Forms of Knowledge
Martin A. Kozloff
Copyright 2006
Our topic is kinds or forms of knowledge. Here is what you will learn.
1.
Teachers communicate specific things, but the goal is for students to
“get,” learn, or acquire general ideas from the specific things. For
example, Ms. Gonzales teaches students to read (sound out, decode) the
words am, ma, at, sat, and mat---not JUST so they can read these words,
but so they learn the general cognitive routine for decoding regular
words, and can APPLY that cognitive routine to ALL regular words.
2.
So, from specific things (examples) we “get” and later use knowledge of
general ideas.
3.
There are four kinds of general ideas, or four kinds of knowledge---verbal
associations (this ONE thing goes with that one thing---facts and lists);
concepts (all these things have some features in common---sensory
concepts and higher-order concepts); rule-relationships (this SET of
things goes with that set of things); cognitive routines (to read all of
these words, or to solve all of these math problems, or to write these
kinds of essays, do steps 1, 2, 3, 4, 5 and 6).
4.
The four kinds of knowledge are about CONNECTIONS. For instance,
a. The name of a city is connected to the words “capital of Missouri”-knowledge of verbal association.
b. All the objects in a box are connected by the fact that they have the
same shape---square-- knowledge of a concept.
c. All the instances of economic development described in a textbook
are connected by the similar WAY they happen. When W, X, and Y
happen, then economic development (revealed in the examples)
happens---knowledge of rule-relationship.
d. All of the solutions to different algebra problems are connected by
the same sequence of steps by which they are solved--- knowledge of
a cognitive routine.
So, your main communication task is to help students to “get”(see, grasp,
figure out, learn) that the examples reveal a connection—a general idea
(verbal association, concept, rule-relationship, cognitive routine).
Remember these sentences.
1.
Knowledge is not about separate things. Knowledge is about connections
among things.
2.
There are four kinds of connections among things.
3.
Therefore, there are four kinds, or forms, of knowledge: verbal
associations, concepts, rule-relationships, and cognitive routines
(Kame’enui and Simmons, 1990. Designing instructional strategies.
Columbus, OH: Merrill Publishing Company)
4.
Some elements of the general procedure for teaching are designed for
each form of knowledge. For example, teaching concepts requires a set
of examples and nonexamples. Teaching cognitive routines requires
teaching the steps and their arrangement into a sequence.
5.
This makes your job as teacher much easier. If you know the form of
knowledge you are teaching, you can simply use the proper procedure for
teaching it.
Four Forms of Knowledge
Now let’s look at each form of knowledge, see what kind of connection it is,
and learn how to teach it. Here is the list.
1.
Verbal associations: Simple facts. Oxygen is an element.
2.
Verbal associations: Lists. There are six New England states……
3.
Basic/sensory concepts: red, square, on
4.
Higher-order concepts: republic, furniture, granite
5.
Rule-relationships: “When (things in the category) X increases, then
(things in the category) Y increases.”
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6.
Cognitive Routines: Steps for solving problems, writing essays,
conjugating verbs, sounding out words.
Verbal Associations: Simple Facts
If you read the word Massachusetts, or if you see Massachusetts on a
map, that’s NOT knowledge. If you read the word Boston, or if you see a little
dot on a map saying Boston, that’s NOT knowledge. But if you answer the
question, “What is the CAPITAL of Massachusetts?” and you say “Boston is the
capital of Massachusetts,” then you have knowledge. You know the
connection between two things that are named. Please read that sentence
again.
If you see a book called Commonsense, is seeing it knowledge? No. If
you see the name Thomas Paine, is that knowledge? No. But make a sentence
that CONNECTS Thomas Paine and the book Commonsense…… Yes, “Thomas
Paine wrote Commonsense.” That statement is a statement of knowledge.
What kind or FORM of knowledge? The answer is verbal association: simple
fact.
Here are some individual “things.” Make sentences that CONNECT
them. The things are not in any special order.
