The (Simple) Logic of Effective Instruction

 

onely add
Deeds to thy knowledge answerable, add Faith,
Add vertue, Patience, Temperance, add Love,
By name to come call'd Charitie, the soul
Of all the rest: then wilt thou not be loath
To leave this Paradise, but shalt possess
A Paradise within thee, happier farr.
[John Milton.

Paradise lost, Book XII, 575-590. 1667]

Dear Readers,

Professor Plum is going out on a limb.  He'll be presumptuous enough to teach you something even though you ain't asked.  I know.  Many of you visit this site to read a good rant.  And believe you me, Professor Plum can rant like nobody's bidness, as we say down south.  When he gets warmed up, he can chew steel and spit .44 magnum hammerheads.

Howsomever, you have an interest--as parents or teachers or as Citizens of these United States--in knowing what it means to teach children well.

The education establishment--through a combination of stupidity, arrogance, vanity, pure self-interest, and power (all requiring that We The People know nothing about what really goes on, and know little about what good curricula and good instruction look like) has turned what is pretty uncomplicated (good instruction) into something unreachably abstract, loaded to the back teeth wiith nauseating fluff, and so esoteric (by esoteric I mean meaningless drivel) that self-appointed priests in ed schools claim only THEY can understand it.   [Why, heck, they don't even know what a concept is!]

But I'm going to try to reveal how uncomplicated good instruction really is.

Therefore, if you've a mind, use what I suggest as a way to teach and as a way to evaluate the teaching your kids are getting.

This is the first shipment.  If there's interest, I'll send more.

Here, as all the nibs say, we go...

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When you teach kids long division, you use problems. 

Of course you want kids to solve each problem. But your BIGGER objective is that they learn the STRATEGY for solving ALL problems of that TYPE.

You want them to learn the STRATEGY, but you can’t teach the strategy by itself.
You must use CONCRETE problems. These problems are examples of how to use the strategy. Once students learn the GENERAL strategy, they can apply it to problems they’ve never seen.

The same goes with reading skills--or anything else. You want students to learn that the letter m says mmm. Not just ONE m, but ALL m’s (all letters that have that shape).  But you can’t teach that CONCEPT (m says mmm) by itself.  You have to use examples of m’s that differ in size and style and placement on the page and placement in words—to show that despite these differences, they all have the same shape and therefore they all say mmm.

Likewise, you want students to learn the STRATEGY for sounding out words. But to do this you have to use EXAMPLES of words. Once they GRASP the strategy using those examples, they can apply it to new words.

So, let’s review. We use examples to teach something general (the sounds that go with letters, the strategy for sounding out words, the strategy for analyzing a poem, the strategy for asking questions about a text so as to comprehend it). But you can’t teach general knowledge by itself. You have to use examples. Students GRASP (or get, or construct) the general idea FROM the examples.

This means, that instruction has to be so (LOGICALLY) clear that it's easy for students
to SEE the general idea (e.g., the way to sound out words, the way to examine history texts and synthesize a big picture) IN the examples.

Teaching is NOTHING more than this...

1.  Communicating in a way that moves students from examples to general knowledge.  This is called acquisition.

2.  Then, teaching them to apply the general knowledge to new examples.  This is called generalization.

What's the best way to organize communication (instruction)?  Easy.  Just know this.

1.  The acquisition of knowledge phase is moving from examples to general ideas. General ideas are concepts (kinds of things); rules (relationships among kinds of things); and strategies (routines for solving problems and for representing complex relationships).

This "movement" is NOTHING more than inductive reasoning. The student's "learning mechanism" figures out (gets, constructs, induces) what is general from the examples.

2. Generalization is moving from a general idea (e.g., a theory of war) to new examples (examining a new war in light of the theory).  This is NOTHING more than deductive reasoning.

This wisdom has been around since Plato and Aristotle and Roger Bacon and Francis Bacon and John Stuart Mill figured it out.  Unfortunately, the education professoriate can't spell any of their names, and so their wisdom has been lost to the field--if you can call organized flapdoodle a field.

So, the job of designing instruction is clear. 

1.  Design the "getting knowledge" phase (acquisition) so that students can EASILY figure out the general idea revealed by the examples.

2.  Design the "applying knowledge" phase (generalization) so that students can easily see that the new examples are really THE SAME as the old ones from which they acquired the general idea.

"Yes, this war looks different, boys and girls, but examine its features carefully.  It has the same features as all the other wars we studied.  So, we can use our theory of war to predict how it will turn out."

How many persons in this field do you think have any idea what Professor Plum is talking about? Would you say 100 in this galaxy? 

I, my mentors (Siegfried Engelmann, Kathy Madigan, Marcy Stein, Nancy Marchand-Martella,  Doug Carnine, Jerry Silbert, Steve Hoffelt) and their students, my students, a few  colleagues (whom I've not gotten permish to name), and now you, Dear Reader, are the only ones. Feeling specccccial?

I say this to express how lucky I am to have known the right people and to have read the right books.  "Theory of Instruction" (Siegfried Engelmann) is the most important piece of applied epistemology in the last 100 years.  Naturally, then, no one in edland knows of it.  And if they run across it, they reject it. 

"That's too hhhaaaarrrrd."

Well, they're right about one thing.  It IS much easier to be an ignoramus.

