Here are the four forms of knowledge and formats for teaching each kind.
M. Kozloff
Furniture. 1. Concepts are the kinds of things in our reality. What our reality has in it. Concepts are sets of things that share defining features.
Concept, class, or category = table. Verbal definition: tells features.
Tables are a kind of furniture (larger category—GENUS--in which tables exist) that consists
of (1) a flat top surface, (2) legs, and (3) you put things on it (the difference between tables, as
Chairs furniture, and other kinds of furniture).
Examples of tables, millions. All have the three defining features, as well as irrelevant features, such as color, size, number and shape of legs, what you put on them.
2. Facts. Facts tell about individual examples of concepts. EVERYTHING is an example of (is a member of) many concepts. Facts tell the features of examples. These features might include the defining features as well as irrelevant features. The LIST of facts/features is a DESCRIPTION.
“This table has three black legs, a flat brown, top surface that is square and is 4 x 4 feet, and you put lamps and books on it.” Note the features that are part of the definition and features that may be interesting or useful to know, but are not part of the definition. “Hey, where do we put the lamps and books?” “On this table?”
3. Rules are statements that tell how classes of things (concepts) are connected: category rules and causal rules.
All dogs are canines. Or, All animals in the class of dogs are in the class of canines. This is a category rule. It tells which is inside another.
Concept, or the class of canines. Canines are mammals (larger category--genus) with snouts and nonretractable claws.
wolves The class/concept of dogs. Definition. Dogs are domesticated carnivorous mammals coyotes that typically have a long snout, an acute sense of smell, and a barking, howling, or whining voice. They are widely kept as a pet or for work or field sports.
Breeds (Collies, Chows, Mixed) are a smaller category of dogs in the category of canines in the category of mammals.
Ned is a mixed breed dog, canine, mammal with four legs, white and brown spots, 4 years old, and her favorite form of play is biting bubbles. [Facts about Ned.]
Rule. As pressure increases on gas in a closed vessel, temperature of the gas increases. This is a
causal rule. It tells what happens to things in one class when things in another (connected class)
change. Examples of Pressure Corresponding (goes with) Examples of Temperature.
Increases Increases
Decreases Decreases
You can teach rules two ways.
a. By telling the rule and then revealing with examples and nonexamples. This is the deductive way.
Easier for students. All they have to get is that examples INSTANTIATE the rule. Or,
b. You can give examples and nonexamples (of pressure and temperature changes) and help students
figure out the rule from how the two variables change together. The is the inductive way. For this to
work, you have to teach students to example pairs of variables and see how they change.
When pressure is Temperature is “When pressure goes from 100 psi to
100 psi 90 degrees 80 psi, what happens to temperature?”
80 psi 70 degrees “When pressure goes from 80 psi to
60 psi 65 degrees 60 psi, what happens to temperature.”
130 psi 110 degrees Etc.
200 psi 150 degrees
180 psi 130 degrees “So when pressure goes up, what happens
to temperature? When pressure goes down,
what happens to temperature?” [rule figured
out from examples.]
4. Routines are sequences of steps for producing some kind of outcome.
The class or concept of routines for sounding out words. Contains billions.The routine consists of steps. The routine can be applied to all examples of words in the class.
By showing, leading, and having students go through the routines, they figure out
that the routine applies to all words (generalization), and that the letters and their arrangements are irrelevant to the STEPS. Yes, the sounds differ, but the steps are the same.
The table on the next pages reviews what each kind of knowledge is, and gives you one or more
formats for teaching each kind.
1
Note. All of the formats below can be, and usually should be, enhanced with add ons here and here (Table B). Be prepared to correc`````````````t errors
Teaching Concepts with verbal definition, synonym, examples, morphemes, and context.Definition
Concepts carve reality into chunks, or kinds of things.
Concepts are classes of things grouped by certain ways they are the same. Dogs, tables, furniture, red, color, male, female, fast, forest, trees.
Everything (every instance) IN a concept or class is an example.
Note: a word (“red,” “canine,” “republic”) is not the concept. A word is just a signal that points to examples of the concept.
For instance, “red” points to that object over in the corner.
The concept is not the word or name; the concept is the class of examples that share certain features. Therefore, to teach a concept, you teach what features are common to examples in the class, and what features are not.
There are five ways (formats) for teaching concepts. It depends on the nature of the concept and on students’ background knowledge.
a. Basic or sensory concepts. One example shows all the features. Colors, shapes, size, loudness, straight, crooked.
So, all you need to do is show examples that show the defining features.
Name them---“This is….”
Make sure the examples differ in irrelevant ways.
The learning mechanism will figure out that the ways they are the same must be what defines the concept.
Juxtapose a few examples with nonexamples. The two should be the same in irrelevant ways but different in the defining feature. Label them “This is… This is NOT…” The learning mechanism will now be sure that the defining feature is what the examples have and the nonexamples don’t have.
b. Abstract concepts. You can’t see all the features. Examples have too many features spread over time, place, objects and activities. democracy, furniture, comet.
(1) Give a verbal definition that tells the features.
(2) Follow the verbal definition with examples and nonexamples, as with teaching sensory concepts.
c. Synonyms. Define a concept with another word that students know. Divide means take apart into pieces. Succinct means brief. Embolden means to make fearless. Terrify means to scare someone’s socks off.
d. Morphemes. Some words contain parts that themselves have meaning. Teach these meanings and help students to figure out what the word probably means.
entrap. en means to do something. trap means to catch and hold something. So, entrap means to do something to get and hold something.
inspire. In means to put something inside. Spire means spirit. So, inspire means to put spirit into something.
e. By context. Sometimes you can figure out what a word means (the concept) from other sentences.
“He waddles like a duck when he walks.” Ducks walk by rocking side to side. So, waddle probably means he rocks side to side as he walks.