1. The black cat.
1. 4
2. Raleigh
2. Ted Kennedy
3. 2 + 2
3. Midnight
4. President
4. The capital of North Carolina
5. Senator
5. Freedom of speech
6. First Amendment
6. George Bush
The sentences you made connect two particular things. The sentences show
that you KNOW the connections. You know that one thing goes with the other
thing. These simple connections between the things named are called verbal
associations. They are such simple connections that we call them simple facts
(Kame’enui and Simmons, 1990.)
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How to teach verbal associations: simple facts. Here’s the General
Procedure for Teaching that you have seen several times.
Set-up
1.
New material to be taught is properly selected:
a. It is specified by a state standard course of study.
b. It is consistent with scientific research and the work of subject matter
experts.
c. The curriculum standard is clear and concrete.
d. The skill is taught within a proper sequence; for example, students
have the needed pre-skills.
2.
Instructional objectives are derived from the curriculum standard.
Objectives specify clearly and concretely what students will do; the
situation in which they will do it, the criteria for achievement, and any
assists that will be provided. Instruction and assessment are designed on
the basis of and focus precisely on objectives.
3.
Instruction begins with review, especially pre-skills and prior instruction
relevant to the current instruction.
4.
The teacher gains student readiness: attention, sitting properly, materials
handy.
“Boys and girls!”
“Eyes on me.”
“My turn.”
“Get ready to write. Pencils up; sitting tall; feet on the floor; back
against the seat. [check.]
“I love the way you all got ready so fast.”
5.
The teacher frames the instruction by stating the kind of new knowledge
to be taught (e.g., “Here’s a new fact.”), the objectives, and big ideas
that will help students organize, remember or access, and comprehend
the new knowledge, and connect new with prior knowledge.
Focused Instruction
6.
The teacher models or presents new information.
7.
The teacher leads students through the application of the new
information.
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8.
The teacher gives an immediate acquisition test/check to determine
whether students learned the new information. [During-instruction
assessment or progress monitoring]
9.
The teacher corrects any errors and/or firms weak knowledge; e.g., the
rule and procedure for renaming, or carrying.
10. If the new material is a concept, rule-relationship, or cognitive routine,
the teacher provides a set of examples (to teach “These are the same.”)
and juxtaposes examples and nonexamples (to teach “These are
different.”) so that students can compare and contrast them, and identify
the common essential features.
Closing
11. The teacher gives a delayed acquisition test (outcome assessment)--calling on both the group as a whole and then individual students---to
determine whether students learned the concept, rule relationship, or
cognitive routine from the examples and nonexamples, or that students
remember the set of verbal associations presented.
12. The teacher reviews the instruction (e.g., main things taught) and states
how what was taught is relevant to next lessons.
13. The teacher uses information from the delayed acquisition test and review
to determine whether students have sufficiently mastered the new
material and can advance to the next step of instruction, or whether
reteaching or more intensive instruction for some students is needed.
Elements 5-9 and 11 are the ones that are special for teaching verbal
associations: simple facts. Since a verbal association: simple fact is that one
thing or name goes with another thing or name, that’s all you have to teach
and test. For example,
Procedure for Teaching Verbal Associations: Simple Fact
(Thomas Jefferson  Declaration of Independence)
Set up
The class has already learned about events leading up to the writing of the
Declaration of Independence (which was a public statement of the
decision to separate from British rule). The teacher reviews these
events. Soon the class will be learning a general cognitive routine for
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comprehending historical documents; studying the Declaration will be
the first example of using that routine. Before reading the
Declaration, the teacher wants students to learn a few facts.
2.
Objectives
When the teacher says, “Who wrote the Declaration of Independence?” or
“Tell me a fact about Thomas Jefferson,” students answer “Thomas
Jefferson wrote the Declaration of Independence.”
5.
Frame.
Teacher. “Boys and girls. New fact.”
Focused Instruction
6.
Model.
Teacher. “Thomas Jefferson wrote the first draft of the Declaration of
Independence.”
7.
