Using a Socratic Dialog To Help Students Construct Fundamental

In the Classroom

Using a Socratic Dialog To Help Students Construct Fundamental Concepts

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Ed DePierro and Fred Garafalo* School of Arts and Sciences, Massachusetts College of Pharmacy and Health Sciences, 179 Longwood Avenue, Boston, MA 02115; *[email protected] Richard T. Toomey Department of Chemistry and Physics, Northwest Missouri State University, 800 University Drive, Maryville, MO 64468

The concept of gravitational mass is usually introduced to chemistry students as a measure of the amount of matter in a given object. Although this definition can be useful as a starting point for quantitative investigations in chemistry, it does not refer explicitly to the direct experimental observations upon which the concept is actually based. This traditional approach also misses an opportunity to help students connect observations in the see–touch world with inferences about the atomic realm, and may contribute to the incomplete understanding exhibited by many high school and firstyear college students of mass and other fundamental concepts, like weight and density (1). This paper presents a Socratic dialog between a hypothetical instructor and student that uses experimental evidence and operational definitions to introduce fundamental concepts. The student’s responses are based on those of many individuals in a college freshman chemistry course, and point out the difficulties associated with learning the concepts. The sequence of 24 questions has evolved to its current form based on student feedback obtained from the course over several years. (Numbered questions provide interested readers with a logical sequence for experimental use of the dialog.) A theoretical basis for this type of instruction is discussed (2), as well as the benefits and challenges associated with its application to this particular material. Learning To Dialog Instructor: Good morning. Student: Good morning to you. Instructor: Today we are going to discuss some fundamental concepts upon which much of our treatment of topics in this course will be based. These include the concepts of mass, weight, and density. Student: Great, I already know about those things, so this class should be a breeze. Instructor: I’m glad to hear that. Why don’t you tell me a little about them, and then I won’t have to bore you by repeating what you already know. We can get right into the exciting and challenging stuff. Student: Mass is a measure of how much matter is in something. You determine an object’s mass by using a scale. The scale tells you its weight in grams or kilograms. The more a thing weighs, the more matter is in it. Instructor: Let’s slow down for a moment. What do we mean by the term matter? Student: That refers to what things are made of. You know—atoms! 1408

Instructor: So according to what you just told me, I can tell which of two objects has more atoms in it just by determining its mass. Student: Yeah, I think so. Wait a minute, maybe not. I was thinking about some really heavy things like mercury. I think something can be heavy and not have as many atoms in it as something that is not as heavy. Instructor: Are feathers heavy? Student: No. Instructor: What if I had a lot of feathers, say 10 tons of feathers. Would that be heavy? Student: Yeah, I guess so... Instructor: You used the terms mass and weight. Is there a difference between mass and weight? Student: I think weight is how heavy something is, mass refers to how much matter is in something. Instructor: Does a heavier object have more matter in it than a lighter one? Student: Sure. Instructor: So weight is also a measure of how much matter there is in an object? Student: I guess so. Instructor: You are aware that things do not weigh as much on the Moon as they do on Earth? Student: Of course, the Moon has less gravity than Earth, so things weigh less on the Moon. Instructor: So if something weighs less on the Moon, does it have less matter in it when it’s on the Moon? Student: I guess so. Wait a minute... I don’t like that. Hmmm... The mass would be the same on the Moon as it is on Earth. If it weighs one kilogram on Earth, it will also weigh one kilogram on the Moon! Instructor: But you just agreed with me that objects do not weigh the same on Earth as they do on the Moon. Student: Hmmm... Maybe we should hold off for a while on the exciting stuff, and I should listen to what you have to say about all of this “simple” stuff. Instructor: OK. Well, why don’t I ask you some questions? Student: You just did, and now I’m really confused. Maybe I should shut up and listen to your lecture. Instructor: I don’t like to lecture. I like to ask questions. What if I ask you questions, and if you can’t answer one, you let me know, and I’ll try to come up with a simpler question that might guide us toward an answer for that more difficult question? Student: OK. I’ll give it a try. Just don’t go too fast. Instructor: I’ll try not to.

Journal of Chemical Education • Vol. 80 No. 12 December 2003 • JChemEd.chem.wisc.edu

