Forms of Knowledge and Phases of Mastery
‘O logoV [ho logos] à Word. Rule. Law. Reason. Discourse.
I repeat. ‘o logoz The Word.
How important IS The Word?
en arch hn o logoz kai o logoz hn proz ton qeon kai qeos hno logoz.
hen arke’ hen ho logos kai ho logos hen pros ton teon kai teos hen
ho logos
“In the beginning was the Word, and the Word was with God, and the Word was God.” (John 1:1)
Imagine that you have no language.
1. You have no way (no words) that transform raw sensation (light, sound, and touch) into STUFF “out there.”
Nothing that does this….
Something there. “What’s dat?”
Or this….
Class of things “What do ya call dem?”
Or this…
This That
(When, If, If and only if, The more) This increases, the (more, the less) That increases.
Stuff that is NOT you. [When you say “That,” you imply that there IS that and there IS you, who are NOT that.]
Stuff that exists on its own. “That is…”
Stuff that you---as a subject OF experience (“I am seeing.”) and as an actor IN the world (“I am rolling a ball.”)---can contact and know about.
What stuff?
(1) Thing.
this, that, it, Muffy.
This is Muffy. [fact]
Muff says that she (a subject and actor) has a sok (a dat), which exists independently of her (I).
(2) Classes of things and happenings.
Muffy, pet, cat, feline, mammal, animal, living being.
A rifle shot, shootings, fire fight, battling, battle, campaign, war, conflict of civilizations
(3) Connections among things, happenings, and classes of things and
happenings
It was a Wednesday when Debbie Jean realized she was out of diapers. [Look at all this says.]
Debbie Jean is out of diapers. [Fact. Connects a thing called Debbie Jean and a condition of being without diapers]
Things that are out of diapers. Debbie Jean. [Categorical rule or
proposition?]
Things that are out of diapers.
Debbie Jean
Debbie Jean realizing Things that happened on
that she’s out of diapers Wednesday. [Fact]
Things that drool. That stinky Debbie Jean. [Categorical rule
or proposition]
Things that make Debbie Jean angry Lack of diapers (?) [Rule?]
Love stinks. [Categorical rule, or proposition]
Things that stink
Love
Debbie Jean
Beans are a musical treat. [Categorical rule or proposition.]
Things that are musical treats.
Things that are beans.
The more you eat, the more you toot. [Causal or functional rule, or proposition]
Formally stated: As the consumption of things in the class of beans increases, the rate of things in the class of tooting increases.
Diagram of (another way to represent) this relationship.
2. Without language you have no way (no words that represent, point to, or signify) STUFF out there.
“That is a tree.” “Look at those birds flying.”
3. Without language you have no way (no words that stand for, or symbolize) stuff out there, and what you know about stuff.
Without words---logoV-- there can be no class of things that are trees, because you have no way (words) to represent SAMENESS that identifies, groups, and is used to communicate about trees. There is only the changing visual image of brown and green. There can be no rules about how trees grow in relation to water because you have no words to transform difference over time into the thing---change---and change in two things into a connection. There is only “this, now.” To see change---as some sort of thing---you need a way to see the sameness in the THING that changes. Without words, there is no WHAT that changes. And there is no such THING as change.
4. Without language you have no way (no words) that you can arrange in sentences and by which you can talk to yourself (think) and examine what you think you know and develop more knowledge. How can you think without words?
5. Without language you have no way (no words) by which to communicate experience and what you know. Besides, you have nothing TO communicate.
In summary, without language you live in the eternal now---of changing light, sound, touch, and feeling. And you are alone. You can never be WITH others because you have no way to connect with the MINDS of others. You can gain some knowledge, but it’s mostly reflexes. touch à pain à move hand.
What language makes possible
We use language to:
1. Turn the buzzing confusion of reality into things, classes, and connections.
2. Signify or point to things, classes, and connections.
3. Symbolize (stand for) things, classes, and connections. With language symbols we can store our representations, think about them (look at them, rearrange them, analyze them, improve them); and communicate them.
