That friend of yours, Jennifer, 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". With this in mind, what would you advise Jennifer to do first? Think about it, and jot your answer below, before you read on! 

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.
 

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? Think about it, and jot your answer below, before you read on! 

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? Think about it, and jot your answer below, before you read on! 

So, 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? Jot your answer below, before you read on! 

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!