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      The pattern of prompt and response is very basic to almost any type of teaching and learning. As I first stated in chapter One and argued again and again, teaching is more than telling. Teaching includes the management of the learners' efforts, and the eliciting of feedback. Prompts are used in two general ways, to provide practice and to test. Practice and testing are certainly not the same thing, but the pattern of prompt and response is very similar in the two situations. The analysis of these prompts is much the same in either situation. A test question in history, for example, might be equivalent in content to a question that was given earlier on a daily assignment. A problem in algebra could be basically the same on a test as in a daily assignment. Therefore I will discuss prompts for practice and prompts for testing together.

      The pattern of prompt and response is perhaps not strictly necessary in order to build a structure of knowledge. When I read a book carefully I am building a structure of knowledge with no external prompts demanding responses from me. There may be internal prompts as a natural part of thinking about what I am reading, but so long as my reading remains a private endeavor, there is no external prompt. However this is not the general pattern for learning in school. If we told the kids in September to go home, study the book for nine months, and come back for a test in May, we should expect little accomplishment. In normal schooling a massive influx of prompts demanding responses begins immediately in September and continues everyday throughout the school year. Therefore it would seem reasonable and beneficial to look closely at prompts.

      I will first divide prompts into five levels. They are:

strict synthesis
open synthesis

      The first level is recognition. A question, or a situation, or stimulus of some sort is posed to the student, along with possible responses. If the student can simply recognize the correct response among the incorrect responses then he gets full credit. Multiple choice tests, at least on the surface, require only recognition.

      The next level is recall. Possible answers are not given. The student must produce the correct response. Fill-in-the-blank or short answer questions are of this kind.

      The third level is strict synthesis, in which ciphering of some form is required. This usually means solving problems. In this situation the response must be a synthesis of parts, but only in a predetermined manner. Thus the student must not only have the parts on hand, he must also be able to assemble those parts in a correct manner. There is a right way and a wrong way to assemble and use the relevant information. The wrong way may be given some credit, but not full credit. Mathematics problems are of this kind, with few exceptions. When doing math problems the student uses the bits of knowledge he has and assembles these bits in a way that produces the correct answer. Science problems sometimes are of this kind, especially when they involve mathematical calculation. Other subjects may sometimes have strict synthesis. Diagramming sentences, for example, is strict synthesis, at least until ambiguous sentence structures are considered..

      The next level is open synthesis. A prompt on this level requires the student to take parts of their structure of knowledge assemble them in some form. However in this case there is not a single objectively correct way to do it. There are several ways, or perhaps many ways, that are correct to one degree or another. Thus, essay questions in history, in which one must explains something, or present an argument supported by facts, are of this type.

      In most situations open synthesis means producing a string of words. I think it is important that open synthesis does not necessarily mean this. There are cases when open synthesis does not mean putting together a string of words. Synthesis, as I am using the term here, means putting ideas together. In most subjects, such as history or literature or science, we cannot know how a students puts ideas together unless that student translates the ideas into a string of words. In mathematical subjects, however, synthesis may consist, or require, translating ideas into a string of symbols, or perhaps a network of symbols. In art, physical education, or shop classes synthesis might consist of translating ideas into a string of motor actions. In all these cases the important part is putting the ideas together

      It is tempting to say open synthesis is the same as creativity. I do not favor this term, because in my lifetime "creativity" has often seemed a euphemism for a lack of synthesis. We can idealize lack of accomplishment, or lack of focus, or even chaos by calling it "creativity". However if we avoid these things then open synthesis certainly can be called creativity.

      The last level of response consists of puzzles. In this situation things are even more unstructured. Often there is a "right way" to assemble and use the relevant information. So one might say that it is like level three, strict synthesis. However as I am using the term "puzzle" here the essential feature is that it can not reasonably be expected to yield to effort. Riddles are puzzles. For example, "How is a one legged dog like a two legged cat?" One might come up with an answer to that very quickly, or one might never come up with the right answer. In my tenth grade world history one prompt on a test was "Two to tango". The answer was supposed to be that two Roman consuls ruled, or something like that. I felt the item was unfair on a test, because one might know the material perfectly well yet not figure out the riddle. One may be smart, or lucky, and solve the puzzle quickly. Or one may be not so smart or lucky and never solve the puzzle. In general I do not think puzzles have any place in formal education. Questions or problems should yield to effort. I consider that implicit in the meaning of teaching. Puzzles may be entertaining at times, but they may also be frustrating and demoralizing. They should be enjoyed when possible, but not assigned, and certainly not be used on tests.