In the Classroom

The Dialog Begins: Questions 1–4 Instructor: Let’s start with this (Question 1). Consider a flat stick (perhaps a ruler) balanced on a triangular base, represented by Figure 1. What happens when I push down on one end of the stick with my finger? Student: The stick tips. It’s no longer in balance. Instructor: Consider the balanced stick once again (Question 2). What happens when I put a wooden block on one of the ends? Student: Well the side with the block now has force on it because the block has weight, so... Instructor: I have an idea. Instead of using technical terms like force, mass, weight, and so forth, let’s for now describe what we observe in the simplest way we can, and then we will introduce technical terms when it is appropriate. So in this case, why don’t we just say that when I put a block on one end of the stick, once again the stick tips and it’s no longer in balance? Student: OK. Instructor: (Question 3) When we place the block on the stick, what is it doing that causes the stick to tip? Student: It’s pushing downward, just as you did with your finger. Instructor: Good, nice and simple. Apparently the block is pushing downward. Now if you take the balanced stick into a spaceship and go into outer space, far away from Earth, Moon, and other heavenly bodies, placing the block on one end of the stick does not result in a sudden movement of the stick and block toward the floor. Based on this information (Question 4) why does the block push downward when the experiment is performed on Earth, or the Moon, but not in outer space, far from heavenly bodies? Student: Gravity. Earth has gravity and there is none in outer space. That’s why the block falls to Earth. Gravity pulls it down, and in the process, the block pushes on the stick! Instructor: Let’s stop for a moment. What do you mean when you say Earth has gravity? ... and when you say that gravity pulls the block down? Student: Gravity is a force, you know, something that pulls or pushes things. Friction is another type of force. You know, when you slide an object across the floor, friction causes it to come to a stop. Instructor: So Earth has this force called gravity? I’m a little confused. Does the floor have friction? Student: Ah....Hmmm. No, not exactly. Instructor: When you push an object across the floor, it may be more appropriate to say that the floor exerts a frictional force on the object. How about that? Student: I like that better. The floor doesn’t have any friction. Instructor: That’s right. Defining Terms: Force, Friction, and Gravity Instructor: You see the word “force” does not refer to a physical object like a chair or a box. The word is used to indicate a type of interaction, during which something causes some other thing to speed up or slow down. Student: So the word “friction” refers to the fact that

Figure 1. A flat stick balanced on a triangular base.

the floor interacts with the object to slow it down? The floor is the thing that slows the object down, not friction? Instructor: That’s right. Friction is the name we give to that type of interaction between objects. If you were to push an object across some very slippery ice, it would not come to rest as rapidly as when it is pushed across the floor. The frictional force exerted by the ice is less than that exerted by the floor. In outer space, where we could push the object without it being in contact with a surface like the floor or ice, it would move at constant velocity after it left your hand. It wouldn’t come to a stop until something interacted with it, to slow it down. Student: But doesn’t it run out of force eventually? Instructor: Remember, objects do not possess force. Is there anything to create a change in the motion of the object after it leaves your hand, far from any other objects, when you push it in outer space? Student: I guess not. Hmmm.... No interaction, no force, so it keeps going. Instructor: It’s important to keep in mind that the general term we give to interactions during which something creates a change in the motion of something else is “force”. Student: How does the floor interact with the object to slow it down? Instructor: We will talk more about this at a later time when we consider how the atoms in two objects interact with one another. For now we can say that the atoms on the surfaces of the two objects stick to each other, and this leads to the moving block coming to rest. We have gotten a little off track. Let’s get back to placing blocks on the balanced stick. Gravity is another type of force. Student: So Earth does not really have any gravity, in the same way that the floor does not have any friction? Instructor: Correct. We can say that Earth exerts a gravitational force on an object, but Earth does not possess gravity. In general, things do not possess forces. When one thing, X, creates a change in the motion of some other thing, Y, we say that X exerts a force on Y. Student: So I should interpret the phrase, “exerts a force”, as “creates a change in motion”? Instructor: Yes, or perhaps as “has the potential to create a change in motion”. Student: Yes, I remember something about opposing forces, where you see no change, but the forces are still there. But isn’t gravity the reason an object falls toward Earth? Instructor: Not really. The object falls toward Earth because Earth pulls on it. Student: But why does Earth pull on it? Instructor: Nobody knows. Not even Newton or Einstein knew. The word gravity is used to describe the fact that objects attract one another, not to explain why they attract one another. Student: I see. You know this isn’t so boring after all. And some things that I thought I understood are now becoming more clear. How about another question?

JChemEd.chem.wisc.edu • Vol. 80 No. 12 December 2003 • Journal of Chemical Education

