and Making Sense When You Teach Martin Kozloff You need to know this, and you need to teach it to your students. 1. Do a knowledge analysis of whatever you want to teach. What are the smaller chunks of information in the new thing to learn? What pre-skills are needed to learn the new thing?
2. Think of a logical sequence for firming the pre-skills and teaching the new thing.
“This sequence makes sense. If they FIRST get the concept of political system, they will THEN be able to get the concept of monarchy, which IS a political system.”
3. Teach or firm each chunk using model, lead (maybe), test.
Then give more examples (model, lead, test) and a few nonexamples (contrast with examples).
Then test them all (delayed acquisition test).
“Is this an X? How do you know?”
4. Then give new examples to teach and test generalization.
5. Make sure to integrate the smaller chunks into something larger; e.g., a new concept or rule/proposition could be added to an explanation of something. Now that they get the concept—monarchy—they can use it when they read the Declaration of Independence.
How would you teach the information below? Think of objectives first.
See the Advance organizers here… scroll down
There are only six kinds of information, skills, or knowledge contained in language (spoken and written), and that can be communicated and learned. No matter what the subject or content is (math, history, science), the information or knowledge will always boil down to six kinds.
Each kind of knowledge represents some kind of CONNECTION. To “get” the knowledge is to “get” the connection. To USE the knowledge (to apply it to possible examples of it) is to apply the connection. Here are the six kinds of knowledge.Remember, that knowledge represents connection.
“The U.S. Constitution was written in Philadelphia.”
Notice that this is a (true, verifiable) statement that connects one specific thing (Constitution) and another specific thing (Philadelphia).
[Teach it. What a fact is.]
“The elements of sugar are carbon, hydrogen, and oxygen.”
“Here is a list of facts about the U.S. Constitution. Written in Philadelphia between May and September, 1787; the draft was sent to the various states for ratification; the Constitution plus the Bill or Rights is a compromise between advocates of strong central government (Federalists) and advocates of strong state governments with a limited central government (anti-federalists); the Constitution was finally ratified in 1789. [How many facts?] Notice that these statements connect one thing (elements of sugar, Constitution) and a list.
Sensory concepts. blue, on.
The specific things (examples) of the concepts differ in many ways (size, shape), but they are connected by a common feature---color, position. All of the defining features of the concept are in ANY example. Therefore, the concept can be shown by one example. However, a range of examples is needed for the learner to see what the common feature is and to cover the range of variations (e.g., from light to dark red). [Teach it.]
Higher-order concepts. Democracy, society, mammal.
The specific things (examples) of the concepts are connected by a common feature or features; e.g., making societal decisions through elected representatives (representative democracy).
However, the defining features are spread out. Therefore, you can’t simply show examples to teach a higher-order concept. You have to give a definition (that states the common, defining features) and then give examples and nonexamples to substantiate the definition. [Teach it.]
Rules or propositions. These are statements that connect not specific things but whole groups of things (concepts or categories).
1. Some rules or propositions state (assert, propose) how one kind of thing (concept or category) is part of or is not part of another kind of thing (concept of category). These are called categorical propositions. For example,
All dogs (one kind of thing) are canines (another kind of thing).
No birds (one kind of thing) are reptiles (another kind of thing).
Some bugs are delicious.
2. Other rules or propositions state, assert, or propose how one kind of thing (concept or category) changes with another kind of thing (concept or category). These are called causal or hypothetical propositions. You can tell that a statement asserts a causal or hypothetical proposition because it says (or suggests) something like “If…. If and only if.… Whenever…. The more… The less….one thing happens, then another thing (happens, comes into being, changes, increases, happens more often, decreases).
Now the “thing” (variable, condition, antecedent event) that is the alleged cause of something else can work (have an effect) in different ways. For example, the alleged cause might be considered a necessary condition for something else to happen or change. This would be stated something like, “If X does not happen, then Y will not happen.” Or, “If and only if X happens will Y happen.”
