The Elegant Simplicity of Effective Instruction. Part 1

And therefore each of you, when his turn comes, must go down to the
general underground abode, and get the habit of seeing in the dark; for
all is habit; and when you are accustomed you will see ten thousand times
better than those in the den, and you will know what the images are, and
of what they are images, because you have seen the beautiful and just and
good in their truth. And thus the order of our State will be a waking reality,
and not a dream, as is commonly the manner of States; in most of them men
are fighting with one another about shadows and are distracted
in the struggle for power, which in their eyes is a great good.
But the truth is, that the State in which the rulers are most reluctant
to govern is the best and most quietly governed, and that in which they are most willing, the worst.
[Plato. The Republic. Book VII, 520]

Dear Reader,

Imagine a school--any level--where everyone is focused on education.  On students being led from superficial, overgeneralized, simplistic, largely wrong, ego-centric and disconnected opinions, to knowledge of and skill at using more general and more enduring truths.

Imagine a school were teachers can say exactly what every student will be able to do at the end of the course (western civ), at the end of each unit (the Persian Wars), at the end of every lesson (on Greek combat), at the end of every instructional communication (defining panoply). And teachers continually assess students' acquisition and application at every juncture.

Imagine a school where no program and no method is used but that has been field tested and shown to be highly effective.

Imagine a school were the words "authentic," "diverse," "wholistic,"  "self-esteem," "faciliate," "learning styles," and "relative" from a visiting eduquack produce howls of laughter from staff and students and an invitation to the quacker to leave.

Imagine a school where self-esteem and character are the result of hard work and success, and are not smarmy "objectives" of special workshops taught by psychobabblers.

It's all possible.  It's all real.  It's done in the inner city.  It's done in the sticks.  It's done in public schools, religious schools (Baptist, Catholic, Hebrew), charter schools, and home schools.

The common feature of all of these, and a necessary feature I think is the first item, above.  Sound epistemology--theory of knowledge.  Staff know what knowledge means and how it is most efficiently acquired and applied, or they use curricula whose design principles are derived from a sound epistemology.

At least 4000 readers [well, three] have asked that I fulfill a promise, made here, 
to discuss how to teach in the service of an ideal--to make the rare sort of school, above, into the common one. So, I'll do it.

But it'll have to be in short installments--sort of like the young ladies I dated in high school.

Here's the list.

1.  What is knowledge; how is it acquired?

2.  What is a highly effective communication format for teaching almost anything?

3.  What are the special versions of the general format that are used to teach verbal associations, concepts, rules, and strategies?

If there is sufficient interest, Professor Plum will unload more bilge, on topics such as

4.  How to design (or evaluate and select) an effective curriculum.

5.  How to design an effective chunk (say, a three-week unit) in a curriculum.  [For example, the one my class did on the Persian Wars.]

6.  How to improve a curriculum or curriculum materials.

7.  Others

Well, that oughta hold us till next week?

Here goes...

I.  What is Knowledge?  How Do We Know?

If I communicate well you will see differently.  You will be among a few hundred persons in this world who know the logical basis of learning and instruction--right from Plato, Aristotle, Roger Bacon, Frances Bacon, John Stuart Mill, and Siegfried Engelmann.  I didn't invent it, you understand.  [I'm not near smart enough.]  I got it from all the folks who mentored me.

The true project of an educator is philosophy.

1.     We live in two worlds: (1) the world of things and events: and
        (2) the world of knowledge (ideas) by which we study and communicate
        about the world of things and events.

2.    The world of things and events is superficial, ever-changing, and particular.
        You can't see oranges in general; only particular oranges that are
        transforming every instant.

 3.     However, knowledge (for example, concepts and rule relationships) is anatomical. Knowledge describes the structure and interconnections among things and events, and explains how they come into being, change, and pass away. Knowledge is enduring and is general. Individual persons and their actions come and go, but the concept of humankind and the rules of moral behavior can exist forever and can remain constant—in the form of ideas, or knowledge.

 4.     The classical role of teacher is to educate—to lead students out of the cave of self-interested beliefs, to knowledge of what is general--universal, stable, and enduring. For example…

You teach about the Revolutionary War, Civil War, First and Second World       Wars, Cold War, and war with Islamic totalitarianism—not ONLY so your students can think and talk about these particular wars, but MORE IMPORTANTLY so they can think and talk about concepts, rules, and theories of war and geopolitics generally, and apply this general (i.e., not limited to particular cases) knowledge to other wars in other times and places.

 Likewise, you teach students to sound out slip, slim, man, rim, lip, lamp, and ram, not so they can read these words only, but so they learn the general strategy for sounding out all regular words.