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Dialog on Questions 5–8 Instructor: OK. So to review, Earth attracts the block, pulling it downward. This results in the block pushing on the stick. Now consider what happens if the stick is balanced on the triangular base, and two identical blocks are added, one on either end, exactly the same distance from the center of the stick. This is shown in Figure 2. We find that the stick does not tip one way or the other. It is balanced. Since the blocks do not move, we might conclude that there is no longer any pull by Earth. (Question 5) What could you do to test whether the blocks are still attracted by Earth? Student: Remove one block; the other then pushes the stick downward. Instructor: Very good. Instructor: (Question 6) What can we conclude about the attraction by Earth for each of the blocks when they are balanced on either end of the stick? Student: The blocks must be exerting the same push on either side, since the stick remains balanced. So Earth must be attracting the blocks equally, otherwise the stick would tip one way or the other. Instructor: Good. (Question 7) What will happen when one of the blocks is replaced with another made of the same material, but occupying twice the volume? Suppose we have a one-liter copper block and a two-liter copper block, as shown in Figure 3. Student: The stick will tip downward on the side with the larger block. Instructor: (Question 8) What can we conclude about Earth’s ability to attract the larger block compared to the smaller block? Student: Earth apparently pulls harder on the larger block. Instructor: Yes. Defining Terms: Gravitational Attraction Instructor: I also want to mention that objects like these blocks are attracted by other objects besides Earth. In fact all objects attract all other objects. This type of attraction is called gravitational attraction. Student: If that’s the case, why don’t we see all of the objects in this room stuck to each other? Instructor: We do not normally see evidence of objects gravitationally attracting each other because their gravitational attraction to Earth is so much greater than it is to each other. All we usually see is the effect produced by Earth. However, experiments can be conducted to show these smaller gravitational attractions that objects exert on one another. For example, when a large lead block is moved close to a lead block that is hanging from a rope, the hanging block moves, ever so slightly, in the direction of the large block. The larger the block, the more the hanging block is attracted. Student: I never really considered that. Interesting... all objects attract all other objects. So the more we have of a given substance, the more it is attracted by Earth, or other objects? Instructor: Yes. And the more it attracts Earth and other objects. That summarizes what we have been discussing. The simple stick we have been considering can be used 1410

Figure 2. Two identical blocks balanced on a stick.

Figure 3. A one-liter copper block and a two-liter copper block placed on either end of the stick.

4 blocks small rock

large rock block

Figure 4. Rocks and blocks placed on two balances.

to measure the extent to which different objects are attracted by Earth. When the stick is used in this way, the apparatus is called a balance (not a scale!). Suppose we put some object, perhaps a rock, on one end of the stick and then add identical blocks to the other end until the stick is balanced. This is shown for two different cases in Figure 4. Dialog on Questions 9–11 Instructor: (Question 9) What is Earth’s ability to attract the small rock compared to its ability to attract the block? Student: They are equal, since the stick is balanced. Instructor: Correct. (Question 10) What is Earth’s ability to attract the large rock compared to one block? Student: Since it takes four identical blocks to balance the stick when the large rock is on the other end, I would conclude that the large rock is attracted four times more than one block is. Instructor: Good. And since objects attract each other, we can also say that the large rock’s ability to attract Earth is four times as great as a block’s ability to attract Earth. Student: Yes. Instructor: (Question 11) What is Earth’s ability to attract the large rock compared to its ability to attract the small rock? Student: I would conclude that it is four times as great. Instructor: Good. Now let’s do a little reviewing. Remember that when we measure, we compare, we count, and we report some number. Remember also that the number is


In the Classroom

based on some standard unit. For distance measurements, this is the meter. When we make a distance measurement, we count off spaces all of equal size—which we define as meters—and report the separation between two points in terms of this number of meters. Student: Yes, we discussed that a couple of days ago. Measurement always involves comparison, counting, and reporting a number. Instructor: Recall that the standard for distance measurements (the meter) is the space between marks on a rod in a glass case in France.1 In a similar fashion, there is a block (like the blocks we used in the questions we just discussed) kept in a glass case in France that is used as the standard for measuring how strongly objects are attracted to other objects, like Earth. We compare Earth’s ability to attract some object X with its ability to attract the standard block. We do this by counting the number of these standard blocks (all of equal size, and made of the same material) that must be placed on one side of the stick in order to balance the attraction that X undergoes (just as we did before, with the rocks). Student: I see. So the greater the attraction by Earth for X, the more of these standard blocks we would have to use to achieve balance, and the greater the number that we would report. Instructor: You’ve got the idea. When we determine the separation between different locations, we report a number that we call the distance, which indicates how far apart the locations are compared to the standard unit of distance, one meter. When we compare Earth’s ability to attract some object X with its ability to attract the standard block, we call this a gravitational mass measurement. The gravitational mass of the standard block in France is defined as being one kilogram. Dialog on Question 12 Instructor: (Question 12) If an object, X, has a gravitational mass of 2 kilograms, what do you think that means? Student: That would indicate that this object is attracted to other objects twice as strongly as our standard object, which is defined to have a gravitational mass of one kilogram. Instructor: Good. So you see that gravitational mass is a direct measure of an object’s ability to attract or to be attracted by other objects. Student: So when we take the object to the Moon or some planet other than Earth, it experiences a different attraction? Instructor: That is correct. Student: And then the object has a different gravitational mass? Instructor: That is not correct. Student: But the Moon does not attract the object as strongly as Earth does. Instructor: That is correct. Student: That seems contradictory. Defining Terms: Weight vs Mass Instructor: To help us, consider the following observations, summarized in Figure 5. The large rock we had talked about previously and a standard one-kilogram block are hung from identical springs on Earth and then on the Moon. As you can see, the rock

hanging from identical springs on the Moon

hanging from identical springs on Earth

block block

rock

rock

balanced on the Moon

balanced on Earth 4 blocks

4 blocks rock

rock

Figure 5. Comparison of the gravitational attraction and mass of two different objects on Earth and the Moon.

