Procedure for Teaching Higher-order (abstract) Concepts:
[Needs verbal definition and then examples and nonexamples]
Systematic, Explicit, Focused, Direct Instruction
First, you need to know about verbal definitions.
Genus and difference. Here’s the 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.
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
Constitutional republics
Monarchies
Aristocracies
Democracies
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, 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
virtue of hereditary ascension], often for life or until
of state [by
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 terms 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
same thing. So, the definition is just saying Fear is an
emotion at involves fear.]
Procedure for Teaching Concepts: Higher-order
[Needs verbal definition and THEN examples/nonexamples]
Systematic, Explicit, Focused, Direct Instruction
Simile
Set up
1.
Objective
mean the
The teacher presents examples and nonexamples of simile and asks, “Is
this a simile?” When students answer, the teacher asks, “How do you
know?” Student correctly identify similes and nonsimiles, and use the
definition to explain their answer.
2.
Frame.
Teacher.
“New figure of speech. Simile. [writes on board or refers to
guided notes.]
Spell simile.”
Class.
“s i m i l e .”
Teacher.
“What word?”
Class.
“Simile.”
Teacher.
“Write it in your notebooks, or guided notes.” [Check to
make sure they do this.]
Focused Instruction
3.
Model—lead—test/check.
Teacher. “Listen. A simile is a figure of speech in which two unlike
things are compared, using the words like or as.” [Model]
Teacher. “Listen again. A simile is a figure of speech in which two
unlike 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.]
“Listen. The air was hot as a stove. The air was hot as a
stove. Are two things compared?” [The teacher focuses on
the details of the definition.]
Students. “Yes.”
Teacher. “What two things?”
Students. “Air and stove.”
Teacher. “Is like or as used to compare them?” [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.]
[Now the teacher presents a NONexample so that students (comparing the
two previous examples with the nonexample) can see the
comparison of unlike things, using like or as—
difference---the
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?”
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
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. Dos 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.]
using
Students. “Compares unlike things.” “Two unlike things.” Air and hot
stove.” “Uses as.”
Teacher. “Correct!! A class full of geniuses!!”
Procedure for Teaching Concepts: Higher-order
[Needs verbal definition and THEN examples/nonexamples]
Systematic, Explicit, Focused, Direct Instruction
Granite
Here’s another example of teaching higher-order concepts. Notice that the instruction
is highly scaffolded---the teacher does a LOT to make sure that students are firm on the preskills (things they have to know to learn the new stuff), that many examples are used, and that
students are getting (figuring out, inducing) the concept. Do you have to teach everything this
way—so thoroughly? Well, how do you think they do it in medical school? Do you think the
professor makes sure that med students know exactly what different kinds of cancer cells look
like? Why?
Rule: If it’s important that students learn it, then teach it this way.
Objective for acquisition. (1) The teacher presents examples and nonexamples of granite.
Students correctly identify 9 out of 10, each within 10 seconds. (2) Students correctly answer
the follow-up question (“How do you know?”) 9 out of 10 times, each within 10 seconds.
1.
Firm pre-skills
Teacher.
“We’ve been studying igneous rocks. Here’s our definition.
Igneous rocks form from the crystallization of minerals in magma.”
“Everyone, say that definition of igneous rocks.” [Check]
Class.
“Igneous rocks form from the crystallization of minerals in magma.”.]
Teacher.
“Yes, igneous rocks form from the crystallization of minerals in
magma.” [Verification]
2.
Frame Instruction
Teacher.
“Today we’ll examine an igneous rock called granite. Everybody, if
granite is an igneous rock, what else do you know about it? Think….”
Class.
“It forms from the crystallization of minerals in magma.” [Teacher
asked students to make a deduction about granite from the definition of
igneous rocks. This helps firm their knowledge of the definition, and prepares
students to USE of the definition to examine rock samples. “Hmmmm. Is this
igneous? No. Then it can’t be granite.”]
Teacher.
3.
“Excellent deduction!!”
Focused Instruction: Model—lead—test/check---verification
First the teacher teaches the verbal definition of granite.
Teacher.
“Here’s the definition of granite. Get ready to write the definition on
your note cards.” [Check to see if they are ready.]
“Granite is an igneous rock consisting primarily of the minerals quartz,
feldspar, and mica. Again, granite is an igneous rock consisting
primarily of the minerals quartz, feldspar, and mica.” [Model]
“Say it with me.” [Lead]
Teacher/
“Granite is an igneous rock consisting of the
Class.
minerals quartz, feldspar, and mica. [The teacher probably could have
left out the lead.]
