3. How do Human Beings (We) Construct Knowledge of Nature?
Martin Kozloff
2012
Please read “What is reality?” and then “What is knowledge? first.
Human beings construct knowledge---which is our representation of reality. We do this using two thinking routines called reasoning. We construct new knowledge (learn something new) through inductive reasoning. WE apply, test, and improve knowledge through deductive reasoning. These are not new ideas. Plato wrote all about them in his dialogues.
Aristotle….
took it farther (in Prior analytics, Posterior analytics, and Rhetoric), and showed the thought processes (thinking routines) by which human beings reason in ways that are valid (leading to useful knowledge) vs. invalid (leading to nonsense and baloney).
John Stuart Mill…
wrote a massive book describing valid and invalid forms of thinking, or reasoning, in A system of logic. (1882). Chapter VIII. Of The Four Methods Of Experimental Inquiry. P. 278.
Constructing Knowledge Through the Cognitive Routine of Inductive Reasoning
Let’s look first at how human beings construct new knowledge (learn something new) through inductive reasoning. I think this diagram is pretty accurate.
Reality Energy Sense organs Human Learning Mechanism Knowledge: Four and only four kinds/forms
Uses Logic (Reasoning) to can be known and communicated.
Transform Sensory Experience 1. Concepts: there are kinds of things (“raw data”) into a. Sensory, or basic concepts: red, straight
b. Abstract, or higher-order concepts:
furniture, democracy, canine
2. Facts: Things (subjects) have features (predicate).
3. Rule-relationships, or Propositions: Classes of things (concepts) are
connected:
a. Categorical relationships: Some classes are, or are not, INSIDE other classes.
(1) “All (things in the class of) pine trees are (in the class of evergreens.” (2) “Some (things in the class of) bacteria are (in the class of things that are) harmless.”
(3) “No (things in the class of) dogs are (in the class of) felines.”
b. Some classes cause or are predicted by other classes:
“If things in class X increase, things in class Y will increase.”
“Whenever things in class X happen, things in class Y happen.”
4. Cognitive routines: sequences of steps
for producing an outcome. Solving problems, describing, explaining,
analyzing, evaluating, organizing
Let’s look closer at inductive reasoning
Inductive reasoning is not a mysterious process that happens in your mind. Inductive reasoning is a cognitive routine (a sequence of steps leading to an outcome)---just like any other cognitive routine, such as solving an equation. The outcome of a successfully solved equation is an answer. The outcome of successfully done inductive reasoning is a valid inductive inference (generalization from facts).
The teacher states the following facts.
This is red. This is red. This is red. This is red. This is not red. This is not red. This is red.
The student reasons from the facts.
“I bet ‘red’ means color.” …………….. “Yup, now I’m sure. ‘red’ is color.”
All the objects called “red” had ONE feature in common. All the objects called “not red” did NOT have the ONE feature that all the “red” objects had. Therefore, “red” must mean (point to) that one feature. And so, the concept---things that are red---is constructed.
1.What’s inductive reasoning for? A routine for making generalizations that summarize what is common to examples.
2. What kind of routine is inductive reasoning? A thinking routine, usually using language.
3. What performs the routine called inductive reasoning? The “learning mechanism” (Engelmann and Carnine, Theory of instruction. Association for Direct Instruction Press, 1991).
4.What is the learning mechanism? The brain, plus sense organs, and other body parts for helping us make contact with the environment.
5. What are the steps in the inductive reasoning routine? What does the learning mechanism do?
a. Examine a particular thing and identify its features.
b. Examine more particular things and identify their features.
c. Compare and contrast the features of the particular things examined. What features are the same in all instances? What features are different? The ways they are the same may be important! The ways they are different may be irrelevant.
d. Make (induce, figure out, construct) a generalization that summarizes what you learned.
Example 1. Developing a concept. The ancient Greek mathematician Pythagoras---who was known for his neat caps……
You’ve heard of the Pythagorean Theorem?
This is the Pythagorean cap.
“discovers” triangle---the class of things (concept) that are triangles.
“Hey, fellas! Look! All of these things that I’ve seen in nature or have drawn on paper have three straight lines that intersect to form angles. The angles add up to 180 degrees. I think I’ll call these things ‘triangles’.”