Or, the alleged cause might be considered a sufficient condition for something else to happen. This would be stated something like “Whenever X happens, Y will happen.”
Whenever temperature increases (one kind of thing), pressure increases (another kind of thing). [This proposition suggests that a rise in temperature is a SUFFICIENT CONDITION---by itself--to cause an increase in pressure.]
If and only if there is sufficient oxygen, fuel, and heat (one category of thing) will there be ignition (another category of thing. [This proposition suggests that sufficient oxygen, fuel, and heat are a NECESSARY CONDITION for ignition.]
The higher the reading fluency (accuracy and speed---one concept or category), the greater the reading comprehension (another concept or category).
[Do you think that this proposition suggests that fluency ALONE causes higher comprehension (that is, is a SUFFICIENT CONDITION)? Don’t you also need VOCABULARY? Do you think that this proposition suggests that fluency is a NECESSARY condition for comprehension? You can comprehend if you read slowly, can’t you? So what does it suggest? What KIND of connection? We would say that there is a correlation----one variable (kind of thing) goes with the other variable, but we are not sure WHAT ELSE is involved or WHY they go together.]
Note: When you have identified all of the necessary conditions, you now have a set of variables that are a sufficient condition.Think of a causal model of fire, a cold, and a revolution. [Teach it.]
Routines. Routines are sequences of steps that usually must be done in a certain order. Solving math problems, sounding out words, and stating a theory or making a logical argument (each proposition in the theory or argument is like a step that leads to a conclusion). [Teach it.]
This is very important! A routine is a connection of a number of events, such as steps in solving a problem or a listing of events leading up to a war. There are different arrangements of steps or events in routines. You want your students to see what these arrangements are. 1. Sequence in one direction. A leads to B leads to C leads to D
Examples: sounding out words; solving math problems. [Teach it.]
2. Sequence with feedback loops. A leads to B and the change in B produces a (reciprocal) change in A
which produces more change in B until some limit is reached. Outbreak of
war, onset of illness, falling in love, divorce, getting porky and out of
Group A Group B
Provocation Anger, fear
Reaction and counter-provocation
3. Stages or phrases. A sequence of events or steps can be seen as a process divided into stages in a process.
Load rifle: a—b—c--d
Fire rifle: e—f—g
Clear rifle: h—i
Clean rifle: j—k, etc.
In history: If you examine enough (examples of) genocidal movements, you notice that one group has some features (e.g., property, social status) that produces envy in another group, or does something that threatens another group (e.g., resists power). This might be seen as the background (first) phase. Then (phase 2) the genocidal group demonizes the first group with racial slurs and propaganda. Then (phase 3) the genocidal group begins to mistreat the victim group; e.g., attacks, job loss, confiscating weapons, special (degrading) clothing. If (phase 4, escalation) the victim group fights back, this provokes worse treatment. If the victim group submits, it furthers the genocidal group’s perception of the victim as degraded. The genocidal group then (phase 5) creates an organization for killing or transporting. Then the killing begins (phase 6).
4. Logical argument.A text might be arranged as a logical argument. There are two sorts of logical arguments.
a. Inductive. Facts are presented. Then the facts are shown to lead to a general idea, such as a conclusion. For example, examine five examples of genocide and INDUCE (see, figure out) the common phases and the activities in each phase.
Or, the prosecuting attorney argues that the defendant, Miss Betty Boop….
1. Had motive. She hated Barney O’Reilly. She was overheard saying, “One day I’m gonna beat him senseless, boop boopeedoo.”
2. Had the means. Barney was beaten senseless with a large blunt object that left dents on his bald head, shaped like the words “Betty Boop.” Miss Boop has a 25 pound purse with her name in steel on the side. The nameplate fits perfectly with the marks on Barney’s head.
3. Had the opportunity.Miss Boop was with Barney O’Reilly the night he was beaten to a pulp.
4. Eye witnesses saw her beat Barney to a pulp. “Oh, yeah,” says Mrs. Tilly Wideload, “she smacked the living %$#@Q out of him.”