You want to apply the ideas, above?

Okie dokie.

First, here's how NOT to teach sound-symbol relationships (or ANY concept).

"Boys and girls, I'm going to teach you the sound made by another letter.  We'll learn the sound made by the letter m.  It makes the same sound as a cow.  What sound does a cow make?  [Depends which end is talking.  Notice how the communication has become UNFOCUSED!  Most kids have no idea what she's doing.]  Billy?  [mooo]  Yes, Billy knows.  [Is that the point?  What Billy knows?]  Cows say moo.  And the letter m makes that sound.  [WHAT SOUND?  mmmm or oooo or mmmooo?  Three fourths of the kids are now gone.]  So, look.  [She points to m in a big book that has LOTS of words.]  Here's m and it says mmm, just like a cow.  [Is that the point?  To confirm the nonsense she talked about earlier?]  And look at this m [in the word man.] It says mmm, too.  [Yeah, but some kids were looking at the n!]

Get the point?  Not focused on the objective!!  m says mmm.  Period.   

Also, all the m's look the same--so kids may not generalize mmm to m's that are in red.

Also, the m's look like the n's.  Half the kids will say mmm when they see an n.

Understand why so many kids are illiterate?

The instruction is illogical.  It does not assist children to induce the concept--all squiggles that look like this--m--say mmm.

Here IS what you want to see...

Ms. Jones is teaching beginning readers the sounds that go with letters--phonics, or sound symbol relationships.  She will use the same FORMAT for teaching every sound-symbol relationship.  In fact, she will use this same format for teaching ANY concept (which is the kind of knowledge that sound-symbol relationships is).

Frame/Model:
"New sound. (Points to letter m on easel.) I will point to the letter and say the sound. My turn." (Teacher places finger under the letter m on the easel.)

"This letter says mmmm."

"Listen again. (points) This letter says mmmm."

Lead:
"Say it with me. (Points to the letter m). Get ready." (Taps the letter as a signal to respond)  Kids say mmm

"Again." (Signal)  Kids say mmm.

Test/Check:
"All by yourselves." (Pause to make sure students are attending.)
(touches under the letter) "What sound? (Signal)  Kids say mmm.

Verification:
"Yes, mmmm."

Examples/nonexamples:
Teacher puts more m's on the board--different colors, sizes, and fonts.  She points to each one and says, "This is mmm."

She JUXTAPOSES m's with a few other letters (a, s, t), points to each NONexample of m = mmm, and says, "This is NOT mmm."

Then she tests/checks to see if students GET the difference.  She points to each letter and asks, "Is this mmm?"

If a student is correct, she verifies it.  "Yes, mmm."

If a student is wrong (which is NOT likely at this point), she says, "This is NOT mmm."  Then she goes back and forth between m and the not m and labels each one.

"Look. This IS mmm.  This is NOT mmm."

Then she tests again.  "Is this mmm?"

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Notice. 

She focused on one thing--the objective. 

She moved from teacher gives information to students USE the information. 

She tested again and again to ensure that they got it. 

She used several examples that differed in UNessential features to reveal (and enable students to INDUCE) the SAMENESS (shape) that makes them the same.

She juxtaposed examples of m and a few nonexamples of m to reveal the DIFFERENCE between all examples of m and all examples that are not m (shape).

This format will teach almost any kid--from the kid who has a terribly tough time making inductions (getting it) to the kid who gets it with only two examples. 

There is a slightly different format if you are teaching a concept (red, democracy, m says mmm), a rule ("When demand increases, price increases."), or a strategy (how to make a model that depicts an economic system, how to sound out words, how to do long division).  And every concept, rule, or strategy would be taught with its particular format--because the LOGIC for inducing a concept, rule, or strategy is the same no matter what the concept, rule, or strategy is.

In our next installment, if you WANT another, I'll give you more examples AND I'll point out what is general about this strategy--which we call model-lead-test.

 

 

Comments

[tc]

Are there any books that explain how to make instruction like this?

[Plum]

There sure are!

Edward Kame'enui and Deborah Simmons. Designing instructional strategies. Merrill.

Marcy Stein et al. Designing effective mathematics instruction.

Skills for school Success AND Advanced Skills for School Success. Anita Archer. Curriculum Associates.

Douglas Carnine and others. Direct Instruction Reading. Merrill.

Any of the Series Guides here...

http://www.sraonline.com/index.php/home/curriculumsolutions/di/9

PP

[Ariztophanes]

I did some looking on Amazon.com for these. The first book is unavailable, though it looks like the best one there. The Stein book on mathematics instruction also looked good, but dealt only with arithmetic.

Which brings me to a question:

Why do Direct Instruction advocates not suggest DI for upper levels of instruction? Is it because current high school methods are effective with well-educated students? Is the answer for upper grades dealing with these uneducated students remediating with DI?

From personal experience, this seems to work. However, with our "self esteem" and "social promotion" culture seems to thing this is bad for kids. Care to start a public education campaign to advocate the need for remediation of kids at ALL levels who are lacking basic skills in reading, writing, and arithmetic?

[Ariztophanes]

BTW, YES, I'd like to see the method for teaching each of the objectives you mentioned (concept, rule, strategy). Is "fact" an objective you would allow? IOW, what is the ontology of instructional objectives, and how does logic dictate they be taught?