Teaching Procedures, page 8
Try It: Practice What You've Learned: This is your opportunity to try the skills covered in this section of the lesson. As the Wikiversity is a collaborative learning space, you will contribute your original ideas to the work of those who have come before you by enhancing and adding to the possible responses within the case scenario laid out below. Are you saying to yourself, "...but, isn't looking at the answers from a fellow learner the same as cheating?" Not in this case. In fact, contributing your original ideas while participating with fellow learners and building upon their work is the intended goal of this Skill Builder exercise. The desired outcome is to build an ever evolving working document filled with not just one possible response to each question, but a host of instructional strategies that you can use on your next instructional design project. Have fun and get creative!
What to Teach? How to Teach It?
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". With this in mind, what would you advise Jennifer to do first? Think about it, click "edit" for this section, and add your answer below:
- First of all, she need to have a clear idea of the cope of the lesson. She would look at the textbook and handouts from the school teacher which indicate what to cover. Then, she would know the goal of the instruction. Next, she would text the current knowledge and skills of Joe. She can do this by getting him take a quiz on the previous contents. Finally, she can plan a lesson which fill a gap between the Joe's goal and Joe's current ability. Kei (discuss • contribs) 21:32, 20 February 2014 (UTC)
- The mom explained what Joe needed to know regarding the fractions so we know the goal, but it would be important to conduct a learner analysis to determine what Joe's current levels are prior to instruction. She could talk to Joe or collect some of his past work to determine current levels. Together these would constitute the necessary needs analysis. Once we know what to teach, Jennifer will need to know what the steps are for calculating fractions. This may require a content analysis if she isn't familiar with the content and then specifically a task analysis to break down the steps for calculation. Sometimes job aids are used with pictures that can be taped to a notebook that include each step in a task analysis gdysard 22:06 (EST), 15 February 2015.
- My first suggestion would be to look at Joe's homework, textbook, and class notes. This should help you to identify exactly what it is that his teacher is wanting him to learn. You then can work through the sample problems he copied in his notes and find a sequence of steps that the teacher has been using. I would then write the steps out in sequence for Joe to use so that as he is becoming accustomed to solving these problems, he can use these steps as a sort of "checklist". Providing a sample problem that shows how to utilize each step would be helpful for him to visualize the steps as well. Smccorma 03:01, 3 February 2012 (UTC)smccorma
- If possible, I would advise Jennifer to talk to Joe's teacher and find out exactly what they're learning in class in regards to adding fractions. At the same time, I would suggest that Jennifer ask Joe's teacher what he is struggling with. This will help Jennifer figure out what she needs to focus on in their tutoring session. Hatch.nicole 02:46, 4 February 2012 (UTC)
- We can suggest that Jennifer draw up a simple set of fraction problems to test Joe's current knowledge, employing both variable characteristics and dimensions of divergence. For example, two each of of adding, subtracting, dividing and multiplying fractions, finding common denominators and reducing fractions the lowest denominator. One Joe takes the pretest, she can interview him about what he thinks he knows and doesn't know, and what makes him uncomfortable about working with fractions. Jennifer can pair this knowledge with an interview with Joe's mother about Joe's struggles with fractions.Kevmcgra 03:49, 4 February 2012 (UTC)
- Apparently the content that Jennifer is going to teach is adding fractions. I am hoping that in the beginning the purpose (goals) of hiring her has been made clear just like whether or not it's getting caught up with homework or preparing for standardized testing etc. If not, she should definitely ask questions in order to identify what Joe needs to be able to do after completing the tutorials and so she will be able to know at the end if it turns out successful with the tutorials. Next, Jennifer probably could speak to Joe, Joe's parents or teachers, look at Joe's existing formative and/summative evaluation items, and maybe also give some problem sets for Joe to solve in order to find out where Joe stands, what type of learner he is, what works for him, and about his abilities and deficiencies in the skills. If Jennifer's expertise is not in the specific area, she can also look for resources (i.e. from a SME) about the procedures Joe needs to learn about adding fractions. After that Jennifer can start to analyze the content/task by breaking the goals down further into substeps. By comparing all these tasks with the information from earlier steps ("learning analysis"), for example - what Joe already knows, Jennifer may determine what Joe does not know as to teach him the content, what routine tactics work for Joe in the basic skills as well as the power tactics to enhance his skills. Y.Zhang 04:43, 4 February 2012 (UTC)