Example 2. Mr. Dragul teaches the higher-order concept, republic---the class of things that are republic. A student---Debbie Lynne Vampire-Goth---describes how Mr. Dragul communicated (taught), and how kids “got” the concept from the communication. Here’s Debbie Lynn… Tell it, Debbie Lynne!
“Our history teacher, Mr. Dracul, is named after Vlad Dracul, III, Prince of Wallachia, 1431–1476. He’s so cool.”
“Well, he gave examples, and told us to figure out what a republic is from the examples. All of the political systems that Mr. Dracul called republics were in different times, spoke different languages, were of different sizes, and were in different places in the world. However, all of these instances of what Mr. Dracul called republics were the same in two ways: (1) the government was considered a public matter, and (2) government officials were elected. So, the kids thought (inferred, induced, generalized) that the concept or class of republic is DEFINED by the two features that are the same: (1) government being considered a public matter, and (2) government officials being elected. But we weren’t sure. This was sort of an hypothesis about what defines republic.”
“So then Mr. Dracul gave instances of what he called NOT republics. These not-republics were of the same time periods, sizes, languages, and places in the world as the examples of republics, but NONE of the not republics had a government that was considered a public matter, and had elected government officials.”
“So, now we were certain (we concluded) that the concept or class of republics is defined by a government that is considered a public matter, and government officials are elected. And therefore, any government that does NOT have these two features is NOT a republic. Now, if you’ll excuse me, I have to nail a horseshoe to my face.”
“Thanks, Debbie. You’ve been a big help.”
Here’s an exercise. Do it and you’ll see the steps in constructing knowledge using a ROUTINE called inductive reasoning. After each entry below, write down what you’re thinking as you try to figure out what foozle is from the examples of foozle and not foozle.
%$#!)( This is foozle. What is foozle? ………….
(%#@) This is foozle. What is foozle? ………….
&$+=)% This is foozle. What is foozle? …………..
&$=+%# This is not foozle. What is foozle? …………..
(%#@) This is foozle. What is foozle? …………….
(%#@ This is not foozle. What is foozle? …………….
Did you figure out that ) is foozle, or that ) is what makes an example foozle?
If you did figure it out (construct knowledge that ) is foozle), I bet you used the following routine that consists of these logical operations.
(1) Examine the examples called foozle and identify their features.
(2) Compare the foozle examples, and identify which feature is always there when the example is called foozle---the common feature.
(3) Hypothesize (bet, suspect) that since there is only one common feature in the foozle examples, that feature is logically what makes an example a foozle. The features that are different from one foozle to another can’t be what causes an example to be foozle.
(4) Contrast features of the foozle examples with features of the not foozle examples.
(5) Identify the feature common to the foozle examples that is not in the not foozle examples. And
(6) Draw the conclusion (or make the inductive inference), that foozle is ) . Because whenever ) is there, it is a foozle, and whenever ) is NOT there, it is not a fozzle.
If you didn’t figure out that foozle is ), USE the above routine and see if that works.
Now, let me ask you something. If you know that plants grow best under certain conditions, would you provide those conditions if you wanted plants to grow best? Of course. Well, if human beings learn something new (construct knowledge) by performing the above sequence of logical operations with examples, doesn’t it make sense to teach in a way that makes it easy for students to DO that sequence by (1) using several examples that CLEARLY SHOW the important features; (2) and putting examples (foozle) and nonexamples (not foozle) next to each other so examples and nonexamples can be contrasted to reveal the important features?
Yes!
That’s what we mean by instruction that is well-designed---that communicates clearly.
Can you see how important it is to teach your students to USE inductive reasoning to figure things out? To make generalizations from specific examples of some concept, or rule, or routine? Here’s an example of teaching students to use inductive reasoning to construct or figure out a rule relationship from examples. Ms. Ironabs, whose kids are VERY well behaved,….
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….says,
“Boys and girls. Here are facts that connect the number of orders for gold (the demand) on the first day of the month, with the price of gold one week later. You compare the facts (see how they are the same) and contrast these facts (see how they are different), and find (induce, discover) if there is a connection between change in demand and change in price. Does price change after demand changes? Here’s the routine for finding out.