Lead.
Teacher. “Say it with me.”
Teacher/ “Thomas Jefferson wrote the first draft of the
Class.
Declaration of Independence.” [You don’t always need the
Lead. It depends on whether your students need to hear the
model more than once.]
8.
Test/check
Teacher. “Your turn. Who wrote the first draft of the Declaration of
Independence?” (or “Tell me a fact about Thomas Jefferson?”)
Class.
“Jefferson wrote the first draft of the Declaration.”
Teacher. “Yes, Jefferson wrote the first draft of the Declaration.”
[Verification]
9.
Error correction.
A student answers, “Jefferson wrote the decoration of independence.”
The teacher correct the error with this simple procedure: model, lead,
and test.
Model: “Jefferson wrote the DECLARATION of Independence.”
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Lead: “Say it with me. Jefferson wrote the DECLARATION of
Independence.
Test:
“What’s our new fact about Thomas Jefferson?
Jefferson wrote the DECLARATION of Independence.
Verification: “Yes, now you’ve got it! Jefferson wrote the DECLARATION
of Independence.”
Closing (at the end of the lesson)
11. The teacher reviews and tests all the facts taught.
“Okay, let’s review all our facts. Who wrote the first draft of the
Declaration of Independence?.... When was the Declaration signed?... How
many persons signed it?”
Verbal associations: Verbal Chains
A simple fact connects two things or names. In a verbal chain, one thing
is connected to a list of several other things. For instance,
The six New England states  Maine
New Hampshire
Vermont
Massachusetts
Rhode Island
Connecticut
“The six New England states are Maine, New Hampshire, Vermont,
Massachusetts, Rhode Island, Connecticut.”
You teach verbal chains the same way as simple facts, but you may have to
present the information in smaller chunks. For example, students learn to say
Maine, New Hampshire, and Vermont. And then Massachusetts, Rhode Island,
and Connecticut. And then all six in a chain. Here’s an example. [Remember,
most elements of the general procedure for teaching are the same. The big
differences are the steps 5-8---frame, model, lead, test/check.]
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Procedure for Teaching Verbal Associations: Verbal Chains (Mitosis)
Set up
The science class is studying cells. Students have already learned the structure
of cells and certain cell processes, such as osmosis. This is some of their
background knowledge. [Please see these websites.]
http://training.seer.cancer.gov/module_anatomy/unit2_1_cell_functions_2.html
http://training.seer.cancer.gov/module_anatomy/unit2_1_cell_functions_1.ht
ml
The teacher reviews these structures and processes. Now it’s time to study
another cell process; namely, cell division.
http://biog-101-104.bio.cornell.edu/BioG101_104/tutorials/cell_division.html
The first objective is that students say the names of the phases of cell
division, in order. [Why is this first? Because the teacher will be showing
slides and discussing the phases. Students need to know WHAT she’s talking
about.]
2.
Objective
When the teacher says, “State the phases of mitosis in order,” students do
this correctly within 10 seconds.”
5.
Frame.
Teacher. “Boys and girls. Now we’re going to study division in somatic
cells. The name of that process is mitosis.” [Writes mitosis on
the board.]
“Spell mitosis.”
Class.
“m i t o s i s.”
Teacher. “Write mitosis in your notebooks at the top of a new page.”
[Check]
“Now you will learn the phases of cell division in somatic cells,
or mitosis.”
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Focused Instruction
6-8. Model—lead—test/check.
Teacher. “Listen, the five phases of mitosis are interphase, prophase,
metaphase, anaphase, telophase.”
“I’ll say the first three. interphase, prophase, metaphase.”
[Model]
Teacher. “Say them with me.” [Lead]
Teacher/ interphase, prophase, metaphase.
Class.
Teacher.
“Your turn.” [Test/check]
Class.
“Interphase, prophase, metaphase.”
Teacher.
“Again.” [This is a judgment call, whether to do it again to
firm the chain.]
Class.
“Interphase, prophase, metaphase.”
Teacher.
