What Analogies to Use in an Electronic Tutoring System and When to Use Them Evelyn Lulis ([email protected]) CTI, DePaul University 243 S. Wabash Avenue, Chicago, IL 60604 USA

Martha Evens ([email protected]) Department of Computer Science, Illinois Institute of Technology 10 West 31st Street, Chicago, IL 60616 USA

Joel Michael ([email protected]) Department of Molecular Biophysics and Physiology, Rush Medical College 1750 W. Harrison St., Chicago, IL 60612 USA

Abstract We are building a new version of our intelligent tutoring system, CIRCSIM-Tutor, using Freedman's APE Planner. APE's powerful planning capabilities make it feasible to implement a number of new features. This paper focuses on adding the capability of generating analogies. Once the system can generate analogies it is possible that students will generate them too. Recognizing student analogies is likely to be even harder than generating them. We begin by describing some of the analogies used by human tutors and showing how they use these analogies in requesting inferences, how they point out the scope of these analogies with the goal of avoiding student misconceptions, and how they follow up on student errors. Then we explain how we chose a list of analogies for implementation using Gentner's structure mapping model and the APE formalism. Each analogy requires a set of plans, one for proposing the analogy, one for requesting inferences, one for limiting the scope of the analogy, and one or more for carrying out the structure mapping process in case the student does not understand. Finally we address the problem of recognizing student analogies, representing them using Forbus and Gentner's Structure Mapping Engine, and responding appropriately.

Introduction Our goal is to add analogies to the repertoire of teaching strategies used in the CIRCSIM-Tutor system. This paper describes how we decided which analogies to implement and how we determined when to employ them. CIRCSIM-Tutor is an intelligent tutoring system (Michael, Rovick, Glass, Zhou, & Evens, 2003; Evens & Michael, 2006) designed to help first year medical students learn to solve problems involving the baroreceptor reflex, the negative feedback system that works to keep the blood pressure constant in the human body. Medical students tend to find the baroreceptor

reflex particularly confusing, along with other negative feedback systems. CIRCSIM-Tutor begins by describing a perturbation to the cardiovascular system and then asks the student to predict how this change will affect seven key variables during three different periods of time as the response occurs. These periods are the Direct Response (DR) stage, before the baroreceptor reflex begins, the Reflex Response (RR) stage, and the Steady State (SS), which is achieved after a few minutes. After the student has made all seven predictions for a phase of the response, the system identifies the errors. It then launches a natural language dialogue designed to help the student think the problem through and correct the errors. The tutoring strategies and the language used in our system are based on eighty-one human tutoring sessions in which Joel Michael and Allen Rovick, Professors of Physiology at Rush Medical College, tutored their first year students solving baroreceptor problems. The tutoring dialogues carried on by CIRCSIM-Tutor have been shown to be effective in teaching students to solve problems using causal reasoning (Michael et al., 2003; Evens & Michael, 2006). They are more effective than reading a passage chosen from a standard textbook and carefully edited to cover the same material for the same amount of time. The system is in routine use in the first year physiology laboratory and it is available in the computer laboratory year round for students studying for boards or wishing to review this material for any reason. Transcripts of sixty-six student sessions with the system are available on the CD-Rom accompanying (Evens and Michael, 2006). The student inputs are obviously restricted in range by the students’ low expectations of the conversational capabilities of the system (Lee, Evens, & Glass, 2004). We hope that extending those conversational capabilities will provoke a wider range of inputs from the system. There are seventy-five sessions in which the tutoring was done in keyboard-to-keyboard style, with tutor and student sitting in different rooms interacting only through their computers. The keyboard sessions are numbered K1, K2,