Number or Orders Price of Gold per Ounce
For Gold One Week Later
Jan 1 5,012 $1023
Feb 1 5,867 $1233
March 1 6,212 $1445
April 1 7,333 $1654
May 1 6,862 $1400
June 1 6,390 $1340
July 1 6,011 $1200
August 1 7,082 $1800
Sept. 1 7,088 $ 1800
“1. Look at January 1. What is the demand and what is the price?
“2. Now compare January 1 with February 1. Did demand go up, down, or stay the same? And what did price do? Did it go up, down, or stay the same?
“3. So make an hypothesis: When demand_____, then price_____.
“4. Now look at March, and the rest of the months to see if your hypothesis is supported or if you have to change it.
“5. Now, summarize the relationship, if there is a relationship? Is there a change in price after there is a change in demand? If so, state the relationship as a rule, in the form “When……, then…..”
That is one version of the inductive reasoning routine that humans use to construct knowledge---in this case, knowledge of the relationship between two classes (concepts): demand and prince.
Humans apply (generalize), test, and improve knowledge through deductive reasoning. “When (things in the class of) demand for gold increases, (things in the class of) price of gold increases.” Or “Price of gold varies directly with demand for gold.”
Applying (generalizing), Testing, and Improve Knowledge Through Deductive Reasoning
Humans apply, test, and improve knowledge through deductive reasoning.
Now that we know what foozle is (we know a definition of the CONCEPT foozle), what the concept republic is, and the rule-relationship (connection) between the demand for gold and price of gold, we can apply this knowledge to new situations. Imagine what the learning mechanism says as it reasons.
“So, here’s what I know. All things that have feature ) are foozle. This is concept knowledge. The concept is things that are foozle. Foozle is defined by the feature ). Here’s the new situation. This new thing has these features----- %^$#)*!
One of the features is ).
Now I make a deduction, or deductive inference. Conclusion. %^$#)*! is foozle.”
Here’s deductive argument (syllogism):
All things with feature ) are (in the class of) foozle.
This new thing has feature ).
Therefore, this new thing is (in the class of) foozle.”
You can easily see whether your mind is using deductive reasoning to draw the conclusion. Just ask yourself, “How did I conclude that %^$#)*! Is foozle?”
Your answer is probably this, “Because %^$#)*! has ), and all things that have ) are foozle.”
Imagine that it turns out that the new example %^$#)*! Is NOT a foozle. That means you have learned something new. The definition of foozle is NO LONGER “All things that have ) are foozle.” The revised definition (more accurate knowledge) is “SOME things that have ) are foozle.”
Can you see how important it is to teach your students deductive reasoning---to apply knowledge to new situations? For example, you use many examples to teach your students how to do long division---they figure out (induce) the GENERAL routine from the examples. Now that they have learned the general routine, give them new examples to which they can APPLY (GENERALIZE) the routine.
How could you teach your students to make deductions from the rule about demand and price of gold?
“Boys and girls. What is the rule about demand and price of gold?”
When the demand for gold increases, the price of gold increases.
When the demand for gold decreases, the price of gold decreases.
Price of gold varies directly (changes in the same direction as) with the demand for gold.
“Yes, that is the rule about the demand and price of gold.
“Look at the data. Let’s say the demand for gold goes from 7,000 orders one month to 8,000 orders the next month. What will happen to the price of gold? Use our rule! What does it say?”
When demand increases, so does price.
“Correct. Now use it!
Increase. Go up.
“How do you know?”
The rule. When demand increases, so does price.
“Excellent deduction from the rule.”
“Let’s say that demand goes from 8,000 to 5,000. Use the rule. What does it say?”
When demand increases, so does price.
“Use it!”…..
The next unit tells about the four kinds of knowledge that humans construct through inductive reasoning and apply through deductive reasoning:
1. Concepts: kinds of things defined by shared features.
2. Facts: statements of the features of INDIVIDUAL things. “This table (subject) is beige (predicate).”
3. Rules or propositions: how classes of things [concepts] are connected), such as “All cats are felines” and “When ocean temperature increases, it releases carbon dioxide into the atmosphere.”
4. Cognitive routines.