Designing Instruction
Selecting and Using Examples During Instruction and Assessment
Martin A. Kozloff
Copyright 2006
Quick (and Final) Review
Here are the tools and steps in designing instruction. Let’s review them---one LAST time.
1.Learn what your state standard course of study requires you to teach.
If standards are not concrete and clear, improve them. If (according to scientific research, expert opinion, and your own knowledge) important standards are missing, add them.
2.Determine what KIND of knowledge a standard is, as described in “Designing Instruction: Forms of Knowledge.”
Verbal association. The U.S. Congress consists of the Senate and the House of Representatives.
Concept. red, republic, colony, alliteration, amphibian, under.
Rule-relationship. “When X, Y, and Z happen, economic development becomes likely.”
Cognitive routine. The sequence of steps for long division or for sounding out words.
The difference in how you teach these four forms of knowledge is mostly whether you teach steps (in cognitive routines) and how you use examples to communicate the idea—the concept, rule-relationship, or cognitive routine.
3.Use task analysis to determine which pre-skills and new skills students needto achieve the curriculum standard. See “Designing Instruction: Task Analysis,” for review.
4.State clear and concrete OBJECTIVES for each phase of mastery, as described in “Designing Instruction: Objectives” and “Designing Instruction: Phases of Mastery.” Specify
a. What students will DO to show whether they have achieved the standard---regarding acquisition of new knowledge, fluent USE of knowledge, generalization of knowledge to new examples, and retention of knowledge.
b. In what situationthey will demonstrate acquisition, fluency, generalization, and retention.
c. The criterion for achievementregarding each phase of mastery.
d. What assistance, if any, students will receive.
e. How to assess whether students have achieved the criterion for each phase of mastery. [Please see the tables on pages 22-33 in “Designing Instruction: Instructional Objectives” and your assignment for that document.]
6.Then, select sets of EXAMPLES that clearly communicate the information students need to acquire new knowledge, become fluent, generalize knowledge, and retain knowledge. Also select examples to assess achievement in each phase.
7.Finally, with all this information,plan procedures for delivering instructionfor each phase of mastery. [The next part of this course.]
It’s very important at this time to review the document, “Designing instruction: Forms of knowledge.” Make sure you are firm on the following ideas.
1.The goal is for students to acquire knowledge (general ideas); to use their knowledge fluently and with new examples;and to retain knowledge.
2.There are four kinds of general ideas or cognitive knowledge. General ideas connectspecific things and events. These specific things or events (e.g., the thirteen original states in America) are EXAMPLES of the general idea (colony).
A company of people transplanted from their mother country
to a remote province or country, and remaining subject to
the jurisdiction of the parent state; as, the British
colonies in America.
3.General ideas (forms of cognitive knowledge) connect specific things. Notice the connections here:
Verbal associations. This ONE thing goes with another thing.
Concepts. All these things have certain commonfeatures---redness.
Rule-relationships. This SET of things goes with that set of things.
Cognitive routines. All these words are sounded out the same way; all these math problems are solved the same way; all these poems are analyzed the same way.
4.You can’t communicate a general idea (the connection) by itself. You can only presentexamples. For instance, students can’t learn (grasp, get, figure out) the concept of---square---unless they see examples of square. Students can’t learn the routine for sounding out words, unless they see and perform examples of the routine for sounding out words WITH words. Students can’t learn the fact that Jefferson City is the capital of Missouri unless someone communicates an example of that fact---by saying it (“Boys and girls, new fact….”) or by showing it on a map.
5.Students learn (grasp) general ideas by performing “logical operations” with the examples(Engelmann, S. & Carnine, D. 1991. Theory of instruction. Eugene, OR: ADI Press). Specifically, the “learning mechanism” (eyes, ears, brain)
a. Examines the examples and observes (and perhaps describes with words) their features; for example,color, shape, size.
b. Compares and contrasts examples, and identifies features that are the same. [Let’s imagine that the learner is talking to herself and knows the words to describe the objects.]
“This one is a circle and small, and called ‘red.’”
“This one is a circle and large, and called ‘red.’”
“This one is a triangle and small and called ‘red.’”
“This one is a triangle and large, and called ‘red.’”
“This one is a diamond, and called ‘red.’”
“Therefore, ‘red’ MAY mean the way these are the SAME---color.”