- first of first, conduct a need analysis, which includes goal analysis and learner analysis.Being aware of what Joe should be able to do about adding fractions after the tutoring and what his current knowledge or skill level is. Zhaomeng 21:18, 4 February 2012 (UTC)
- First, Joe needs to start creating a domain map that specifies what to learn and how things are related with each other. And then, Joe needs to identify what are the goal of the task, and what needs to be learned to perform the task. And then, Joe needs to test the learners to decide what they already know and what they should learn. Dablee 21:45, 5 February 2012 (UTC)
- If possible, I would suggest Jennifer to acquire curricular standards for Joe to learn adding the fraction. With the standards inventory that come before, at, and after the adding the fraction, she can have some diagnostic exercise with Joe to identify his current stage of knowledge and what area he needs more attention to in terms of adding the fraction instruction.Yeolhuh 22:24, 5 February 2012 (UTC)
- I'd suggest Jennifer to check Joe's current grades and scores on the recent test that conducted in the previous semester. Jennifer can figure out what is the strength and weakness. Then, Jennifer can analyze how Joe could show a good performance on the strength part, and not a good performance on the weakness part. Songd (discuss • contribs) 14:39, 20 February 2014 (UTC)
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What are the recommended teacher actions?
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, click "edit" for this section, and add your answer below:
- Presentation-practice-feedback should be good in this case. However, in order not to overwhelm Joe, the content for the presentation and practice should start easier ones then gradually become more complex. It would be good to start with adding fractions of same denominators. Jennifer can teach Joe that he has to just add numerators in cases where the denominator of the fractions are same. Then, get him to practice the calculation of adding fractions of same denominators and give him feedback. Jennifer, then, can show how to calculate adding fractions of same denominators. She should start with small numbers. Especially cases like this 2/3 + 1/6 where Joe just has to multiply the first fraction. Kei (discuss • contribs) 21:48, 20 February 2014 (UTC)
- Joe could be making errors at one point of the task analysis. If you are using a checklist that is taped to his notebook, you can highlight this step and have him specifically practice this in different contexts. Maybe give him some authentic practical examples that he may be familiar with like cooking or measurements needed for building a dog house for his dog. gdysard 22:12, 14 February 2014
- If Joe is struggling with this concept, I would start by using the checklist/sequence of steps and showing him how to follow it as I go back through his notes and show him how to solve each of those problems (whose final answer we already know) using the checklist/sequence of steps. In doing so, you should be able to see where he is having difficulty. After you have solved a few and Joe is starting to tell you what to do, allow him to show you how to solve a problem that you already know the correct answer to (and use that as feedback for him). Once he has correctly solved a number of problems to which he does not know the answer (this way, the tutor can provide feedback based on his steps and work), remove the checklist and see what he can recall using even more new problems that Joe does not know the answer to. Smccorma 03:05, 3 February 2012 (UTC)
- Jennifer will want to make sure that she identifies all the dimensions of divergence for adding fractions to ensure that Joe receives enough variation in examples and practice exercises. Joe might be okay adding 1/2 + 1/2 but have difficulty solving 1/2 + 2/3. Hatch.nicole 03:18, 4 February 2012 (UTC)
- Jennifer's analyses should have revealed how Joe will be expected to use fractions at school, and the dimensions of divergence he will be asked to demonstrate mastery of. She should match her presentation and practice to these dimensions, establishing both the generality for the procedure(s)and the equivalence classes for the dimensions. Does Joe need to know how to add simple fractions with one-number or two-number numerators and denominators, or must he also know the divergent dimensions of adding and subtracting both positive and negative fractions, or fractions with positive numerators but negative denominators? In each case, practice must encompass the dimensions in their totality, and match the complexity of the expected performance. Kevmcgra 04:06, 4 February 2012 (UTC)
