The Road to Proficiency

This document first identifies the main knowledge elements of proficient teaching. Then it examines each element in more detail. Links take you to documents that provide even more information. Part I. How Human Beings Construct And Organize Knowledge Good Teachers are Applied Logicians.

1. What is Reality, or Nature?

2. Knowledge is a representa-tion of Reality, or Nature, constructed by human beings.

3. How do humans construct knowledge---a representation of reality?

Humans use:

1. Inductive reasoning to acquire new knowledge.

2. Deductive reasoning to apply, test, and revise knowledge.

4. There are four kinds or forms of knowledge by which we represent reality.

1. We invent classes of things that have common features. [Concept knowledge]

2. We know the features of things. [Fact knowledge]

3. We discover how classes of things are related to each other. [Rule or proposition knowledge]

4. We know that performing a sequence of steps has an outcome. [Routine or strategy knowledge]

There is an effective procedure for (1) acquiring; (2) generalizing; (3) using fluently; (4) integrating; and (5) retaining knowledge = phases of learning/instruction.

5. Humans construct, save, store, and communicate knowledge (our representation of reality) with language and other forms of communication, such as music, dance, painting, and sculpture.

Knowledge (of facts, concepts, rules, and routines) is most clearly and efficiently communicated with simple declarative statements: subject…predicate

6. Humans organize knowledge into knowledge systems, such as math, science, history, religion, economics, literature, farming, building, medicine, law, education, and many others.

7. Some ways of acquiring (constructing) and applying knowledge are logical, and lead to valid beliefs (sound reasoning).

Other ways of acquiring (constructing) and applying knowledge are illogical, and lead to invalid and false beliefs (fallacious reasoning). Teachers need to know this and teach it to their students.

Part II. Using Principles Of Knowledge [Part I] And More Ideas To Design Curriculum [What To Teach] And Instruction [How To Teach]

“Crank it, Loretta!”

Principles of Well-designed Curriculum

1. What is a curriculum?

2. Some curricula teach tool skills (reading, math, language, and reasoning). Other curricula teach content or subject matter knowledge systems (literature, history).

3. Develop a curriculum by considering: a. Scientific research, experts in the subject, and your own knowledge.

b. Curriculum strands---main kinds of knowledge to be taught; e.g., in literature, poems, plays, religious writing, and fiction of different periods.

c. The sample of knowledge to be taught in each strand.

d. Curriculum standards, goals, or objectives---and the knowledge students need to achieve the objectives---for (1) the whole curriculum, (2) units (sequences of lessons) in the curriculum, (3) lessons, and (4) short tasks in each lesson.

e. Using knowledge analysis to identify all the elementary (component) skills in a complex skill.

f. Teaching component skills or knowledge elements (pre-skills) before teaching complex skills that USE these elements (logically progressive sequence).

g. How elementary knowledge will be integrated into larger and coherent wholes; e.g., in an arithmetic curriculum, integrating counting, subtraction, and estimation to form the routine of long division

Principles of Well-designed Instruction

1. When and how to use (1) explicit, systematic, focused, teacher-directed instruction; and (2) discussion, inquiry, and independent student learning and application.

2. How to collect information from student performance (assessment), and use it to make decisions about curriculum and instruction.

3. How to use the proper for procedure or format for teaching the different kinds of knowledge: facts, concepts, rules, routines.

4. How to work systematically on all five phases of learning: (a) acquisition of new knowledge; (b) generalization of knowledge to new examples and materials; (c) fluent use of knowledge; (d) retention of knowledge; (5) strategic integration of knowledge elements into larger wholes.

5. How to corrects errors, firm up weak knowledge elements, reteach as needed, and provide intensive instruction as needed.

6. How to design lessons.

7. How to teach at a brisk pace.

8. How to give frequent opportunities for group (choral) and individual responses to test/check learning.

9. How to use pre-corrections, or reminders, to prevent errors.

10. How to use a questioning technique such as Socratic dialogue.

Part III. Destination---Four Teaching Activities. Now it all comes together.The four activities are connected. 1 is used to do 2; 1 and 2 are used to do 3; and 4 is the context in which you do 1-3.

1. Planning instruction and teaching daily lessons from textbooks and other materials, such as internet documents.

Much of the knowledge in your curriculum is in textbooks that your school and district want you to use. Skilled teachers know how to:a. Improve textbooks with supplements, glossaries, outlines, big ideas, and guided notes.b. Divide the materials into units (sequences of lessons on a topic).c. Identify exactly what they want students to learn in each unit (objectives).d. Divide each unit into a logical sequence of lessons.e. Plan exactly how to communicate TO students (instruction formats), and how to help students THEMSELVES to

get and apply knowledge.f. Find out if students are learning (assessment, progress monitoring).g. Help student to organize all they’ve learned (strategic integration).

2. Evaluating, improving, and teaching from programs.

With textbooks, YOU have to select and organize their content into lessons. However, programs are curriculum materials already organized into a sequence of lessons. Programs might be for teaching beginning reading, math, spelling, remedial reading, and writing (tool skills). Programs usually tell you exactly how to communicate knowledge to students (instruct); how to correct errors; how to assess progress; and what to do if some students aren’t learning well (remediation). Many programs are poorly designed. For instance, they don’t use enough examples of math problems to solve; don’t work on fluency (going fast) or generalization (new examples); don’t provide enough review (to build retention of knowledge); don’t tell you the errors students are likely to make, and how to correct errors. Some programs are pretty well designed, but you have to make them better. And a few programs are very well-designed, but can be improved for certain students. Skilled teachers don’t just USE programs they are given. They carefully examine how the programs are designed; they find the strong and weak FEATURES; they decide if the programs are good enough to use at all; and then they use knowledge of good design to make pretty good or very good programs more effective for all students. You will learn how to do this!

3. Planning, teaching, and evaluating a semester or a year-long curriculum.

In elementary schools and special education classes, the curriculum is many subjects (knowledge systems). In secondary schools, the curriculum is usually one subject. Either way, you need to know:1. What your state curriculum, district curriculum, scientific research, and subject matter experts say your students should learn (curriculum objectives, or standards).2. What your students should DO at the end (final objectives) that shows whether they learned.3. What exactly to teach in each subject of the curriculum that will enable student to meet the objectives.4. What textbooks, programs, and supplemental materials contain the knowledge students need to learn.5. How to organize the knowledge in textbooks, programs, and supplements into a logical sequence of units and lessons within units.6. Exactly how to help your students acquire the knowledge during each lesson (instruction).7. How to find out if your students are learning (assessment, progress monitoring), and how to improve curriculum, materials, and instruction if students are not learning easily or quickly enough (remediation via error correction, part firming, reteaching, or intensive instruction).

4. Planning and running the class as a social group.

You can have the best curriculum, textbooks, and programs, but that’s not enough. You need students to respect and trust you, are energized and want to learn, take part, try hard, and know how to learn (e.g., know inductive and deductive reasoning; know how to develop and evaluate concept definitions; discover and apply rules; develop and evaluate theories, descriptions, solutions, and arguments (routies). So, you need to know how to turn a number of individuals into a team or “learning community,” who are fluent (accurate and fast) at doing the class business (getting ready to learn, doing and handing in assignments, taking notes).

Here’s a diagram of the route.

Reality

Constructing Knowledge Applying (Generalizing)/testing and Improving Using Inductive Reasoning. Knowledge through Deductive Reasoning.

“I see instances where “Whenever C happens, Y happens. [Rule] ABC is followed by XYZ An instance of C just happened. [Fact] AC is followed by WGY Therefore, Y will happen. [Conclusion from fact LMC is followed by TRDY in light of rule] BJUC is followed by HWSY

I (infer, conclude, generalize) that whenever C happens, Y

happens.” [rule] Develop

Four Kinds of Knowledge

Concepts: Facts: Rule-relationships/ Cognitive Routines: 1. Sensory Individual things have propositions: Sequences of steps that

2. Higher-order features, communi- Connections among produce known outcomes. Classes of things that cated with declarative classes (concepts). Solving equations; using share certain features statements. “Boston 1. Categorical a list of facts to describe; revealed by examples (subject) is the capital (All, some, nothing) using a diagram to explain;

and specified by of Massachusetts in one class is inside using a set of rules to definitions. (predicate) (is a member of) explain; sounding out

another class. words. X

Some A is (inside) X. No A is (inside) XAll A is (inside) X.

2. Causal, hypothetical, Functional rules/conections.

Change in examples of one class (ocean temp.)

cause or merely predict change in examples of

another class (atmos- pheric CO2.

As ocean temperature rises (change in X), the amount of CO2 in the atmosphere rises (change in Y).

Routines for Acquiring, Generalizing, Fluently using, and Retaining Knowledge:a. Explicit, systematic, focused instruction---for tool skills, complex knowledge, needed fastb. More inquiry and independent via projects and discussions, but still rests on tool skills and

essential pre-skills taught explicitly

Knowledge Represented, Stored, and Communicated in the form of Language [most effectively and efficiently with simple declarative statements of subject…predicate] but also in media such as sculpture, music, dance, painting.

Knowledge Systems: Personal and Shared Stock of Knowledge

A. Tools Skills for Acquiring, Using, Improving, and B. Content/Subject Matter Needed to Communicating Conduct and Reproduce Society, and for

Enjoyment 1. Language: especially simple declarative statements 1. Sciences 2. Reasoning 2. History 3. Reading 3. Literature 4. Math 4. Medicine 5. Procedures, formats, or routines for acquiring, 5. Law generalizing, fluently using, integrating, and 6. Arts retaining knowledge 7. Religion and Philosophy

Stored or available in textbooks, programs, art, internet, your own brain, etc.

State curriculum District/school curriculum Research and Expert Opinion Your own expertise

If you are skilled at (1) designing curricula; (2) designing instruction; (3) Planning instruction and teaching daily lessons from textbooks and other materials, such as internet documents; (4) Evaluating, improving, and teaching from programs, you will develop and provide technically proficient (logical),

1. Curriculum and instruction for Elementary grades. Several knowledge systems, each taught during special lessons and all integrated. Each follows a scope and sequence.

2. Curriculum and instruction for Secondary grades.

Part I. Construction of Knowledge

Here’s what this section covers.

1. What is Reality, or Nature?

2. Knowledge is a representation of Reality, or Nature, constructed by human beings.

3. How do humans construct knowledge---a representation of reality? Humans use: a. Inductive reasoning to acquire new knowledge.

b. Deductive reasoning to apply, test, and revise knowledge.

4. There are four kinds or forms of knowledge by which we represent reality.a. We invent classes of things that have common features. [Concept knowledge]b. We know the features of things. [Fact knowledge]

c. We discover how classes of things are related to each other. [Rule or proposition knowledge]

d. We know that performing a sequence of steps has an outcome. [Routine or strategy knowledge]

There is an effective procedure for (1) acquiring; (2) generalizing; (3) using fluently; (4) integrating; and (5) retaining knowledge = phases of learning/instruction.

5. Humans construct, save, store, and communicate knowledge (our representation of reality) with language and other forms of communication, such as music, dance, painting, and sculpture.

Knowledge (of facts, concepts, rules, and routines) is most clearly and efficiently communicated with simple declarative statements: subject…predicate

6. Humans organize knowledge into knowledge systems, such as math, science, history, religion, economics, literature, farming, building, medicine, law, and many others.