stretches the spring more than the standard block does, whether we perform the experiment on Earth or on the Moon, but the amount the spring is stretched is greater on Earth than on the Moon. However, if we set up a balance on Earth and on the Moon, we find that in both cases, four of the standard blocks just balance the rock. Earlier you said that weight indicates how heavy an object is. Weight is actually a measure of the force (pull) exerted on the object by Earth or some other huge heavenly body, like another planet or the Moon. The greater the force exerted, the heavier the object. For now, we can get a qualitative idea about the size of the pull exerted by a planet on an object by hanging the object on a spring, and observing the extent to which the spring is stretched downward. The more the spring is stretched, the greater the pull that the planet exerts on the object and the greater the object’s weight. Dialog on Questions 13–16 Instructor: (Question 13) In the experiments described above, on Earth, which weighs more, the rock or the standard block? Student: Since the rock stretches the spring more than the block does, the rock weighs more. It looks like this is the case on the Moon, as well. The rock weighs more than the block on the Moon. Instructor: Correct. (Question 14) Where does the rock weigh more, on Earth, or on the Moon? Student: Since it stretches the spring more on Earth than on the Moon, it weighs more on Earth than on the Moon. And again, it looks like this is the case for the standard block as well. It weighs more on Earth than it does on the Moon. Instructor: Very good. (Question 15) On Earth, which object has the greater gravitational mass, the rock or the block? Student: The rock does, since it takes four blocks to balance the rock. The rock has a mass of four kilograms compared to the block, with its defined mass of one kilogram.


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Instructor: Correct again. (Question 16) And where does the rock have a greater gravitational mass, on Earth or on the Moon? Student: Well... according to the picture, four standard blocks are required to balance the rock on Earth and on the Moon. So I guess the mass is the same, whether it is on Earth or the Moon? Now I see! The attraction of the rock and of the block are both less on the Moon, but the rock is still attracted four times more than the block is. Instructor: Correct. It is important to realize that the gravitational mass is a property exhibited by the object. It does not matter if we observe the object being attracted to Earth, the Moon, or a block of lead hanging from a rope. The fact that the rock has a gravitational mass of four kilograms means that it is attracted to any other object four times as strongly as the standard object with a mass of one kilogram. Student: So gravitational attraction and gravitational mass are not the same thing. Instructor: Correct again. The objects experience a greater gravitational attraction to Earth than to the Moon, but their masses are always the same. The key idea that we are focusing on when we consider gravitational mass then is relative strength of attraction. Defining Terms: F = ma Student: But now I’m confused again. I’m used to saying an object weighs so many kilograms. If the rock is four kilograms on Earth and four kilograms on the Moon, this sounds like its weight is not changing, and since weight is the force exerted on it, this sounds like the force exerted on it is not changing Instructor: Do you recall the unit used when reporting force? Student: I think it’s newtons, named after Isaac Newton. Instuctor: Good. There is a relationship between mass and force, do you recall it? Student: F = ma? Instructor: And what is a? Student: Acceleration. I recall that for objects that are attracted to Earth, a = 9.8. Instructor: That number is the acceleration, the change in velocity, that any object undergoes as it falls. For each onesecond interval that passes, the velocity of a dropped object increases by 9.8 meters per second. We write this as 9.8 m/s/s or 9.8 m/s2. For objects that are attracted to planets, scientists usually write F = mg. Student: Oh, now I remember. g means the acceleration due to Earth’s gravity...I mean Earth’s gravitational attraction. And m is the mass. Instructor: On the Moon, g is only about one-sixth of 9.8 m/s2. Student: So the force exerted by the Moon is less, and objects do weigh less there! Instructor: Yes. To find the weight of an object—in other words, the gravitational force it experiences—we multiply its mass by g. Student: So I really shouldn’t refer to an object as weighing 4 kilograms, but as weighing—let’s see—4 ⫻ 9.8 = 39. 2 newtons on Earth?...and one-sixth this number for its weight on the Moon? 1412