Teacher.
“All by yourselves.” [Immediate acquisition test/check]
Class.
“Granite is an igneous rock consisting of the minerals quartz,
feldspar, and mica.”
Teacher.
“Excellent saying that definition with so much enthusiasm.”
Now the teacher firms up background knowledge of minerals that are the DEFINING features of granite,
before she presents examples that contain the minerals and nonexamples that do not.
Teacher.
“We have already studied the minerals quartz, mica, and feldspar.
Let’s review them before we go on….” [Now the teacher shows examples of
each mineral and asks students to identify them. Structure (flakes, crystalline,
what defines each mineral. When students are firm on this—that
define and identify examples and nonexamples of each
flat planes) is
is, when they correctly
mineral---the teacher moves to
the next step.]
Teaching the new concept, building on background knowledge
First the teacher shows examples of granite that differ in NONessential ways (e.g., color and shape) but
are the same in the defining features. Logic: Comparison to identify sameness.
Teacher.
“Now, I’ll show you how to use the definition of granite, and your
knowledge of what mica, quartz, and feldspar look like, to identify
rock samples.”
[The teacher holds up or shows slides of granite, and names each one as
granite. The examples differ in size, shape, and color of minerals; e.g., pink and
quartz. But they share the essential and defining features—the structure
grey
of quartz, mica,
and feldspar.]
Teacher:
“This is granite…Notice the mica (black flakes), feldspar (white
with flat planes), and quartz (pink and crystalline).”
Quartz [Crystalline]
Mica [Black]
Teacher.
Feldspar [Flat planes]
“And this is granite… Quartz is orange and crystalline, feldspar is
whitish with flat planes, and mica is black flakes. There are different
colors than in the first example, but they all have the structure of
mica, feldspar, and quartz.”
Mica
Feldspar
Quartz
Teacher.
“And this is granite… Quartz is green and crystalline, feldspar is
yellow with flat planes, and mica is black flakes. There are different
colors than in the last example, but they all have the structure of
mica, feldspar, and quartz.”
Mica Feldspar
Teacher.
Quartz
“And this is granite… Quartz is pink and crystalline, feldspar is grey
with flat planes, and mica is black flakes. There are different colors
than in the last example, but they all have the structure of mica,
feldspar, and quartz.”
Quartz
Mica
Feldspar
Notice that the WORDING is the same each time!
Next the teacher juxtaposes (puts next to each other) examples of granite and not granite, and labels
them. Examples and nonexamples are similar in NONessential features (e.g., color and shape) but are
different in that examples have the defining features and nonexamples do not. Logic: Contrast to
identify the differences that make the difference.
Teacher.
“This is granite. Notice the mica, feldspar, and quartz….”
Granite
Teacher.
“This is not granite. Notice that it has no quartz. So it can’t be granite.”
Not granite
Teacher.
“This is granite… Again, see the mica, quartz, and feldspar.”
Teacher.
“But this is NOT granite. It is chunky, like the last example of granite, but there
is no quartz or feldspar. So it can’t be granite.”
4.
Closing
Reread the objective above. The teacher has completed the focused instruction portion. Now the
teacher gives an acquisition test/check to see if instruction was effective; that is, to see if students
achieved the objective. So---just as the objectives states---the teacher presents examples of granite and
nongranite; asks students to identify them; and asks students to justify their
answer, using the
definition of granite.
Teacher. “Everyone. Is this granite?”
Class.
“ Yes.”
Teacher. “How do you know?”
Class.
“There is mica, feldspar, and quartz.”
Teacher. “Yes, it is granite. Good use of the definition to explain your answer.”
Teacher. “And is this granite?”
Class.
“No.”
Teacher. “How do you know?”
Class.
“There is no quartz.”
Teacher.
“Correct! No quartz. So, it cannot be granite. .”
The teacher repeats the test with several more examples and nonexamples.
The teacher corrects any errors. For example, if a student says “Granite,” but the sample is NOT
granite, the teacher uses the model, lead, test (or just model and test) correction procedure.
Teacher.
“This is NOT granite. Granite consists of three minerals: mica,
quartz, and feldspar. [Model] Does this sample have mica, quartz,
and feldspar?”
Student.
“It has mica and feldspar, but no quartz.”
Teacher.
“So can it be granite?”
Student.
“No.”
Teacher.
“How do you know?”
Student.
“It has to have quartz, too.”
Teacher.
“Correct. It does not have quartz. So it can’t be granite.”