“Now the last two.” Listen. anaphase, telophase [Model]
Teacher.
“Say it with me.” [Lead]
Teacher/
Class.
“Anaphase, telophase”
Teacher.
“Your turn.” [Test/check]
Class.
“Anaphase, telophase”
Teacher. “Now all of them with me.” [Lead]
Teacher/ “Interphase, prophase, metaphase, anaphase, telophase.”
Class
Teacher.
“Again, with me.”
Teacher/ “Interphase, prophase, metaphase, anaphase, telophase.”
Class.
9.
Teacher.
“Your turn.” [Test/check]
Class.
“Interphase, prophase, metaphase, anaphase, telophase.”
Error correction.
If a student makes a mistake in ANY of the above instruction, the teacher
immediately corrects it with the procedure: model-lead-test/check. For
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example, the teacher hears one student leave out anaphase. The teacher
directs the correction to the whole group.
Teacher.
“Interphase, prophase, metaphase, ANAPHASE, telophase.”
[Model]
Teacher.
“Say it with me.” [Lead]
Teacher/ “Interphase, prophase, metaphase, ANAPHASE, telophase.”
Class.
Teacher.
“Your turn. Everybody. [Test/check]
Class.
“Interphase, prophase, metaphase, anaphase, telophase.”
Application. When would you teach verbal chains? Let’s say you are preparing
lessons in science or history or literature. There are many verbal chains you
want students to learn. For example
1.
What rights are guaranteed by the first five Amendments to the
Constitution?
http://www.law.cornell.edu/constitution/constitution.billofrights.html
2.
List six of the most important events leading up to the colonists’ decision
to separate from Britain? (Stamp Act, Sugar Act, Battle at Lexington
Green…) http://www.historyplace.com/unitedstates/revolution/revprel.htm
3.
List six main kinds of fungi. http://tolweb.org/tree?group=fungi
4.
Name seven figures of speech, or tropes.
http://www.nipissingu.ca/faculty/williams/figofspe.htm
Note that learning simple facts and verbal chains is usually an
introduction to instruction on important concepts and rule-relationships
and cognitive routines that involve the facts and verbal chains. For
instance, you would teach students to list the five phases of mitosis before you
teach them what is happening IN each phase, to identify cells in each phase,
and to describe changes from one phase to another. Likewise, you would teach
students to list the main events that came before the Colonists’ decision to
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separate from Britain so that you can THEN make a diagram of the SEQUENCE
leading to the War of Independence, and then DISCUSS how the events
gradually produced more and more resentment in the colonists.
You may wonder “Do you have to teach everything with THIS much
scaffolding (bit by bit, modeling, leading, testing/checking to see if students
learned it, correcting errors)? The answer is, WHENEVER THE KNOWLEDGE IS
SO IMPORTANT THAT YOU MUST ENSURE THAT STUDENTS LEARN IT, THEN YES,
TEACH THAT WAY. This is especially important for diverse learners. But the
more students learn and the more they learn HOW to pay attention to the
important elements in your communication, the LESS scaffolding they will
need.]
Concepts: Basic
A verbal association is a statement that connects one or more things or
names. A concept is a set of events or things that have one or more
common features. The common features are the concept. The word (“red”) is
not the concept. It is merely a name for the concept. “Red” signifies or
points to the feature—the redness. So, to teach a concept, you must teach
students what are the common features of the examples; and you must teach
them the name of the features (“red”) so that students can communicate the
concept to other persons.
What is basic about basic concepts?
The “stuff” of basic concepts is right in front of your eyes, ears, or skin.

Red. Not the word “red”; the stuff you see on a “red” apple.

On. Not the word “on”; the way things are arranged that is called “on.”

Hot. Not the word “hot”; the way your skin feels when you touch “hot.”