Instructor: Very good. Note that since objects do not possess force, it is technically incorrect to talk about an object as having a weight. It would be better to refer to the weight experienced by, or undergone by some object, rather than the weight possessed by the object. Student: That’s amusing, I can say that I have no weight! Instructor: I also want to mention that we could turn the spring we were stretching into a measuring device by noting how much it is stretched for a given number of newtons exerted on it. On Earth, the stretch produced by a one-kilogram object corresponds to 9.8 newtons. The stretch produced by a two-kilogram object corresponds to 19.6 newtons, and so on. Do you know what we call such an instrument? Student: I think it’s a scale? Now I see the difference between the two devices, scales and balances. The scale gives a different reading on Earth and on the Moon for a given object, but the balance doesn’t. But what about gravitational mass as a measure of the amount of matter in an object? Where does that come in? Instructor: Do you know what the word inference means? Student: Yes, I think so. It means a conclusion you make, based on observation. But I think the conclusion may be an interpretation; it does not necessarily have to be correct. Instructor: That is correct. Dialog on Questions 17–20 Instructor: Let’s go through one last sequence of questions. Consider that even thousands of years ago, people were speculating that matter is made of tiny particles. Let’s go back to our one-liter and two-liter blocks of copper for a moment. (Question 17) If matter is composed of tiny particles, which would have more, the one-liter block, or the two-liter block? Student: The two-liter block. Instructor: And why do you say that? Student: Because it has a greater mass. Mass is a measure of the amount of matter in something. Instructor: You remember that statement from high school. Forget it for the moment, and just look at the blocks. Without using technical terms, (Question 18) why might we conclude that the two-liter block has more particles in it? Student: Well it’s twice as large. So presumably it has twice as many tiny particles? Instructor: Yes. Now remember that we have just discussed the idea that gravitational mass is a measure of how strongly an object is attracted to other objects, compared to our standard object. (Question 19) What do we observe about the two-liter block compared to the one-liter block in terms of the gravitational attraction that Earth exhibits for each? Student: The attraction is greater for the two-liter block. Instructor: Suppose we observe that the two-liter block has a mass of 10 kilograms and the one-liter block has a mass of 5 kilograms. (Question 20) What can you infer about the relationship between the gravitational mass of an object and the number of tiny particles (the amount of matter, if you will) in it? Student: The greater the mass, the greater the amount of matter? But I can tell which has more matter just by looking at the objects. You just pointed out that there is more in the bigger one. I don’t need to make a mass measurement to determine that!


In the Classroom

Dialog on Questions 21–24 Instructor: Hold on a moment. Now consider two blocks of metal, X and Y, with the same volume, but that result in the balance tipping when they are placed on either end. Let’s say that the balance tips downward on the side where X rests. (Question 21) Which is more massive? Student: Object X. Instructor: (Question 22) How do you refer to an object that has the same volume as another, but has a greater mass? Student: It’s denser? Instructor: Yes. Very good. (Question 23) Now based on your inference, which would have more particles in it, X or Y? Student: Well, for objects made of the same material, the larger object, with more particles, is attracted more strongly to Earth. If X and Y have the same volume, but X is attracted more strongly to Earth, it suggests that there is more matter, more tiny particles, in the block of X than in the block of Y. Instructor: That is a reasonable inference. (Question 24) Now, what does this suggest about the proximity of these particles to one another in X and in Y? Student: They would be closer together in the block of X than in the block of Y? Instructor: Very good. They would be closer together in the denser block. The word density is often used when discussing the amount of something there is in a given space. For example, we say that the population density of New York is greater than that of Boston. Do you see that you made your conclusion about the number of particles in a given volume of the different materials, X and Y, based on information about the attraction of Earth for objects made of the same material, but of different size. We did not determine that there are more particles in X directly. Student: We made an inference. It seems reasonable, but it is based on what I can see, and on an assumption about what things are made of. Instructor: Very good. You are starting to think like a scientist. Dialog on Atoms Student: If block X does have more particles, does this mean that it has more atoms in it than block Y? Instructor: That is an interesting question, and we shall encounter it on several occasions during the year. For now, let’s consider a related, but less-challenging question. Tell me something about atoms. What about their composition? Student: They are made of smaller particles, called proton, neutrons, and electrons. And the protons and neutrons are made of.... Instructor: Let’s just consider the protons, neutrons, and electrons. Now we cannot see any of these particles directly. You know about these things because you have read books, and listened to teachers, who have read books. Do you know something about the masses of these particles? Student: The protons and neutrons are much more massive than the electrons. Instructor: Yes. The protons and neutrons are about