Teach concepts before lessons that USE the concepts.
Teach concepts as a lesson itself---“Language time.”
Decide which format is appropriate for the concept and the kids. / Teaching Facts
Definition
Facts tell features of a subject that is a single thing.
“This table (singular subject) is brown (predicate).”
The subject part of the statement tells what the statement is about---this table.
The predicate part of the statements tells more about the subject---is brown. / Teaching Rules
Definition
Rules are statements of connections among concepts. Today, there were 1400 orders for gold in the world; and the price of gold was $1500 an ounce. That is two fact statements.
1. “The number of gold orders today (a singular subject) is 1400 (predicate, tells more about the subject).”
2. “The price of an ounce of gold today (a singular subject) is $1500 (predicate, tells more about the subject).
But what if we had daily facts on the number of orders and the price of gold for 200 days? We might find a connection between the class of things that are orders for gold (2 orders, 500 orders, 100 orders, 1400 orders, 3 orders) and the price of an ounce of gold ($1000, $900, $1500, $750).
We might find—and state a rule: “The higher the number of orders per day, the higher the price of gold per ounce.” Or, “The price of gold varies directly with orders for gold.”
Since this rule states how change in one class of things (concept) is connected to change in another class of things (concept), teach rules by:
a. Telling the rule; showing and identifying examples and nonexamples; having students identify examples and nonexamples.
Or
b. Show examples and help students figure out and then state the connection.
“As you go from one example to the next, is it the case that when one variable changes, the other variable changes?”
Yes.
“How?” / Teaching Routines.
Definition
A routine is anything performed as steps:
1. Sounding out words,
2. Solving a math problem,
3. Searching for words in a text (“ant” “said”) in order to answer a literal question (What did the ant says?”
4. Finding and identifying figures of speech in a poem.
5. Stating 6 rules that constitute a theory.
6. Stating 8 facts that constitute a description.
Routines are a sequence of steps that do something. But you must already know certain knowledge elements in order to perform the steps. Therefore, when teaching routines, do a knowledge analysis to determine the steps, and the knowledge elements needed for each step.
Knowledge analysis of sounding out words.
Steps / Knowledge elements
1. Put finger or focus on spot to the left of the first letter.
2. Move finger or direct focus to the first letter.
3. Say the sound that goes with the first letter.
4. Move finger or eyes to the second letter.
5. Say the sound that goes with the next letter.
Repeat. / 1a. What a letter is.
1b. Where the first letter is.
1c. Where the spot to the left of the first letter is.
2a. How to move finger or eyes to the right, and to stop at the first letter.
3. Know the sound that goes with the first letter (i.e., has said the correct sound reliably before).
4a. Where the second letter is.
4b. . How to move finger or eyes to the right, and to stop at the first letter.
5a. Know the sound that goes with the second letter (i.e., has said the correct sound reliably before).
Formats or Procedures
Gain attention. “Boys and girls. Eyes on me. Show me ready.”…
“Yes, I love the way…”
“Now you’re ready to learn!”
Frame the instruction.
1. Tell what you’ll be working on. “Now we’ll…”
2. Tell what they’ll do when you are done (objective). “When we’re done, you will…”
Here are the five ways to teach concepts after you’ve gained attention and framed instruction.
a. With Synonym.
Define a concept with another word that students know. Divide means take apart into pieces. Succinct means brief. Embolden means to make fearless. Terrify means to scare someone’s socks off.
You’ll often use synonyms while students read or while or you are reading to students.
“We hold these truths to be self-evident (means pretty obvious)… that all men (he means human beings) are created (born) equal (equal in their rights).”
“New word. embolden. What’s our new word…. Spell embolden…. Sound it out if you have to…. What word?
“Listen, embolden means to make fearless. What does embolden mean? What’s another word for embolden? To make fearless. Yes, embolden is another word for fearless.
“For instance. Her coach made her fearless to sky dive.
“I’ll say that with our new word. Her coach emboldened her to sky dive.
“Listen, his human made Spot the dog fearless about hunting wild pigs. Say that with our new word. His human made Spot the dog emboldened about hunting wild pigs. Yes, you used emboldened in a sentence!”
b. With Examples and nonexamples.
Teach with a set of examples and nonexamples when the concept is a basic or sensory concept. It has few defining features, and you can see or hear or feel them all in one example. Of course, you need to show variations.
(1) “New word/concept---elliptical. What’s our new word/concept?.... Spell elliptical. … Sound it out if you have to….What’s our new word/concept?”...
(2) Examples.
“This is elliptical.”
“This is elliptical.”
“This is elliptical.”
“This is NOT elliptical.”
“This is NOT elliptical.
“This is not elliptical.”
“This IS elliptical.”
(3) Test. Show all examples and nonexamples, and ask, “Is this elliptical?” Correct errors or verify.
Later, work on generalization.
c. With Verbal definition plus examples and nonexamples.
Use this method when a concept has a lot of features and they are so spread out in time, space, activities, and objects that you can’t show examples, as you can show examples of sensory concepts, such as colors.
So, start with a verbal definition that tells the features, and then instantiate the features with examples and nonexamples.
Basically, the examples and nonexamples tell the learning mechanism, “This is what I mean.”
Orbit
(1) “New word. Orbit. What’s our new word?... Spell orbit… Sound it out (if they need to). What’s our new word?”…
(2) Tell the new word and its definition. “Listen, an orbit is a path (genus or larger category) that is: (1) shaped like a flattened circle, and that (2) one thing travels around another thing (the features that make the difference between orbits, as a kind of path, and other kinds of paths, such as trails through the woods). Again, an orbit is…..”
Note, we taught the features one by one! Hold up fingers or use a numbered list.