      There is a general correlation between levels of prompts and levels of responses. A low level prompt generally requires a low level response. A recognition or recall prompt generally applies to learning that is on a look-say level. However that is not always the case. There may be some ciphering of one sort or another involved before recognition or recall can take place. A higher level prompt may involve elements of recognition or recall.

      In order to illustrate these different levels of prompts I will use an example of a seventh grade history class. In this example the class is studying a chapter on the Civil War. As a written homework assignment, or as a test question, the students might be given this prompt:

      How did the Civil War affect America as a growing world power?

      This is an essay question, a very high level prompt. It would be on the open synthesis level. Students may take their knowledge of the chapter and construct an answer in any number of different ways that would have merit. And it is a very easy prompt for the teacher to construct. Contrast this with a somewhat lower level prompt. This again could be a homework assignment or test questions:

      1. Explain the advantages the North had over the South in the Civil War.

      2. Did slavery cause the Civil War? Explain why or why not.

      3. What battle do you think was the most important one in the Civil War. Explain why you think so.

      These prompts are still on the open synthesis level, but they are considerably more specific than the first example. Also the fact that there are three questions instead of one tells the students that shorter answers are expected. In question one the students know tha they should mention that the north had more population and industry than the south. They can add details, or offer opinions, but that basic information is definitely called for. In question two they must definitely mention that states' rights was the issue identified by the south. In Question three they must remember a few battles.

      The teacher could get more specific than these questions and still remain on the open synthesis level. But when the questions get very specific, or become multiple choice or fill-in-the-blank questions then the exercise is down on the recall and recognition levels. An example of prompts on this level might be:

      1. The first shots of the Civil War were fired at ________________ in the year ________.

      2. Who was President of The United States during the Civil War?

      3. The Southern states called themselves the _____________.

      4. The (North, South) had a military tradition that was an advantage to them.

      5. Jefferson Davis was (commanding general, president, ambassador to England) of the (Union, Confederacy).

      6. The Gettysburg Address was a (place, time, person, book, document, speech).

      7. Who was the commanding general of the North at the end of the War?

      8. Who was the commanding general of the South at the end of the War?

      9. Which side won the Civil War?

      10. What Union General split the Confederacy by driving through Georgia to the Sea?

      11. In what year did the Civil War begin? In what year did it end?

      12. The Emancipation Proclamation was a (place, time, person, book, document, speech).

      The specificity of the questions depends on the abilities of the students. In my 12 questions above I did not include the multiple choice question:

      Slavery existed in the (North, South).

For the class I envision in this example, that question would be too basic. But of course for some classes it would not. I did include the question:

      Which side won the Civil War?

This question would be too basic for many classes. Such questions would certainly be a waste of time for a class of intelligent students with a good background in history. They would not be a waste of time for some classes not so well endowed.

      To construct these short answer and multiple choice prompts is no easy matter. A number of prompts are required if all the material is to be covered, and any prompt carelessly constructed may be misleading to the students, or may be redundant, or inefficient, or in yet other ways problematic. Dedicated teachers may put in a great deal of time producing assignments consisting of these low level prompts. Hopefully the teacher would have them ready made in a workbook or at the end of the chapter. Such considerations should be kept in mind when choosing a textbook.

      An essay question is easy for the teacher to construct, but hard for the students to respond to. The short answer questions are hard for the teacher to construct, in terms of time required, but easy for the students to respond to, once they have actually learned the information. But which is better for learning?

