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.
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“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,
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“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. Model lead  test 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.
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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.
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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.
http://www.kidsastronomy.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
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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
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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
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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.
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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.
1. Which concepts could you teach with synonyms WHILE you and students reads the text? List
them.
2. Which concepts should you teach with verbal definitions and examples---BEFORE you work
on the text? Both:
a. Which should you teach MUCH earlier in the curriculum—because they are relevant to
most all of the curriculum? List them.
b. Which might you teach a few days earlier and then review before you started on the
Declaration? List them.
Here’s how I see it.
Let’s say you’re going to read the text it aloud while the class reads along. I would use
[synonyms] to teach the concepts in brackets and italics WHILE we read the text. I would use
verbal definitions to teach the concepts in bold face. I would teach some of these much
earlier, because they are relevant throughout the curriculum, and I would teach others for a
few days before we deal with the Declaration. Like this.
We hold these truths [rules of nature] to be self-evident [obvious to anyone], that all
men [human beings] are created equal [equal in their rights], that they are endowed
[provided, given] by their Creator [God] with certain unalienable Rights, that among
these are Life, Liberty, and the pursuit of Happiness [the right to pursue your own
interests]. That to secure these rights, Governments are instituted among Men,
deriving their just powers [not just plain power, but power that is considered just by
the citizens] from the consent of the governed [rulers don’t take power; they are
given power by those who consent TO be governed].
That whenever any Form of Government becomes destructive of these ends [to
secure unalienable rights of the governed], it is the Right of the People to alter or to
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abolish it, and to institute new Government, laying its foundation on such principles
[rules of how the government will be organized and operated] and organizing its
powers [such as different branches will have power to do different things, such as war
and legislation] in such form, as to them shall seem most likely to effect their Safety
and Happiness….But when a long train of abuses [acting against the unalienable right
of the people]and usurpations [taking power not consenting to by the governed],
pursuing invariably the same Object evinces a design to reduce them under absolute
Despotism, it is their right, it is their duty, to throw off such Government, and to
provide new Guards for their future security.
So, I would teach the following concepts:
1. Rights, form of government (monarchy, aristocracy, democracy, republic), power, and
branches of government much earlier in the curriculum, and then review these right before
we worked on the Declaration. But I would teach the concepts
2. Declaration (as a form of argument), absolute despotism, and unalienable rights shortly
before working the document, because it is only NOW that they are relevant.
Whether much earlier or right before, I would concepts 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, here are
The Basics Of Teaching Higher-Order Concepts With Verbal Definitions And Examples
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What does a good verbal definition look like? Genus and difference. Here’s a VERBAL
definition of the higher-order concept—constitutional republic.
A constitutional republic is a state where the head of state and other officials are
representatives of the people and must govern according to existing constitutional law
that limits the government's power over citizens.
http://en.wikipedia.org/wiki/Constitutional_republic
The definition has two parts: genus and difference.
Genus. A constitutional republic is a STATE (a political relationship between government and
citizens).
The genus is the larger category or concept in which constitutional republic in located. The
genus tells you what KIND of thing something is and what KINDS of things it isn’t. A
constitutional republic is not a society. Not a geographic thing, like mountains. And not
anything that other species do. However, constitutional republics are not the only kind of (not
the only member of the class of) states. Other kinds of states are monarchies, democracies,
and aristocracies. So a full definition has to tell the difference between constitutional republic
states and other kinds of states. This is the difference part of a verbal definition.
Difference. …. where the head of state and other officials are representatives of the people and
must govern according to existing constitutional law that limits the government's power over
citizens.
The difference part of the definition tells the difference between constitutional republics (as
ONE example of state) and OTHER kids of states, such as monarchies, democracies, and
aristocracies.
A diagram of the verbal definition looks like this.
Political states [largest category]
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Constitutional republics
Monarchies
Aristocracies
Democracies
Particular, individual examples of democracies, aristocracies, etc., are INSIDE each smaller
circle.
Note: There is no such thing as a true definition. Rather, some definitions are better
than other definitions; they are better at directing attention to the right events. So, definitions
are better when:
1. They state the genus and the difference.
2. The difference part of the definition contains enough descriptors (features of the
thing defined) that it can easily be distinguished from other kinds of things in the
class (genus).
Here’s a poor definition.