 When you show your students how to solve 10 equations having one unknown (x = 3 + 12; or 6 x 5 = y) you are not teaching the solution to those 10 particular equations only. You are at the same time teaching the general strategy for solving all equations of that TYPE.  The 10 problems and their solutions are examples of the general type of problem and its general method (strategy) of solution.  That (the general—the idea) is what you really want students to learn. (Otherwise, how can they generalize to new examples?)

 5.     However, we’ve got a problem. We can’t teach or learn what is general, constant, or universal (a concept, rule relationship, or strategy) directly or by itself. We can’t see (and a teacher can’t show) the concept (idea) red—only red things that are examples of the concept red.  The concept is in the head. It is cognitive. It is an IDEA abstracted from (taken out of) the examples of red things. 

         Likewise, we can’t teach or learn the word sounding out strategy itself—without particular words to sound out. We can’t see a rule relationship. We can only abstract a rule (that we can say or draw) from particular examples of the rule relationship. Again, as teachers, we can only present examples. The students’ minds have to see (“get,” “grasp”) the connections among the examples and then abstract (induce, figure out) what is general—a verbal association (e.g., fact), concept, rule, or strategy. [PLEASE read that sentence again.]  Our job is to present information (examples via demonstration and explanation) in such a clear way that it is easy for our students to INDUCE (“get”) the idea—the general.

 6.     Cognitive knowledge (i.e., how we represent and communicate about the world of things and events) consists of

      a. verbal associations--knowledge of names  (or descriptors).

b. concepts--knowledge of kinds.

c. rule relationships--knowledge of connections.

d. cognitive strategies--knowledge of

(1) big pictures; e.g., theories and models that describe, explain, and predict; and  

(2) routines for getting answers; e.g., deductive and inductive reasoning, methods for solving problems, methods for analyzing documents. 

Everything you say, think, read, and write boils down to these four forms of knowledge.  This makes instruction elegantly simple.  If everything you teach (e.g., the Greek panoply--armor and weapons carried by the Greek hoplite) is either a verbal association, concept, rule, or strategy; and if the mind, or learning mechanism, performs a number of step-functions to move from examples to knowledge (to induce a verbal association, concept, rule, or strategy); and if there is a communication format whose logic matches the logic "used" by the learning mechanism, then, regarding instruction, all the teacher has to know is WHAT form of knowledge she is teaching, and know the proper communication format for teaching it.

7.     The question is, How does a teacher help students move from examples (particular things and events) to general knowledge (of verbal associations, concepts, rule relationships, and strategies) that represents and enables students accurately to communicate about things and events? The answer is: The teacher helps students to apply a series of logical, mental steps (operations) to examples. If this is done well, students get the concept, rule, or strategy that is revealed by the examples.

8.     You might say that the mind (learning mechanism) performs certain logical operations, or mental steps, to move from examples (particular things) to cognitive knowledge (general). Therefore, the fastest and most effective way to teach (help students acquire and apply knowledge) is to make it easy for their minds to follow the logical steps. For example…

a. The logic of a verbal association is THIS ONE THING GOES WITH THAT ONE THING. To “get” a verbal association means to get THAT THIS ONE THING goes with THAT ONE THING. Therefore, the most effective and fastest way to teach a verbal association is simply to say, THIS ONE THING goes with THAT ONE THING.

“That (point) is a door…. What is that?... door…. Yes, point to door.”

“Thomas Jefferson wrote the first draft of the Declaration of Independence. Say that with me…  [Test.  Who wrote the first draft of the Declaration of Independence? Tell me a fact about Thomas Jefferson?]

b. The logic of a concept is ALL OF THESE EXAMPLES HAVE SOMETHING(S) IN COMMON. THEY SHARE A SAMENESS in their features.

 So, to get a concept means to get (induce) the sameness common to the examples (particulars) but NOT found in the NONEXAMPLES. 

 Therefore, the most effective and fastest way to teach a concept is to teach WHAT THE SAMENESS IS that is COMMON to the EXAMPLES but NOT found in the NONEXAMPLES. Specifically,

 (1) Teach students how to examine examples and nonexamples. For example, students see and identify the features of rocks that are crystalline vs. not crystalline (size, shape, color, and structure).

  (2) Show examples one at a time, label them as examples, and point out the common features that make them “same.” “See the planes in the structure.”

  (3) Juxtapose examples and nonexamples of crystal and noncrystal; label the nonexamples (“This is NOT crystalline.”) and point out the absence in the nonexamples of the features common to crystal. “See, unlike crystal there are no planes in the structure.”