      I believe for the vast majority of students the lower level prompts are much better for the bulk of everyday learning in most subjects. I am quite aware that I am going against educational ideology in taking this position. We like to think we are "teaching them to think." Indeed this is a worthy goal, in so far as it is possible. However it does not follow, I believe, that the way to do this is to use only high level prompts. In fact I think just the opposite is true. We "learn to think", among other ways perhaps, by being lead to give careful consideration to a multitude of small details. We also learn to think, of course, by also giving attention to the big picture. High level prompts can contribute to high level thinking. But low level prompts can also contribute to high level thinking. But most importantly, one does not rule out the other. We must do both. We must give attention to the big picture, and we must give attention to the fine details. There is a place for both high level prompts and for low level prompts. But it is the low level prompts that I think merit our close attention at this point. If our students are to give attention to fine details then we must draw their attention to fine details. This implies, again perhaps among other things, a great many low level prompts.

      I will present five lines of reasoning that argue for the importance of low level prompts.

      First, we must consider intelligence versus effort. An adequate response to the high level prompt, the essay question, requires high intelligence. The lower level prompts require less intelligence. But the lower level prompts will yield to effort. The high level prompt may not. I have previously mentioned this idea, but I think it needs emphasis. In fact I would consider it to be a basic principle of teaching, as well as a basic principle of prompts or testing. Whatever we ask students to do should be something that they can, with effort, do, not something impossible for them.

      The distinction between intelligence and achievement is very basic and important in teaching. Intelligence, in the sense I am using the term here, is fixed. I cannot will myself to be more intelligent. I cannot become more intelligent by study. I cannot prepare for an intelligence test. Intelligence will not yield to effort. If a teacher gives an intelligence test rather than an achievement test then the students have no motivation to put forth effort. One might as well give a blood test, and give good grades to type A people and poor grades to type O people. Achievement, on the other hand, is a result of effort. Achievement, to one degree or another, is possible for everyone. People can achieve knowledge and understanding. Achievement will yield to effort. Therefore in normal classroom teaching we should test for achievement, not intelligence.

      Unfortunately it is seldom possible to test only for achievement. Every test will inevitably have components of intelligence involved. To pass any test in arithmetic requires a certain degree of intelligence. We might teach a dog to respond to "2 + 2" by pushing one button and respond to "2 + 3" by pushing another button. But a dog is not capable of learning arithmetic. And we should not confuse a dog's conditioned response with actual understanding. Some subjects, such as higher math or physics, require intelligence of an order that is simply beyond most people. Even algebra requires an intelligence that is simply beyond many people. When we give an algebra test that includes a problem such as:

How many pounds of nuts containing 20% peanuts must be mixed with how many pounds of nuts with 35% peanuts to make 10 pounds of nuts with 28% peanuts?"

we are depending heavily on intelligence. Would it be possible to change this test so that it would not require intelligence? Could we teach an algorithm that students could apply without understanding that would allow them to solve problems such as this? Perhaps we could, but that seems to be self defeating. We want students to solve problems by applying principles of algebra, not by following a formula or recipe. Therefore I conclude that an intelligence component of any algebra test is just about inescapable.

      But if the intelligence component is allowed to become predominant then students certainly have a basis of complaint. If normally intelligent algebra students study a chapter, understand the concepts, and can do the exercises in the chapter, but then all flunk the chapter test because the teacher chose particularly hard problems, they will feel cheated. This could happen if the teacher is intent on teaching at a level of abstraction that is higher than the textbook's level of abstraction, and that is beyond of ability of the average student to attain. We can not engineer all intelligence out of an achievement test, but it is certainly a worthwhile principle to always keep the intelligence component of a test to a minimum. One way to do this is to use lower level prompts rather than higher.

      A second reason for using lower level prompts has to do with feedback and diagnosis. I discussed this at some length in Chapter Three. I would argue that the high level prompt is a poorer method for the teacher to evaluate the student's knowledge. A student's knowledge of the Civil War, for example, consists of a good many facts, concepts, and associations. The lower level prompts can isolate individual parts of this structure of knowledge. The higher level prompts cannot. Consider this analogy: A radio can be tested by simply turning it on to see if it works. If sound is produced, if it brings in a station, we can say that it works. This is a high level test. The radio can also be tested by a technician probing each individual component with electronic test equipment. This would be low level testing. The high level test has its place perhaps. If one has no intention of fixing the radio once it fails, then the high level test is all that is needed. You turn the knob, and either listen to the radio or throw it out and get a new one. But if the radio is worth fixing and fails to work, or if the radio works, but with noise or distortion, then the lower level testing is essential. You cannot fix it without detailed testing of individual components. In teaching, the essay test corresponds to the high level test of the radio. If the student has a good deal of knowledge, and if the student has the intelligence to understand how the parts of this structure of knowledge fit together, and if he or she has the verbal skills to assemble that knowledge into a good essay, then the student will do well on the test.