equal in mass, but an electron is only about 1/2000th the mass of a proton or a neutron. To keep things simple for now, let’s assume that the protons and neutrons are equal in mass, and that they are responsible for all the mass in an object. What do you think would be the case in terms of numbers of these particles for two objects of equal volume, but made of different material, if one is denser than the other? Student: The denser one will have more protons and neutrons. Instructor: Yes. That is a reasonable inference to draw, at this time, based on what you know about subatomic particles.2 Closing the Dialog: The Limits of Understanding and the Joys of Active Learning Student: I never realized how important it is to understand the meaning of all of these terms—mass, density, weight, force, even atom versus particle. I think I understand them now. Instructor: Be careful. When one understands a concept, it suggests that that individual is comfortable with various situations in which that concept is used. These include verbal, pictorial, mathematical, and graphical expressions. We have just been talking about a few terms, and considering the results of a few experiments. We have not confronted problems where we must do a lot of calculating, or interpreting of graphs. Nevertheless, being able to recognize what these terms refer to, and being able to use these terms properly is an important first step. Hopefully this will make it easier for you when you revisit these concepts in this and other courses. Student: Also, it seems that I learn better when we are engaged in a conversation about the concepts, rather than when I just sit and listen. Instructor: That has been shown to be true. It is a process called active learning. Our time is up. Hopefully we will engage in more active learning when we meet again. Student: That sounds good. I’m looking forward to next time. Discussion

Theoretical Background Curriculum development in freshman chemistry at the Massachusetts College of Pharmacy and Health Sciences (MCPHS) has been guided by constructivist learning theory for the past twelve years (1, 3). The curriculum is traditional in the sense that it comprises a survey of topics, although concept development is based on prior introduction of experimental evidence or operational definitions. This work is based on an action research methodology (4, 5), which consists of planning and implementing specific classroom activities, observing and evaluating the results, and then using the conclusions to revise the activities and perform another cycle of the process. A key issue in developing this type of curriculum is the trade-off between greater time spent on developing concepts, and the resulting need to eliminate topics. A more detailed description of the freshman chemistry sequence at MCPHS and its evaluation are described elsewhere (3, 6). The approach used in the student–instructor dialog is described as inquiry teaching (2). The term guided inquiry is


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appropriate because lines of questioning provide direction and focus. Such dialogs can be used to help students establish basic vocabulary, discover and dispel misconceptions, explore multiple representations of concepts, and develop formal reasoning skills. The latter include distinguishing observation from inference, creating and testing hypotheses, and predicting consequences using facts and a hypothesis (hypothetico– deductive reasoning). The instructor can control the process in a number of ways. These include: 1. Helping students to trace the consequences of an answer to a contradiction 2. Suggesting incorrect hypotheses in order to get students to reveal underlying misconceptions 3. Generating hypothetical cases to get students to reason about situations that are difficult to reproduce naturally 4. Helping students to realize that they hold a certain view based on authority (prior factual information from a book or teacher)

Within such a dialog, the instructor can also draw upon techniques that are used in more conventional types of instruction, such as providing positive and negative exemplars, or varying cases systematically (2).

Using Dialog with First-Year Chemistry Students The dialog presented in this paper is based on a series of questions, which has been presented to students each year since academic year 1998–99 in the freshman chemistry sequence at MCPHS. The nature and sequence of the questions has evolved to its current state, based on student written responses generated in class or as homework assignments, and oral responses made during class or in help sessions. Although the dialog has the instructor interacting with just one student, this individual’s responses are really a composite, based on responses collected from many individuals throughout the years. Numbered questions provide interested readers with a logical sequence, should they choose to experiment with using part or all of the dialog. Vocabulary Difficulties Hamper Understanding The initial conversation between the student and the instructor demonstrates the lack of command of scientific vocabulary typically demonstrated by first-year students, and how easily they can be entrapped by the instructor. It is challenging for an instructor to direct the flow of this presentation in a constructivist fashion, because students are eager to invoke partially understood technical vocabulary, as the response to question 2 above suggests. The actual presentation currently includes an explicit request for students to avoid technical vocabulary at the start. Question 4 often elicits the technical term gravity and the subsequent discussion presented above demonstrates some of the important misconceptions associated with the concept of force. Touger discusses the impact on student understanding of poor locutions by instructors; this paper should prove useful to any science educator (7). Rephrasing question 4 delays these issues in the actual presentation. By asking what Earth is doing that results in the stick tipping when the block is placed on it, the student is cued to respond that Earth, and not gravity, pulls on the block. Gravitational attraction is introduced as a descriptive phrase, not as an explanation. A somewhat more 1414

