Teaching Procedures, page 9
The following are possible responses (prepared by the original authors of this lesson) to the exercise on the Try page. Note that these responses are purposely placed on a separate screen from the exercise to provide general guidance should you become stuck, but NOT to imply a single correct response to the case scenario.
What to teach ? How to teach it ?
Question: That friend of yours, Jennifer, from the Invariant Tasks lesson has now been hired to tutor Sam's younger brother, Joe, in adding fractions. She remembered what wonderful advice you gave her for tutoring Sam, so she is back for more help. After you recover from the flattery, you remember that you should start with the view that the most important concerns in any instruction are "what to teach" and "how to teach it".
Possible Answer: She should do a needs analysis to make sure that Joe really needs to know how to add fractions. Rodger Kaufman (1982) has described this as identifying the gap in knowledge between what should be and what is. This requires both a goals analysis and a learner analysis. Joe's mother has already told Jennifer that he should know how to add fractions. Jennifer could try to confirm this by talking to Joe's math teacher, but it is probably not necessary in this situation. Jennifer could then find out what he already knows with a few questions at their first session together.
But what if she had a group of students and needed to prepare some instructional materials ahead of time ? It would be a lot harder to figure out what they already know. It might be necessary to sample the learners and conduct several interviews to identify the lowest level of entering knowledge. But then you would want to have some mechanism (like a pretest) to avoid teaching the more knowledgeable learners anything they already know. That would just waste their time and demotivate them. However, in many instructional development (ID) situations, you may not have enough time or money to sample the “target” learners, but you may be able to talk to someone who has taught the same content to the same kinds of learners. This is a more cost-effective but less reliable way to conduct a learner analysis.
Let's assume that Jennifer is confident that Joe needs to learn how to add fractions. Can we now turn Jennifer's attention to "how to teach it" ? Have we really spelled out what to teach ? Not exactly. Jennifer will need to be precise (refresh her memory) as to what the procedure is for adding fractions. This is called a task analysis (or content analysis), and entails identifying all the required steps. On your advice, after digging around in the depths of her gray matter, Jennifer comes up with a flowchart like the one on page 3. So now she is all finished with "what to teach," right ?
Not exactly. She really ought to break down some of those steps into substeps (such as steps 2, 3, and 6) until all steps are at a level that Joe can understand. Part of this analysis process is to identify any concepts that Joe may not be familiar with, such as denominator, common denominator, and numerator. Jennifer doesn't have to use those terms (unless the post-instructional situation will require their use), but some term will be needed (e.g., "top number" and "same bottom number") to communicate efficiently. These analysis activities are also called task (or content) analysis, and the term "prerequisites analysis" is often used for identifying such substeps and concepts.
What are the recommended teacher actions ?
Question: Based on your advice, Jennifer has done all these analyses, so now she has truly identified "what to teach" and can proceed to think about how to teach it. You remember how useful the notion of presentation-practice-feedback was for Jennifer to teach the Presidents to Sam. Do you think that notion would help for teaching this procedural skill ? Clearly, practice is important for learning a skill. We all know that "Practice makes perfect." But what should that practice be like ? Joe shouldn't just do the same practice over and over again like memorization practice, should he ?
Possible Answer: The practice should be as similar as possible to the post-instructional requirements (the conditions of performance after the instruction is all over). Joe will probably be given two or more fractions and be asked to add them, in which case that's what Jennifer's practice should require him to do. But the post-instructional requirements may entail reading a story problem and figuring out what mathematical operation is needed, and then using the right procedure, in which case that's what the practice should do. This is called consistency (or authenticity or performance-based learning). Similarly, the post-instructional requirements may call for Joe to be able to handle all kinds of fractions, in which case Jennifer should give him practice adding all kinds of fractions. This is called divergence.
Furthermore, we know that some cases of adding fractions are a lot more difficult than others. To be consistent, Jennifer should include the full range of difficulty required after the instruction is over. But should she start out with difficult practice ? Clearly, it will be easier for Joe to learn from if it is an easy case, unless he already knows how to handle easy ones (in which event he wouldn't learn anything from it!), although it would help you to diagnose his entering skill. If even the easiest authentic case was quite difficult for Joe, it would probably be helpful to compromise on the consistency rule in some ways. This is a form of prompting—what behaviorists call shaping and cognitivists call scaffolding.
What if the learner does it wrong ?
Question: Now, you know well that if Joe is doing a lot of practice and getting them all wrong, it could actually make things worse. His error would become ingrained to the point where it would be much more difficult for Jennifer to correct it. So feedback is clearly also important for skill learning. But what should the feedback be like ?
Possible Answer: Errors most often occur in a single step of a procedure. So Jennifer's feedback should point out the specific step that Joe did wrong and should help him to do it right. The feedback could demonstrate the correct performance of the step, or it could give a hint that helps Joe to figure out what he was doing wrong. When Joe gets the practice right, on the other hand, Jennifer's feedback should probably just confirm that it was right. You should also remind Jennifer that motivational feedback (encouragement when wrong and praise when right) can also be useful.
What else should the teacher do ?
Question: Imagine Jennifer asking Joe to add a couple of fractions. If he couldn't do it in school, it's not likely that he can do it now for Jennifer! So what other guideline should you give Jennifer ?
Possible Answer: Jennifer should probably show Joe how to add two fractions. This is often called a demonstration or example of the skill. But some cases (demonstrations) are a lot more difficult than others. So again, it will be easier for Joe to learn if it is an easy one. Now, if Jennifer just demonstrates the procedure without saying anything, would that be good instruction ? Not exactly. So what should she say ? Think about it before you read on!
She should explain what she is doing. This explanation could be in a form that generalizes to other cases within a given equivalence class, in which event it is called a generality. Or it could be in a form that relates the generality to this particular case, which is called attention focusing.
When is the best time ?
Question: When is the best time to present the generality ?
Possible Answer: There are several options as to when Jennifer could give the generality: before the demonstrations (which is a deductive approach), after several demonstrations (which is an inductive approach), or during a demonstration. No one approach is always best.
What about motivation ?
Question: How often have you heard, "I hate fractions!" ? Joe is probably no exception. What can Jennifer do to keep him from getting discouraged—to keep his attitude positive and his concentration high ? High motivation translates into high effort, and that means quicker and better learning. What would you recommend to Jennifer ?
Possible Answer: Encourage him when he falters: "That's closer!" Give praise when he is correct: "All right! You got it this time! You're smart!"
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Procedure Using by Charles M. Reigeluth. Used by Permission.