All of these are basic concepts. Because all the information that DEFINES a
basic concept is right there. So, teach a basic concept by giving examples
and naming them. Then juxtapose (put next to each other, or one right after
the other) examples with nonexamples (that are the in every way EXCEPT in
the features that make the difference), and name them. For example,
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Procedure for Teaching Basic Concept (Red)
Set up
A kindergarten class has been studying shapes and colors.
Students accurately name examples of blue and yellow, squares and circles.
The teacher reviews these.
2.
Objective
When the teacher points to objects of different colors and shapes and
asks, “Is this red?” students answer correctly within 3 seconds.
4.
Review
Teacher. [Holds up color and shape examples one at a time]
“What color?”
Class.
“Blue.”
Teacher. “Yes, blue.” [Verification]
“What shape?”
Class.
“Circle.”
Teacher. “Yes, circle.” Etc.
5.
Frame.
“Boys and girls. New color. Red.”
Focused Instruction
6.
Model. [Teacher shows a range of examples of red things of various
shapes, and nonexamples (not-red things that are the same shape as
the red examples)—so that the only difference is redness. The teacher
must use a range of red things---light to dark—or else students may
wrongly conclude that red is, for example, only dark.]
“This is red.”
Light red square
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“This is red.”
Light red circle. [By using two light reds but with
different shapes, students see that “red” goes
with (is connected to) color, not shape]
“This is red.”
Dark red circle. [Juxtaposing dark red and light red,
circles—above--shows students that redness—not
dark or lightness—is the defining feature of red.]
“This is NOT red.” Dark blue circle. [Juxtaposing dark red circle—
above--and dark blue circle enables student to see
the contrast. “Red” is color, not shape.]
“This is NOT red.” Dark blue square.
“This IS red.”
Dark red square. [Juxtaposing red and blue squares
shows that color and not shape defines red.]
7.
No lead is needed. [Just model and then test.]
8.
Test/check [Teacher holds up the SAME examples and nonexamples and
tests]
Teacher. “Is this red?”
9.
Class.
“Yes.”
Teacher.
“Yes, it IS red.” [Verification]
Teacher.
“Is this red.”
Class.
“No.”
Teacher.
“No, it is NOT red.” [Verification]
Teacher.
“Is this red?”
Class.
“Yes.”
Teacher.
“Yes, it IS red.” [Verification]
Error correction.
A student makes an error; for example, the student says No---that a dark
red square not red. The teacher corrects this with the modeltest/check procedure.
Teacher.
“This (holds up dark red square) IS red.” [Model]
Teacher.
“Is this (holds up dark red square) red?” [Test/check]
Class.
“Yes.”
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Teacher.
“Yes, it IS red.” [Verification]
[To firm it up even more, the teacher holds up the dark red square and
the dark red circle and names them both red, and then tests again.]
Closing
11. Delayed acquisition test. At the end of the lesson, the teacher holds up
all the red and not red objects and tests. “Is this red?”
Concepts: Higher-order
In basic concepts, such as red, on, and s says sss, the “stuff” that
defines the concept is right there to be seen, heard, or felt. However, the
stuff that defines higher-order concepts is not right in front of your senses.
You can’t see in one place all the stuff that defines democracy, or justice, or
furniture, or symmetry. The stuff that defines democracy (elections, for
example) is spread over time and place and groups. So, to teach a higher-order
concept you first give a verbal definition that draws a big circle around all
the stuff in the concept. And then you give examples and nonexamples so
that students see the actual stuff that defines the concept. For example,
Procedure for Teaching Higher-order Concept (Granite)
http://en.wikipedia.org/wiki/Granite
Set up
2.
Objective
The teacher presents examples and nonexamples of granite and asks, “Is
this granite?” When students answer, the teacher asks, “How do you
know?” Students correctly identify granite and not granite, and use the
definition to explain their answer.
5.
Framing.
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Teacher. “We have 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.”
Class.
“Igneous rocks form from the crystallization of minerals in magma.”.]
Teacher.
“Yes, igneous rocks form from the crystallization of minerals in
magma.” [Verification]
“Today we will 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
asks students to make a deduction about granite given the definition of
igneous rocks. This helps to firm their knowledge of the definition,
and their USE of the definition to examine rock.]