How does the learning mechanism come to this conclusion? Because all of the examples are different (size, shape) but are treated the same way (named) AND they have one SAME feature. Therefore, logically, the way they are the same is likely to be why they are treated the same.
c. Contraststhe examples(that share the same features and have the same name---“red”) with NONexamples that don’t have those features and don’t have that name (“not red”). Then the learning mechanism identifies the difference between the examples and the nonexamples.
“This one is a circle and small, and called ‘red.’”
“This one is a circle and small, and called ‘NOT red.’”
“This one is a circle and small, and called ‘NOT red.’”
“They are all small and all circles, but one is called ‘red’ and the other two are called ‘not red.’ The one way they are different must be what makes the difference in what they are called.”
“This one is a triangle and small, and called ‘red.’”
“This one is a triangle and small, and called NOT red.’”
“They are both small and all triangles, but one is called ‘red’ and the other is called ‘not red.’ The one way they are different must be what makes the difference in what they are called.”
d.Finally, the learning mechanism puts all that information together and “grasps” the connection.
“Ah Ha! ’Red’ means THAT COLOR, which all of the things called ‘red’ have but which NONE of the things called ‘not red’ have.”
It’s exactly the same logical operations if a student watches the teacher sound out different words, or analyze different poems and documents, or solve different equations---and the student finally grasps the general series of steps in the routine.
6.The teacher can’t present examples and nonexamples in a random sort of way. The teacher must present a certain range of examples, that have certain features, in a certain order, and then juxtapose (put next to each other) examples and NONexamples---so that the learning mechanism can quickly and without confusion examine, identify features, compare and contrast, and draw a conclusion---which IS grasping the general idea.
7.There is a general and effective procedure for teaching; e.g., gaining attention, framing the task, modeling new information, presenting examples, correcting errors, etc. However, the general procedure is slightly different depending on whether you are teaching a verbal association, concept, rule-relationship, or cognitive routine. Please notice some of the difference when you review “Designing instruction: Forms of knowledge.” Note how examples and nonexamples are presented. Note how students’ knowledge is assessed in the phase of acquisition, with immediate and delayed acquisition tests.
The next section expands on number 6, above.
Revealing General Ideas with Examples. Acquisition Phase
We’ll discuss the selection and use of examples for each phase of mastery. Let’s begin with acquisition. This is the phase when students FIRST learn (get, figure out, grasp) a general idea (such as a concept) from examples and nonexamples presented by the teacher. In the phase of fluency, the teacher uses examples to help students perform their knowledge more quickly and effortlessly. In the phase of generalization, the teacher helps students learn to apply their knowledge to new examples. And in the phase of retention, the teacher uses examples to help students to retain their knowledge.
1. Use several examples to teach a concept, rule relationship, or cognitive strategy. You can’t use just one example.
Why? Because one example has many features. Mr. Kamal is teaching the concept---civil war. [civil war: A war between factions of the same country.
Mr. Kamal describes the main features of the civil war in the United States. He describes armies, battles, weapons, generals, ships, fortifications, states, events that led to the outbreak, and so forth. So, WHAT IS (what features define) civil war? It’s impossible to know for sure. Why? Because the one example (with all of those features) enables students to draw many logical (but wrong) conclusions.
Fred. “Civil war is when armies fight.”
Joe. “Civil war is when they use cannons.”
Jose.“Civil war is when northern armies fight southern armies.”
Deb.“Civil war is war that kills many soldiers.”
The one example does not communicate which features are the DEFINING features. [A war between factions of the same country.]
If Mr. Kamal later describes the civil war in early Rome (a war that has some of the same features as the American Civil War—weapons, groups, generals), will students easily identify the features that make them bothcivil wars? No.
Here’s another example of how you can’t use just one example. Mr. Smith taught his students the sounds that go with several letters. Now he’s teaching students the cognitive routine for sounding out wordsusing those letters.
“Boys and girls, I’ll show you how to sound out words. Here I go.”
m a
o------>
He puts his finger on the ball, slowly slides his finger to the right, and says mmmmaaa.
Willthis one example of the routine teach all students (especially diverse learners) the GENERAL set of steps for sounding out words? No. Watch what happens next, when he reverse the letters.
a m
o------>
“Okay, boys and girls. Your turn. Sound it out.”
Ginny. “mmmaaa.” [The one example, above, of ma, taught Ginny that you are supposed to say mmm first.]