7. Some ways of acquiring (constructing) and applying knowledge are logical, and lead to valid beliefs (sound reasoning).

Other ways of acquiring (constructing) and applying knowledge are illogical, and lead to invalid and false beliefs (fallacious reasoning). Teachers need to know this and teach it to their students.

Okay, now we’ll look at each item.

1. What is Reality, or Nature?

Reality, or Nature, just IS. IT exists whether we exist or not. IT has features no matter whether

we know of them, and no matter how or what we think of them.

Physicists say that----waaaayyyyyy down deep----physical reality is waves of energy. No sun,

no earth, no galaxies, no puppies, no music, no colors, no objects, no you. Just waves of

energy.

“Quantum physicists say that the objects we know—including our own bodies—are made of

waves and not particles. Up here in the land of people and puppies and bologna sandwiches,

it’s hard to believe. But down there in the land of protons, electrons, and neutrons, waves

rule the day.” http://scopeweb.mit.edu/?p=294

http://features.caltech.edu/features/363

Here’s diagram of what COMES from Reality (waves of energy), and the small amount

that humans RECEIVE their our senses and USE to “know” Reality.

http://www.mpoweruk.com/radio.htm

What we CAN know of Reality, with the naked senses, is here.

Our sense organs---our eyes, ears, skin, nose---receive only a tiny amount of the Reality of

energy waves.

Imagine if you could shrink WAY way way down down down down. You’d become so small

that the smooth flat floor you stand on would be a mountain range of peaks and valleys.

Bacteria would be the size of elephants. If you kept on shrinking, the world of objects would

disappear and you would be floating amongst molecules that make up the world of objects.

Atoms would be the size of solar systems. Most of Reality would be empty space.

You. “Wow! Duuuude!”

http://apps.teachu.com/innovaeditor/assets/1913_bohr2.jpg

And if you shrunk even smaller than atomic particles, you’d be floating amongst waves of

energy.

“No world, no objects, no sound, no light, no

http://i.ytimg.com/vi/TgGX246kPFc/0.jpg weight, no molecules, no atoms. Just

waves/particles.”

In other words, Reality seems to be organized as levels.

The World of Objects---US---

that we experience through our naked sense.

Molecules organized into

Atoms organized into

Waves and Particles organized into

Even Deeper Stuff organized into

And what or Whom is Behind it ALL?

38:4 Where wast thou when I laid the foundations of the earth?... 38:5 Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it? … 38:17 Have the gates of death been opened unto thee? or hast thou seen the doors of the shadow of death?38:18 Hast thou perceived the breadth of the earth? … 38:25 Who hath divided a watercourse for the overflowing of waters, or a way for the lightning of thunder; 38:26 To cause it to rain on the earth, where no man is; on the wilderness, wherein there is no man; 38:27 [Book of Job.]

Well, we can’t experience molecules and atoms, waves and particles with our naked senses.

So, what we take to be real------the world of objects, colors, shapes, movement----is how our

brains make sense of the energy that stimulates our sense organs. [Notice the narrow band of

visible light in the electro-magnetic radiation spectrum above.] In other words, reality is not

really the way---OR NOT THE ONLY WAY---we experience it. Our HUMAN reality is a

representation. It is a construction.

http://www.youtube.com/watch?feature=player_embedded&v=dtAuEYHaI1w Bill Whittle

http://www.youtube.com/watch?v=AU8PId_6xec

http://www.youtube.com/watch?v=JkxieS-6WuA Imagining the 10the dimension.

“The world is my idea:"--this is a truth which holds good for everything that lives and

knows, though man alone can bring it into reflective and abstract consciousness. If he

really does this, he has attained to philosophical wisdom. It then becomes clear and

certain to him that what he knows is not a sun and an earth, but only an eye that sees a

sun, a hand that feels an earth; that the world which surrounds him is there only as idea,

i.e., only in relation to something else, the consciousness, which is himself. [Arthur

Schopenhauer. 1788-1860. The world as will and representation. Volume 1. Book 1.]

2. What Is Knowledge?

Knowledge is a representation of Reality, or Nature, constructed by human beings so that, as

individuals and groups (from families to civilizations), humans can act effectively (that is, stay

alive and prosper).

But what, exactly IS knowledge? Here’s an excerpt from Plato’s Republic—the allegory of the

cave.

Plato, Book VII, The Republic. Benjamin Jowett translation (Vintage, 1991), pp. 253-261.The Republic consists of a dialogue between Socrates and several young men. The form of the dialogue is called elenchus, or disputation. 1. Socrates asks questions, such as “What is [the definition of, or your definition of] justice?” Or “What should be the qualities of a good ruler?”

2. His students or other persons present answer.

3. Socrates then makes deductions from the definitions. For instance, “You say that justice is whatever is in the interests of the stronger. But sometimes, the stronger are wrong in what they think are their best interests, and so their definition of justice would be counterproductive for them. How can ‘justice’ be that which has adverse consequences?”

4. This challenges the other persons to think about their beliefs and perhaps change them until they are logical; that is, beliefs flow from valid reasoning (not speculation, the opinions of important persons, or the opinions of the mob).

This form of conversation is today called “Socratic instruction.”

This portion of dialogue shows that teaching---what Socrates is doing---is NOT about fun and clever activities. Teaching is about helping students to examine the world, and their own beliefs, using inductive reasoning (“What generalization can I make from these examples?”) and deductive reasoning (“What are the consequences of USING my generalizations?”) to go beyond ever-changing experience and arrive at enduring Truth.

Why? Because by approaching Truth, we approach the Divine.

And, only persons who use reason to approach Truth should be in the position of rulers and teachers.

And, an ignorant and irrational mob (democracy) will invariably do things that

are suicidal. Sure enough, the Athenian democracy not only voted to put Socrates to death (for teaching young men to think in ways that challenged common beliefs) but voted to go to war with Sparta---a real dumb idea.

http://faculty.washington.edu/smcohen/320/platoscave.gif

[Socrates] And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: --Behold! human beings living in a underground cave, which has a mouth open towards the light and reaching all along the cave; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets. [Glaucon] I see. [Socrates] And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.[Glaucon] You have shown me a strange image, and they are strange prisoners. [Socrates] Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave? [Glaucon] True, he said; how could they see anything but the shadows if they were never allowed to move their heads? [Socrates] And of the objects which are being carried in like manner they would only see the shadows? [Glaucon] Yes, he said. [Socrates] And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?

This is the condition of ordinary humans. We live in a world of shadows projected onto a wall by puppeteers; e.g., teachers and political figures who: (1) are ignorant; (2) are trying to keep ordinary humans ignorant and believing falsehoods.

It is as if humans were chained to a wall and could not look around to SEE how they are being stupidified by shadows, which they TKE to be reality.

In other words, humans don’t know the rules of valid reasoning, and so they can’t criticize and debunk what they are told and what they have come to believe.

[Glaucon] Very true. [Socrates] And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow? [Glaucon] No question, he replied. [Socrates] To them, I said, the truth would be literally nothing but the shadows of the images. [Glaucon] That is certain. [Socrates] And now look again, and see what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision, -what will be his reply? And you may further imagine that his instructor is pointing to the objects as they pass and requiring him to name them, -will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him? [Glaucon] Far truer. [Socrates] And if he is compelled to look straight at the light, will he not have a pain in his eyes which will make him turn away to take and take in the objects of vision which he can see, and which he will conceive to be in reality clearer than the things which are now being shown to him? [Glaucon] True, he now. [Socrates] And suppose once more, that he is reluctantly dragged up a steep and rugged ascent, and held fast until he 's forced into the presence of the sun himself, is he not likely to be pained and irritated? When he approaches the light his eyes will be dazzled, and he will not be able to see anything at all of what are now called realities. [Glaucon] Not all in a moment, he said. [Socrates] He will require to grow accustomed to the sight of the upper world. And first he will see the shadows best, next the reflections of men and other objects in the water, and then the objects themselves; then he will gaze upon the light of the moon and the stars and the spangled heaven; and he will see the sky and the stars by night better than the sun or the light of the sun by day? [Glaucon] Certainly. [Socrates] Last of he will be able to see the sun, and not mere reflections of him in the water, but he will see him in his own proper place, and not in another; and he will contemplate him as he is. [Glaucon] Certainly. [Socrates] He will then proceed to argue that this is he who gives the season and the years, and is the guardian of all that is in the visible world, and in a certain way the cause of all things which he and his fellows have been

The reality of enduring Truth---the IDEAS of justice, love, beauty, manhood, womanhood, duty, morality, courage, time, space, mathematics---is outside the cave, and can be approached only by crawling up and out--becoming educated in logical thinking.

However, ordinary persons are comfortable in their ignorance---especially if living is easy for them. Illogical farmers starve to death. But if someone else grows the food you eat, you can remain an idiot.

These are the stages of education: growing accustomed to using logic, seeing things more clearly, and finally achieving knowledge of what is behind mere APPEARANCE in everyday life---namely, Laws—Truths—that come from ? God?

accustomed to behold? [Glaucon] Clearly, he said, he would first see the sun and then reason about him. ….

[Socrates] This entire allegory, I said, you may now append, dear Glaucon, to the previous argument; the prison-house is the world of sight, the light of the fire is the sun, and you will not misapprehend me if you interpret the journey upwards to be the ascent of the soul into the intellectual world according to my poor belief, which, at your desire, I have expressed whether rightly or wrongly God knows. But, whether true or false, my opinion is that in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which he who would act rationally, either in public or private life must have his eye fixed.[Glaucon] I agree, he said, as far as I am able to understand you….

[Socrates] Whereas, our argument shows that the power and capacity of learning exists in the soul already; and that just as the eye was unable to turn from darkness to light without the whole body, so too the instrument of knowledge can only by the movement of the whole soul be turned from the world of becoming into that of being, and learn by degrees to endure the sight of being, and of the brightest and best of being, or in other words, of the good. [Glaucon] Very true.

There are two worlds: 1. The everyday world of the senses---which continuously changes---the world of becoming.Therefore, anything we believe about the everyday world is an illusion. Just as any objects and relationships you “see” in a kaleidoscope are an illusion---not really there.

The “power and capacity of the soul” is logic.

2. The world of eternal Ideas—the world of being---concepts (e.g., Justice, Beauty), rules or Laws (cause and effect, of how some class are part of larger classes); and routines (e.g., valid explanations—sequences of rules).

Notice how Socrates says that moving from the everyday world of illusion and ignorance to the world of enduring truths is NOT a mere addition to the person. A person who basis beliefs and actions on Reason (rather than opinion) has changed his whole orientation to Reality.

Our sense organs (eyes, ears, nose, skin) take in only a tiny amount of Reality. Humans have a

learning mechanism---brain, limbs, plus senses (Engelmann and Carnine. 1991. Theory of

instruction. ADI Press)----that transforms this tiny amount [sensations: color, sound, touch] into a

representation of Reality or Nature. We call these representations knowledge. It looks

something like this.

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

Of course, each person constructs knowledge (represents Reality). But persons usually do this

together, slowly but surely within a group and across the whole history of our species. The

shared construction of reality (all of the beliefs---both valid, as knowledge, as well as myths,

superstitions, nonsense, falsehood, lies, and baloney) is part of the CULTURE of a group—

family, community, social class, nation, civilization, human kind.