Dogs are canines (genus) with four legs (difference).
The genus part is okay. Dogs ARE in the class of canines---along with wolves, foxes, and
coyotes. But the difference part is so skimpy that you can’t USE this definition to distinguish
dogs (as canines) and foxes, wolves, and coyotes (as canines) because all of them have four
legs.
Here’s another poor definition.
Monarchy is a form of government (genus) in which one person rules (difference).
Yes, monarchy IS a form of government (or state) in which one person rules, but the difference
(one person rules) does not tell enough to distinguish monarchies and other forms of
government in which one person rules. Dictatorships are also rule by one person. So, if a
student reads about a dictatorship, the student might WRONGLY judge it to be a monarchy. So,
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the difference portion should include more features of monarchies (in contrast to
dictatorships). Here’s a more descriptive definition.
A monarchy is a form of government (genus) in which supreme power is absolutely or
nominally lodged with an individual, who is the head of state [by virtue of hereditary
ascension], often for life or until abdication…The person who heads a monarchy is called
a monarch (difference). http://en.wikipedia.org/wiki/Monarchy
Now look at a good definition of dictatorship. It is good because it is useful---it enables you to
distinguish monarchy (rule by one person) from dictatorship (also rule by one person).
A dictatorship is defined as an autocratic [one ruler. MK] form of government in which
the government [means the same as “supreme power is absolutely or nominally lodged
with an individual”] is ruled by an individual, the dictator, without hereditary ascension.
http://en.wikipedia.org/wiki/Dictatorship
3. All of the words have clear meaning; that is, the words in the definition clearly point to the
events named.
Poor definitions.
A donut is a kind of pastry that is shaped like a donut. [Yes, but what is a
donut shaped like?]
Fear is an emotion that involves being afraid. [Fear and afraid mean the same
thing. So, the definition is just saying Fear is an emotion at involves fear.]
Here’s an example. Student talk is in italics.
Procedure for Teaching Higher-order Concept: Simile
Set up
1.
Objective
The teacher presents examples and nonexamples of simile and asks, “Is this a simile?” When
students answer, the teacher asks, “How do you know?” Students correctly identify similes and
nonsimiles, and use the definition to explain their answer.
2.
Frame.
Teacher. “New figure of speech. Simile. [writes on board.]
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Spell simile.”
Class.
s i m i l e.
Teacher. “What word?”
Class.
Teacher.
s i m i l e.
“Write it in your notebooks.” [Check to make sure they do this.]
Focused Instruction
3.
Model—lead—test/check.
Teacher. “Listen. A simile is a figure of speech [genus] in which two unlike things
are compared, using the words like or as [difference between similes, as figures
of speech, and other figures of speech, such as metaphors.]” [Model]
The larger class [genus] of figures of speech
The class of metaphors. “His temper is volcanic.”
The class of similes. “His temper is like a volcano.”
The class of hyperbole. “His breath comes straight from
hell.”
Teacher. “Listen again. A simile is a figure of speech in which two unlike
things are compared, using the words like or as.” [Model]
Teacher/ “Say it with me. A simile is a figure of speech in which two
Students
unlike things are compared, using the words like or as. [Lead]
Teacher. “Your turn. Define simile.” [Test/check]
Students. A simile is a figure of speech in which two unlike things are
compared, using the words like or as.
Teacher. “Yes, you said that perfectly!” [Verification]
Teacher. [Students know the verbal definition. Now the teacher uses examples and
nonexamples to display the defining features of the concept that are IN the
examples and NOT in the nonexamples.]
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“Listen. The air was hot as a stove. The air was hot as a stove. Are two things
compared?” [The teacher ensure that students recall the details of the
definition.]
Students. Yes.
Teacher. “What two things?” [The teacher makes sure students USE these features to
examine examples.]
Students. Air and stove.
Teacher. “Is like or as used to compare them?” [Ensuring students focus in another detail
of the definition.]
Students. Yes.
Teacher. “So, is ‘The air was hot as a stove’ a simile?” [Students use the
definition to judge an possible example.]
Students. Yes.
Teacher. “Yes, The air was hot as a stove a simile?” [Verification]
Next, the teacher does exactly the same thing with a second example to firm up the features of
the definition and students’ use of the definition to judge a possible example.