Maria. “aaa…..mmmm” [The one example, above, did NOT teach Maria the rule that you blend the sounds together.]
Chuck. “Huh?” [The one example was not enough for Chuck to learn the steps.]
Therefore, during the phase of acquisition---when you are trying to teach a new concept, rule-relationship, or cognitive routine, use several examples. [Note. This does not apply to teaching verbal associations. Because there IS only ONE example. There is only one example of the fact that The six New England states are Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut. So, you merely STATE the verbal association and students memorize it. But for concepts, rule-relationships, and cognitive routines you DO need several examples in an acquisition set.
Acquisition Set. In the phase of acquisition, the examples are called an acquisition set. In each lesson you use part of the set. How do you select examples for the acquisition set? Here’s a guideline.
Select a range of acquisition examples (of concepts, rule-relationships, and cognitive routines) whose FEATURES represent the examples to which students will later generalizetheir knowledge. [You may want to read that again.]
Do you want students easily to generalize the concept---red---to the whole range of red---dark to light; reddish orange to reddish blue? Yes. Therefore, when you teach---red---use examples whose features range from lighter to darker, and from orangish to plain red to bluish red. [But start with the most common red.]
If you teach the routine for sounding out words, do you want students to be able to generalize the sounding out routine to words that are vowel-consonant (am, it); consonant-vowel (ma); consonant-vowel-consonant (cat); consonant blends (flow, snap); words with stop sounds (cat) and words with continuous sounds (fun)? Yes. Therefore, your acquisition set should include examples of all of these. [But start with the easiest---am]
If you teach students the routine for multiplication, do you want students to generalize the routine to problems with odd and even numbers, and to problems where the larger number is sometimes on top and sometimes on the bottom? Yes. Therefore, your acquisition set should include examples of all of these. [But start with the most common examples.]
Stipulation errors. Ms. Ruger used medium redonly as her acquisition set for teaching the concept red. What do these examples tell students red is? Medium red. What do you think happened when she later showed dark red and asked, “Is this red?” Many of her students said, “NO. Not red.” They made an error. Why? Because the medium red examples communicated (STIPULATED) that “red” means medium red. This is called a stipulation error. The range of examples was BIASED in some way. Too narrow. What students learned (“red” means medium only) did not match the WIDER RANGE of red. So when asked about red examples that were outside of their definition, they did not see these as red.
Mr. Kimber used the following to teach students what fractions are.
3/4 5/7 12/34 1/3 9/15 3/5 4/9
Do these represent the whole range of fractions? No. Are they biased in some way? Yes. The denominators are all larger than the numerators. Later, Mr. Kimber says,
“Boys and girls, is this a fraction?”
4/3
Some students will say “No. Not a fraction.” Why? Because his biased set of examples above, stipulated (taught) that fractions have larger denominators.
To avoid stipulation errors, and to make it easier for students to generalize knowledge to unfamiliar examples, make sure your acquisition set covers the variety of features of whatever you are teaching. But when you FIRST start teaching, use the most common examples.
2. Teach students that things that look DIFFERENT in many ways are the SAME in the essential ways, and therefore should be treated (named, solved, sounded out, analyzed) the same way.
You don’t want students to get stuck on unimportant details. You have to teach them that, for instance: (1) the letters are different, but you sound out these words the same way because they are all regular words; (2) the numbers and the unknowns are different, but you solve these algebra problems the same way because they are all equations with one unknown; (3) their outer appearance is different, but you can use the same concepts to describe these animals because they are all vertebrates; (4) the letters may be different, but you can conjugate these French verbs the same way because they are all “er” verbs. In other words, present examples from the acquisition set in a way that shows how the examples are the same (in the essential features) despite differences (in unessential features—letters, numbers).
How do you teach that “these (words are sounded out, problems are solved, poems are analyzed, verbs are conjugated) the sameway even though they are different in certain features”? [Please look at the five examples of red on pages 3 and 4, above.] The rule is:
Show examples that are greatly different in irrelevant features, but treat (name, solve, sound them out, analyze) them the same way.
For instance,
Mr. Garand is teaching his eighth graders the concept---amphibian.
He can’t do it with only one example. If he shows the example below and says, “This is an amphibian,” some students may “get” (conclude) that “amphibian” means thing with bulging eyes.