  (4) Acquisition test. Present the examples and nonexamples just shown.  Ask, “Is this (crystalline)? Yes. How do you know?” [Student uses the definition to justify his answer--his deduction.]

  (5) Later, work on generalization/discrimination with new examples and nonexamples.

 c. The logic of a rule relationship, or proposition, is THIS CLASS (group, set) of examples/things (CONCEPT) GOES WITH THAT CLASS (group, set) of examples/things (CONCEPT).

 All mammals are vertebrates. [All of the class of mammals is INSIDE the class of vertebrates.]

No terrorist can be trusted in peace negotiations. [No person in the class of terrorist is in the class of persons that can be trusted in peace negotiations.

The more the enemy’s infrastructure (fuel, transportation, communication) is destroyed, the less the enemy resists after defeat. [The class of events that involves destroying enemy infrastructure CAUSES the class of events that involves resistance.]

Therefore, the most effective and fastest way to teach a rule relationship is to teach THE RELATIONSHIP (GOESTOGETHERNESS) COMMON to the EXAMPLES. Here’s how.

     (1) Pre-teach students how to examine examples and to identify sameness and difference in the features; e.g., poems, historical documents, rocks, slides of phases of cell division, wars (weapons, size of armies, duration, amount of destruction of soldiers, amount of destruction of infrastructure, amount of enemy resistance after defeat of main forces).

     (2) Either state the rule relationship (and have students repeat and write it) OR tell them that they are to compare and contrast examples and discover (induce) and state the relationship.  [Of course, the second  REQUIRES that you FIRST teach students how to do the steps of induction.]

     (3) Show examples and point out the goestogetherness (co-variation) among certain variables—that is, point out the relationship across the examples. Or, show examples and have students identify the goestogetherness. [It is better for you to do this first—model—and then have students do it with new examples.] For example,

“Boys and girls, here’s a rule. The more the enemy’s infrastructure (of water, waste, power, communication, roads, food) is destroyed, the less  resistance the enemy will mount after defeat of its military.”

“Here is an example of the rule. In the Third Punic War (149-146 BC) Rome totally destroyed Carthaginian infrastructure. Down to the ground. Even salted the fields. Carthage then put up no resistance."

“Here’s another example. In the War Between the States, Union General William Tecumseh Sherman burned southern cities, homes,materials, and fields. The Confederate soldiers put up little resistance after that.”

“Here’s a contrasting example. Union General Grant killed soldiers, but unlike Sherman, did not destroy  cities. Even though  Confederate soldiers died by tens of thousands, they kept on fighting.

 [Of course, students can get these examples from various texts.]

  (4) Have students identify and state the relationship (goestogetherness) common to the examples. “The greater….the less…”

  (5) Give new and/or hypothetical examples and/or have students invent them. Ask what will happen if (there is more or less destruction of infra-structure). Then ask, How do you know? (Students give rule.) And give new examples of more and less resistance after defeat, and ask why. Again, students apply the rule.

 d. The logic of a cognitive strategy is a sequence of LOGICALLY ARRANGED, OR PROGRESSIVE STEPS (each next step depends, logically, on accomplishing the earlier ones; and each step, logically, makes the next steps possible), GOVERNED BY RULES (“If the product is ten or more, write the…”), and USING CONCEPTS (product, tens, ones, column, times, carry) AND VERBAL ASSOCIATIONS (seven times five is 35).

 So, to get a cognitive strategy is to get (induce) the logical arrangement of steps (and to see the necessary progression) and the concepts, rules, and verbal associations needed.

Therefore, the fastest and most effective way to teach a cognitive strategy is to teach the sequence of steps, the logical necessity of the progression, and all of the concepts, rules, and verbal associations needed. You should teach most of the concepts, rules, and verbal associations beforehand, so that during instruction on the strategy, you are mostly teaching the steps.

 You may have to teach a strategy in chunks (forward chaining). 1; 12; 123; 1234.... Or 1; 2; 12; 3; 123; 4; 1234… It is also important to describe what you are doing as you demonstrate the routine so that students learn to verbalize the concepts, rules, and steps (conspicuous strategy instruction).

This ends whatever we were doing. 

Review....

We saw that there are four and only four kinds of cognitive knowledge.  [Fogive me for asking, but what are they?]  Notice that some forms have a simpler logical structure than others.  In a verbal association, This implies That.  In a strategy, one step requires knowledge of rules, concepts, and verbal assocations, and logically implies the next.  Getting (inducing) a verbal association, concept, rule, or strategy from examples involves a logical routine performed by the "learning mechanism"  (Engelmann and Carnine.  Theory of Instruction).  There is a communication format that is designed to make it EASY for the learning mechanism to perform the logical routine and to induce knowledge of what is general from the examples.