Teacher.
“Excellent deduction!!”
Focused Instruction
6-8. Model—lead—test/check.
[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 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!”
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[Now the teacher firms up background knowledge of minerals 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, flat planes) is what defines each mineral.
When students are firm on this—they correctly define and identify examples and
nonexamples of each mineral---the teacher moves to the next step.]
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
grey quartz. But they share the essential and defining features—the structure
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
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example, but they all have the structure of mica, feldspar,
and quartz.”
Mica
Feldspar
Teacher.
Quartz
“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
Teacher.
Feldspar
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.”
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Quartz
Mica
Feldspar
[Do you 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. This assists students to compare and contrast the
examples----all have mica, quartz, and feldspar---with the nonexamples of
granite---which are missing one or more of the defining minerals. This reveals
the defining features of granite.]
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.”
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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.”
Closing
11. Please read # 2, above---the objective. The teacher has completed the focused
instruction portion. Now the teacher gives an acquisition test/check to see if her
instruction was effective; that is, to see if her students have achieved the
objective. So---just as the objectives states---she 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?”
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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 sample 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?”
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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.”
Rule-relationships
Rule–relationships are knowledge NOT of how one thing goes with another
thing (verbal association), but of how one set of things goes with (is connected
to) another set of things. Sometimes rule-relationships are called principles, or
laws, or correlations. Rule-relationships are stated in several ways. For
example,
1.
When the demand for a product increases, the price increases.
2.
Behavior that is reinforced will occur more often.
3.
Democratic nations tend not to make war against other democratic
nations.
4.
The more members of a religious group share beliefs, the more members
of the group feel protection by the group.
The sciences contain many rule-relationships. A course in physics, for
example, is almost entirely about “laws,” such as laws of motion.
There are at least two ways to teach rule relationships.
1.
State the rule-relationship and then present examples that back it up.
This is the same as defining a concept (granite) and then presenting
examples of granite.
2.
Present examples of the rule-relationship and then help students to
examine the examples, find the connection, and state the connection.
Here’s an example. The question is, Is there a connection between how steep
an inclined plane is and how long it takes a ball to roll down it?
http://www.mcm.edu/academic/galileo/ars/arshtml/mathofmotion1.html
[Please skim the text and watch the videos.]
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You could TELL students the rule-relationship (the steeper the inclined plane,
the less time it takes the ball to roll down the inclined plane) and then show
examples using inclined planes of different angles. These examples would
confirm the rule.
Or, you could have students do an experiment by rolling balls down inclined
planes of different angles, measuring how long it takes each ball to roll down,
and then draw a conclusion. The first way requires fewer skills. Students
merely compare examples with the rule. “Yup, the ball takes less time when
the angle is steeper.” This second way involves more skills than the first
method. For example, student have to change the angles, measure the times,
write the measurements, compare and contrast the instances, and figure out
the connection. This means you would have to teach these pre-skills BEFORE
students do the experiment. Here’s an example.
Procedure for Teaching Rule-relationships
Set up
A middle school science class is studying pressure. The teacher wants
students to learn a rule-relationship that connects pressure and temperature, but
even more importantly, the teacher wants students to learn HOW to figure out how
things are connected.
http://www.chm.davidson.edu/chemistryApplets/KineticMolecularTheory/PT.html
The teacher reviews background knowledge (taught earlier) on molecules,
gasses, and certain laws of kinetic molecular theory.
http://www.chm.davidson.edu/chemistryApplets/KineticMolecularTheory/Basi
cConcepts.html
2.
Objectives
Students are presented with examples of measurements of the pressure of
gas in a closed cylinder and corresponding measurements of the
temperature of the gas. Students compare and contrast each example
and summarize them with a statement of the rule-relationship. “The
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greater the pressure (or when pressure increases), the higher the
temperature (or temperature increases).”
5.
Frame
Teacher.