To the infant, the world is a buzzing confusion of changing light, sound, touch, and

feelings. There are no objects. There is no idea that there are kinds (classes) of objects and

activities that are the same in some way. There are no relationships or connections. However,

spoken and written language enable human beings to---in a way---STOP the ever-changing

stream of light and sound and feeling (sensations) , and to GET that (1) there is a world “out

there” and that (2) this world has:

1. Kinds or classes of things (concepts) that have similar features. family, blue, on, food.

2. Individual things, and these things have features. Kitty (subject)is eating. This (subject) is

Mommy.

3. Relationships or connections among classes of things (concepts), stated as rules or

propositions. All (things in the class of) cats (are in the class of things that) say meow.

When water gets real hot, it boils.

If you run fast in the house, you will break something.

4. Sequences of steps (routines by which things happen or can be accomplished. Solving

math problems. Getting dressed. Analyzing a document to identify the propositions in a

theory.

The diagram, below, represents the development of personal and collective (shared)

knowledge, or representation of reality.

Personal knowledge/reality and Collective knowledge/reality

A developing conception of reality (stock of knowledge) for each person, and for the social groups of which the person is a member, consists of four kinds of things that are known, stored, used, taught, and shared/communicated, in the form of language music, dance, and graphic arts.Concepts = The kinds of thing there are. Colors, shapes, objects, actions, places, times, groups.Facts =The features of individual things.Rules or propositions = The way things are connected. Sequences, causation, parts and wholes, processes.

Cognitive routines = The way to get things done. Solving, analyzing, predicting, explaining, theorizing, organizing, fixing.

http://texashideout.tripod.

com/alfred_e_newman.jpg

We call our representation of Reality, or Nature, knowledge. However, we SHOULD call it

knowledge ONLY when beliefs are valid (that is, are logical, reasonable, supported by strong

evidence). Beliefs and statements that are NOT logical, reasonable, supported by strong

evidence are not knowledge. They are just baloney, speculation, rumor, bias, bunk, nonsense,

false, and flapdoodle. How can we tell if beliefs and statements are knowledge (valid) or are

false (invalid)? The answer is, we use principles of sound reasoning---called logic. See # 7

below.

3. How do Human Beings (We) Construct Knowledge of Nature?

Humans construct new knowledge (learn something new) through inductive reasoning. See the

figure in #2 above.

Humans apply (generalize), test, and improve knowledge through deductive reasoning.

Let’s start with inductive reasoning.

a. Humans construct new knowledge (learn something new) through 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

“discovers” triangle---the class of things 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 concept, republic---the class of things that are republic. A

student---Debbie Lynne Cupcake---describes how Mr. Dragul communicated (taught), and how

kids “got” the concept from the communication. Here’s Debbie Lynn…

http://mygothfashion.blogspot.com/

“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 where 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 get a horseshoe inserted in 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 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

“Look at January 1. What is the demand and what is the price? 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? So make an hypothesis: When demand_____,

then price_____. Now look at March, and the rest of the months to see if your

hypothesis is supported or if you have to change it.

“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…..”

b. Humans apply (generalize), test, and improve knowledge through deductive reasoning.

Now that we know what foozle is (we know a definition of foozle), what republic is, and the

rule-relationship (connection) between the demand for 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 ) 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 these features----- %^$#)*!

One of the features is has is ).

Now I make a deduction or deductive inference. Conclusion. %^$#)*! is foozle.”

Here’s deductive argument (syllogism):

All things with ) are (in the class of) foozle.

This new thing has ).

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!”…..

4. What Kinds Of Knowledge Are There In Our Human Representation of Reality?

1. There are only four kinds of things we can know about reality---four kinds of knowledge.

2. These four kinds of knowledge are the only kinds of things students can learn and that you

can teach.

3. These are the only knowledge that is storted IN programs, textbooks, supplementary

materials, and your own mind.

4. There is a simple method for teaching each kind of knowledge.

5. So, if you know each method, and if you know what kinds of knowledge you are teaching,

then you know exactly how to teach! Simple!

Here are the four kinds of knowledge.

1. Concept knowledge. There are kinds (classes) of things with common features. “All of these

things are evergreens.”

2. Fact knowledge. Things have features. “The tree is brown.”

3. Rule or proposition knowledge. There are relationships among classes of things.

“All (things that are) pine trees are (in the class of things that) are evergreen trees.”

“No (things that are in the class of) pine trees are (in the class of things that) are deciduous

(leaves fall off in the fall).”

“When the demand for a commodity increases, the price of the commodity increases.”

4. Routine or strategy knowledge. Performing a sequence of steps has a specific result.

Remember this well! To learn a concept, rule, or routine is to learn something general—

something common to examples. You figure out just WHAT is common to examples of

1. A concept. “What do examples of the class of evergreens have in common?” = What are the

shared features?r

2. Rule. “What do these instances of stroke and high blood pressure have in common?” = How,

if at all, do measures of blood pressure and the occurrence of stroke go together? And

3. Routine. “What are the common steps by which this gets done?”

And you figure this out through inductive reasoning---by comparing examples to identify what

is the same; by contrasting examples and nonexamples to find out what is different; and by

stating the generalization that summarizes the observations.

1. Rule. “From these examples of persons who had a stroke, and these nonexamples of

persons who didn’t have a stroke, I conclude (induce the generalization that), The higher the

blood pressure above 130/90, the higher the probability of a stroke in the next year.” Or,

2. Routine. “From all these examples of solving equations of the form a(bc) x d = X, I get it that

first, you….., next, you…” And

3. Concept. “From all these examples and nonexamples of granite, I infer (make the

generalization) that granite is (the class of granite has the features of) the minerals mica,

feldspar, and quartz.”

Since concepts, rules, and routines are learned by comparing examples, contrasting examples

and nonexamples, and figuring out what was common to the examples and what was different

aboiut examples and nonexamples, THAT is exactly how to teach concepts, rules, and routines.

Let’s look at each form of knowledge.

1. Kinds of things exist: classes, categories, concepts = concept knowledge. Some objects and

events have common features that we INDUCE by comparing and contrasting them. We might

group objects and events BY their common features—things with a flat top surface on which

you put things, and that have at least one leg holding up the flat top surface. You could the

concept of table by presenting the examples and the nonexamples below, and labeling each

one. The person’s “learning mechanism” would compare the examples and find what’s

common, contrast the examples and nonexample and notice what’s different, and then draw

(induce, figure out) a conclusion.

“This is a table.”

“This is a table.” “This is a table.” “This is a table.”

“This is not a table.”

What is the inductive inference? “Tables (or the class of tables) have a leg or legs and a flat top

and you can put things on them.”

These groups are called concepts (or classes or categories). Things that are red. Things

that are square. Things that are dogs. Things that are canines. Things that are animals. Things

that are alive. Things that are plants. Things that are processes of economic development.

Things that are monarchies. Things that are republics. And millions more.

There are two kinds of concepts: (1) sensory or basic concepts, and (2) higher-order or

abstract concepts.

A sensory or basic concept (Kame’enui and Simmons, 1990) is a concept (class of things)

whose examples have features that can be seen, smelled, touched, tasted, or heard all at

once and in one place—right before your eyes and ears.

1. ANY example of a sensory concept shows all the defining features. One triangle shows

triangularity.

2. However, any example has many features. The triangle shown might be equilateral, blue,

and have sides three inches long. If the teacher points to the triangle and says, “This is a

triangle,” the words are ambiguous. The statement could MEAN (point to) several features

besides triangularity. So, students logically might INFER that “triangle” means blue, or thing

with lines, or three lines, or things three inches long.

3. Therefore, you can’t teach a sensory concept with one example. You have to show several

examples that show the SAME triangle but differ in the UNessential (irrelevant) features---

size, color, angles. By comparing and contrasting the examples, students see that the only

ways they are the SAME is that they are all called “triangle” and they all have three lines

that intersect to form three angles. Therefore, it’s logical to conclude that the one way

that they are the same is what “triangle” means.

4. But showing examples is not enough. You also have to show NONexamples, so that

students learn what NOT triangle is. So, you put next to one another---you

JUXTAPOSE—one of the examples and a NONexample that has the same UNessential

features as the example. Put a blue square with three inch sides next to a blue triangle

with three inch sides, and say “This is triangle…This is NOT triangle.” Now the students

can compare and contrast the two and INFER that “triangle” MUST mean three-sides

figure with intersecting lines, because that’s how it differs from the thing called “NOT

triangle.”

Here’s an example.

http://reading.uoregon.edu/big_ideas/voc/voc_skills_oral.php

Here’s another example of teaching a sensory concept.

1. Gain attention and focus; frame the task.

“Boys and girls. Get ready. New shape. [write the word on the board]

triangle.”

“What shape?” triangle.

“Spell triangle.” t r i a n g l e

“What word?”

triangle.

“Yup, triangle is our new shape.”

2. Model.

a. Present/model and name (“This is a triangle.”) a range of examples that differ in

NONdefining features (size, color, etc.), but are the same in the defining feature (e.g.,

shape)—so students can (1) compare the examples, (2) notice the differences between

examples, and then (3) see that the examples---called the same thing-- are the same in

one way (shape) and are all CALLED the same thing. Therefore, by inductive reasoning,

the learning mechanism figures out that the one way that they are the same (shape) is

logically why they are called the same thing (“triangle)---that is, are in the same class.

“This is a triangle.” “This is a triangle.” “This is a triangle.” “This is a triangle.” “This is a triangle.”

b. Now pair up (juxtapose---present next to each other or one after the other) an example

just shown and a nonexample. The nonexamples must be the same as the examples in

the NONdefining features, but the example has the defining features and the

nonexample does not. Name each one.

This contrast tells the student what is the difference (shape, not color or size) that

makes the difference in whether the instance is a triangle or not.

“This is a triangle.” “This is NOT a triangle.” “This is not a triangle.” “This IS a triangle.”

3. Test/check acquisition with all the examples and nonexamples spread out.

“Is this a triangle?” Yes

“Is this a triangle?” Yes

“Is this a triangle?” No

“Is this a triangle?” No

“Is this a triangle Yes

4. Correct any errors.

a. Model. “This is NOT a triangle.” “This IS a triangle.”

b. Start over and re-test. Back up a few examples and nonexamples, and retest.

4. When students (finally) get all the acquisition examples and nonexamples right,

work on generalization. Show NEW triangles and nontriangles, and test.

“Is this a triangle? “Is this a triangle? “Is this a triangle? “Is this a triangle? “Is this a triangle? “Is this a triangle?

Correct any errors with model, start over, and retest.

HYPERLINK TO DOC FOR PRACTICE.

Higher-order, or abstract concepts (Kame’enui and Simmons, 1990). Remember

sensory concepts. The thing about sensory concepts is that:

1. Their defining features (the sameness in certain features in all examples) are tangible; you

can see, hear, smell, feel, or taste the features; and

2. Any example shows all of the defining features; the features are all right there in front of

your face or ears or nose.

So, you can teach basic concepts just by showing and naming examples.

“This is a triangle.” Or,“This is red.” Or, “This is straight.”

And then you show contrasting examples (“This is red.”) with nonexamples (This is NOT red)

that are the same in NONdefining features, but are the same in the DEFINING features.

“This is red.” “This is not red.”

However, higher-order or abstract concepts have features that are spread out and can’t be

seen or heard all at once.

1. Some defining features are NOT tangible; they are themselves abstract; you can’t

directly see, hear, smell, or feel then.