- The practice can be very motivating when a specific context is provided. An example is as follows: Joe, imagine that several boys and girls are visiting your family. Your mother prepares a big round cake. She asks you to help her divide the cake, in order to treat those little friends. There were three kids. You planed to divide the cake equally into three pieces. Right after you finished cutting, two more boys arrived. There seems not enough cakes. So you cut each piece into two. Now there are six pieces. But we have five kids. You give the extra piece to one of them, your best friend. Finally, how much of the whole cake did your best friend eat? (The problem can be made easier or harder) Shuya Xu 07:21, 4 February 2012 (UTC)
I think the "presentation-practice-feedback" should work here. But if Joe has learn adding fractions in school, Jennifer may go ahead to let him practice on couple of questions first, and based how he did, present the general procedure. In this way, Joe will be more engaged and Jennifer would be able to emphasize on the steps where Joe needs more help.Zhaomeng 21:35, 4 February 2012 (UTC)
- Joe needs to create practices to accomodate all the divergent and variable instances and categorize them into equivalence classes. After that, the equivalence classes should be sequenced from easy to difficult. Joe needs to provide easy example followed by easy practice within the same equivalence class. If successful, Joe can proceed to more difficult equivalence class. Dablee 21:50, 5 February 2012 (UTC)
- Jennifer should make the practice definitely align with the content, full of practice opportunities or new contexts to allow Joe to apply his skills - the right procedure dealing with fractions. The practice items can be arranged from the easiest difficulty to the hardest level.Y.Zhang 04:07, 6 February 2012 (UTC)
- She needs to design practices with various equivalent classes examples based on divergent problems. Ranging from easy to difficult divergent problems, Joe gets to practice with various equivalent classes practice questions.Yeolhuh 15:04, 6 February 2012 (UTC) 18.104.22.168 15:03, 6 February 2012 (UTC)
- I'd suggest Jennifer to gather instructional materials for a subject area that Joe could not get a good mark. After that, Jennifer can organize the instructional materials in order to teach Joe based on the decision on what should be the first and what should be the later. Songd (discuss • contribs) 14:42, 20 February 2014 (UTC)
- ADD YOUR ANSWER ABOVE THIS BULLET POINT. SIGN IT WITH YOUR NAME USING THE SIGNATURE WIKICODE Phonebein 18:15, 18 December 2011 (UTC)
What if the learner does it wrong?
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, click "edit" for this section, and add your answer below:
- Jennifer should get Joe to show all steps of the procedure he pursued, and tell him in which step in the procedure he did wrong. Kei (discuss • contribs) 21:50, 20 February 2014 (UTC)
- I would find out where in the task analysis of steps the error is occurring to provide him feedback with the specific step in the process. That way feedback can be provided immediately during that particular step. So, he isn't completing fraction problem after problem. The issue can be isolated and corrected gdysard 22:16, 14 February 2014
- Initially, if you are solving problems he has already seen in his notes, the feedback is immediate as he always knows the correct answers. When he is first starting to solve them on his own (without the final answers being known), I would provide feedback after every step. Once he can make it through a few problems without needing any more feedback after every step, then allow him to solve an entire problem and provide feedback only when he has reached the final solution. Smccorma 03:07, 3 February 2012 (UTC)
- I would make sure that Joe writes out each step he takes to solve the problem, so that it's easy to tell when a mistake was made and provide corrective feedback at that exact step. Hatch.nicole 02:56, 4 February 2012 (UTC)
- Jennifer can stop Joe when she sees him make an error and demonstrate the correct procedure, explaining each step to him as she makes it. As she does so, she can equip him with the generality for the specific problem. For example: "When you add two fractions, always remember to look first at whether the denominators are the same. If so, you can add the numerators straight across and keep the denominator. Then you can check whether you can reduce it to a smaller fraction."Kevmcgra 04:15, 4 February 2012 (UTC)
- Jennifer can prompt Joe by reminding him of the principles of adding fractions; or by making the fractions concrete problems, so that the task is imaginable (e.g. asking him to think about the total pieces of cake, and the number of pieces his friend ate). Shuya Xu 07:27, 4 February 2012 (UTC)
- Once an error appears, Jennifer should correct instantaneously or provide hints to help Joe find out the way to correctly go through the whole procedure. Jennifer may also repeat the generality of the procedure, and encourage Joe "you are getting it. Follow the steps, you must be able to make it!" Zhaomeng 21:39, 4 February 2012 (UTC)