So, what is knowledge?
Knowledge is OF things, classes, and connections. It is answers to the questions what, who, how, when, why. It is used when we describe, explain, make a case for some conclusion, evaluate, predict, plan. In all of these language activities, we use the same kinds of knowledge. But first….
How do we get knowledge?
Here’s a picture of how human beings develop knowledge though language.
Experience: Seeing, hearing, touching. But what is it that we see, hear,
and feel that is more than just lights and sounds?
The “learning mechanism” figures out what is there---things, classes of things, and relationships.
There are only five kinds of “figurings out” of what is there. Only five kinds of knowledge that reasoning gives us.
Only five kinds of knowledge that we represent with words, store (in our minds, books, art, and computers), and communicate.
These kinds of knowledge (representations of reality) are:
(1) concepts; (2) facts; (3) lists; (4) rules or propositions;
(5) routines.
Human beings (in a culture) organize knowledge into systems---knowledge systems---that are important to their lives. So, we have plumbing, food preparation, teaching, mathematics, law, medicine, philosophy, logic, music, religion, physics, geology, building construction, war, and many more.
Each person in a culture---through language and communication with others in the culture---gradually develops a similar way of representing and communicating knowledge in the culture’s systems of knowledge.
Fact. One specific thing is connected to another specific thing.
The name of a city (Jefferson City) is connected to the words “capital of Missouri.” The name of a place (Boston) is connected to an even event (Boston Massacre).
List. A number of events, features, dates, persons, etc. are enumerated ina series. Phases of cell division. New England states. Thirteen original states. The first ten Amendments (Bill of Rights).
Sensory concepts. Things are connected by their common feature or features, such as color, shape, sound. Any example shows the features.
Abstract or higher-order concepts/categories. Things are connected by their common feature or features, but the features are not easily presented together. Examples can’t be held up for display. monarchy, cosmos, galaxy, igneous rock.
Rules, rule-relationships, propositions. Statements of how categories (not specific things) are connected. How the category of price (in general) increases when the category of demand (in general) increases. How the category of dogs (in general) are part of the category canines.
Routines. How actions (physical and mental) are connected in a sequence of steps. Stating a theory, solving a math problem, writing a paper.
Knowledge (of connections) is acquired (learned) through a process of inductive reasoning. What is glerm?
1. This is glerm. (/’_ What is glerm?
2. This is glerm. &*)’_ What is glerm?
3. This is glerm. \*^#( What is glerm?
4. This is NOT glerm. /’^# What is glerm?
5. This is NOT glerm. _&\* What is glerm?
6. This IS glerm. _&\*) What is glerm?
7. This IS glerm. /’(^# What is glerm?
What feature makes something glerm?
What was the logical process by which you figured it out, or induced the generalization: Glerm is……..?
Did you compare and contrast examples and nonexamles?
“Whenever it’s called glerm, there is………”
“Whenever it’s called NOT glerm, there is NOT….”
“Glerm must be whatever is always there when it’s called glerm and
what’s NOT there when it’s called NOT glerm.
“Therefore, glerm is…..”
In summary, the “learning mechanism” performs a sequence of logical operations--beginning with examples and ending with a general idea.
Since reasoning involves comparing and contrasting, vocabulary (to describe), and logical inferences (Since…., therefore…), persons who lack skill at comparing and contrasting, vocabulary, and logical inferences, will have a harder time learning. What should you do?
This figure summarizes.
http://people.uncw.edu/kozloffm/jpglearning.doc
There are different sets of logical operations for comparing and contrasting examples and nonexamples, and then drawing a conclusion about what is connected to what, or what causes what.
These logical operations are called inductive reasoning. Here are three common forms of inductive reasoning when we ACQUIRE knowledge.
a. 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).
Glerm examples 1, 2, 3, 6, 7 are the method of agreement.
b. Method of difference.