2. Each example may not show all of the defining features. For instance, any example of

red (a basic concept) will show THE defining feature---redness. But every example of

democracy (an abstract concept) may not show all the defining features at once. For

example, voting is a defining feature of democratic political systems (the concept). You

might show an example of Athens in the fifth century BC (a democracy), but Athenians were

NOT having a vote at the time. Maybe they were at war.

So, basically, you can’t bring an example of an abstract concept into class and say,

“Here’s (a democracy, a forest, a galaxy, plate tectonics, volcano).

Instead, to teach an abstract concept you have to:

1a. Give a synonym (a common word meaning the same thing) for the concept.

“Huge means real big.”

“Unalienable rights are rights that can’t be taken away.”

“Monarchy is rule by one person.”

Use synonyms when the FULL meaning (more features) is not needed for students to GET

what they are working on. So, you might give quick definitions with synonyms while you are

reading a poem.

“…headpiece fill with straw… Like a scarecrow with a cloth head fill with straw.”

1b. Give a verbal definition that TELLS the defining features. Use verbal definitions for

fundamental concepts (students really need to know them); for concepts that are

connected to other concepts (monarchy, political system, oligarchy, democracy) and may be

compare and contrasted with them; and when concepts have many features and can’t be

captured by a synonym.

2. And then show examples that ALL have the defining features (and call them the same

thing--“This is a democracy.”) and NONexamples that do NOT have the defining features (and

call them something different from the examples---“This is NOT a democracy).

3. The test/check by giving all the examples and nonexamples; asking students to identify each

one (“Is this a democracy?” or “What is this?”); and then asking a follow up question (“How do

you know?”) to make sure students use the definition when they make their judgment.

What does a good verbal definition look like? A good verbal definition states the genus

and difference. Here’s the VERBAL definition of the higher-order concept—constitutional

republic.

A constitutional republic is a state where the head of state and other officials are

representatives of the people and must govern according to existing constitutional law

that limits the government 's power over citizens.

http://en.wikipedia.org/wiki/Constitutional_republic

The definition has two parts: genus and difference.

Genus. A constitutional republic is a STATE (a political relationship between government and

citizens).

The genus is the larger category or concept in which constitutional republic in located. The

genus tells you what KIND of thing something is and what KINDS of things it isn’t. A

constitutional republic is not a society. Not a geographic thing, like mountains. And not

anything that other species do. However, constitutional republics are not the only kind of (not

the only member of the class of) states. Other kinds of states are monarchies, democracies,

and aristocracies. So a full definition has to tell the difference between constitutional republic

states and other kinds of states. This is the difference part of a verbal definition.

Difference. …. where the head of state and other officials are representatives of the people and

must govern according to existing constitutional law that limits the government's power over

citizens.

The difference part of the definition tells the difference between constitutional republics (as

ONE example of state) and OTHER kids of states, such as monarchies, democracies, and

aristocracies.

A diagram of the verbal definition looks like this.

Political states [largest category]

Constitutional republics

Monarchies

Aristocracies

Democracies

Particular, individual examples of democracies, aristocracies, etc., are INSIDE each smaller

circle.

Note: There is no such thing as a true verbal definition. Rather, some definitions are

better than other definitions; they are better at directing attention to the right events. So,

definitions are better when:

1. They state the genus and the difference.

2. The difference part of the definition contains enough descriptors (features of the

thing defined) that it can easily be distinguished from other kinds of things in the

class (genus).

Here’s a poor definition.

Dogs are canines (genus) with four legs (difference).

The genus part is okay. Dogs ARE in the class of canines---along with wolves, foxes, and

coyotes. But the difference part is so skimpy that you can’t USE this definition to distinguish

dogs (as canines) and foxes, wolves, and coyotes (as canines) because all of them have four

legs.

Here’s another poor definition.

Monarchy is a form of government (genus) in which one person rules (difference).

Yes, monarchy IS a form of government (or state) in which one person rules, but the difference

(one person rules) does not tell enough to distinguish monarchies and other forms of

government in which one person rules. Dictatorships are also rule by one person. So, if a

student reads about a dictatorship, the student might WRONGLY judge it to be a monarchy. So,

the difference portion should include more features of monarchies (in contrast to

dictatorships). Here’s a more descriptive definition.

A monarchy is a form of government (genus) in which supreme power is absolutely or

nominally lodged with an individual, who is the head of state [by virtue of hereditary

ascension], often for life or until abdication…The person who heads a monarchy is

called a monarch (difference). http://en.wikipedia.org/wiki/Monarchy

Now look at a good definition of dictatorship. It is good because it is useful---it enables you to

distinguish monarchy (rule by one person) from dictatorship (also rule by one person).

A dictatorship is defined as an autocratic [one ruler. Synonym. MK] form of

government in which the government [means the same as “supreme power is

absolutely or nominally lodged with an individual”] is ruled by an individual, the

dictator, without hereditary ascension. http://en.wikipedia.org/wiki/Dictatorship

3. All of the terms have clear meaning; that is, the words in the definition clearly point to the

events named.

Poor definitions.

A donut is a kind of pastry that is shaped like a donut. [Yes, but what is a

donut shaped like?]

Fear is an emotion that involves being afraid. [Fear and afraid mean the same

thing. So, the definition is just saying Fear is an emotion at involves fear.]

You have to learn how to identify concepts to teach---both concepts that are in class materials

and concepts that are not, but that students need to know. And you need to help students to

figure out the definitions of concepts that are in text materials.

3. That classes of things (concepts) are connected. Statements of these connections are called rules or propositions. For example, some classes or concepts are inside another class or concept.“All (things in the class of) republics are (in the class of) political systems.”

Some classes or only partly inside of another class.“Some (things in the class of) fungi are in the class of things that are) harmful.”

Some classes are totally not part of another class.“No uninformed citizenry makes wise decisions.”

rules or propositions (connections among classes of things/concepts), descriptions, hypotheses, explanations, theories, arguments for or against a conclusion] , painting, music, sculpture, dance, and other media1. Most of human knowledge (our representation of reality) is of two things: (1) what sorts of stuff IS there; and (2) how is this stuff CONNECTED. Think of it as putting together a jigsaw puzzle but with no picture on the box top to guide you. No, really. Think about it. How would you do it. “I think this piece goes here.” (hypothesis) “Nope. It doesn’t fit.” (acting on hypothesis) “Maybe here.” (new hypotheses). “YES! They fit!” Now you learned how a small part of reality is connected.

There is an effective procedure for teaching each kind of knowledge.

How to Teach Sensory Concept Knowledge: Pre-k or Kindergarten

We’re going to teach kids a shape—triangle. A procedure that’s effective (that is, most kids

learn from it) and efficient (that is, most kids learn fast and with hardly any mistakes) is pretty

simple. We’ll teach triangle during several tasks in one Lesson. Watch how FAST it goes.

Teacher talk is in “quotation marks.” Student talk is in italics. Here we go!

“Boy and girls. Everybody show me ready. …..[Kids sit up straight, stop talking, and look at the

teacher.] Ys, you’re ALL ready to learn. I love how you got ready so fast!!”

“Boys and girls. Let’s review our shapes. Then you’ll learn a NEW one. When I point to a

shape, you tell what it is. Remember to say the WHOLE thing.”

[Teacher points to one at a time.]

“What is this?”

This is a line.“Yes, thisIS a line.”

“What is this?”

This is a line.”

“Yup, this IS a line, too!”

“And what is this?”

This is a line.

“Correct. This is a line.”

“And this?” This is a circle.

“Yes, this IS a circle.”“And what is this?”

This is a circle.

“You’re so smart. This IS a circle.

“What is this?” Points

This is an angle.

“Correct, this is an angle.”

“And what is this?

Teacher points This is an angle.

“You’re so smart. This IS an angle.”

“And what is this? This is a circle.

“Correct, this is a circle.”

“And what is this?”

This is a line.

“Yes, this IS a line.”

“And what is this?”

Two students say, This is an angle.

Teacher points.

“This is a LINE. An angle is formed when TWO lines come together. [Teacher point.] Does this have TWO lines coming together?” No. “How many lines does this have? [Teacher traces line.]This has one line.“Yes, this has ONE line. So can this be an angle?”

No.

“So what IS this?” This is a line.“Yes, this IS a line.”

“And this? Don’t get fooled. Count how many lines this has? This is an angle.

“Yes, two lines come together [points]. So, this is an angle.”

“And what is this?” This is a line.

“Yes, this is a line. You got it now!” “Boys and girls. Get ready to learn a new shape…..[Kids sit up straight, stop talking, and look

at the teacher.] “Yes, now you’re ready.”

“Here’s our new shape. [write the word on the board] triangle.”

“What shape?” triangle.

“Spell triangle.” t r i a n g l e

“What’s our new shape?” triangle.

“Yup, triangle is our new shape.”

“When we’re done, I’ll show you things and you will tell me if they are triangles. You’ll be

sssoooo smart!”

[Teacher shows one example at a time.]

“This is a triangle. “This is a triangle. “This is a triangle. “This is a triangle. “This is a triangle. It has 3 straight It has 3 straight It has 3 straight It has 3 straight It has 3 straightlines that come lines that come lines that come lines that come lines that cometogether, and 3 together, and 3 together, and 3 together, and 3 together, and 3angles?” angles?” angles?” angles?” angles?”[Point and count. [Point and count. [Point and count. [Point and count. [Point and count.Have students Have students Have students Have students Have studentscount.] count.] count.] count.] count.]“What is this?” “What is this?” “What is this?” “What is this?” “What is this?” This is a triangle This is a triangle This is a triangle This is a triangle This is a triangle“Yes, this is a “Yes, this is a “Yes, this is a “Yes, this is a “Yes, this is a triangle.” triangle.” triangle.” triangle.” triangle.”

[Teacher shows one at a time.]

“This is a triangle. “This is NOT a triangle. “This is NOT a triangle.” “This IS a triangle. It It has 3 straight A triangle has 3 lines. A triangle has 3 lines. This has 3 straight lines lines that come This has 4 lines. So, this is is a circle. It has ONE line. that come together, together, and 3 NOT a triangle. This has 4 and 3 angles. One, two, angles. One, two, angles. A triangle has 3 three.” three. angles. So it is NOT a [Point and count. triangle.” Have students [Point and count. Have [Point and count. Have [Point and count. count.] students count.] students count.] Have students count.]

“Is this a triangle?” “Is this a triangle?” “Is this a triangle?” “Is this a triangle?” Yes, this is a triangle. No, this is not a triangle No, this is a circle. Yes, this is a triangle.”

“Yes, this is a “It IS NOT a triangle” “Correct. This is a circle.” “Yes, this is triangle”

“Is this a triangle?” Yes

“How do you know?” Three straight lines. Come together. Three angles.

“Yes, this IS a triangle.”

“Is this a triangle?” Yes

“How do you know?” Three straight lines. Come together. Three angles.

“Yes, this IS a triangle.

“Is this a triangle?” No

“How do you know?” “Four lines, not three. Four angles, not three.”

“Correct! This is NOT a triangle.”

“Is this a triangle?” No

“How do you know?” “One line. Not three angles.”

“Correct! You’re so smart. NOT a triangle.”

“Is this a triangle?” Yes

“How do you know?” Three straight lines. Lines connect. Three angles.

