the science strand in our curriculum, because these concepts apply to just about everything ON the strand. However,
2. We would teach solar system, star, planet, minor planet, moon, comet, asteroid, and solar wind only a few lessons earlier (and review up to the current lesson) because it is only NOW that these concepts are relevant.
And we would do this teaching by:
1. Giving a verbal definition.
2. Making sure students SAY that definition and define each main concept IN it.
3. Giving an acquisition set of examples that show the features identified in the definition, and
nonexamples that don’t have the features identified in the definition.
4. Testing students by asking them either: (a) whether each instance is or is not an example,
with a follow-up question (“How do you know?”) that requires students to USE the definition to judge each instance; and/or (b) to identify each instance. “Is this a monarchy?.... How do you know?”

Okay, let’s begin.

Teaching Higher-order Concepts with Synonym Definitions Followed by Examples

The easiest way to teach the definition of a higher-order concept is with SYNONYMS.
Huge means real big.
Equal means the same.
Ignorant means lacking knowledge.

Using synonyms is fine for concepts or vocabulary words used in everyday life. Or for getting through a novel.

“Hey, Joe, what’s obtuse mean?”
“It means a block head, like you.”

Here are examples of teaching higher order concepts with synonyms.

Teaching the Concept—Practice--with Synonyms

Student talk is in italics.

Gain attention and frame task

Boys and girls. Here’s a new word [point to word on board.] practice.

What’s our new word? practice.

Spell practice. p r a c t I c e

What word? practice.

Yes, practice!

Model. Practice means to do something over and over to get better.

Test. What does practice mean?... doing something over and over to get better.

Verification. You got it. Practice means doing something over and over to get better.

More models. He sings a song over and over to get better at singing. He practices singing.

She paints pictures over and over to get better at painting. She practices painting,

Test

She jumps rope over and over to get better at jumping rope. Tell me….she practices or not practices?... practices.

How do you know? She jumps rope over and over to get better.

Verification. Correct! To practice is to do something over and over to get better. And she jumps rope over and over to get better. So, she practices.

Test. They do NOT read books over and over to get better at reading. Tell me…they practice or not practice?... Not practice.

How do you know? Practice means to do something over and over to get better. They don’t do something over and over to get better. So, they don’t practice.

Verification.

Excellent! You said the definition of practice so you could tell if the kids practiced or did not practice reading!

Application

I’ll say a sentence with old words and then I’ll say that sentence with our new word.

She is writing her letters---a b c’s---over and over to get better and better at writing letters.

I’ll say that with our new word. She is PRACTICING writing her letters.

TEST. Your turn.

I’ll say a sentence with old words and then YOU’LL say that sentence with our new word.

He is riding his bike over and over to get better at riding his bike.

Say that with our new word?

He is practicing riding his bike.

Etc.

If you are reading stories with little kids, it’s easy to tell which words/concepts you could teach with synonyms. kitten = very young cat. garage = a building where you park cars. sofa = couch rodent = rats, mice
But some text will have some concepts that can be taught with synonyms and other concepts that should be taught with verbal definitions plus examples.

So, you have to decide when: (1) you can just give synonyms; versus (2) you need to give a more complete definition. Let’s practice.
Here’s the second paragraph of the Declaration of Independence. The objectives are:
1. Students will define a set of concepts (e.g., unalienable rights, just powers, consent of the
governed, despotism, and others); and
2. Students will identify the main rule statements, restate them as simple declarative
statements, and arrange these statements into the theory of representative
government. For example, this long sentence,…

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness…

…becomes this:
“All human beings are created equal.”
“All human beings have unalienable rights.”
“The unalienable rights if all human beings come from their Creator.”
“All human beings have the unalienable rights to life, liberty and the pursuit of happiness.”

Now, which concepts can be defined with synonyms WHILE you teach, and which should be defined EARLIER (pre-taught) with verbal definitions and examples? Which of these pre-taught concepts would you teach MUCH earlier because they are relevant throughout the course, and which could you teach a few days before you work on the declaration?

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.
That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.