Talk:Teaching Procedures, page 5

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Consider adding some content from the following to the Practice section:

"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.

"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.

"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. 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. " - Reigeluth

--Lzinsmei 03:20, 16 April 2007 (UTC)