“Yes, it IS a triangle!”

Done!

The question is, Can you quickly and easily design a task (in a lesson) like this one? Maybe.

Maybe not. So, I’ll show you what you need to know to design instruction for the same kind of

knowledge---a sensory concept, such as shape, color, texture (rough, smooth), sound (loud,

quiet), smell.

What We Need to Know

Here’s a list of what we need to know.

How teaching shapes fits in your curriculum.

What a lesson is. What lessons look like.

How you teach shapes depends on what kind (form) of knowledge shapes are.

A concept is NOT the same as a word, or vocabulary word.

What the learning mechanism does to “get” a sensory or basic concept.

What the learning mechanism does to get a sensory concept tells us how we should teach a

sensory concept.

We are working on the first phase of learning and teaching---the acquisition of knowledge.

Our procedure for the phase of acquisition will be explicit instruction.

1. Before you plan how to teach shapes, or anything else, you have to plan the curriculum---

what kinds of knowledge you will work on (strands) and when you will work on them. See

curriculum.

2. What a lesson is. What lessons look like. We’ll be teaching our new concept during a

lesson in the curriculum. So, we must design the lesson. See lesson.

3. How you teach shapes depends on what kind (form) of knowledge shapes are. Shapes

are concepts. A concept is a set, class, category, or group of particular things that have

one or more features that are the same. These features (same) define the concept. These

features are HOW the individual things were put IN the group. So, all of the things in the

concept are EXAMPLES of it. Also, these individual things are different in many ways.

These differences do NOT define the concept. For example, the concept table is defined

by legs, a flat top surface, and a purpose (to put stuff on top). All examples of table have

those features, but examples differ in size, shape, how many legs, and color. So, to learn a

concept simply means to learn the defining features and to learn the NOT defining

features. Students would use or show that knowledge by saying IF an object is or is not an

example of the concept (“Is this a table?” yes. “How do you know?” It has three legs,

and flat top, and you put stuff on it.), or by sorting things (“Pick all the ones that are

red.”), or by naming things (“What is this called?”).

Shape is a kind of knowledge called sensory concept, or basic concept (Kame’enui and

Simmons, 1990). The thing about sensory concepts is that: (1) their defining features (the

sameness across examples) are tangible; you can see, hear, smell, feel, or taste the

features; and (2) any example shows all of the defining features; the features are all right

there in front of your face or ears or nose.

4. A concept is NOT the same as a word, or vocabulary word. A word is just sounds that

SIGNIFY (point to) the set of things that ARE (that define) the concept. When someone

says, “How do you like this table,” a person who knows what “table” means (what

FEATURES the word points to), and so the person looks at a table, and not at a chunk of

cheese. So, if you just point to a table and say “That’s a table,” you are not teaching the

concept, table. Why not? Because you have to teach the FEATURES that make something

(define) a table. If you point to a table and say, “Table,” the other person may INFER that

“table” is the NAME of the object, not the KIND of object that it is.

5. What the learning mechanism does to “get” a sensory concept. To get a concept---to get

the definition (“The word ‘table’ means---points to has legs, flat top, and you put stuff

on it.”)---the learning mechanism performs the routine called “inductive reasoning” or

induction. The learning mechanism:

a. Examines individual things and identifies their features. Teacher points to an object

and says, “This is a table.” Students look at it and identify the features it has.

Note: To identify features of something, a person has to notice (discriminate, see,

hear, feel, smell) the features a part from the background. For instance, to identify the

melody in a tune, you have to distinguish certain notes from the rest of the notes. To

identify the sunset in a painting, you have to distinguish certain parts of the painting from

the rest of the painting. To discriminate the legs of a table (to see those parts), you have

to see that the legs part is different from the top part. This sounds like a simple matter,

but that is only because you learned how to do it long ago. Persons with certain

disabilities have a hard time making discriminations (seeing certain particular stuff) from a

background. With shapes, a person has to distinguish the features that make up the

shape from other features, such as color and size.

b. Compares individual things and identifies features that are the same and features

that are different. For instance, the student notes how (1) each time the teacher says,

“This is a table,” the object has legs, a flat top, and has stuff sitting on it; and also (2) each

thing that she calls something a table, it has a different number of legs, different color,

different shape, different size, and different thing on top. So, logically, can the word

“table” mean (point to) color, shape, size, or kind of stuff on top? No. Because all these

features are different, but the teacher calls the OBJECT by the same name. Or, logically,

must “table” mean legs, flat top, and put stuff on it? Yes. Because these are always the

same, at the same time that the teacher calls the object by the same name.

c. Makes a generalization (inductive inference) based on a and b (please read a and b

again). Basically, the student’s learning mechanism says, “I get it. ‘Table’(means, is)

anything with legs, a flat top, and you put stuff on it.”

6. What the learning mechanism does to get a sensory concept tells us how we should

teach a sensory concept. Here’s why. The learning mechanism “gets” a concept by using

the above steps----a, b, c---in inductive reasoning. So, it makes sense to make it easy for

the learning mechanism to do the steps. How? Easy peasy!

a. Use examples that clearly communicate (show) the important information directly.

“THIS is (a triangle).” The defining features (three straight lines, the lines

connect,

there are three angles) must be OBVIOUS. This helps students to distinguish each

feature from the background of other features---size, color, shape. If it is hard for

some kids to see the defining features, they will make errors. Is that a good idea? We

want them to learn! Later---when kids are skilled at examining things, identifying

features, comparing and contrasting the features of things, and making

generalizations (“I get it. All triangles…”)---THEN you can teach them the skill of

“looking real close and finding what is hard to see.” But THAT skill is different from

just knowing the concept, triangle.

b. Select a range of examples (called the acquisition set, because this is the acquisition

phase of instruction) that reveal clearly the important information (Kame’enui and

Simmons, 1990). You can’t use triangle examples that are ONLY equilateral.

Why? Because all triangles are NOT equilateral. If you use only equilateral triangles, you

will be teaching “All triangles look like this.” So, when your students see triangles that are

NOT equilateral, they MAY make a deductive inference (judge) that these new ones are

NOT triangles! Their (incorrect) deductive reasoning would go like this.

(1) “All triangles look like this. “ [Because that’s what you taught them with the narrow

range of examples.]

(2) “This does not look like this.”

(3) “Therefore (deduction from #1), this is NOT a triangle.”

This is called stipulation error. The narrow range of examples (all equilateral) stipulated

(told) that “triangle” means “only like these.”

But if you use a wide range of examples that cover most of the range of triangles, and

THEN you show this one… and ask, “Is this a triangle?” your students

are likely to say “Yup!” because they have seen IT in the range of examples you used.

c. Make sure that the examples are DIFFERENT in features that do NOT define the

concept (number of legs, color, size, shape of top, kinds of objects in top) but are the

SAME in the defining features (all examples have legs, a flat top, and something on them).

This way, students will see that the word “Table” goes with certain same FEATURES. So

these must be important.

c. Each time you present an example, treat it a certain way, and treat all examples that

same way. Show triangles and say, “This is a triangle….And this is a triangle….And this is a

triangle.” Why? Your students will get it that the sameness in how you treat the

examples is connected to the sameness that is IN the examples. Please read that again.

d. Also use NONexamples to show contrast with the examples. Squares, circles,

rectangles, hexagons. Each time you show a NONexample, treat it UNLIKE you treat the

examples. “This is NOT a triangle.”

Make sure that the NONexamples have the same NONdefining features as the

examples. For instance, show a red triangle (“This is a triangle.”) and a red square (“This

is NOT a triangle.”). Make sure to put the example and nonexample next to each other in

time or in place. This is called “juxtaposing examples and nonexamples. “ This

juxtaposition makes it easier for the learning mechanism to CONTRAST the example and

nonexample.

“This is a triangle.” “This is not a triangle.”

Think of the inductive reasoning here. If you show a red triangle and say “Triangle” and

then a red square and say “Not triangle,” logically, “triangle” can’t mean color, because

the example and nonexample were the same color. And “triangle” can’t mean the square

one, because you said “NOT triangle” when you showed the square one.

Note. We will call the NONexamples “NOT a triangle.” We will NOT call them by their

names---square, circle. Why? Because we are teaching only ONE concept now. All we

want NOW is for students to get the definition of triangle. Later, after we have taught

triangle, square, and circle, we could have students use all the concepts at the same time:

(a) draw them (“Draw one square and two circles.); (b)sort them (“Put all the circles here

and all the triangles there.”); (c) find shapes in the room (“Find me triangles…. Now find

circles.”).

e. Test to see if students make the correct induction (that is, “got it”). Show all the

examples and nonexamples, and ask “Is this a triangle?” This is called an acquisition test

(Kame’enui and Simmons, 1990).

f. Correct any errors. If you hold up a NOT triangle and say “Is this a triangle,” and a

student says, “Yes, triangle,” immediately say, “This is NOT a triangle.” Juxtapose the NOT

triangle with a triangle you showed before. “This IS a triangle.” Then show the NOT

triangle again, and ask, “Is this a triangle?” I’ll show you how in a minute.

7. We are working on the first phase of learning and teaching---the acquisition of

knowledge. The objective is that students correctly “treat” examples and nonexamples of

a concept. In other words, when the teacher holds up examples and nonexamples, and

says, “Is this (an example/not an example of the concept) _____?”, students answer

correctly within, say, 3 seconds. When students show that they “get” the concept---

because they make no errors during the acquisition test, the teacher works on the other

phases of learning---generalization of knowledge to new examples and nonexamples;

fluent use of knowledge (for instance, identifying shapes FAST); and retention of

knowledge (being skilled days and weeks later).

8. Our procedure for the phase of acquisition will be explicit instruction, which is the most

reliably effective (it works with most students) and efficient (it works with the fewest

errors and in the least time). Explicit instruction is often needed with so-called diverse

learners---or students who have a hard time learning or who have little background

knowledge needed to “catch on”---that is, they may not be skilled at the steps of inductive

reasoning (describing, identifying features, comparing and contrasting, making

generalizations).

And now!

Here’s the procedure for explicit instruction of sensory concepts.

1. Gain attention and focus; frame the task.

Always gain and focus attention. You might say, “Okay, everyone, show me ready.” Or,

“Let’s get ready to learn.” With little kids, you must teach this from the start. Model what

“Ready to learn” means. For example, sitting up, feet on the floor, hands on the desk,

looking at you, quiet. Have them practice. Point out during lessons that they are “so

ready!” Do NOT teach if ANY student is not ready. “I need to see EVERYone ready.”

2. Then frame the learning task by:

a. Telling what the task is. Make sure students tell YOU what the task is.

b. Tell what the objective is---what students will DO when the task is done, so that

they can prepare to feel pride. The objective also tells YOU: (1) what you have

to

teach; and (2) what you have to assess (namely, whether students met the objective

and your teaching was effective).

Task 1. Review and firm-up prior knowledge, pre-skill elements

Gain attention and frame the task

“Boys and girls. Let’s review our shapes. Then you’ll learn a NEW one. When I point to a shape,

you tell what it is. Remember to say the WHOLE thing.” [These are the objectives. When the

[Teacher points to one at a time.] teacher points to a shape, students

“What is this?” tell what it is with a full sentence.]

This is a line.

“Yes, thisIS a line.” [Teacher verifies the correct answer.]

“What is this?”

This is a line.”

“Yup, this IS a line, too!”