etc. There are also a few face-to-face sessions numbered F1, F2, etc. The number “K44-tu-128-1” at the beginning of a line in the examples below indicates that this line comes from keyboard session K44, that the tutor is typing and that this is turn #128, sentence #1 in this session. Since the tutors and the students were typing as fast as possible for an hour at a time, there are many errors in spelling and some in grammar. We left the data unchanged so that the reader could get a feeling for the experience. Several other papers about Intelligent Tutoring Systems discuss the use of analogies. Woolf (1984) discusses analogy construction as one of a number of alternative strategies. Winkels and Breuker (1990) also include analogy in their hierarchy of strategies for an intelligent help system. Edelson’s (1996) CREANIMATE system proposes analogies as a way of pushing the users to make inferences. But all of these systems used template-driven generation and none of them discuss the problems of generating the appropriate language. Moore, Lemaire, and Rosenbloom (1996) have some valuable suggestions for generating language to remind students of past problems and how they overcame them, which we have found very useful. But the literature does not seem to address the problem of how to follow up on an analogy to make sure that the student really understands it and can use it in problem-solving and no one discusses appropriate ways to block possible student misconceptions. We believe that these are central issues in the use of analogies that deserve immediate attention.

Analogies in Human Tutoring Sessions In the eighty-one human tutoring sessions conducted by our experts, we observed fifty-one analogies proposed by the tutor and ten proposed by the student. Table 1 includes only the analogies proposed by the tutor, as those will be emulated. In nine of the cases, the tutor apparently used the analogy only to enhance the student’s level of understanding. Table 1: Use of observed analogies proposed by tutors Type inference requested total successful inference failed inference success after repair failure after repair no inference requested total successful mapping failed mapping enhancement only Total:

Number present in corpus 37 15 15 7 5 4 1 9 51

The tutor employed analogies in forty-two cases after the student failed to make correct predictions. In five of the forty-two cases no inference was requested by the tutor, but the students successfully mapped the base to the target, on

their own, making four correct inferences. In thirty-seven of these cases, the tutor requested an inference after proposing an analogy, with the student making correct inferences fifteen times and failing to make correct inferences twentytwo times. However, in fifteen of these twenty-two cases, the student was able to make correct inferences after the tutor explained the analogy (made repairs to the mapping of the base to the target). In total, out of the thirty-seven cases where an inference was requested after the use of analogy, students made correct inferences thirty times—fifteen after repairs to the analogy—a success rate of 81%. In only 19% of the cases did the tutor abandon the use of analogy and use a different teaching method. (See Lulis & Evens, 2003 and Lulis, Evens, & Michael, 2003, for further discussion.) Empirical observation convinced us that the use of analogy had positive effects on the students’ ability to understand the material, as Gentner (1983) and Kurtz, Miao, and Gentner (2001) have demonstrated in more formal experiments. In the corpus, the expert tutors followed up on the analogies in a number of complex ways, to make certain that the student understood the analogy and could apply it correctly. The tutors took steps to avoid the kind of misconceptions described by (Feltovitch, Spiro, & Coulson (1989). As recommended by Holyoak and Thagard (1995), the tutors: • • •

•

made certain that students understood the system mapping used a variety of analogies informed the students when an analogy was relevant and when it was not—pointed out the differences, as well as the similarities, between the the base knowledge and the target corrected misconceptions when they occurred

Determining What Analogies to Employ We began the task of determining what analogies to implement by compiling a list of bases occurring in the corpus, which appears in Table 2. We found a wide range of bases. For more discussion and examples see Lulis, Michael, and Evens (2004, a,b,c). The most commonly utilized base, another-neural-variable, appears twenty-nine times. The use of this base was successful in twenty-four cases. In only five attempts did the tutor abandon the use of this analogy and use another strategy. The other bases— balloons as examples of a compliant structure, Ohm's Law, airplane wings, black boxes, dimmer switches, traffic jams, etc.—were not used as frequently, but yielded gratifying mappings and correct inferences. We also collected some idioms that have an obvious analogical basis, like “pulling oneself up by one’s bootstraps.” Michael reviewed the examples of analogies and idioms identified (Lulis et al., 2003). He decided, that while idioms may add to the interest of the language, they do not make a significant difference in student understanding in

the way that the more explicit analogies do. As a result, idioms were eliminated from consideration.