“Ladies and gentleman of the jury. All of the facts lead to the conclusion that this tiny woman with a big head is guilty. Guilty. GUILTY.”
b. Deductive. Or, text may be arranged so that it presents a deductive argument. It begins with a general idea, such as a rule---first premise.
“If X happens, then Y must happen.”
It then presents facts relevant to the first premise—evidence or second premise..
It then draws a conclusion.
“Therefore, Y must happen.”
How Do We Get (Acquire, Learn) Knowledge? In general, We “get” (acquire, learn) new knowledge through inductive reasoning. That is, the learning mechanism (1) observes examples and nonexamples (examples of concepts, or rules/propositions, or routines); (2) performs a series (a routine) of logical operations on what it observes; and (3) arrives at (induces, figures out, discovers, “gets”) general idea (the concept, rule, or routine) revealed by the examples and nonexamples.
It’s as if a kid says,
“The teacher showed all these things (a, a, a, a) and said ‘This letter makes the sound ahhh.’ They all have the same general shape. So, I guess SHAPE is what goes with ahhh.”
Observe examples and [perform series of logical operations] get general idea.
[Teach it. Hint. Color. Letter-sound relationships. Monarchy. FOIL]
We apply or generalize knowledge through deductive reasoning.
Like this….. The learning mechanism (1) has/knows/can say a general idea (concept, rule/proposition, routine); (2) uses the general idea (definition of a concept, or statement of a rule, or features of the things handled by the routine; e.g., math problems, words) to examine a possible new example using the information in #2; (3) “decides” whether the new thing FITS (is an example of) the definition, rule, or routine (“Can you solve this with FOIL?”); and (4) “treats” the example accordingly---names it (concept), explains it (with the rule), solves it (with the routine).
“If (so far) all things that look like these (a, a, a, a) say ahhhh, then this new thing (a) probably says ahhhh, too.”
Notice: general idea predict example.
Let’s apply this stuff to learning the six kinds of information. In the case of facts and lists (statements that connect specific things), we simply memorize the connection.
Teacher. “There were thirteen original states.”
Student. “I get it. Thirteen original states.”
But in the case of concepts, rules or propositions, and routines, we have to figure out the GENERAL idea that is revealed by examples. How do we get from examples (specifics) to the general idea embedded in the examples? The answer is, inductive reasoning.
Knowledge of concepts, rules/propositions, and cognitive routines is acquired through inductive reasoning (which is itself a routine).
[See John Stuart Mill’s A system of logic.
http://www.gutenberg.org/etext/27942 and especially
Or Irving Copi’s Introduction to logic.]
The “learning mechanism” performs a sequence of logical operations,
beginning with examples and ending with a general idea.
a. Identify what is common to examples and NOT found in nonexamples.
What is common IS the general idea; e.g., redness. Method of agreement. Examples differ in nonessential features but AGREE in the essential feature. If they are all “treated” the same way (named, solved), it must be because of the way in which they agree.
So, present a range of examples; help students to compare and contrast, and to identify the sameness---which IS the general idea (concept, rule, routine).
b. Identify what is different between examples and nonexamples. What is different must be what MAKES the difference. This FEATURE that is different (present in examples, missing in nonexamples) must be the
general idea. Method of difference.
Examples and nonexamples are t. If they are treated differently, the
difference (feature) must be what makes the difference. This
difference IS the general idea.
So, juxtapose examples and nonexamples that are the SAME in nonessential
features but DIFFER in the essential feature; treat the examples and
nonexamples differently (“This is red. This is NOT red.” Or, “You can use
FOIL to solve this one, but NOT that one.”); help students to compare
and contrast examples and nonexamples, and to identify the difference
that makes the difference.
c. Identify how one kind of thing changes along with (in the same or different
direction as) another kind of thing. Method of concomitant variation.