      The low level prompts correspond to the detailed testing of individual components. Just because the student cannot assemble a coherent body of knowledge into an essay does not mean he or she has no knowledge of the subject. The student is like the radio that is not working right, but is very much worth fixing. The low level prompts will reveal a considerable amount of knowledge, even if that knowledge is in bits and pieces more than as a coherent structure. Much of teaching is like this. We transmit bits and pieces of our subject to the students. We try to make those bits and pieces as coherent and structurally solid as we can, but there are limits to what can be done. Seventh graders' knowledge of history is very patchy compared to their knowledge of history at the end of twelve or sixteen years of schooling. Thus testing at the seventh grade level needs to employ much lower level prompts than testing at the higher levels.

      Low level prompts are desirable for motivation as well as for diagnosis, and this is the third reason for using them. Students need to be able to "nail down" the individual components of their structure of knowledge. When they write down the answer to the question "Who was the commanding general of the Confederacy at the end of the Civil War?" they are nailing down that element. Getting one question right is success. It is only partial success, of course, in relation to the task as a whole, but one bit of success can be a stepping stone to more bits of success. When that question is one of 20 questions on a homework worksheet then they can think to themselves, "One down, nineteen to go." This is motivating. In contrast, staring at a blank piece of paper and not knowing quite how to begin, or where to go to, is not motivating. In other words, students don't like essay tests.

      Efficiency is a fourth reason for sticking primarily to the lower levels of prompts. The higher levels of prompts require tremendous effort on the part of the students. Synthesis, as I mentioned, usually means choosing bits of knowledge and translating them into a string of words. Synthesis usually means writing, and writing is hard. If a teacher is interested in checking on a particular element in a structure of knowledge, like do they know when Andrew Jackson was elected president, then an essay question is not a quick way to get to that fact. Recognition and recall may be primitive, but they require comparatively little effort on the part of the students. So in this sense recognition and recall are efficient. Specific elements in the structure of knowledge can be tested with a minimum of time and effort.

      And finally, the lower levels of prompts are suitable in many situations because that is the way the knowledge is used. When learning to drive, for example, simple recognition and a bit of recall is all that is needed for a stop sign. We simply recognize it and respond to it. It could certainly be argued that even a stop sign requires some synthesis. When I see a stop sign I use my knowledge of stop signs, along with my knowledge of where I am, and where I am going, and so on, and synthesize a response. But this is a very small synthesis, quickly and easily done, and, very importantly, it does not need to be translated into a string of words and subjected to the scrutiny of a teacher.

      As another example, I have had to learn a great deal about the particular word processing program I am using on my computer right now. My knowledge consists of many bits and pieces. I could synthesize these bits and pieces into a reasonably coherent essay, explanation, report, or even a textbook, but normally I do not have to. I do not have to translate my structure of knowledge into a string or words. I could do so if I had a good reason, but it would take hours and hours of effort. The effort would, I suppose, give me a surer knowledge and greater fluency in what I am doing. I have long said that a good way to really understand a subject is to teach it. But the effort would not be worthwhile if all I am going to do is use the word processor. Recall is sufficient for my purposes. When I want to cut a paragraph and place it somewhere else I can do it. I can recall the method. When I want to save the text to disk I can do it. Synthesis, beyond a very low level, is not normally what I do with my knowledge of my computer, and synthesis is not normally what we do with most of our knowledge. We apply that knowledge. We use it. We even synthesize it into new and different forms. But we seldom explain it.

      When we do synthesize our bits and pieces of knowledge in everyday life, the synthesis is often easy and automatic, because it is on a very limited scale. I know the way to the grocery store, but I do not normally synthesize a string of words to represent that knowledge. If someone asks me directions to the grocery store then I will turn that knowledge into a string of words. I may say "Go east to the stop light, turn right, and it's about a mile south." That synthesis is not long. It seems pretty easy. Very few concepts and relations are involved. However when the directions are more complicated the synthesis can quickly become more difficult.