“Okay, now let’s see IF there is any connection between
pressure and temperature.”
Focused Instruction.
Teacher.
“I’m going to change the pressure of the gas in this
enclosed cylinder. You will see the measurement on the
screen. You will also see the corresponding temperature of
the gas that goes with the pressure. You will record the
measurements in a table, like this.”
[Teacher varies the pressure five times. Students record
pressure and temperature.]
Teacher.
When Pressure Is
Temperature Is
200 lbs/square inch
120 degrees
150 lbs/square inch
100 degrees
170 lbs/square inch
110 degrees
230 lbs/square inch
150 degrees
80 lbs/square inch
90 degrees
“Okay, boys and girls. Let’s arrange pressure from lower to
higher. Which measure of pressure is lowest?”
Class.
“80 pounds.”
Teacher.
“Next?”
Class.
“150 pounds.”
Teacher.
“Next.”
Class.
“170 pounds.”
Teacher.
“Next.”
Class.
“200 pounds.”
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Teacher.
“Next.”
Class.
“230 pounds.”
Teacher.
“Now rewrite the table with the lowest pressure on the
bottom.”
When Pressure Is
Temperature Is
230 lbs/square inch
200 lbs/square inch
Teacher.
150 degrees
120 degrees
170 lbs/square inch
110 degrees
150 lbs/square inch
100 degrees
80 lbs/square inch
90 degrees
“Start at 80 pounds. What’s the corresponding
temperature?”
Class.
“90 degrees.”
Teacher.
“Yes, 90 degrees.”
Teacher.
“Now, how up to 150 pounds of pressure. What happens to
temperature?”
Class.
“It goes up.”
Teacher.
“Now look at the rest of the pressures, one at a time.
What happens to the corresponding temperature?”
Class.
“It goes up.”
Teacher.
“So is there a relationship between pressure and
temperature?”
Class.
“Yes.”
Teacher.
“State the relationship.”
Class.
“When pressure increases, temperature increases.”
Closing.
The teacher reviews the data and the rule-relationship. The teacher also
reviews the steps that the students followed to find the rule relationship.
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1.
Measurement of both variables.
2.
Arrangement of the measurements in an order that would make change
easy to see.
3.
Comparison of one set of corresponding measures with another to see if
and how a change in one variable was connected to a change in the other
variable.
Cognitive Routines
Cognitive routines are the fourth form of knowledge. Examples include
solving math problems, conducting experiments, writing papers, analyzing
documents to identify the main points, and even sounding out words. These
are so different; how can these be the SAME form of knowledge? Well, do they
all involve a sequence of steps? Yes. Does the sequence lead to something
accomplished? Yes. Then they are all cognitive routines. And this means that
despite differences in the subject matter (math problems, reading words), you
use the same procedure for teaching them. The difference would be that some
cognitive routines have few steps and involve fewer background skills. Here is
an example.
Procedure for Teaching Cognitive Routines:
Decoding or Sounding out Words
Set up
What are the steps and pre-skills involved in sounding out words, such as
run and sit? [We find out what these are either by reading the scientific
research or by doing task analysis---which you will learn more about later in
the course.]
1.
Look at the letter on the far left. r
2.
Say the sound of that letter. rrr
3.
Shift your eyes to the right, focus on the next letter (u), but continue
saying the first sound. rrr
4.
Now say the next sound. uhh
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5.
Shift your eyes to the right, focus on the next letter (n), but continue
saying the second sound. uhh
6.
Now say the last sound. nnn
The teacher has already taught students the pre-skills needed to decode
words: (1) say sounds; (2) say the sounds that goes with the letters; (3)
shift eyes to the right. These are some of the pre-skills USED in the
sounding out routine. So, the main NEW skills and steps that are
taught are in steps 3-6---mainly, shifting eyes to the next letter and
saying the next sound. Students don’t know how to do this yet.