“And what is this?” [Notice that the wording is the same.]

This is a line.

“Correct. This is a line.” [The teacher presents a sample of shapes

“And this?” worked on in earlier lessons to ensure kids

This is a circle. are firm. The shapes—lines, angle, circle--

“Yes, this IS a circle.” are pre-skills for learning triangle---lines

“And what is this?” and angles DEFINE triangle vs. other shapes.]

This is a circle.

“You’re so smart. This IS a circle.”

“What is this?” Points [Pointing helps to focus attention and

connect the word—angle---with the

object.]

This is an angle.

“Correct, this is an angle.” [Notice that the examples DIFFER in NONdefining

“And what is this? features---color, size—but are the same in

Teacher points This is an angle. defining features---shape.]

“You’re so smart. This IS an angle.”

“And what is this? This is a circle.

“Correct, this is a circle.”

“And what is this?”

This is a line.

“Yes, this IS a line.”

“And what is this?”

Two students say, This is an angle. [Error! Teacher immediately

Teacher points. corrects by modeling

“This is a LINE. An angle is formed when TWO correct answer and statinglines come together. defining features so kids[Teacher point.] Does this have TWO lines see WHY the example iscoming together?” a line and not a triangle.

No. Teacher make sure kids“How many lines does this have? use the defining features[Teacher traces line.] (number if lines) to judge forThis has one line. themselves.“Yes, this has ONE line. So can this be an angle?”

No.

“So what IS this?” Teacher retests the example.This is a line.“Yes, this IS a line.”

“And this? Don’t get fooled. How many line does this have? Teacher uses another example to This is an angle. check whether kids get it right

“Yes, two lines come together [points]. So, this is an angle.” this time. Retest.

“And what is this?” Another example that looks like

This is a line. the one where they erred, to Check whether kids get it right

“Yes, this is a line. You got it now!” this time. Retest.

Task 2. Teach new knowledge: acquisition

Gain attention and frame the task

“Boys and girls. Get ready to learn…..Yes, now you’re ready!”

“New shape. [Write the word on the board] triangle.”

“What shape?” triangle. [Check to make sure they say

what they will learn.]

“Spell triangle.” t r i a n g l e [You point to each letter and students say

the name---if they have been taught the

NAMES of the letters.]

“What’s our new shape?” [Firming up what was just taught.]

triangle.

“Yup, triangle is our new shape.” [Verifying that students are right.]

“When we’re done, I’ll show you things and [Stating the objective.]

you will tell me if they are triangles.

You’ll be sssoooo smart!”

3. Model.

a. Present/model/show, and name (“This is a triangle.”) a range of examples that differ in

NONdefining features (size, color, etc.), but are the same in the defining feature (e.g.,

shape)—so students can (1) compare the examples, (2) notice the differences between

examples, and then (3) see that the examples---called the same thing-- are the same in

one way (shape) and are all CALLED the same thing. Therefore, by inductive reasoning,

the learning mechanism figures out that the one way that they are the same (shape) is

logically why they are called the same thing (“triangle)---that is, are in the same class.

You could also TELL and POINT to the features that make these examples of the concept,

triangle.

[Teacher shows one at a time. Teacher tells the concept and the defining features. Checks to

make sure kids can do the same thing. Model (this is) Test (What is this?) Verification of

correct answer.]

“This is a triangle. “This is a triangle. “This is a triangle. “This is a triangle. “This is a triangle. It has 3 straight It has 3 straight It has 3 straight It has 3 straight It has 3 straightlines that come lines that come lines that come lines that come lines that cometogether, and 3 together, and 3 together, and 3 together, and 3 together, and 3angles?” angles?” angles?” angles?” angles?”[Point and count. [Point and count. [Point and count. [Point and count. [Point and count.Have students Have students Have students Have students Have studentscount.] count.] count.] count.] count.]“What is this?” “What is this?” “What is this?” “What is this?” “What is this?” Triangle Triangle Triangle Triangle Triangle“Yes, triangle” “Yes, triangle” “Yes, triangle” “Yes, triangle” “Yes, triangle”

b. Now pair up (juxtapose---present next to each other, or one after the other) an example

just shown and a nonexample. The nonexamples must be the same as the examples in

the NONdefining features, but the example has the defining features and the nonexample

does not. Name each one.

This contrast tells the student what is the difference (shape, not color or size) that

makes the difference in whether the instance is a triangle or not.

[Teacher shows one at a time, names it, states defining features, models the reasoning process,

tests, and verifies correct answers. ]

“This is a triangle. “This is NOT a triangle. “This is NOT a triangle.” “This IS a triangle. It has 3 straight A triangle has 3 lines. A triangle has 3 lines. It has 3 straight lines lines that come This has 4 lines. So, it is This has ONE line. So, it is that come together, together, and 3 NOT a triangle. This has 4 NOT a triangle. A triangle and 3 angles. One, two, angles. One, two, angles. A triangle has 3 has 3 angles. This has NO three.”

three. angles. So it is NOT a angles. So, it is NOT a

triangle.” triangle.”

“What is this?” “What is this?” “What is this?” “What is this?”

Triangle Not a triangle Not a triangle Triangle

“Yes, triangle” “Yes, it is NOT a triangle” “Yes, it is NOT a triangle” “Yes, triangle”

4. Test/check acquisition with all the examples and nonexamples spread out. This is an acquisition test (Kame’enui and Simmons, 1990).

[Teacher shows examples and nonexamples, asks what they are examples of, checks reasoning

process (did students make judgment using definition?), and verifies correct

answers.]

“Is this a triangle?” Yes

“How do you know?” Three straight lines. Come together. Three angles.

“Yes, this IS a triangle.”

“Is this a triangle?” Yes

“How do you know?” Three straight lines. Come together. Three angles.

“Yes, this IS a triangle.

“Is this a triangle?” No

“How do you know?” “Four lines, not three. Four angles, not three.”

“Correct! This is NOT a triangle.”

“Is this a triangle?” No

“How do you know?” “One line. Not three angles.”

“Correct! You’re so smart. NOT a triangle.”

“Is this a triangle?”

“Is this a triangle Yes

“How do you know?” Three straight lines. Lines connect. Three angles.

“Yes, it IS a triangle!”

5. Correct any errors. For instance,

“Is this a triangle?” Yes.

a. A student misidentifies an example or nonexample. You

Model the difference.

“This IS a triangle.” “This IS NOT a triangle.”

“It has 3 straight lines. “It does NOT have 3 lines. The lines come lines. It has FOUR lines.

together. And 3 angles. It does not have 3 angles.Then RETEST with THAT example.“Is this a triangle?” NO. “Correct. This is NOT a triangle.”Then back up (start over) and RETEST several more to firm up the concept.

b. A student correctly identifies the shape, but forgets to mention angles when you ask

“How do you know?” You say,

“Yes, it IS a triangle. It has three straight lines (point). The three straight lines connect

(point). AND it has THREE angles. See? 1, 2, 3. Tell me. How do you know this is a

triangle?” [Verify the part of the answer the student got right, and ADD the part that

the student forgot. Then RETEST.]

Student gets it right.

“Yes, it has three straight lines. The line connect. And it has three angles!” [Verification]

6. When students (finally) get all the acquisition examples and nonexamples right,

work on generalization. Show NEW triangles and nontriangles, and test. These new

examples and nonexamples of triangles are called a generalization set (Kame’enui and

Simmons, 1990).

“Is this a triangle? “Is this a triangle? “Is this a triangle? “Is this a triangle? “Is this a triangle?

“Is this a triangle?

Correct any errors with (1) model, (2) retest; (3) back up a few/start over.

What are we going to do the next days? Easy!1. Work on retention of knowledge. Let’s say shapes is part of your curriculum strand on

language, and you work on language during the second lesson of the day---9:00 to 9:30.a. So, the next day after you worked on the acquisition of the concept, triangle, you REVEW the examples and nonexamples of triangles---both the examples in the acquisition set and the generalization set.

“Okay, boys and girls. She me how smart you are.”

“Is this a triangle? How do you know?” “Is this a triangle? How do you know?”

etc.

Correct any errors with model (“This is….” This is NOT…”), back up/start over, retest.

b. Do the same thing as in a., with a sample of all the shapes so far. Notice that you use

both examples and nonexamples.

“Is this a square? How do you know?”

“Is this a circle? How do you know?”

“Is this a circle? How do you know?”

“Is this a rectangle? How do you know?”

Always immediately correct errors:

1. Model the right answer. “This is a square. This is not a square.”

2. Restest. “So, is this a square?” Yes. “Yes, you’re right. It IS a square. (verify).

3. Backup a few/start over. “Starting over…. Is this a circle?... Is this a triangle?”

2. Work on fluency----accuracy (as in the phase of acquisition) plus speed. During next lessons, add more shapes, work on generalization to new shape examples, AND have some short tasks where you go fast.

“Let’s play a game. Let’s go fast! Try not to make mistakes. THINK before you answer. Here we go.” Do a sample of all shapes. Correct errors: model, retest, back up/start over.3. Work on generalization or application to new materials. This is where students apply

knowledge. You could have color and shape hunts. “Find me as many things that are circles.” “Find

things that are blue.” You could have students draw shapes plus colors. “Draw a house. Use squares and rectangles.”

4. Work on integration of knowledge. For instance, show examples that consists of several shapes. Have students outline, name, and count the shapes. To do this, students must use all of their knowledge of shapes---lines, angles, and figures.

5.We humans construct, save, store, and communicate knowledge (our representation of reality) with language and other forms of communication, such as music, dance, painting, and sculpture.

Knowledge (of facts, concepts, rules, and routines) is most clearly and efficiently communicated with simple declarative statements: subject…predicate

The clearest and cleanest way to construct, save, store, and communicate what we’ve learned about reality is with simple declarative statements of subject predicate. “All these things (subject) are red (predicate).”“All cats (subject) are felines (predicate).”

“The price of a product increases (subject) when the demand for the product increases (predicate).”Jefferson (subject) was the third U.S. President (predicate).”“To sound out a word

If we are examining a painting or sculpture, watching a dance performance, or listening to a symphony, we still TRANSLATE these communications into the ordinary language of simple declarative statements.

Even if you look at a painting or sculpture, or listen to music, however, you STILL make sense of it with WORDS. “What does this say? What is the meaning? What knowledge can I get from this?”

Mary Stevenson Cassatt (……May 22, 1844 – June 14, 1926) http://en.wikipedia.org/wiki/Mary_Cassatt

“This painting (subject) shows the mother infant bond of tenderness and trust (predicate). Tenderness and trust (subject) are shown by the way she holds the baby’s foot (subject), and the mother and her baby are looking at each other’s eyes.”

6. We humans organize knowledge into knowledge systems, such as math, science, history, religion, economics, literature, farming, building, medicine, law, and many others.

There are two kinds of knowledge systems:1. Subject matter or content knowledge: history, economics, botany, literature, philosophy.

Subject matter knowledge is loosely coupled; you don’t have to know all about poetry in order to comprehend fiction.

2. Tool skills are knowledge needed to acquire and use content knowledge. Tool skill examples: language, inductive and deductive reasoning, reading, math.

Tool skill knowledge is tightly coupled. In arithmetic, the skills of counting, adding, subtracting, and multiplying all work together (and therefore must all be learned first) in order to do long division.