- Jennifer needs to stop Joe and examine his misunderstanding. After she identifies the misunderstanding, she can explain the procedure and highlight what has been done wrong. Depending on the misunderstanding, she can also provide some power tactics such as giving a mnemonic device, prompts, etc. Dablee 21:53, 5 February 2012 (UTC)
- Jennifer can point out what went wrong (by circling the mistake in another color, for example) as to have Joe's attention. In the mean time, the correct step(s) should be demonstrated again if giving prompts for correction did not work for Joe. Informative and motivational feedback should be used like it's in other scenarios (learner response => wrong/encouragement, correct/praise).Y.Zhang 03:55, 6 February 2012 (UTC)
- To identify where Joe is having a hard time exactly or where Joe has misunderstanding, Jennifer would encourage him to think aloud when he solves a practice problem. Once she identifies the area that Joe needs feedback on, she can ask him pause the activity and revisit the area that Joe needs clarification or correction.Yeolhuh 15:07, 6 February 2012 (UTC)
- First of all, finding specific reasons why Joe did it wrong. It is not a good idea to provide feedback that includes correct answers or right procedures. Jennifer can analyze why Joe did wrong, and then modify Joe's thought pattern based on the analysis. Songd (discuss • contribs) 14:44, 20 February 2014 (UTC)
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What else should the teacher do?
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? Think about it, click "edit" for this section, and add your answer below:
- If Joe becomes overwhelmed if he tries to add three fractions, then Jennifer can get Joe concentrate on the two of the three fractions and get him add the two. Then, add the answer and the third fraction. Kei (discuss • contribs) 21:53, 20 February 2014 (UTC)
- This example is asking Joe to do something that he couldn't do originally. Jennifer should provide a clear example by showing him how to do it by demonstrating completion of a problem successfully. She could complete and entire problem and then break it down step-by-step and have Joe repeat each step after Jennifer repeats each one. gdysard 22:15, 15 February 2014
- Start by asking Joe to read the steps to you as you roleplay being the student and show him how you would solve a problem. Since he is reading the instructions, it is as if he is the teacher. Ask him guiding questions with everything you do so that he is engaged in "helping" you (although you are solving the problem-this allows you to quickly assess what he knows and what he doesn't know). Being that he is now the teacher and not the student, this may take some pressure off of him so that he doesn't feel that he needs to do it all perfectly. Smccorma 03:09, 3 February 2012 (UTC)smccorma
- I would write out the steps and suggest that we complete a problem together by following the steps. Then I would complete the problem with input from Joe. I would prompt Joe for direction whenever moving onto a new step to draw his attention to the procedure. Hatch.nicole 03:23, 4 February 2012 (UTC)
- On thing Jennifer can do is relate fractions to Joe's prior knowledge. She can tell him that if he can add, subtract, multiply and divide ordinary numbers, he can work with fractions because the skills are exactly the same. The only thing that changes is the procedure: what you do first or second, or which number you multiply or divide another by. Then she can demonstrate one or two simple examples to reinforce the generalities, and ask him to tackle similar examples. Kevmcgra 04:28, 4 February 2012 (UTC)
- The difference between learning in school and learning from a tutor is the latter is a one-on-one type of learning, therefore, Jennifer could based on her analysis of Joe's current skill of adding fractions find out the specific obstacles which Joe is facing. For example, Joe can do pretty well when the two denominators are same and one denominator could be a multiple of the other, but he stumbles when two denominators have a common factor. If it is like this, Jennifer can tailor the presentation of the generality and practice by focusing on this type of fraction adding. Zhaomeng 22:04, 4 February 2012 (UTC)
- She can ask Joe to explain the procedure and the principles behind them while performing the task. Dablee 21:55, 5 February 2012 (UTC)
- Jennifer can explain the steps again and write all the steps on a piece of paper with the label of the procedure (if any) as well as the goal, and then demonstrate an example following the steps. After that Joe can try to practice again. Y.Zhang 03:46, 6 February 2012 (UTC)
- Jennifer would create a cheat sheet type of material with all the necessary steps to follow for solving the problem. With the material, she can go over the sample problem with Joe together and let him refer to the material with steps for supplementary material.Yeolhuh 15:10, 6 February 2012 (UTC)
- I'd suggest Jennifer to demonstrate a couple of example questions. Showing how to do it first, and then letting Joe to do that by himself. And then, Jennifer can give him feedback. Songd (discuss • contribs) 14:47, 20 February 2014 (UTC)
When is the best time?