extensive discussion of the subtleties associated with the concept of force are presented by choice in the next block of material in this curriculum. However, this is not essential for helping students to construct the concepts of gravitational mass and weight, using a question sequence like that given above. An article by Krim provides useful information on the concept of friction at the atomic level, should an instructor decide to pursue this (8). The concept of gravitational mass emerges from the concrete measurement activities of comparing, counting, and reporting a number (questions 5–12). While the response rate for questions 5–9 has been well over 90%, these simple and seemingly obvious questions are needed to provide guidance so that students can draw correct inferences like those expected in questions 11, 16, and 24. This is consistent with the ideas expressed by Arons (1). Comparing the process for gravitational mass measurement with that of distance measurement serves to generalize the measurement process. Introducing Gravitational Mass and Attraction While the dialog above has the instructor distinguishing between weight and mass in a quantitative way, this is again delayed in the actual presentation until the next block of material in the curriculum. Instead, the presentation just stresses the difference between the idea of gravitational mass as a measure of relative attraction, and weight as an indication of extent of attraction. This approach is simpler for students who have not had physics, but the distinction between gravitational mass and weight can be challenging even for those who have had a physics course. Arons notes the difficulties associated with the concept of equal and opposite forces being exerted on one another by two interacting objects (1). No pretense is made about our brief mention of an object and Earth undergoing mutual attraction as being sufficient to completely clarify this concept. The challenges that students face in constructing the ideas of gravitational mass and weight within the time constraints of this chemistry curriculum suggest that such efforts should be delayed until discussion of Newton’s Third Law in a physics course. Further discussion of approaches to these concepts in physics instruction can be found in papers by Brown and Clement (9), and by Minstrell (10). The extreme difficulty that students can exhibit when confronting the concepts of velocity and acceleration should also be noted (1). Many students can invoke the fact that mass is related to the amount of matter in an object, and do this when comparing the two-liter and one-liter blocks of copper. However, questions 18–20 are important to get students to draw the inference that greater mass suggests greater number of particles. This points to the fact that students at this level are not blank slates, and that their prior knowledge can complicate an instructor’s efforts to help them construct concepts and draw inferences. It can also disguise their lack of knowledge. For example, in an earlier question sequence, which was not as extensive as the sequence given in questions 13– 16 above, 80% of the class answered “no”, when asked if the mass of an object changed when it was brought to the Moon. However, such a question does not probe for understanding of the idea of constant relative attraction. On closer inspection, the responses suggested that most students were merely parroting the statement that constant mass means constant


In the Classroom

amount of matter, without really having internalized the idea of constant relative attraction. At this point in the curriculum (week two of the first semester), it is sufficient for students to come to the conclusion that greater density suggests a greater number of particles. Essentially all of the students know about protons and neutrons, but the concept of atomic structure is delayed until the second semester in this development (3). The student in the above dialog seems to know that density is a ratio, but many students have difficulty with the concept when asked questions that go beyond plugging numbers into the equation: density equals the mass of an object divided by the volume of object. Some questions that probe for deeper understanding of the concept 3 are included in the Supplemental MaterialW in this issue of JCE Online. The last part of the dialog serves as an introduction to some applications of the density concept that appear later in the curriculum. For example, once Avogadro’s law has been introduced, but before the introduction of atomic structure, greater density of one gas compared to that of another can be used to suggest the existence of more massive individual units (atoms or molecules) in the denser gas. This leads to the Dumas method of molar mass determination (3). In the second semester, students use density data to support claims about the nature of atomic structure and bonding. For example, students are sometimes surprised to find that magnesium is denser than calcium, although the atomic mass of calcium atoms is greater than that of magnesium atoms. The density and molar mass of the two elements can be used to show that calcium has the greater molar volume, which is consistent with the greater number of electronic shells proposed for calcium atoms. Since the electrons occupying the shells have negligible mass, the lower density of calcium becomes less of a puzzle. Similarly, copper is denser than zinc, but zinc atoms are more massive than copper atoms. The density and molar mass of the these two elements can also be compared. In this case, the smaller molar volume of copper suggests that atoms are bonded more tightly in copper than they are in zinc. This is consistent with other experimental evidence, such as enthalpies of vaporization of these two elements. Practicing Dialog The numbered questions treated in the above dialog are currently introduced in one classroom period (in a class of typically more than 100 students), reviewed in a second period, and reinforced in part of a laboratory session introducing the concept of measurement. A sequence of questions very similar to questions 1–16 above is presented in class with two blocks of time set aside for students to discuss questions 9–11, and then 13–16. During these times, the instructor and two classroom facilitators circulate through the room listening to the discussion, and engaging the students in conversation (6). These sessions are followed by immediate feedback given by the instructor to the entire class. Questions 17–24 are currently given in the laboratory, where students have access to manipulatives to help them with the concept of density (11). This approach represents an improvement over that used in past years. Although many students participated when the entire sequence was presented in class, not enough time was available for extensive student discussions, and oral and written feedback from help sessions and