Table 2: Bases present in the corpus Base Airplane wing Another algorithm Another neural variable Another procedure Balloon as a compliant structure Black box Bootstrap Brake & accelerator Compliant structure Dimmer switch Elastic reservoir Flight or fight Gravity Ohm’s Law Physician Pump Reflex Sugar or glucose Summation Traffic jam

No. present in corpus 1 2 29 4 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2

Due to their effectiveness, we decided immediately to implement the another-neural-variable and anotherprocedure analogies. The work of Kurtz et al. (2001) and Katz’s series of experiments at Pittsburgh (Katz, 2003; Katz & Albritton 2002; Katz, O'Donnell, & Kay 2000) have confirmed the importance of this kind of explicit discussion of meta-knowledge and of reflective tutoring in general. Michael, while reviewing the analogies in the corpus (Lulis et al., 2003), identified five common student misunderstandings that were successfully addressed by evoking analogies: • • • • •

student makes incorrect predictions of changes in neural variables student does not understand relationship between the change in cardiac output and resultant change in CVP student has problems with understanding the determinants of MAP student predicts that MAP will be completely restored in the steady state student makes an incorrect prediction of HR, or the dialogue with the student indicates that student does not understand the determinants of HR

Some of the explicit analogies that involve bases outside the domain—the balloon analogy and Ohm’s Law—

correspond to the general models that are described in Modell’s (2000) paper and discussed in more detail in Michael and Modell (2003). Taking these models into consideration, Michael identified the following bases for implementation because they demonstrated to be effective in correcting misunderstandings in the corpus: • • • • •

another neural variable and another procedure the reservoir model (Modell, 2000; Michael & Modell, 2003) compliant structure (with balloons as an example - Modell, 2000; Michael & Modell, 2003) the pressure/flow/resistance model—Ohm's Law (Modell, 2000; Michael & Modell, 2003) accelerator and brake

Developing Rules for Employing Analogies For implementation purposes, the chosen analogies were described in schemas in detail (Lulis, Michael, & Evens, 2004abc). Since expert tutors use different analogies in different ways, the corpus was examined for patterns of use. Based on these patterns, we developed rules to determine when to employ each analogy. In the CIRCSIM-Tutor system these rules are expressed in terms of the APE discourse planning engine developed by Freedman (2000a,b, 2001). The analogies that use bases outside the domain may require a more powerful approach to analogical inference to follow up on proposed analogies or to recognize analogies proposed by the student.

Another Neural Variable The another-neural-variable analogy was the analogy used most frequently by the expert tutors. It was used to help students understand how and when the baroreceptor reflex causes changes in the neural variables. Its use also helped students group variables into important categories as well as to make correct predictions. The process of using analogies in category formation is described in detail in (Loewenstein, Thompson, & Gentner, 1999). Following is a successful example from our corpus: K1-st-29-1: During the DR period it would remain unchanged. K1-tu-30-1: Correct. K1-tu-30-2: What other variables are neurally controlled? K1-st-31-1: CC, HR K1-tu-32-1: Again correct The rule governing the another-neural-variable analogy is evoked in any phase, whenever a student has predicted one neural variable correctly, but but failed to predict the change in one or two of the other neural variables, or whenever the system has just persuaded a student to correct one neural variable, but another one remains to be corrected. The rule asks the student to name the other neural variables and then to infer how those variables will change.