[In other words, if you know that eventually you want students to learn a
complex cognitive routine, such as sounding out or decoding words,
solving equations, and writing essays, you first do a task analysis of
these skills to see what students have to know in order to do the
routines. Then you teach the pre-skills. Therefore, teaching the
cognitive routine itself should be little more than teaching students the
steps. You do NOT want students trying to learn the pre-skills or the
elementary skills at the SAME time that they are learning to assemble
these skills into a routine. This will be too big a load for many
students, and they will fail.]
2.
Objective
The teacher writes on the board words whose letter-sounds students
already know (a, m, s). The teacher points to each word and says, “Sound
it out.” Students sound out each word within 3 seconds.
3.
Review.
Three pre-skills are reviewed. Why? Because they are PART of the
cognitive routine for sounding out. If students don’t have these pre-skills,
they can’t sound out words.
Teacher.
“Get ready to say some sounds. First I’ll say a sound and
then you’ll say that sound. Get ready. ahhh.”
Class.
“ahhh.
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Teacher.
“mmm.”
Class.
“mmm.”
Teacher.
“sss.”
Class.
“sss.”
Teacher.
“Individual turns. Julie…aaa.” [The teacher makes sure to
call on students who may need the extra practice.]
Julie.
“ah.”
Teacher.
“Yes, ah.”
“Sammy…mmm”
Sammy.
“mmm.”
Teacher.
“Yes, mmm.”
“Phyllis…sss.”
Phyllis.
“sss.”
Teacher.
“Yes, sss.”
“Okay, let’s review our letter-sounds. [Teacher writes
letters on the board. Notice that they are the same ones
whose pronunciation was just reviewed.]
“Everybody. What sound?” [Teacher points to each letter.
Students say the sound. If any student makes an error, the
teacher corrects it, with model, lead, test/check. “That
sound (points) is ahhh. Say it with me… What sound?...”
The teacher makes sure to come back to that sound to
retest the student who erred.]
“Now let’s read our sounds.” [Teacher writes letters on
the board. The letters are the ones in the words students
will sound out.] “When I touch under a letter, you say the
sound.” [Teacher starts at the ball and moves her finger
under the letter.]
a
m
o---->
o---->
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s
o---->
[The teacher corrects any errors. “That sound is aaa. Say
it with me… What sound?]
4.
Readiness.
Teacher.
“Everybody, sit big. Eyes on me. Feet on the floor….Oh,
you are such good students. You got ready so fast.”
5.
Frame.
Teacher.
“Now you are going to learn how to SOUND OUT words!!”
Focused Instruction
6-8. Model—lead—test/check.
Teacher.
[Writes am on the board.]
a m
o-------->
“I’ll read this word the slow way. When I touch under a
sound I will SAY the sound. I WON’T stop between sounds.
Here I go.” [Touches under edach letter] “aaammm.”
[Model] “Again. aaammm.”
“Do it with me. Get ready.” [Lead]
Teacher/
Class.
“aaammm”
Teacher.
“All by yourselves. Get ready.” [Touches under each
letter] [Test/check]
Class.
“aaammm.”
Teacher.
“Yes, aaammm.” [Verification.]
[Teacher repeats these steps with ma, and sa.]
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Closing
The teacher reviews all the words students have sounded out and corrects
errors. The teacher decides if some children need extra practice later that day
and before the next lesson on sounding out. If they are not firm on these first
words, surely they will never be firm on newer and longer ones.
Summary
You have learned that knowledge is general, but that we can only learn
general ideas through examples. You have learned definitions and examples of
the four forms of cognitive knowledge. You have also examined procedures for
teach each form of knowledge. In each case, instruction and assessment were
tied directly to the objective. We taught what students were to DO and we
assessed whether they learned to do it. You also learned a few principles
about examples used to teach concepts, rule-relationships, and cognitive
routines. You learned about using a wide enough range of examples; about
using examples that vary in many ways except for the essential features; and
about juxtaposing examples and nonexamples so that by comparing and
contrasting them students can identify the essential features. We will return
to all of these issues later, after you have learned a few more tools for
designing effective instruction.
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