Examples and nonexamples are the SAME in nonessential features but
DIFFER in the essential feature. 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; help students to compare
and contrast, and to identify the difference that makes the
difference.
Contrasting glerm examples 1, 2, 3, 6, 7 with nonGlerm examples 4 and 5 is the method of difference.
c. 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.
1. When A, B, and C are unchanged and D is 10, Y is 23.
2. When A, B, and C are unchanged and D is 5, Y is 12.
3. When A, B, and C are unchanged and D is 20, Y is 34.
4. When A, B, and C are unchanged and D is 15, Y is 30.
5. When A, B, and C are unchanged and X is 50, Y is 70.
You can see that Y varies in value. If A, B, and C do NOT vary, then can you INFER that A, B, and C are associated with change in Y? No? How can something that does NOT change produce a change in something else?
If only D varies in a REGULAR way when Y varies, does that appear to show an association between D and Y? Yes. D and Y are the only things that change together---co-vary.
Can you state the relationship?
How we apply knowledge.
Knowledge (of a general idea) is applied or generalized (to specifics, to new examples) through a process of deductive reasoning. If a general rule (learned either via inductive reasoning or via being told) is that when demand increases, price increases, and if you notice that the demand for ammunition is increasing, your learning mechanism will deduce (predict) that the price of ammunition will increase.
It is a simple deductive syllogism,
When demand increases, price increases. [rule]
The demand for ammo is increasing. [fact]
Therefore, the price of ammo will increase. [prediction of another fact]
“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.”
There is an effective and efficient procedure for teaching each of the six kinds of knowledge in the phase of acquisition. The procedure is the same regardless of the content. Each procedure is effective because it facilitates the learning mechanism’s USE of inductive reasoning.
However, each procedure is a simple variation of a general procedure for teaching (during the phase of acquisition).
Forms of Knowledge see p. 7-11
**Gain attention.
**Frame instruction---say what you’ll be teaching.
**Present information with the first example (model).
**Have students do it with you (lead).
**Check to see if they got it (immediate acquisition test/check).
**Use model, lead, test with more examples and nonexamples (for contrast).
**Test/check with all examples and nonexamples (delayed acquisition test)
**Correct all errors and retest.
Four-Level Procedure for Remediation
Forms of Knowledge see p. 7-11
Variations of this general procedure are: (1) how many examples and nonexamples are used (for concepts and rules); and (2) whether you teach a sequence of steps (routine) or items (list).
See Forms of Knowledge
Here’s a list.
1. Facts. Boston -- Massachusetts
2. Lists. Prophase, anaphase, metaphase, telephase
3. Concepts/categories.
a. Sensory concepts/categories red(ness), on(ness), loud(ness), circle
(circularity)
b. Higher-order, abstract concepts/categories. democracy, canine, cell
4. Rules, rule-relationships, propositions
a. Categorical rules.
All dogs are canines.
No cats are canines.
Some fungi are poisonous.
b. Causal/functional rules. You have to consider the function and effect of each variable or factor in a relationship, and the direction of change.
(1) What does each variable/factor/condition do in the relationship? What is its function?
“When temperature of kindling material increases to 600 degree F (given 20% oxygen), there is combustion.”
Independent variable, antecedent. Temperature.
Dependent variable, consequent. Combustion.
Intervening variable. Oxygen.
(2) What influence does the independent variable have on the dependent variable? The independent variable is
(a) Merely correlated with subsequent change in the dependent
variable We can’t prove that change in Y requires change in X.
“The more coffee you drink (to a point) the less likely you are to have a heart attack.” Does coffee DO anything? Or is it something else?
(b) Is sufficient for a change in the dependent variable.
“When a government increases income or property taxes by 5% or
more and taxpayers see no benefits to themselves, the legitimacy of
the government [all other things constant] decreases.
(c) Is necessary for change in Y.
“You can increase the amount of positive reinforcement for good
tries, but a struggling student will not “get” the information until