If one thing changes, and everything else stays the same, and then
another thing changes in a regular way, then it is reasonable to infer
that they go together---they are in a functional or causal
relationship. This form of inductive reasoning is used especially in
discovering rule relationships or propositions.
Knowledge is applied or generalized through a process of deductive
reasoning. If a general rule or proposition (learned either via inductive reasoning or
via being told) is that when demand increases, price increases, and if
you notice that the demand for .45 caliber ammunition is increasing,
your learning mechanism will deduce (predict) that the price of .45
caliber ammunition will increase.
It is a simple deductive syllogism.
When demand increases, price increases.
The demand for ammo is increasing.
.45 caliber ammo is a kind of ammo.
Therefore, the price of .45 caliber ammo will increase.
“How do you know?”
“Because when demand increases, price increases, and an increase in
the demand for ammo is an EXAMPLE of an increase in demand.”
Deductive Reasoning Deductive reasoning, or deduction, or deductive argument is merely a way of thinking or communicating---a routine. There are three parts to what is called a deductive syllogism.
1. General idea, rule, or proposition. (first premise)
2. Facts or evidence relevant to the general idea. (second premise).
3. Conclusion based on how the second premise fits with the first premise.
Some deductive syllogisms are called categorical---these syllogisms use categorical propositions. Others are conditional—these syllogisms use hypothetical or causal propositions.
Categorical deductive syllogisms All dogs are canines. [first premise: general idea or proposition]
Larry is a dog. [second premise: fact or evidence]
Therefore, Larry is a canine. [Conclusion]
No birds are reptiles
Chirpy is a bird.
Therefore, Chirpy is not a reptile.
[You diagram it.]
No birds are reptiles.
Micky is a reptile.
Therefore, Micky is not a bird.
[You diagram it.]
Some snakes have teeth.
Sammy is a snake.
Some dogs have four legs.
Larry has four legs.
Therefore, Larry is some dog? [Huh?]
Conditional deductive syllogisms Whenever the temperature of a gas in an enclosed space increases, the pressure of the gas will increase.
The temperature of the gas in an enclosed space increased.
Therefore (I predict that) the pressure of the gas will increase.
If and only if X happens will Y (happen, increase, decrease).
X (did not, will not) happen.
Therefore (I predict that) Y will not (happen, increase, decrease).
Extracting Information and Re-stating as Facts, Lists, Definitions of Concepts, Rules/propositions, and Routines (e.g., explanations, arguments) Following are excerpts that contain facts, lists, definitions of concepts, rules or propositions, and routines. Find these, identify what they are, and then state them in a simpler form.
1. ...a state is a human community that (successfully) claims the monopoly of the legitimate use of physical force within a given territory. [Max Weber. "Politics as a vocation." 1918]
2. No living being can be happy or even exist unless his needs are sufficiently proportioned to his means. [Emile Durkheim, Suicide. 1897]
3. If the state is to exist, the dominated must obey the authority claimed by the powers that be. [Max Weber. "Politics as a vocation." 1918]
4. ...the term suicide is applied to all cases of death resulting directly or indirectly from a positive or negative act of the victim himself, which he knows will produce this result. An attempt is an act thus defined but falling short of actual death. [Emile Durkheim, Suicide. 1897]
5. If therefore industrial or financial crises increase suicide, this is not because they cause poverty, since crises of prosperity have the same result; it is because they are crises, that is, disturbances of the collective order. [Emile Durkheim, Suicide. 1897]
6. Where the State is the only environment in which men can live communal lives, they inevitably lose contact, become detached, and thus society disintegrates. [Emile Durkheim. The Division of Labor in Society. 1893]
7. There is the authority of the extraordinary and personal gift of grace (charisma), the absolutely personal devotion and personal confidence in revelation, heroism, or other qualities of individual leadership. This is charismatic domination... [Max Weber. "Politics as a vocation." 1918]
8. Quoting Esquirol (with whom Durkheim disagrees):
"Suicide shows all the characteristics of mental alienation." (p. 58)
9. Again quoting Esquirol:
"A man attempts self-destruction only in delirium..." (p. 58)
10. "(N)o psychopathic state bears a regular and indisputable relation to suicide." (p. 81)
11. "(T)he degenerate is more apt to commit suicide than the well man; but he does not necessarily do so because of his condition. This potentiality of his becomes effective only through the action of factors which we must discover." (p. 81)
12. "Man prefers to abandon life when it is least difficult." (p. 107)
13. "Imitation exists when the immediate antecedent of an act is the representation of a like act, primarily performed by someone else; with no explicit or implicit mental operation which bears upon the intrinsic nature of the act reproduced intervening between representation and reproduction." (p. 129)
14. "(I)mitation is not an original factor of suicide. It only exposes a state which is the true generating cause of the act and which probably would have produced its natural effect even had imitation not intervened" (p. 141)
15. Average No. of
Ave. 192 Ave. 135 Ave. 75
What propositions can we draw from the above table?