In a later installment, we will examine those formats.

Thanks for reading.  Have a beer and a shot of tequila.

 

Comments

[slimedog]

YES! This is exactly what I--a humble statistician--have been looking for. Parts 2, 3, and 4, please.

[Dr. Cookie]

Professor, is this really rhetoric? I mean in the old fashioned sense. Logic set forth in rules of language, in order to persuade, offer evidence, etc.

In my quest to understand how to teach reading comprehension, sometimes I wonder if it's really just old-fashioned rhetoric with a new name.

[Zippy The Pinhead]

Professor Plum:

No offense intended, but back in the day when I suffered through all those silly credential classes, one of my main beefs with the professors who taught them was that most-- if not all of them-- were ivory-tower types who had no real experience teaching in the K-12 arena. In other words, they were basically pushing theories which they had never themselves tried to implement. So I'm curious to know if you have any personal experience "from the trenches," as it were, or not.

When I did my tour of duty in K-12, which consisted of a semester at a middle school, followed by three years at a high school, I found that such work could be profoundly depressing. I came to believe that the public schools-- at least in the district where I worked-- had passed the point of no return. In other words, fighting over curriculum at that point was analogous to fighting over how to best re-arrange the deck chairs on the Titanic.

When I read articles like the one which follows, I remember my days working in K-12, and I remember feeling like my own efforts to teach well and make demands on my students were basically a waste of time. As I recall, in most of my classes, I spent probably 75-90% of my time and energy dealing with a small minority of kids who just didn't want to be there.

====================

Saturday, November 13, 2004
Fires ravage limping Baltimore schools
Number of small blazes set by students rises. Some say the arson is evidence of larger problems.

By FOSTER KLUG
The Associated Press

BALTIMORE – Four firefighters and a firetruck are stationed outside Walbrook High School every day. The chances are good they'll be needed.

Two months into the school year, Baltimore's public schools have been hit with at least 76 fires - most of them small, most of them set by students - compared with 168 in all of last year. Walbrook High alone has reported about 20 blazes, versus 24 in 2003-04.

"I've never seen it this bad before," says math teacher Eugene Chong Qui, who has taught in the city school system for eight years. "I don't know what it stems from, but it's systemic. It really seems as if the students are so far gone out of their minds, they'll do anything for attention."

In a school system struggling with a $58 million deficit, some say the surge in fires is alarming evidence of deeper problems - staff shortages, cutbacks in extracurricular activities, overcrowded classrooms and rising alienation among the 95,000 students.

So far, the fires have caused little damage and no serious injuries. But across the city, a pattern has emerged: Firefighters get a call about a fire in a trash can or locker, a toilet or stairwell; the students are evacuated, and they stream outside; with so many people in one place, violence sometimes follows; school is usually canceled.

On Oct. 20 alone, firefighters got more than 10 calls from Baltimore schools about deliberately set fires.

At Walbrook High, school officials decided not to even evacuate the students during the last several fires because of the fights and the lost class time, Chong Qui says.

So far, there have been 61 fire-related arrests, compared with 144 last year, says city fire spokesman Kevin Cartwright.

The Fire Department is offering rewards of up to $500 for information leading to a conviction, and has stationed four-person crews at three high schools as a deterrent and to enable firefighters to get to the scene more quickly. Also, the school board last month voted to spend $1.5 million to enable 15 schools to hire 37 more hall monitors and 34 more security officers.

Fire officials have encouraged teachers to patrol in or around toilets, stairwells and empty lockers between classes. And school officials have been talking with parents to try to put a stop to the fires and other troublemaking.

"We are asking all of those concerned about the city that they join us, help us, work with us as we work to create better, safe schools," school board chairwoman Patricia Welch said last month. "We can't do it by ourselves."

At Walbrook High, situated in the city's working-class West Baltimore section, 16-year-old junior Christopher Spruill says students are setting the fires to get out of class. "They want to be out on the corner instead of getting an education," he says. He says students are too afraid to speak up, reward or not: "People know who's doing it, they're just not saying."

Chong Qui says Walbrook High's fires "probably started out with a handful of kids. But that handful has contaminated maybe three or four other handfuls who aren't strong enough to say 'No' ."

Part of the problem, says Bebe Verdery, education director at the American Civil Liberties Union of Maryland, is that officials, trying to fix the financial crisis, have increased class sizes - 40 or more in some classrooms - and cut staff - more than 1,000 people last year, with 250 fewer teachers.