      Even in the classroom synthesizing is usually on a small scale. In a history class, for example, the class may be discussing the Civil War, and this discussion may range over a variety of topics. The teacher, to continue this example, may ask the students if slavery was the cause of the war. Johnny may venture the opinion that it wasn't really, because the book said that the South said they were fighting over states rights, not slavery. In expressing this opinion Johnny is using recall of what he has read, and he does combine what he recalled with other ideas. He synthesizes. But his synthesis, his expressed opinion, is not large. It is translated into a string of words, but it consists only of perhaps two or three sentences, and these sentences can be halting and disjointed. The situation does not call for a larger synthesis, or for polished language. Other students want to talk, and the teacher has an agenda she wants to cover. Recognition and recall provide us with the facts we need at the moment. Synthesis is seldom required to a large degree. This is true of most knowledge in everyday life. We get full use of most of our knowledge with little more than recognition and recall, so it would seem reasonable that we make extensive use of these low levels of prompts.

      There are many possible criticisms of using only a low level of prompting. It could certainly be argued that the learning could degenerate into a catechism. Yes, it could. Whether it does or not depends on the teacher. For some classes of low ability students it would degenerate into a catechism, because that is all they are capable of. It might be argued that if that is all they are capable of, then perhaps trying to learn history (or whatever the subject is) at all is a waste of time. That indeed might be the case. But in general it is not. For most of the less able, history (and other subjects) is still worth studying. A great deal of meaningful and worthwhile knowledge can be gained with the use of low level prompts.

      And it could be argued that students will never learn higher level thinking unless they are asked to do higher level thinking. Therefore, according to this argument, we should use high level prompts. As stated, I agree with this 100%. However I have worded those two sentences very carefully. This argument can easily slip to the idea that we should use high level prompts, and only high level prompts. With this I would very much disagree, based on the reasoning of the previous paragraphs. We can do both. We must do both. But I also think that low level prompts will always constitute the bulk of teaching for normal students in everyday learning.

      It could also be argued that high level prompts are better for motivation, that low level prompts do not provide a challenge to students and are therefore boring. I disagree with this in general. To say that children like high level prompts is about the same as saying children like to write. Some English teachers may convince themselves of this, and indeed some children do like to write, but I think they are in quite a minority. (And some people like to do math. I am one of them. But I do not delude myself that most people are like me in that regard.) For average Jane and Joe facing a blank page is one of the more unpleasant parts of life. Facing a workbook page of blanks to fill in is far less onerous.

      Of course low level prompts can be tedious if poorly chosen. The "just right challenge" is a very important concept in motivation. Low level prompts certainly can be boring or tedious if they offer no challenge at all. But that is a matter of the choice of prompts in an individual situation, not a matter of the prompts being low level.

      Now I will turn to a discussion of prompts by their purpose. .

      In Chapter Three I talked about eliciting feedback from the student, about diagnosing the emerging structure of knowledge and acting on that diagnosis. This is a very important use of prompts, to elicit a response upon which diagnosis may be made. Such prompts may be called "diagnostic prompts". In a moment I will subdivide this category.

      In chapter Four I talked about correction of learning problems, and in other chapters I talked about presentation of information. Some of this is done by simple communication. "Telling" is indeed an important part of teaching. But often one does not simply give a bit of information. Instead one gives a prompt that will elicit a response that will somehow produce the bit of information in the student's mind. I will call these "Socratic prompts", referring to the "Socratic method" of teaching by asking questions.

      In chapter Five I talked about "structure building" and "brain packing". The "brain packing" part of this requires lots of prompts. This is what drill consists of. Thus we may speak of "drill prompts", or "practice prompts".