"(S)uicides are found to be in proportion to "
"and in proportion to " (p. 153)
18. "(W)hen religious intolerance is very pronounced, it often produces an opposite effect. Instead of exciting the dissenters to respect opinion more, it accustoms them to disregard it." (p. 156)
19. "(A) religious society cannot exist without a collective credo." (p. 159)
20. "(T)he more extensive the credo the more unified and strong is the society." (p. 159)
21. "(T)he greater concessions a confessional group makes to individual judgment, the less it dominates lives, the less its cohesion and vitality." (p. 159)
22. "Man seeks to learn and man kills himself because of the loss of cohesion in his religious society; he does not kill himself because of his learning." (p. 169)
23. "(T)he desire for knowledge wakens because religion becomes disorganized." (p. 169)
24. "As suicides diminish, family density regularly increases." (p. 199)
25. "(T)he density of a group cannot sink without its vitality diminishing." (p. 201)
26. "(C)ollective force is one of the obstacles best calculated to restrain suicide, its weakening involves a development of suicide." (p. 209)
27. "Excessive individualism not only results in favoring the action of suicidogenic causes, but it is itself such a cause. It not only frees man's inclination to do away with himself from a protective obstacle, but it creates this inclination out of whole cloth and thus guves birth to a special suicide which bears its mark." (p. 210)
28. "(W)oman can endure life in isolation more easily than man." (p. 215)
29. "...they are crises, that is, disturbances of the collective order." (p. 246)
30. "Every disturbance of equilibrium...is an impulse to voluntary death." (p. 246)
31. "It is not true, then, that human activity can be released from all restraint." (p. 252)
32. "...more depressed and anxious pregnant teenagers, who perceive their social relationships to be less satisfying, and who have less knowledge of child development, have more negative expectations for their infants." J.M. Contreras et al. (1995). Journal of Applied Developmental Psychology, 16, 283-295.
33. High mother support was associated with more secure infant attachment only for those adolescents living with partners." S.J. Spieker (1994). Developmental Psychology, 30, 1, 102-111.
34. This problem--the experience of the irrationality of the world--has been the driving force of all religious evolution...(H)e who lets himself in for politics, that is, for power and force as means, contracts with diabolical powers and for his action it is not true that good can follow only from good and evil only from evil, but that often the very opposite is true. Anyone who fails to see this is, indeed, a political infant... [Max Weber. "Politics as a vocation." 1918]
35. Man seeks to learn and man kills himself because of the lack of cohesion in his religious society; he does not kill himself because of his learning. It is certainly not the learning he acquires that disorganizes religion; but the desire for knowledge wakens because religion becomes disorganized. Knowledge is not sought as a means to destroy accepted opinions but because their destruction has commenced. To be sure, once knowledge exists, it may battle in its own name and in its own cause, and set up as an antagonist to traditional sentiments. [Emile Durkheim. Suicide. 1897]
35. We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. [Declaration of Independence]