Another Procedure This analogy was used in a reflective tutoring mode in the SS phase when the student can look at the entire pattern of predictions, to help the student understand the relationships between blood volume, CVP, SV, and CO. In the following example the tutor and the student are solving the broken pacemaker procedure and the tutor refers back to what happened in the hemorrhage procedure in order to get the student to understand these relationships. K53-tu-63-4: If BV changes then CVP changes direclty with it, as in hemorrhage. K53-tu-63-5: OK? K53-st-64-1: yes, but if they both change, which has the greater effect, co or bv? K53-st-64-2: or does it depend on the extent of the change? K53-tu-65-1: No. K53-tu-65-2: It depends on the order. K53-tu-65-3: Let's try hemorrhage. K53-tu-65-4: You lose BV. K53-tu-65-5: CVP falls. K53-tu-65-6: SV falls. K53-tu-65-7: CO falls. K53-tu-65-8: That fall in CO would not undo the direct effect of the BV loss. K53-tu-65-9: CVP remains down. Our rule applies when the student has a problem with one or more of these relationships. The system looks through the procedures that the student has already solved for one in which MAP changes in the same direction. If it succeeds in identifying an appropriate procedure, it reminds the student about it and then recapitulates the pattern of changes in blood volume, CVP, SV, and CO.

Balloon/Compliant Structure This analogy is used when a student has problems understanding the relationship between CO and CVP. Compliance, the pressure volume relationship, is a source of misconceptions in practicing physicians as well as students, who tend to view the circulatory system in terms of rigid household plumbing (Feltovich et al., 1989). Most people are familiar with balloons and can visualize them easily, making them an appropriate base for an analogy. It is common knowledge that if you blow into the balloon it expands and that it will contract if the air is released. This model is effective in helping students understand that pressure and volume increase (and decrease) together. In the example below, the tutor proposes the balloon as a base to tutor the relationship between CO and RAP. K14-tu-41-1: For a compliant structure (like a balloon filled with air) the pressure inside is a function of the compliance of the structure (how "stretchy" it is) and the volume it contains. K14-tu-41-2: what parameter in the predictions table relates

to the volume that will be present in the central venous compartment? K14-st-42-1: Co and sv K14-tu-43-1: Well co certainly does (sv is a determinant of co). K14-tu-43-2:Do you know how rap will change if something produces a change in co? K14-st-44-1: If co increases then rap should also increase K14-tu-45-1: No. K14-tu-45-2: When a change in co is the independent variable (the thing changed) then rap changes as the dependent variable IN THE OPPOSITE DIRECTION (co and rap are inversely related under these conditions). K14-tu-45-3: Since you predicted that co i what will rap do? K14-st-46-1: D K14-tu-47-1: Right. Students often experience great trouble understanding compliance, or the way an elastic structure changes size and shape. Since just about everyone is familiar with balloons, this is a place where the balloon analogy can be a big help. We all know that if you blow harder into the balloon it gets bigger, but if you let the air out it will get smaller again. This model seems to be very effective in helping students understand that pressure and volume increase (and decrease) together. In the example below the student proposes to use a sink as an analogy and the tutor counters with a better analogy. Balloons are compliant like the right atrium, unlike a sink. F1-st-62-1: If I make an analogy of you try to fill a sink with water and you... F1-tu-63-1: Try to fill a balloon with water, since that's what we're dealing with, a distensible object. F1-st-64-1: OK. The balloon analogy also makes it easy for students to visualize the often confusing inverse relationship between Cardiac Output and Central Venous Pressure. If you increase Cardiac Output, you decrease Central Venous Pressure (just as the pressure goes down when you let air out of the balloon). If you decrease Cardiac Output (you don't let as much air out of the balloon) the Central Venous Pressure (the pressure inside) will be higher.

Reservoir Model Like the balloon/compliant structure model, the reservoir model enables students to deal with the relationship between CO and CVP, the most difficult relationship for students to understand. The model can be most easily understood in terms of a bathtub. The level of water in a tub is directly related to the flow of water in and out of the tub. For example, the water level is constant if the rate of water entering the tub is equal to the rate of water leaving the tub. The tutor evokes this analogy in the following example from session K12:

K12-st-44-1: I was thinking that if you increased map, co and if tpr did not change then blood is returned to the right atrium with agreater pressure. K12-st-44-2: I. E apercentage increase of increased map K12-tu-45-1: Well let's think about this again. K12-tu-45-2: When CO increases, the rate of blood removal from the central veins goes up immediately. K12-tu-45-3: Does venous return go up immediately? K12-st-46-1: Does the rate of blood removal from the central veins mean that blood entering the right atrium, if so ithink venous return does go up immed. K12-tu-47-1: We need to get our terminology straight. K12-tu-47-2: Venous return means blood returning from the systemic circulation to the heart. K12-tu-47-3: That does not go up immediately. K12-tu-47-4: It takes about a minute after CO I. K12-tu-47-5: Does more blood enter the ventricale for CO to I, Yes. K12-tu-47-6: But it's coming from the blood content of the ventricles (end systolic volume -- reserve), pulmonary blood volume, central venous volume. K12-tu-47-7: Immediately after CO I, the entire central blood chamber decreases in volume. K12-tu-47-8: That's because CO exceeds VR. The rule that we developed applies whenever the student has trouble understanding the relationship between CO and CVP. Since the example in K12 seems rather hard to emulate we decided to use the bathtub as an example reservoir. The bathtub analogy does not appear in the corpus, but the experts have successfully developed it for use in lectures. Bathtubs, while not compliant, are easier to visualize than a reservoir. We may need to add a step to block any student misconceptions.

Ohm's Law and the Pressure/Flow/Resistance Model

K44-tu-130-2: That being the case, in the ci rculation, what does v represent? As in this example, our rule starts by asking whether the student knows Ohm’s Law. If so, the system asks the student to carry out the steps in the analogical mapping process explicitly. This rule can be applied in any phase when the student makes an error in predicting MAP or shows confusion about the determinants of MAP in the tutorial dialogue.

Accelerator and Brake Model This accelerator and brake model was used in our corpus when the student made incorrect predictions for HR, or indicated a misunderstanding of the determinants of HR. This analogy is also meant to help the students understand that neural inputs are always present and always interacting to determine what HR is. It is important, but not obvious, that HR is the result of a balance between the sympathetic nervous system (the accelerator) and the parasympathetic nervous system (the brake). Normally, a person's heart rate without any neural input is 100/min. There is usually more input from the parasympathetic system causing a resting heart rate of 70/min. In this example the tutor asks for the determinants of HR: K44-tu-106-2: What I mean is, w hat physiological signals reach the heart that determine the value of hr? K44-st-107-1: Action potentials from the ans either para or sympathetic K44-tu-108-1: So, if parasymp. Signal increases to heart what happens to hr? K44-st-109-1: Decrease K44-tu-110-1: And if sympath. signal to heart decreases, what happens to hr? K44-st-111-1: Decrease K44-tu-112-1: Right, think of P and S as the brake and accelerator.

Ohm's Law and the pressure/flow/resistance model are used when a student experiences difficulty understanding the determinants of MAP. Students typically have difficulty applying the equation MAP = CO * TPR (Mean Arterial Pressure is the product of the Cardiac Output and the Total Peripheral Resistance). It is the cardiovascular version of the pressure/flow/resistance model, which states that the pressure is the flow times the resistance. This equation is familiar to most of us in the guise of Ohm's Law (V = IR), which says that the voltage (the electrical pressure) is the current (the flow of electrons) times the electrical resistance. In this example the tutor goes on to make sure that the student understands the mapping between the cardiovascular parameters and the ones that appear in Ohm's Law.

As we explained above, if our only goal is to implement a capability for the tutor to deploy a short list of analogies, we can do that by developing a set of plans for each analogy using Freedman’s APE planner, which we are using to implement the rest of the system. The implementation of each analogy needs at least three plans: a plan for proposing that analogy, a plan for requesting an inference from it, and one or more plans for limiting the analogy, coping with possible student failures to understand and student misconceptions. We now turn to the more difficult question of recognizing student analogies, which seems to require a more sophisticated approach.

K44-tu-128-1: Do you know ohm's law for electrical circuits? K44-st-129-1: V=ir K44-tu-130-1: Well, the circulation is exactly analogous.

We actually glimpsed a student analogy in the example from F1 shown above.