EXPLCIT

7. Some ways of acquiring (constructing) and applying knowledge are logical (sound reasoning), and lead to valid beliefs.

Other ways of acquiring (constructing) and applying knowledge are illogical (fallacious reasoning), and lead to invalid and false beliefs.

“We know that, in general, the price of a product increases when the demand for the product increases.” (rule)

“The demand for gold has increased for three days in a row.” (fact relevant to the rule)

“Therefore, I predict that the price of gold will increase.” (deductive inference or generalization based on the fact in relation to the rule)

“Sure enough, the price of gold just increased! I’m glad I bought gold before the price went up. I guess the rule so far is correct.”

This way, we add to our stock of knowledge of how reality works.

There are ways of inductive and deductive reasoning that are valid and that lead to useful information, and help us to make wise decisions. There are also ways of inductive and deductive reasoning that are invalid---sloppy, superficial, biased, closed-minded---that lead to errors, fooling ourselves, false beliefs, and nonsense, and help us to make poor decisions.

Scientific thinking is a combination of inductive reasoning (discovery, construction) and deductive reasoning (application, prediction, test of beliefs). It is simply more rigorous (concerned with validity and steps of reasoning) than ordinary thinking.

Content Subjects Politics Community Values Scientific ResearchOfficial Curriculum (State, District, School)

PART II. USING PRINCIPLES OF KNOWLEDGE [PART I] AND MORE IDEAS TO DESIGN CURRICULUM [WHAT TO TEACH] AND INSTRUCTION [HOW TO TEACH]

Principles of Well-designed Curriculum

Here’s what this section covers.

1. What is a curriculum?

2. Some curricula teach tool skills (reading, math, language, and reasoning). Other curricula

teach content or subject matter knowledge systems (literature, history).

3. Developing a curriculum by considering:

a. curriculum strands---main kinds of knowledge to be taught.

b. The sample of knowledge to be taught.

c. Curriculum standards, goals, or objectives---and the knowledge students need to achieve

the objectives---for (1) the whole curriculum, (2) units (sequences of lessons) in the

curriculum, (3) lessons, and (4) short tasks in each lesson.

d. Using knowledge analysis to identify all the elementary (component) skills in a complex

skill.

e. Teaching component skills or elements (pre-skills) before teaching complex skills that

USE these elements (logical sequence).

f. How elementary knowledge will be integrated into larger and coherent wholes; e.g., in

an arithmetic curriculum, integrating counting, subtraction, and estimation to form the

routine of long division

Okay, now let’s look at each item in designing a curriculum.

1. What is a curriculum? It is the knowledge to be taught, and the sequence in which the knowledge will be taught.

8:00-8:30 Lesson

8:40-9:20Lesson

9:30-10 10:05-10:40Lesson

10:45-11:15Lesson

11:15-11:45Lesson

11:50-12:30

12:40-1:20Lesson

1:25-2:00Lesson

2:05-2:30Lesson

Common Knowledge and LanguageSpeaking in full sentences with proper grammar.

Names of persons and places.

Colors, shapes, prepositions.Days of the week; times of day; months; seasons.

Materials (wood, stone, paper, etc.) and qualities (hard, smooth, etc.)

Clock time.

Reading 1Saying words fast (blending sounds) and saying words slowly (segmenting).

Letter-sound correspondence(sound that go with letters).

Sounding out words and saying them fast.

Story comprehension (retelling) and vocabulary.

Reading sentences and longer text.

Story comprehension (retelling, predicting)

SnackRules and routines for setting table, passing food, cleaning up.

SciencePlants: Kinds Life cycle

Astronomy: Solar systems: sun, planets, orbits, moons.

Light years

Galaxies

MathRote counting(“one, two, three…”)Rational counting(“One, two, three blocks.”Group counting (3 red blocks and 2 blue blocks).

AdditionSubtraction

Reading 2Continue from Reading 1.

LunchRules and routines for setting table, passing food, cleaning up.

StoryVocabularyRetell and predict, using proper grammar and syntax.

ApplicationsTeachReal-world activities to generalize and apply knowledge:Find shapes, colors

Draw storiesGardenMake mobiles of solar system

Daily ReviewNote weak knowledge to firm or reteach now and to review the next day.

So, the day is divided into periods of around 30 minutes; each period is a lesson; each lesson

focuses on a subject matter or curriculum strand as suggested (1) by research on what kids

need to know; and (b) as mandated by a state or district course of study. Teaching shapes

might be during Lesson 1. But the teacher would help kids to USE their knowledge of shapes

during other times, such as story (“Is the barn door a square?” “Find circles in the room.”).

2. Some curricula teach tool skills (reading, math, language, and reasoning). Other curricula teach content or subject matter knowledge systems

(literature, history).

3. Develop a curriculum by considering the following

1. Curriculum strands---main kinds of knowledge to be taught.

Curriculum strands (main kinds of knowledge to be taught) are drawn from a state standard

course of study, scientific research, expert opinion of what is important, and the teacher’s own

skills. Curriculum standards, goals, or objectives from a state or district course of study are

restated so that they tell teachers exactly what students will do (clear and concrete).

2. The sample of knowledge to be taught.

The teacher selects a sample of knowledge that gives wide coverage of the strands.

3. The teacher establishes curriculum standards, goals, or objectives---and the knowledge

students need to achieve the objectives---for (1) the whole curriculum, (2) units (sequences of

lessons) in the curriculum, (3) lessons, and (4) short tasks in each lesson.

When planning a curriculum for a tool skill or subject (please read # 1 again), the teacher first

identifies what students will DO at the end of a semester, year, or course (a final performance

and assessment), and HOW the students will do the final performance so as to show proficiency

(fluency, generalization, retention).

Teachers also develop objectives (what students will learn) for the end of the each unit

in the curriculum, for each lesson in a unit, and even for each task in a lesson. In other words,

students DO something to show whether they learned what the teacher tried to teach.

Teachers use the objectives for the curriculum, units, lessons, and tasks to:

a. Identify exactly what students need to learn, and therefore what teachers must teach in the

unit, lesson, and task.

b. Give students review and practice.

c. Give students another chance to integrate what they have learned; and

d. Enable teachers and students to assess learning and their own teaching.

Assessment after a sequence of lessons (unit) is sometimes called a “mastery test.”

4. The teacher uses knowledge analysis to identify all the elementary (component) skills in a

complex skill.

5. The teacher arranges a logically progressive sequence.

A logically progressive sequence means that:

a. Component skills or elements (pre-skills) identified by knowledge analysis are taught early

and continually, and are reviewed and firmed up before teaching complex skills that USE

these elements. For example, sounding out words

see “run,” say “rrruuunn

consists of certain knowledge elements: saying sounds, saying the sound that goes with a

letter, saying sounds from left to right, and not stopping between sounds. These elements

(pre-skills) are taught early and continually BEFORE the students are taught the ROUTINE

(sounding out) that integrates and uses these skills in a sequence.

b. Component knowledge is taught in a way that tells a story (as in history), or so as to make a

logical argument leading to a conclusion (such as moral or political lessons).

6. The teacher plans how elementary knowledge will be integrated into larger and coherent

wholes.

For example, in an arithmetic curriculum, integrating counting, subtraction, and estimation to

form the routine of long division. Likewise, elementary students learn to say sounds (mmmm,

aaaa), to say words slowly and then to say words fast, to say the sounds that go with letters (r

says rrrrr). Then they learn to integrate this knowledge in the routine of decoding words: run

say “rrruuunnn” Now say it fast “run.”

Secondary students learn concepts, facts, rules, and theories, and then integrate them by

writing essays and having discussions of how the U.S. Constitution was written.

Principles of Well-designed Instruction

1. When and how to use (1) explicit, systematic, focused, teacher-directed instruction; and (2) discussion, inquiry, and independent student learning and application.

2. How to collect information from student performance (assessment) , and use it to make decisions about curriculum and instruction.

3. How to use the proper for procedure for teaching the different kinds of knowledge: facts, concepts, rules, routines.

4. How to work systematically on all five phases of learning: (a) acquisition of new knowledge; (b) generalization of knowledge to new examples and materials; (c) fluent use of knowledge; (d) retention of knowledge; (5) strategic integration of knowledge elements into larger wholes.

5. How to corrects errors, firm up weak knowledge elements, reteach as needed, and provide intensive instruction as needed.

6. How to design lessons. What lessons look like.

a. A lesson is a number of tasks (a minute or more long) in a sequence. Each task has a specific instructional function---each task DOES something. Here are instructional functions. In a task, you might:(1) Review and firm up earlier-taught knowledge elements needed to learn something new (pre-skills. What’s a knowledge element? Riding a bicycle is a WHOLE. But when

you perform the whole—riding---you perform certain ELEMENTS: sitting steady, grasping and moving handle bars, peddling, observing the road and adjusting your weight. The whole is an INTEGRATION of these parts. Multiplication of 2-digit numbers 86

x12is a whole; it is a complex skill. It consists of knowledge element PARTS. What are the knowledge element parts? We find out by doing a knowledge analysis. We ask,

What do kids have to know in order: (a) to get what the teacher is talking about when she teaches this whole---this complex skill?

“First we multiply the numbers in the one’s column.” Huh? One’s column? What’s that?

So, kids need to know what “multiply,” “numbers,” and “one’s column” mean; and

(b) to do the complex skill, or whole---to actually multiply?

Knowledge analysis tells us that kids must know the following knowledge elements: (1) the numerals (squiggles) that go with numbers (quantities); (2) how to write the numerals; (3) how to count forward; (4) how to multiply single-digit numbers; (5) place value; (6) renaming (12 is one 10 and two 1’s); and (7) carrying.

Well, when should the kids be taught these elements? (1) Before the teacher starts working on 2-digit multiplication? Or (2) At the same time the teacher is working on 2-digit multiplication? When should you learn the elements of swimming? Before or while you are in the ocean? Duuuhhhh. BEFORE! Way before! And you practice the elements, and get stronger, every day until the day you get in the ocean.That is why ONE instructional function is reviewing and firming-up the knowledge elements, or PRE-SKILLS, of a new WHOLE to be taught.

(2) Teach something new---acquisition phase of learning. So, after reviewing and firming up the pre-skill elements of multiplication, the teacher begins to teach it.

(3) Teach students to generalize knowledge to new examples---generalization phase. When the kids ACCURATELY multiply the numbers in the ACQUISITION SET of numbers used to teach 2-digit multiplication, the teacher gives the kids a NEW set of problems that they will solve using the knowledge that they just acquired. This new set is called a generalization set.Knowledge acquired from the is applied to The generalization setacquisition set of problems of new problems

(4) Teach students to use their knowledge accurately and quickly---fluency-building.Using examples from the acquisition set (the examples used to teach multiplication) and from the generalization set (the new examples that the kids worked CORRECTLY), the teacher says, “Okay, now for some fun. Let’s solve out problems FAST. Try not to make silly mistakes. Think! But let’s go faster. Ready? Go!”

(5) Add new examples; e.g., teach additional historical facts to give more details.For instance, every day, the kids work some earlier problems (review, to build retention) and some new ones (to strengthen generalization).

(6) Review both earlier knowledge and newly-taught knowledge---to build retention and to prepare kids for learning something new that USES earlier taught knowledge elements.

“Okay, we’re going to do something new. We’re going to find out the surface area of the big tables in our room. But first, we have to make sure we remember our BASIC skills. So, let’s practice measuring, and then multiplying, and then adding. Here are some problems. Let’s do them. THEN we’ll measure our tables!”