      I will classify prompts as:

diagnostic prompts
existence prompts
category prompts
differential prompts
isolating prompts
prioritization prompts
hierarchization prompts

Socratic prompts

practice prompts

      I have subdivided diagnostic prompts into a number of categories. First one may use a prompt to simply determine if a particular element of a structure of knowledge exists in the student's mind. Fill-in-the-blank questions usually test for the existence of a certain bit of information in the student's mind. When we ask "Who shot Lincoln?" we are probing for a specific element in the structure of knowledge. This prompt may be called an "element existence" prompt. A more subtle variation of this same thing can be called a "slot existence prompt" . Instead of asking "Who shot Lincoln?", we might be wondering if the student knows that Lincoln was shot. Asking "Who shot Lincoln?" provides the information that he was indeed shot. It will take a different question to test whether the students know that. John Wilkes Booth is an answer to fit a slot. But perhaps that slot is missing. Perhaps the student's doesn't know that Lincoln was shot. To test this one might ask "How did Lincoln die?" Or one might use a much more indirect approach. One might start weaving an improbable tale and see if someone in the class picks up on the error. The teacher might begin, "Some historians say that what Lincoln did in the 60's was not nearly as important as what he did in the seventies. Do you think that makes sense?" At this point the teacher ought to see a lot of hands go up. If instead most of the students sit impassively then the teacher may conclude that there is a lot missing in their structures of knowledge. This is a rather high level prompt, in one sense, and I have just spent considerable time arguing for low level prompts. But this is a diagnostic prompt, and the diagnosis may be made very quickly by observing the body language of the students. The criticisms I previously made about high level prompts do not apply in this case. It does not remain a high level prompt for the student who knows the relevant information, and is accustomed to this type of method.

      "Category prompts" are an important type of prompt that is, I think, often overlooked, because we fail to recognize that students sometimes have faulty categorization. This question, for example,

The Emancipation Proclamation was a (time, place, person, document, policy).

is a category prompt. It does not ask the students to know anything other than the proper category of the Emancipation Proclamation. It is easy to forget that students may not know that. In many cases categorization may be assumed. In history we probably don't need to put on homework the item,

Columbus was a (person, place, time, thing, way of storing wheat).

The category is obvious. Columbus was a person. But in other cases categorization should not be assumed. It might be very helpful to put in this question on homework:

Manifest destiny was (a document, a law, a time, a place, an idea, a war).

Manifest destiny is not very concrete. I would predict that in the average seventh grade history class a substantial number of students would choose the wrong answer to this. It can be difficult for students to understand abstract ideas, but it helps if they at least have the right category in mind.

      I remember working with one of my children in about the fifth grade. We were finding countries on the globe. It occurred to me, I don't remember just why, that she may not even know the difference between land and water on the globe, for she was behind in many areas of schoolwork. To test this I could have simply pointed to blue and asked, "Is this land or water?" I decided to try to be a little less direct. I said, "Here's an astronaut flying around the earth in a space ship. He falls down to a landing right here. Does he go 'splash!' or does he go 'splat!!!?'" Using this approach for several minutes I determined that indeed this very basic knowledge was missing. This is a level of diagnosis that would never be needed with a normally competent fifth grader. But not all fifth graders are normally competent. For the less able students this type of diagnosis, using category prompts, is needed.

      A differential prompt is simply a prompt that differentiates in some way, that allows the teacher to test a hypothesis about what is going on in the student's mind. A differential prompt is the basic tool used in diagnosis, as I discussed in Chapter Three. For example in a ninth grade art class the teacher might ask, "name the warm colors". The students obviously know the colors. They learned them long before first grade. Now the teacher is asking them to differentiate between "warm" colors and "cool" colors. This is a very simple level of differential prompting. A more subtle and advanced level of differential prompting is given by this example: Joe completes the following three problems in multiplying decimals.
      Does it follow that Joe knows how to multiply decimals? What will he do with this problem?
      With the premise that Joe will be consistent can we say that he will correctly work this problem? Here are two possible ways in which he might work the problem.
      The first method, of course is incorrect. But there is a logic to it. In the three problems above Joe brought the decimal straight down. Therefore in the next problem he brings the decimal straight down. Of course this is not the logic that Joe should follow. He should follow the logic (or at least the rule) that the number of decimal places in the answer is the sum of the number of decimal places in the factors. It might be argued that the teacher had explained the method. Indeed this will work for many students, and they will work the problem correctly, as on the right. But it is equally true that many students will not understand the explanation and will make an error. The error displayed on the left is a very important error. Teaching is more than telling. Teaching requires the teacher to find out what is going on in the students' minds.