Student Analogies

F1-st-62-1: If I make an analogy of you try to fill a sink

with water and you... F1-tu-63-1: Try to fill a balloon with water, since that's what we're dealing with, a distensible object. F1-st-64-1: OK. How could we model the tutor’s decision to propose substituting a balloon for the sink? We turned to the Structure Mapping Engine, developed by Forbus, Gentner and Law (1995; Forbus, Gentner, Everett, & Wu, 1997), a computer implementation of Gentner’s (1983,1989) model of the analogical mapping process. As a first step we constructed a representation (shown in Table 3) for the analogy involving the heart (or at least the right atrium), the sink, and the balloon from this example. This illustration shows how we can use the Structure Mapping Engine to help the system to retrieve the bases (the sink and the balloon), match them with the description of the right atrium, and propose the balloon as a closer analogy than the sink. In all three of these descriptions, the formalism describes filling a container with a liquid, so the system can recognize the analogy that the student is trying to make between the sink and the heart. When the retrieval module is called to retrieve other descriptions of filling processes, itretrieves the “balloonFill” description as well. The next step is to call on the Structure Matching module to compare the facts from the two bases (sinkFill and balloonFill) with the target (heartFill). The descriptions of ballonFill and heartFill both involve compliant containers, using the facts “(compliant balloon)” and (compliant rightAtrium).” Both involve “distend” relations, while the sink has no facts to match these. The Structure Mapping module then rates the balloon as a much better match. The system can also use these facts as part of the analogy followup process, to emphasize to the student that the issue of compliance is the significant one in this analogy. Table 3. Representation of Balloons, Sinks, and the Right Atrium in the Structure Mapping Engine Formalism (defEntity balloon: type container) (defEntity sink: type container) (defEntity rightAtrium: type container) (defEntity water: type liquid) (defEntity blood: type liquid) (defDescription: balloonFill entities (balloon, water) facts ((compliant balloon) (liquid water) (fill container liquid : name addLiquid) (distend balloon : name >volume) (increase pressure :name >pressure) (and >volume >pressure) (cause addLiquid and1))) (defDescription: sinkFill entities (sink, water) facts ((liquid water) (fill container liquid:name addLiquid) (increase pressure :name >pressure) (cause addLiquid >pressure)) )

(defDescription: heartFill entities (rightAtrium, blood) facts (( compliant rightAtrium) (liquid blood) (fill container liquid :add liquid) (distend rightAtrium :name >volume) ( increase pressure :name >pressure) ( and >volume >pressure ) (cause addLiquid)) ) Our 81 session transcripts contain ten analogies proposed by students. Among the other nine is another student analogy that the tutor turns down: F7-st-268-1: Yeah, and the heart is the pump. F7-tu-269-1: Well, let's stick to this elastic chamber and look at it first more or less in isolation. We suspect that the tutor turned down the student’s proposed analogy for much the same reason as in the example from F1. The tutor believes that the student needs to understand compliance in an elastic chamber. The analysis that we just discussed would, in fact, take care of this case, too. When another student proposes a pump analogy and uses it to draw an appropriate inference about the relationship between CO and CVP, the tutor continues with the analogy, but rephrases the explanation in a more scientific manner. K51-st-53-1: Because the heart pump starts to look like a vacuum to the veins and sucks a lot of blood out of them as its output increases. Two of the analogies proposed by students involve traffic jams. The tutor responds to both in the same way by limiting the analogy, to ensure that the student who uses the term “back up” does not think that blood actually moves backward through the circulatory system. K24-st-41-1: Since hr d, co d, and rap is inversely related to co when co i.e. the variable which is being affected. K24-st-41-2: Qualitatively i know that if less blood is being pumped out per min then there must be a bit of it backed up. K24-tu-42-1: Good thinking (but be careful about this notion of "backed up"). In the second example, the student actually uses the word analogy. K64-st-54-1: Would it be a reasonable analogy to look at the heart like a traffic cop? K64-st-54-2: If it slows down the rate of blood flow (lets fewer cars through) then there will be a backup behind it (a backflow of blood prior to the heart, and therefore an increase in CVP) and fewer cars coming through (less blood coming out of the heart and therefore a decrease in