(7) Use information from review (6) to reteach weak elements. Let’s say that more than a few kids make errors when reviewing 2-digit multiplication. The teacher notes which ELEMENTS of 2-digit multiplication the kids messed up (for instance, renaming) and reteaches these. If the same few kids usually need reteaching, the teacher has short special sessions for them---differentiated instruction.

(8) Teach students to combine or integrate different knowledge elements into a larger whole; for example, (1) measure the length (in inches) of the sides of five tables in the

room (one skill); (2) multiply the lengths to find square inches or area of each table; (3) add the areas to find the total surface area of the five tables. Look at the lesson between 1:25 and 2:00--Application. That’s a good place to do this task that integrates knowledge of elements (measurement, multiplication, addition) into new knowledge of a larger whole.

b. A second feature of lessons is that tasks in a lesson are arranged in a logical sequence:

a. First, review and firm up earlier-taught knowledge to ensure students are ready for

new learning. Then,

b. Teach new knowledge. Then

c. Integrat earlier and new knowledge into a larger whole, such as a discussion or project.

Then

d. Review, firm up, or reteach at the end of the lesson and at the start of the same lesson

the next day.

c. Lessons are usually part of a larger sequence of lessons, called a “unit.” For example,

lessons on the Colonial Period, the Declaration of Independence, the Revolutionary War,

and writing the Constitution would be part of a larger Unit on American Independence in

a course on U.S. History, from Colony to Civil War.

d. Most lessons will teach several kinds or forms of knowledge that are IN the curriculum

materials (textbooks, internet, programs)—forms of knowledge such as facts, concepts,

rules (how things are connected), and routines (sequences of steps, such as descriptions

and explanations).

7. How to teach at a brisk pace.

8. How to give frequent opportunities for group (choral) and individual responses to test/check learning.

9. How to use pre-corrections

Principles of Well-designed Instruction

1. Explicit, systematic, focused, teacher-directed instruction is used when teaching a curriculum for a tightly-coupled knowledge system (e.g., beginning reading, math).

However, instruction that involves more discussion, inquiry, and independent student activity is used when teaching a curriculum for a more loosely-coupled knowledge system (e.g., literature, history).

2. Teachers use information from student performance at the end of every task in a lesson, every lesson in a unit, every unit in a curriculum, and at the end of a curriculum, to decide if students (a) are ready to go one to the next task, lesson, unit, or grade level; (b) need more practice; (c) need to have certain weak knowledge elements firmed up (such as the multiplication part of long division); (d) need reteaching of a whole skill; (e) need supplementary materials (such as a glossary to help students learn vocabulary); or (f) need a different kind of instruction, such as intensive instruction.

3. Teachers use the proper for procedure for teaching the different kinds of knowledge in a curriculum: sensory concepts (colors, shapes), higher order concepts (republic, igneous rocks, consumer demand, linear), facts (The U.S. Constitution was written in 1787), rules, or propositions (“All igneous rocks crystallize from magma.”), and routines, or strategies (descriptions, explanations, theories, logical arguments leading to a conclusion, analyses of documents, solutions to math problems, evaluations of explanations and arguments).

4. Teachers work systematically on all four phases of learning for everything they teach. The four phases are: acquisition of new knowledge; generalization of knowledge to new examples and materials; fluent use of knowledge; retention of knowledge; strategic integration of knowledge.

5. The teacher corrects all errors, firms up weak knowledge elements, reteaches as needed, uses supplements as needed, and provides for intensive instruction as needed.

6. Teachers use the proper for procedure for teaching the different kinds of knowledge: sensory concepts, higher order concepts, facts, rules (propositions), and routines (strategies).

7. All four phases of learning are taught: acquisition of new knowledge; generalization of knowledge to new examples and materials; fluent use of knowledge; retention of knowledge; strategic integration of knowledge.

3. Instruction begins with review, especially elements and background knowledge relevant to the current instruction (pre-skills). The teacher corrects errors and firms knowledge or reteaches before introducing new material that requires this background knowledge.

teacher gains student readiness: attention, sitting properly, materials handy.

Strengths, Weaknesses, Improve How?

5. The teacher frames the instruction by stating the kind of new knowledge to be taught, the objectives, and big ideas that will help students organize, remember or access, and comprehend the new knowledge, and connect new with prior knowledge.

The teacher models or presents new information clearly and focuses on the objectives. The teacher: (a) Shares his or her thought processes. (b) Uses clear wording. (c) Repeats the information as needed. (d) Presents one step or item at a time in a list or routine, depending on how many steps or items students can handle.

The teacher leads students through the application of the new information.

Strengths, Weaknesses, Improve How?

8. The teacher gives an immediate acquisition test/check to determine whether students learned the new information. The teacher tests/checks every time new information is presented to be sure that students learned it. This is especially important when teaching diverse learners, essential material, and difficult material.

The teacher corrects all errors and/or firms weak knowledge.

**Matter of fact way and directed to the group.

**Model. Teacher immediately gives the answer or demonstrates the step.

** Lead. Students say the answer or do the step with the teacher.

**Test/check. Teacher asks the question or gives the problem step again.

**Verification. Specific praise.

** Retest/starting over.

**Delayed test. Teacher comes back and checks again.

11. The teacher gives a delayed acquisition test (calling on both the group as a whole and then individual students) to determine whether students learned the concept, rule, or cognitive routine from the examples and nonexamples, or whether students remember the set of facts presented.

12. The teacher reviews the instruction (e.g., main things taught) and states how what was taught is relevant to next lessons.

The review:

** States what was learned, how it built on what came before, and how it will be built on by next lessons.

** Has students once more reveal essential knowledge.

14. The teacher teaches at a brisk pace by speaking more quickly; staying on task; using words whose meanings are clear; using the same instructional vocabulary from one task to another; cutting out unnecessary words.Strengths, Weaknesses, Improve How?

15. The teacher gives frequent opportunities for group (choral) and individual responses to test/check learning.

The teacher asks the question first, and then calls on the group or an individual. The teacher think time before calling on the group or an individual. After presenting new information, the teacher calls on the group as a whole. After calling on the group, the teacher calls on individual students, and makes sure to

call on students who have made errors or who in general have a harder time learning.

16. The teacher uses pre-corrections, or reminders, to prevent errors. For example, “When we see an x between two numbers or parentheses, we multiply. What do we do when we see an x between two numbers or parentheses? Multiply. Yes, multiply.”

17. The teacher uses a questioning technique such as Socratic dialogue as an instructional/communication procedure. Asking questions that probe students’ knowledge. Asking questions that require students to use rules of reasoning. Helping students revise their knowledge.

INSTRUCTION/EDUCATION

transmission, preservation and advancement

Principles of Well-designed Curriculum Principles of Well-designed Instruction

1. What is a curriculum?

2. Some curricula are for teaching tightly-coupled knowledge systems. Other curricula are for teaching more loosely-coupled knowledge systems.

2. Curriculum strands (main kinds of knowledge to be taught) are drawn from a state standard course of study, scientific research, and expert opinion of what is important.

3. The sample of knowledge to be taught gives wide coverage of the strands.

1. Explicit, systematic, focused, teacher-directed instruction is used when teaching a curriculum for a tightly-coupled knowledge system (e.g., math).

However, instruction that involves more discussion, inquiry, and independent student activity is used when teaching a curriculum for a more loosely-coupled knowledge system (e.g., literature).

2. The curriculum for a year or semester is divided into units (sequences of lessons on a topic). Lessons are divided into tasks. Each task has a clear function.

4. Curriculum standards, goals, or objectives are restated so that they tell exactly what students will do (clear and concrete).

5. The curriculum teaches in a logical sequence. This means: a. The knowledge elements (pre- skills) of more complex skills are taught earlier and continually. These knowledge elements or pre- skills are identified by knowledge analysis of the complex skill. b. The most common and most useful knowledge is taught first. 6. Knowledge is integrated to form larger wholes, or skills. For instance, elementary students learn to say sounds (mmmm, aaaa), to say words slowly and then to say words fast, to say the sounds that go with letters (r says rrrrr). Then they learn to integrate this knowledge in the routine of decoding words: run say “rrruuunnn” Now say it fast “run.”

Secondary students learn concepts, facts, rules, and theories, and then integrate them by writing essays and having discussions of how the U.S. Constitution was written.

3. Instruction functions include: a. Review and firming up prior knowledge.

b. Teaching new knowledge (acquisition).

c. Teaching students to apply knowledge to new examples and materials (generalization).

d. Teaching students to use their knowledge quickly and smoothly.

e. Reviewing and firming up new knowledge taught.

f. Integrating elements into larger wholes.

g. Expanding knowledge by, for example, adding more examples.

6. Teachers develop terminal objectives (what students will do) for the curriculum and for each unit in the curriculum.

Teachers use the terminal objectives for the whole curriculum and for each unit in the curriculum to:a. Identify exactly what students need to learn, and therefore what teachers must teach.

b. Develop terminal performances (something that students will DO) for each unit and for the end of the curriculum so that students can show whether they have met the objectives. These terminal performances: (a) give students more review and practice; (b) give students another chance to integrate what they have learned; and (c) enable teachers and students to assess learning.

Assessment after a sequence of lessons (unit) is sometimes called a “mastery test.”

4. After teachers have planned what to teach in each unit of a curriculum, they plan lessons within each unit. Teachers develop terminal objectives for the end of each lesson, and a terminal performance that enables students to show whether they learned enough to achieve the lesson objectives. The terminal lesson performance might be in the form of review.

5. Teachers use information from these assessments to decide if students (a) are ready to go one to the next task, lesson, unit, or grade level; (b) need more practice; (c) need certain weak knowledge elements firmed up (such as the multiplication part of long division); (d) need reteaching of a whole skill; (e) need supplementary materials (such as a glossary to help students learn vocabulary); or (f) need a different kind of instruction, such as intensive instruction.

6. Teachers use the proper for procedure for teaching the different kinds of knowledge in a curriclum: sensory concepts (colors, shapes), higher order concepts (republic, igneous rocks, consumer demand, linear), facts (The U.S. Constitution was written in 1787), rules, or propositions (“All igneous rocks crystallize from magma, and routines, or strategies (descriptions, explanations, theories, logical arguments leading to a conclusion, analyses of documents, solutions to math problems).

7. All four phases of learning are taught: acquisition of new knowledge; generalization of knowledge to new examples and materials; fluent use of knowledge; retention of

knowledge; strategic integration of knowledge.

8. The teacher corrects all errors, firms up weak knowledge elements, reteaches as needed, uses supplements as needed, and provides for intensive instruction as needed.

6. Teachers use the proper for procedure for teaching the different kinds of knowledge: sensory concepts, higher order concepts, facts, rules (propositions), and routines (strategies).

7. All four phases of learning are taught: acquisition of new knowledge; generalization of knowledge to new examples and materials; fluent use of knowledge; retention of knowledge; strategic integration of knowledge.

8.

Assessing and Improving Teaching from Textbooks Designing curriculum andPrograms and Supplements instruction for elementary

Principles of Effective ClassesBeginning

readingArithmetic State [Scientific

Curriculum research]Algebra Language

Writing

B. Content

Subjects

Literature

Biology

Chemistry

History

CivicsLet’s look.