assignments indicated that many students were not getting the key ideas from just one exposure. Such feedback has been an important factor in creating the current question sequence and its presentation. Although a question sequence like that given here can be very useful in introducing operational definitions and vocabulary, and encouraging the development of reasoning skills, it cannot anticipate every difficulty, nor is it instantaneously effective for all students. Immediately after these classes some students seek clarification on the difference between mass and weight. Such clarification is usually realized by repetition of appropriate portions of the question sequence. Distinguishing between fact, hypothesis, and deduction is also particularly challenging for many students (3). For example, when exposed two years ago to a sequence of questions similar to those in questions 17–24 above, more than half of the students answered “true” when asked if this line of questioning proved that matter is made of tiny particles. This is despite the fact that the sequence started by asking the student to hypothesize that matter is made of such particles. This question has now been added to the sequence given in the lab, where students have more time to engage in discussion and reflection. Concluding Remarks Although there are challenges associated with presenting this material in a Socratic fashion, there are also benefits. The approach connects the operational definition of gravitational mass that is used in the discipline of physics with inferences about the atomic realm that are important to the discipline of chemistry. The operational definition presented in physics refers to a Cavendish (torsion) balance (1, 12), while the approach described in this paper relies on an equalarm balance, which is easier to use in active learning and easier to represent on a chalkboard. Student attention in this approach is focused explicitly on the important idea of constructing an operational definition, and on the correct use of vocabulary, while the active learning environment provides the instructor with important feedback. Finally, this approach is consistent with several recent constructivist approaches to the development of the concepts of density and specific gravity (11, 13, 14), and could easily be connected to any of them. Our observations indicate that approaches like this, which actively engage students, anticipate the needs of novice learners better than a conventional lecture format. For this reason, such approaches will continue to be used as a foundation for further curriculum evolution. Readers interested in the link between chemistry teaching and physics teaching may be interested in a recent article on this subject (15). WSupplemental

Material

Additional questions to probe for deeper understanding of these concepts are available in this issue of JCE Online. Notes 1. At this point, students are not introduced to the modern definition of the meter, given in terms of a certain number of wavelengths of a particular electromagnetic radiation.


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In the Classroom 2. This inference can lead one to conclude that different objects with equal masses and equal volumes should have equal numbers of nucleons (protons and neutrons). However, in addition to ignoring the slight mass differences between protons and neutrons, more important relativistic effects have also been ignored in this discussion. Fusion of protons and neutrons results in complex atomic nuclei with masses that are less than the sum of the individual masses of the protons and neutrons. If we consider two containers of equal mass and volume, one containing O16 atoms, the other H1 atoms, the container with oxygen atoms actually has more nucleons per liter, even though the densities are the same. Such discussions are best left until later in a course. The present course avoids them entirely. 3. An alternative approach to that presented in this part of the dialog could have the student conclude that block X has more particles per unit volume than block Y, and then introduce the concept of density to describe this situation. This, however, has the drawback of defining density in terms of one unobservable quantity (number of particles) and one observable quantity (volume).

Literature Cited 1. Arons, A. A Guide to Introductory Physics Teaching; Wiley: New York, 1990; Chapter 3. 2. Collins, A. A Sample Dialogue Based on a Theory of Inquiry Teaching. In Instructional Theories in Action, C.M. Reigeluth, Ed.; Lawrence Erlbaum Associates: New Jersey, 1987. 3. Toomey, R.; DePierro, E.; Garafalo, F. CERAPIE 2001, 2, No. 3, 183–202. http://www.uoi.gr/cerp/2001_October/03.html

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(accessed Sep 2003). 4. Nakhleh, M., Lowery, K., Mitchell, R.; J. Chem. Educ. 1996, 73, 758–762. 5. Towns, M; Kreke, K.; Fields, A. J. Chem. Educ. 2000, 77, 111– 115. 6. Cohen, J.; Kennedy-Justice, M.; Pai, S.; Torres, C.; Toomey, R.; DePierro, E.; Garafalo, F. J. Chem. Educ. 2000, 77, 1166– 1173. 7. Touger, J. The Physics Teacher 1991, 29, 90–95. 8. Krim, J. Friction at the Atomic Scale. Scientific American 1996, 275 (4), 74–80. 9. Brown, D.; Clement, J. Classroom Teaching Experiment in Mechanics. In Research in Physics Learning: Theoretical Issues and Empirical Studies, Duit, R.; Goldberg, R.; Niederer, H., Eds.; Institute for the Pedagogy of the Natural Sciences, University of Kiel, Germany, 1992. 10. Minstrell, J. Facets of Students, Knowledge, and Relevant Instruction. In Research in Physics Learning: Theoretical Issues and Empirical Studies, Duit, R.; Goldberg, R.; Niederer, H., Eds.; Institute for the Pedagogy of the Natural Sciences, University of Kiel, Germany, 1992. 11. DeMeo, S. J. Chem. Educ. 2001, 78, 201–203. 12. Haber-Schaim, U. Physics, Physical Science Study Committee; D. C. Heath and Co.: Boston, MA, 1960. 13. Samsa, R. J. Chem. Educ. 1993, 70, 149–150. 14. Curtright, R.; Ricketts, J. J. Chem. Educ. 1993, 70, 489–490. 15. Toomey, R.; Garafalo, F. CERP 2003, 4, No. 2, 189–204. http://www.uoi.gr/cerp/2003_May/07.html (accessed Sep 2003).


Using a Socratic Dialog To Help Students Construct Fundamental

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