4. Then the teacher presents a NONexample so that students (comparing the two previous
examples with the nonexample) can see the difference---the comparison of unlike things, using
like or as—between the examples and the nonexample.]
Teacher. “Listen. The evening sun was red ruby. The evening sun was
red ruby.”
Teacher. “Are two things compared?”
Students. Yes.
Teacher. “What two things.”
Students. Evening sun and red ruby.
Teacher. “Is like or as used to compare them?”
Students. No…. It said the evening sun WAS red ruby.
Teacher. “So, it compares unlike things, but it does NOT use like or as.
So, is it a simile?”
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Students. No.
Teacher. “Correct. It is NOT a simile. A simile compares unlike objects
AND uses like or as.” [Restates the definition to firm it.]
The teacher then juxtaposes a few more examples and nonexamples using the SAME WORDING
as above.]
5.
Error correction.
The teacher corrects errors immediately. For example.
Teacher. “Her eyes shined like diamonds. Simile?”
Students. A few students say No.
Teacher. “Her eyes shined like diamonds. Does it compare two things?” [Uses the
definition to help students make the judgment.]
Students. Yes.
Teacher. “What two things?”
Students. Her hair and diamonds.
Teacher. “Does it use LIKE or as?” [Uses the definition to help students make the
judgment.]
Students. Yes.
Teacher. “So, is it a simile?” [Has students make the judgment.]
Students. Yup!
Teacher. “Yup, it IS a simile.” [Verification]
[The teacher will return to this example later, to retest.]
6.
Delayed acquisition test.
The teacher tests all the examples and nonexamples used.
Teacher. “The air was hot as a stove. Simile or not simile?”
Students. Simile.
Teacher. “How do you know?” [This requires students to use the definition to judge
examples and nonexamples.]
Students. Compares unlike things….Two unlike things…. Air and hot
stove…. Uses as.
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Teacher. “Correct!! A class full of geniuses!!”
Here’s another example.
Teaching a Higher-order Concept: Convection Cell
Here’s an example of teaching an abstract or higher-order concept: convection cell. Notice how
every single statement from the teacher does something to (1) prepare the class to learn; and
(2) communicate the concept. And every response from the class does something to
communicate what they’ve learned or not learned. See explicit instruction. This is several tasks
in a science lesson. [Explanation of what’s going on is in brackets. I put numbers in to show
main parts of the instruction.] The procedure for teaching convection cells is longer than the
procedure for teaching similes. Why? Because (1) there is a lot more background knowledge
elements involved in convection cells that must be reviewed and integrated into the concept
(e.g., system); (2) the concept of convections cells must be examined thoroughly (lots of
examples) because they are have so many features and because examples vary widely (ocean,
atmosphere, pot of boiling water)----while similes are defined by a few words.
Task 1. Set up [First, we make sure students (1) are paying attention, (2) have their materials
ready, (3) are told the objectives, and are (4) firm on any pre-skills/background knowledge
needed.]
1. “Boys and girls.” [Gain attention and focus] “Okay, great. Your eyes are on me and you’re
sitting up nice and tall, ready to learn. What a great class I have!!”
“Please open (your text book to chapter 12, science lesson 12 on your computer) for today’s
lesson. Also, open your guided notes to lesson 12.”
2. “New concept: convection cell. We’ll USE the concept of convection cell in our study
tomorrow of weather and ocean current. Look at your guided notes to see what we studied
earlier, what we’re studying today, and what we’ll study next. Now we’ll review background
knowledge. Second, you’ll learn what convection cells are. You’ll tell the definition of
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convection cell and identify examples. [Objectives] And third, we’ll do an experiment on
convection cells.”
3. “First, let’s review.” [Firm up pre-skills. Also see compound.]
3a. “The concept, fluid. Read the definition with me in your guided notes. [Students read with
the teacher to increase their attention and involvement.] A fluid is a continuous (not broken
into parts), amorphous substance (amorphous means without a specific form) whose molecules
move freely past one another and that has the tendency to assume the shape of its container.”
http://www.thefreedictionary.com/fluid
[Teacher gave a quick definition of continuous and amorphous. If these concepts were brand
new or tough, the teacher would have defined them before saying the sentence.]