MAP) K64-tu-55-1: The analogy is OK. K64-tu-55-2: But just as a traffic jam does not occur because cars back up, the increase in CVP caused by a fall in CO is not the result of blood BACKING UP. It would seem as though we could emulate this behavior with an SME representation and by adding the phrase “back up” to our list of misconception triggers. Another student uses the word “analogous” to propose an analogy. This should alert the system to turn on the analogy machinery. Here the student is expressing the belief that right atrial pressure should behave in the same way as right ventricular volume and therefore that stroke volume should increase when RAP does. The human tutor ignores the analogy and explains the actual relationship. This is typical tutor behavior when the student seems to be really off the track. K20-st-69-1: SO CO. K20-st-69-2: IS THE INDEPENDENT VARIABLE. K20-st-69-3: BUT I AM STILL UNCOMFORTABLE BECAUSE I THOUGHT THAT RAP IS ANALOGOUS WITH THE AMOUNT THAT CAN BE POURED INTO THE RV SO I WANT SV TO GO UP WHEN RAP GOES UP. K20-st-69-4: DOES THIS MAKE SENSE. K20-st-69-5: OR IS IT SV GOES UP EVEN IN THE FACE OF D RAP, WHEN CC. K20-st-69-6: I Another analogy is proposed by a student who apparently associates the sympathetic nervous with the “fight or flight” response and tries to use this association to explain what is going on. The tutor provides a better explanation. Our misconception fighting routines might be able to handle this problem successfully, without recognizing the student analogy. F5-st-223-5: I just think of sympathetic is like flight or fight and hich would be needing more blood flow to like muscles but less blood flow though... F5-tu-224-1: OK. F5-tu-224-2: I understand how you're thinking about this.. F5-tu-224-3: Um.. F5-tu-224-4: In fact increased sympathetic activities to the blood vessels causes them to constrict. F5-st-225-1: OK Students also make use of two of the tutors’ favorite analogies, another neural variable and another problem. Here is a student making a successful inference about another neural variable: K12-st-54-1: Sympathetics, i now think this will stay the

same too during dr K12-tu-55-1: Super. Can we recognize the analogy here by analyzing “stay the same too,” properly? Maybe it is good enough to just recognize the correct answer and acknowledge it with enthusiasm. In the next example the student uses the results of a previous problem to infer the answer to this one. K33-st-229-1: I figured it was like the last problem and DR is greter than RR K33-tu-230-1: And you were correct. Here another student asks if the rule inferred by the previous student holds all the time or not: K35-st-151-4: When would ss be the same as rr and not dr? K35-st-151-5: Or is there never a time like that? In this situation the student is asking about an important generalization and it is clearly important to answer this question. The human tutor tells the student that it holds for the cardiovascular system, but not always for the respiratory system. We suspect that the best that the system could do here is what it does now when it does not understand the student – it changes the subject.

Conclusion Experiments in the literature and the evidence from our own corpus have convinced us of the importance of adding analogies to the repertoire of strategies employed in our intelligent tutoring system, CIRCSIM-Tutor. In this paper we have described how we chose the list of strategies to be implemented in the first round and how we developed the rules for when to propose each one, by analyzing the tutoring sessions in our corpus. The analogies that we have chosen include two that ask the student to generalize from previous experience with the system (another neural variable and another procedure), so they involve a kind of reflective tutoring. We have also a handful that involve familiar objects and ideas from the outside the world of cardiovascular physiology: balloons and bathtubs, Ohm’s Law, accelerators, and brakes. We hope that these familiar notions will serve as a gateway to understanding some important general models of physiology. Acknowledgments This work was partially supported by the Cognitive Science Program, Office of Naval Research under Grant 00014-00-10660 to Stanford University as well as Grants No. N0001494-1-0338 and N00014-02-1-0442 to Illinois Institute of Technology. The content does not reflect the position or policy of the government and no official endorsement should be inferred.

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