      A differential prompt is simply a prompt that will differentiate between correct thinking and incorrect thinking. The problem number four is therefore a differential prompt. Another problem of the same type as the first three problems would not be a differential prompt. It could, of course, be a practice prompt. "Differential" is a rather broad term when applied to prompts. Whether or not to call a particular prompt differential or not depends on the context, and often on subjective judgment. The terminology itself is not too important. The important thing is that the teacher have a knowledge of how the learner's thinking can be defective and have some skill in eliciting feedback.

      Very similar to the differential prompt is what I will call the "isolating prompt". Consider this example, which I have repeated many times in recent years: I am teaching guitar to a 12 year old. He is working on a difficult measure. It is hard for him to get his fingers in the right place at the right time to produce the desired result. I am wondering why he is playing the rhythm wrong. There are two possibilities, and it is important that I find out which it is so I can help him. Is it because he doesn't know how the rhythm goes, or is it that he knows the right rhythm but can't produce it because of the difficulty in getting all the motor actions together to produce the required result. If it is the latter case then I won't expect him to get the rhythm at the moment, but he will be able to get it right when he practices by himself over the next week. In this situation I don't really have to do anything more. But if he doesn't know how the rhythm should be then I want to help him with it. I don't want him to go home and practice the wrong rhythm for a week. So in order to diagnose which case it is I ask him to play the rhythm on an open string. This isolates the rhythm problem from the problem of finding the right places to put his fingers. The rhythm is still not right, indicating he probably doesn't understand the rhythm. I check this by isolating further. I tell him that I will play the rhythm, and he is to tell me whether I played it correctly or incorrectly. After a few tries I can play it one way or another, and he can tell me if it is the desired rhythm or not. This last step not only isolated the correct rhythm from possible other rhythms, but it also isolated the rhythm from his ability to produce the rhythm. Thus I have crafted a "motor-free" prompt, just as one might craft a "culture-free" IQ test. I used a low level prompt. Only recognition was required. I isolated the learning that I was concerned about.

      In Chapter Three I talked about faulty prioritization. There is also such a thing as faulty hierarchization. Thus we have "prioritization prompts" or "hierarchization prompts". In biology it is obvious to the teacher that mammals are a subdivision of the vertebrates. Indeed it may be so obvious that the teacher fails to realize that it may not be obvious to the students. Thus a prompt such as

          "(Some, All, Few, No) mammals are vertebrates."

may be useful. I think this is not at all as subtle or hidden as the example of manifest destiny given above. Generally in biology taxonomy is consciously and carefully taught. But it is subtle enough to be easily overlooked. Most importantly, understanding the hierarchical nature of taxonomy is crucial. If the hierarchizaton of taxonomy is not understood then the whole chapter on taxonomy is wasted on the student.

      The example I gave of a hierarchization prompt can also be considered a category prompt. A slot in a hierarchy, after all, is a category. But there are many categories that are not slots in a hierarchy.

      All of the prompts I have discussed may be direct or indirect. When the teacher holds up multiplication flash cards the prompt is very direct. Drill prompts generally are very direct. There are times, however, when prompts need to be indirect. In the example I gave about Lincoln's death the indirect prompt is needed in order to avoid providing the answer with the question. A slot-existence prompt, such as this, generally would be indirect. At other times the indirectness is beneficial for one reason or another. There is a danger in using indirect prompts. An indirect prompt can turn into a puzzle, something that may or may not respond to effort. Students may feel they teacher is playing games at their expense. Prompts should be direct unless there is a clear benefit of being indirect.

      In everyday teaching and learning it is very often hard to say that a given prompt is either a differential prompt, or a category prompt, or a practice prompt, and so on. It may be on the borderline between two types, or it may fit several types at the same time. Usually the distinction is only academic. I think these labels are useful, but only as descriptive vocabulary. The important thing is to be aware of the many possible ways in which thinking and knowledge can be faulty, to have ways of finding these faults, and to develop in the students' minds extensive and coherent structures of knowledge.