“So, water is a fluid. [Uses water as an example of fluid because water will be the fluid in one of
the examples of convection cell.] It is continuous and amorphous. Its molecules move freely
past one another. And in its liquid state, it conforms to the shape of its container. Give me an
example of how water conforms to the shape of its container.” [Test/check. If students
generalize to a new example, they must know the concept so far.]
Bathtub….sink…swimming pool…..ocean.
“Excellent. Yes, those examples show how water is a fluid. Its molecules move past one
another. It is continuous. And it conforms to the shape of its container.” [Teacher verifies the
correct answer by repeating the answer.]
“Oxygen is a gas. It is continuous and amorphous. Its molecules move freely past one another.
And it conforms to the shape of its container. Give me an example of how oxygen conforms to
the shape of its container.” [Another example of fluid. Test/check. If students generalize to a
new example, they must know the concept so far.]
Fills a room…Fills a refrigerator…Fills a tank.
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“Yup. Great examples. The gas, oxygen, is a fluid. Its molecules move past one another. It is
continuous. And it conforms to the shape of its container. [Teacher verifies the correct answer
by repeating the answer.]
3b. Next. Here’s a rule from yesterday. Check your guided notes….. As a substance becomes
cooler, it becomes more dense. As a substance becomes warmer, it becomes less dense. [Have
students read that rule with you.] So, if you heat water, will it become more or less dense?”
[Test/check students’ using the rule about heat and density to make a deduction.]
Less dense.
“Correct. As the water is heated, it becomes less dense.” [Verification]
“If you let the water sit there in the pot, it will cool. Will it become more or less dense?”
[Test/check students’ using the rule about heat and density to make a deduction.]
More dense.
“That is correct. As a substance cools, it becomes more dense.” [Verification]
3c. “Another rule. Among objects (solid or fluid) that are the same size or volume, the denser
objects are heavier than the less dense objects. [Have students read that rule with you.]
So, there are two containers that each contain one cubic foot of oxygen. The oxygen in
container A is more dense than the oxygen in container B. Which container has heavier
oxygen? [Test/check students using the rule about density-weight to make a deduction.]
Container A.
“How do you know?” [Follow up question to check reasoning. Did students use the rule or
were they guessing?]
If it’s more dense, it’s heavier.
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“Correct. If it’s more dense, it’s heavier. Good use of the rule.” [Verification.]
“How about water. You have two containers of water, and each container has one gallon of
water. One of the gallons weighs more than the other. And one of the gallons is more dense
than the other. Which container has denser water?” [Another test/check of students using the
density-weight rule to make a deduction.]
The heavier one.
“How do you know?” [Follow up question to check reasoning. Did students use the rule or
were they guessing?]
If it’s denser, it’s heavier.
“And which one is cooler?” [Test/check students using the density-weight rule to make a
deduction.]
The denser one.
“How do you know.” [Follow up question to check reasoning. Did students use the rule or
were they guessing?]
If it’s cooler, it’s denser.
“Yes, you got it. If it’s hotter, it’s less dense, and if it’s less dense, it lighter.” [Summarize the
rules before going on.]
___________________________________________________________________________
The Set-up part is done. Now we move to new material.
___________________________________________________________________________
Task 2. Initial Instruction (Acquisition) of New Concept
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1. “Now for our new concept: convection cell. Follow in your guided notes.” [Gain attention
and focus]
2. “Here’s the definition. A convection cell [SUBJECT] is a loop of moving fluid (such as air, or
water, or even molten rock) [GENUS] in which the motion from the bottom to the top of the
cell, and from the top of the cell back to the bottom of the cell, results from differences in
density caused by differences in temperature [DIFFERENCES].”
http://www.allwords.com/word-convection+cell.html
[Verbal definition Notice that the first part---“A convection cell is a loop of moving fluid”---is
the GENUS part of the definition. It places things that are convection cells INSIDE the larger
class (genus) of things that are loops of moving fluid. Other things that are loops of moving
fluid would be water and air churning behind a propeller; water going down the drain; water
stirred in a pot; and water or gas circulating through pipes. So, the next part of the definition
(the DIFFERENCE) tells how convection cells are different from other things that are in the same
genus of loops of moving fluid. “….in which the motion from the bottom to the top of the cell,
and from the top of the cell back to the bottom of the cell, results from differences in density
caused by differences in temperature.” This is DIFFERENT from a loop of water going down the
drain, or air swirling behind a propeller.]