When is the best time to present the generality? Think about it, click "edit" for this section, and add your answer below:
- After showing four or five examples. Compared to adults, kids tend to get the sense of generality after seeing multiple examples. They do not often get the sense of generality by themselves as kids in this age are still in the process of developing attract thinking. So, after showing several examples, Jennifer should explain about the generalities of the examples. Kei (discuss • contribs) 21:57, 20 February 2014 (UTC)
- It may depend on Joe's prior knowledge. If he has limited knowledge, then the generality could be presented before she demonstrates the process. However, if he has some confidence and experience she could provide demonstrations and then present them, so my answer is it depends...gysard 22:21, 15 February 2015
- If Joe is completely lost, then I would present the generality right away. If he is struggling but not entirely lost, then I would first want to see what he knows, then I would present the generality to help him keep the steps in order and provide feedback about where he is having difficulty. Smccorma 03:10, 3 February 2012 (UTC)smccorma
- In this case, I would probably present the generality and an example at the same time. I would use the generality to work through the example. Hatch.nicole 03:03, 4 February 2012 (UTC)
- The best time is anytime it helps the learner(s) encode the procedure. It could be paired at the front of the lesson with a prototype example, or with a demonstration, to equip a learner facing a difficult (for him or her) or complex procedure. It could be presented when the learner encounters difficulty in practice. It can be presented after practice, but before assessment.Kevmcgra 04:45, 4 February 2012 (UTC)
- One of the best time to present generality I think is at the very beginning of teaching the procedure. The generality should be presented with variant demonstration of examples. Another time to present generality is before practice. This is like giving a kind of review. During practice, the learner may make mistake or get stuck at certain steps. At this time, the presentation of the generality should be repeated, but the focus would be on the certain challenging steps, instead of the whole process. Zhaomeng 00:26, 5 February 2012 (UTC)
- The generality should be presented when they learn something and apply it to different contexts for the first time and when they get things wrong to correct their understanding. Dablee 22:00, 5 February 2012 (UTC)
- One of the solutions can be to begin with presentation of specific examples and ends with the formation of generality. (showing examples again -> compare/contrast -> generality) Y.Zhang 03:36, 6 February 2012 (UTC)
- The best time to present the generality is when they are first exposed to it, which is the beginning of the instruction. Also it can be better understood by being presented with examples at the same time.Yeolhuh 15:12, 6 February 2012 (UTC)
- The best time to present the generality might be when Joe answers correctly a couple of times in a row. That is the point that Joe starts organizing a schema to store that knowledge. Songd (discuss • contribs) 14:49, 20 February 2014 (UTC)
What about motivation?
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? Think about it, click "edit" for this section, and add your answer below:
- Confidence seems to be the biggest variable decides if kids are motivated to learn fractions. Fractions look new and strange and get kids to lose their motivations. In order help Joe to gain confidence, starting with fractions with same denominators should be helpful. Jennifer should emphasize that Joe just has to add the numerators and that he would pursue the exact same procedure which he follows when he is adding integers.