"You have a net reduction of the adults who are able to supervise students," Verdery says. "When you combine that with the increased class sizes, the schools seem much less capable of controlling the violence and the fire-setting."

Robert Balfanz, a research scientist at the Johns Hopkins Center for Social Organization of Schools, says the vandalism stems, in part, from the loss of counseling and extracurricular programs at schools in the city's poorest areas.

"The mismatch between the level of kids' needs and the level of resources available to help solve their problems leads to kids' feeling lost," Balfanz says. "When kids feel lost and frustrated, they act out."

And the misbehavior "is like a contagion."

In August, before the school year started, a judge ordered the city and state to put an additional $30 million to $45 million into the Baltimore schools after the ACLU argued that the system's plan to solve its financial crisis hurt the quality of education. But the state has appealed, and the money has not been released.

[Plum]

Zippy the P asks THE question. "Does any of that guff about the logic of learning/instruction have any conecttion to the real world.

The answer is, Yes.

I taught autistic children for many years; developed and then tested education programs for them and their families for abouot 20 years after that.

Point deux. The giif about the logic of instruction cuts through all the flappdoodle and gets to the heart of the matter. If it came across as airy, tjat would be my fault, but it is as down to earth as you can get. How do you communicate so that kids get it.

This leads to the third point. If teachers taught/communicated more effectively, more kids would experience more success more oftenm and you'd have fewer acting out problems in school.

Of course, talking about the (true) philosophy of education alone doesn't come close disclosing all there is to teaching. There is of course how you pace instruction (fast), how you engage students (act crazy, for one), how you come up with interesting material, etc

I'll get to that if you want.

[Ariztophanes]

We want.

[slimedog]

How ... you communicate so that kids get it.

Yes, please. Bring it on!

[Ariztophanes]

I started reading the Carnine/Englemann book, THEORY OF INSTRUCTION yesterday. The first chapter says the ONLY way kids learn is by induction, and they demonstrate learning by deduction. I'm a big fan of DI, I assure you, but it's the "only" way?

I suspect that for students with language deficits, letting THEM develop the generalization from the specific examples IS the best way to achieve "perfect" knowledge. However, for students with a better grasp of language, I believe they can grasp the generalization from the description (giving them the "rule" they could have induced on their own) and use that knowledge for deduction.

I've often wondered why DI was better suited for learners from "disadvantaged" backgrounds, and this might explain why: kids with language deficits need to induce the concept for themselves from concrete examples in order to achieve anything like "perfect" understanding. To kids with stronger language skills, perhaps just stating the information gives the student enough information to sufficiently "get" the concept.

Granted, I'm not very far into the book, but I experience "disequilibrium" (See? I've learned something in my education classes!!) when I'm told that the ONLY way to learn is induction from expertly chosen examples. Right now I'd have to say it is ONE way, and perhaps is demonstrably the BEST way, but that it surely is not the ONLY way.

They claim it may be the most important education book ever written. Being that I haven't read much (if any) of Piaget, Dewey, or anyone else they mention, I won't be able to say. I AM glad you suggested it.

[Scott W. Woods]

TOI does not say that induction is the only way to learn anything, but that it is the only way to learn a concept. This is not true just in DI programs, or just with disadvantaged children, but with everybody and all concepts. This comes from the nature of concepts themselves. TOI does not say that induction from expertly chosen examples is the only way to learn concepts, just that it is the best way. It does say that all concept learning comes from induction from examples, and that without expertly selected and communicated examples many students will fail to learn the concept, or will learn a misrule about it, for instance, that reading is about looking at the shape of words and guessing what they say.

Regarding rules, some concepts are easier to get if the rule behind them is given first (the method for doing this effectively is given in TOI), others don't have a useful rule. For instance, very basic concepts often are taught best without a rule, since the rule will probably be more advanced conceptually than the concept. How can you teach "getting steeper" with a rule if the learner really doesn't understand "getting steeper"? You will find that TOI goes into considerable detail about which kinds of concepts under which circumstances are best taught with rules or not.

DI programs work well for disadvantaged children because they were designed and tested to work with these children. Have you seen evidence that they don't work well with "normal" children? Please post it if you have.

If by "DI programs" you mean programs written and tested according to the principles of TOI, what possible objections could you have? Who would not benefit from well-designed, thorough, instruction? Quite obviously, excellent instructional design takes skill, intelligence, time, and money. The fact that there are few really well-designed programs available designed for other than disadvantaged children is not a good argument against DI programs, but an argument for designing better instruction for all