“Read that definition with me…” [Lead. Students map their behavior onto the teacher’s
model. Correct any errors by repeating the model and lead.]
“Now read that definition yourself.” [Test/check to ensure they can do it independently.
Correct any errors by repeating the definition and retesting. Why is the teacher doing so
much—model, lead, test, correct errors, repeat? Because this definition is a pre-skill for
achieving the objective. If they don’t know the concept---convection cell—they can’t identify
examples and can’t do experiments on them.]
3. [Now the teacher shows examples that reveal clearly the features that define convection
cells. The examples are different in the irrelevant/nondefining features, such as where the cell
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is and what the fluid is. But they are the same in the DEFINING features---loop of fluid, heating
and cooling. As students examine and compare examples, they identify how they are the same.
When they then contrast examples and nonexamples, they see how nonexamples are MISSING
the festures that all the examples SHARE. This way, the learning mechanism figures out
(induces) the SAMENESS in examples that defines convection cell IN GENERAL. Please see
induction.]
“This is a convection cell. Notice the motion from the bottom to the top of the cell, and from
the top of the cell back to the bottom of the cell, results from differences in density caused by
differences in temperature.” [Teacher labels the example and then identifies features in the
example that match the definition. This shows students WHY an example IS an example. But
the teacher is also teaching a more GENERAL skill---namely, “Examine things; identify their
features; see if the features match the definition.” This teaches students to USE definitions to
guide their attention and inspection.]
http://archive.ck12.org/ck12/images?id=309914
“This is a convection cell. Notice the motion from the bottom to the top of the cell, and from
the top of the cell back to the bottom of the cell, results from differences in density caused by
differences in temperature.”
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http://pubs.usgs.gov/gip/dynamic/graphics/Fig33.gif
“Here’s another convection cell. Use the definition and our rules about temperature, weight,
and density, to tell how it works.” [The students have just seen several examples of convection
cells. The teacher used the definition to help them to examine the examples. Now the teacher
goes a step further---use the rules (reviewed earlier) to explain what is happening. Notice that
THIS example is a lot like the previous one. So, having students generalize to this new example
should be easy.]
http://www.cookingforengineers.com/pics3/640/ND2_6214_LR.jpg
Heat makes the water less dense….Less dense fluid is lighter than more dense fluid…..Lighter
fluid rises….. When warm fluid is at the top, it cools….Cooler fluid becomes more dense…Denser
fluid is heavier….Heavier fluid falls….Then it gets hot again, becomes more dense, becomes
lighter, and rises…. [Correct any errors.]
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“Yes, you told how this convection cells works, and you used the rules and heat, density, and
weight.” [Verification.]
“And here’s another example. It’s water in the ocean. But it’s still a convection cell because
hotter and lighter fluid moves from the bottom to the top of the cell, and from the top of the
cell (where it cools and becomes denser and heavier) back to the bottom of the cell.” [Teacher
helps students to generalize the definition to a new and rather different example.]
http://www.oocities.org/researchtriangle/node/5345/images/convec.gif
Here’s another convection cell. In the one before, a volcano heated the fluid (water) from the
bottom. In this one, the sun heats the ground, which heats a different fluid---air. The kind of
fluid and the source of heat are different, but they are convection cells because hotter and
lighter fluid moves from the bottom to the top of the cell, and from the top of the cell (where is
cools and becomes denser and heavier) back to the bottom of the cell.” [Teacher helps
students to generalize the definition to a new and rather different example. Teacher points out
irrelevant differences but sameness in defining features.]
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http://www.propertiesofmatter.si.edu/images/L5/conv_cell_atmos_labeled.gif
“This is a convection cell in the earth itself. The fluid is liquid rock, or magma, heated by the
hot earth’s core. Tell me what happens as the magma rises.” [Test/check students using the
definition and the rules to explain what is happening in the example.]
http://sriutami88.files.wordpress.com/2012/02/convection.gif
It cools….Get’s less dense…Gets lighter…Rises above the denser magma….Gets to the surface
and cools…Gets heavier…Gets more dense…Flows back down….