- It is important to give him positive reinforcement to add to his own belief that he can do it. Give him stickers next to each part of the task analysis that he gets right. This will reinforce what he does correctly and he can aim at getting his entire sheet filled out. This may give him a goal to work towards and to focus his energy on. gdysard 22:24, 15 February 2015
- Make it a game and give him something to work toward. Each problem can be worth 3 points that he will solve on his own. For every problem that he solves correctly, he earns one point. For every problem where you didn't have to provide any feedback to him until the conclusion of the problem, he earns one more point. For every problem that he does willingly and without complaining, he earns one more point. When he reaches 30 points (10 problems solved correctly, without scaffolding feedback, and willingly...or some combination of more problems) then he earns some prize that he would enjoy: an ice cream cone, $5.00, you will order him a pizza of his choice, etc. (In my experience, this works remarkably well for high school students.) Smccorma 03:14, 3 February 2012 (UTC)
- I think I would just try to stay positive and encouraging by telling him that most people hate fractions initially but that it will get easier. That doesn't seem as motivating as Stacey's idea... Hatch.nicole 03:25, 4 February 2012 (UTC)
- At the moment Joe shows frustration, Jennifer can remind him of her previous appeal to prior knowledge (or present it for the first time if she has not done so), and offer encouragement: "Remember when we talked about how working with fractions is just using addition, subtraction, multiplication and division? That's all we're doing. We just need to figure out what step to take first, second or third. It's easy; you can do this!" Alternatively, she can present Joe with a procedural mnemonic, such as such as the "bow tie" method for subtracting fractions, that will give him confidence that he can complete the subtraction procedure.Kevmcgra 04:54, 4 February 2012 (UTC)
- In order to increase motivation, it's a good way to make Joe feel that adding fraction has much to do with his experience, and that can be interesting. The cake dividing problem may work for the above purpose. It is important to prepare presentation and practices at an appropriate level, so that Joe won't feel too frustrated because of the difficulty, or feel boring with the easyness. Jennifer's praise and encouragement also values in the retention of motivation. Shuya Xu 07:38, 4 February 2012 (UTC)
- There are several ways to motivate Joe: put the description of the procedure of adding fractions into his favorite lyrics, and sing the song with him. Always encourage him when he feels not less confident and when he wants to give up--"I believe you will make it!" Praise him when progress is made either in oral way or giving candies, ice-cream or more entertainment time. Sometimes setting challenging goals and taking away what Joe likes if he cannot achieve the goal is also a way to motivate him, but this should be applied when Jennifer is sure that he has had the capability. Switching teacher and student role, and having Joe describe the procedure he is learning is also a motivation strategy. Zhaomeng 01:02, 5 February 2012 (UTC)
- Making him do something easier will gives him a sense of accomplishment. Also, letting him work with a partner who is eager to learn will be a good way to motivate him. A game in which learners get a positive reinforcement will be another way to motivate him. Dablee 22:02, 5 February 2012 (UTC)
- Giving praise as positive reinforcement immediately: "Thanks for doing the practice questions! You did a great job at answering all the them correctly." Encourage Joe when he's trying to get there but struggled: "Almost!" "Joe can do it!"Y.Zhang 03:28, 6 February 2012 (UTC)
- Using examples around his life for practice can be motivating to him. For example, Jennifer can use candies or pies for practice questions. Also sometimes using examples around him help him reconstruct his schema. For example, Joe may be familiar with batting average of major league baseball players or shooting average of NBA players. Jennifer can use that figure to explain how faction is used to get that figure. In addition, using each to difficult practice approach can help him develop high level of self-efficacy that can boost his motivation as well. Yeolhuh 15:43, 6 February 2012 (UTC)
- It is usually good to provide real-life examples and context-related questions and situations. I would suggest Jennifer to provide Joe with some interesting real-life examples that include a concept of fraction. Songd (discuss • contribs) 14:51, 20 February 2014 (UTC)
To see possible responses to this exercise (prepared by the original authors of this lesson), click here: Example. Note that these responses are purposely placed on a separate screen to provide general guidance should you become stuck, but NOT to imply a single correct response to the case scenario.
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Procedure Using by Charles M. Reigeluth. Used by Permission.