“Perfect. You used the definition and rules to explain the loop of moving fluid.” [Verification]
4. [Now juxtapose examples used earlier, with nonexamples. Make sure the juxtaposed
examples and nonexamples are similar in NONdefining features (e.g., fluid, container), but are
different in the DEFINING features (heat, density), so that the differences that MAKE the
difference (heat, density) are easily seen. “This is a convection cell because it has…..?.....This is
NOT a convection cell because it does not have….”]
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“This is a convection cell.
“This is NOT a convection cell.
Hotter, less dense, a lighter
There is no difference in temper-
fluid rises, cools, and then
ature in the fluid, and therefore
falls.”
it is all the same density and weight,
and therefore there is no loop of moving fluid.”
“This is a convection cell.
“This is NOT a convection cell.
Hotter, less dense, lighter
There is no difference is temper-
fluid rises, cools, and then
ature in the fluid under the ice.
falls.”
And therefore, it is all the same density and weight,
And therefore there is no loop of moving fluid.”
5. [Now give a delayed acquisition test of (1) the rules about heat, density, weight, and motion
of a fluid, and (2) all of the examples and nonexamples in the acquisition set---above. This is
where you assess whether students met the objective. ]
5a. “Boys and girls, tell the definition of convection cell. Check your guided notes….Okay, go!”
[Choral response. Test/check the definition first. It is LOGICALLY prior to examples of the
concept or rules about how convection cells work.]
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A loop of moving fluid…air, or water, molten rock….the motion from the bottom to the top of
the cell, and from the top of the cell back to the bottom of the cell, results from differences in
density….caused by differences in temperature.
[Verify correct answers. “Yes….!” Correct any errors, and have the group repeat until they are
firm.]
[Now ask SEVERAL individual students, especially students who made errors or who need some
success.]
“Individual turns. Define convection cell. Luis?”
[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]
5b. “Everybody. Tell me the rules about heat, density, weight, and motion…. Go!” [Now,
test/check rules, which logically follow the definition of convection cell.]
When the fluid is hotter it is denser…When it’s denser, it rises….When it’s cooler it’s less
dense….When it’s cooler, it falls.
[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]
“Individual turns. Tell me the rules about heat, density, weight, and motion. Debbie?”
[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]
5c. [Now show each example and nonexample, and test. Examples and nonexamples logically
follow checking the definition and then the rules.]
“Is this a convection cell?”
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Yes.
“How do you know?”
Fluid loop….hotter on the bottom….less dense….lighter….water rises….cools at the top….denser
and heavier….fluid falls.
“Correct! Excellent use of the rules and definition.”
“Is this a convection cell?” [Nonexample]
No.
“How do you know?”
Frozen…No heat differences….No part is denser or heavier….No motion.
“Correct again. There are no heat differences. So, no part is more dense or heavy. And so
there is no motion.”
[Repeat acquisition test with several more examples and nonexamples. Verify correct answer
and correct all errors and repeat.]
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6. [Now help students to EXPAND their knowledge by GENERALIZING it to new examples.]
“Here’s a bathtub with hot water running in it. Is IT a convection cell? Think about it using the
words, heat, density, weight, and movement up or down.” [Hints/reminders of how they
answered questions like this earlier.]
http://www.improvisedlife.com/wp-content/uploads/2010/08/bath-1.jpg
Yes.
“How do you know?”
Hot water goes to the bottom, but is less dense and lighter than the cooler water in the
tub….The hot water rises….The water at the top cools….Gets less dense….Gets lighter and falls.
“Wow! You used the definition of convection cell and all the rules!!” [Verification.]
“How about this one? The water has been sitting in the tub all day.” [A second generalization
example.]
http://www.austincahills.com/blog/MasterBathtub_102006.jpg
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Not a convection cell. Fluid is the same all over….No part is hotter or colder…Same density and
weight. No motion.
“You are soooo smart!”
[You could give more generalization examples and nonexamples to the whole group and to
individual students.]
Task 3. Application and Integration.
[Now you could APPLY the knowledge with projects that INTEGRATE this new knowledge AND
prior knowledge of measurement and data collection.]
“Boys and girls. You are SOLID on convection cells. Let’s do some projects on convection cells,
using glass beakers that we will heat from the bottom, blue dye that we can use to see motion,
and thermometers to measure temperature in different parts of the fluid. We’ll use water and
oil to see IF it takes higher or lower temperature to produce motion. We will make videos
showing motion and heat.”
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