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How Students Learn: History, Mathematics, and Science in the Classroom 11 Guided Inquiry in the Science Classroom James Minstrell and Pamela Kraus The story of the development of this piece of curriculum and instruction starts in the classroom of the first author more than 25 years ago. I had supposedly taught my classes about universal gravitation and the related inverse square force law. The students had performed reasonably well on questions of the sort that asked, “What would happen to the force if we increased the distance from the planet?” They supposedly understood something about gravitational forces, resistive forces of air resistance and friction, and the idea of force in general. Then came a rude awakening. I don’t remember why, but we happened to be talking about a cart being pulled across a table by a string attached to a weight over a pulley. The students were becoming confused by the complexity of the situation. So, in an attempt to simplify the context, I suggested, “Suppose there is no friction to worry about, no rubbing, and no friction.” Still the students were confused and suggested, “Then there would be so much wind resistance.” I waved that notion away as well: “Suppose there were no friction at all and no air resistance in this situation. Suppose there were no air in the room. Now what would be the forces acting on this cart as it was moving across the table?” I was not prepared for what I heard. Several voices around the room were saying, in effect, “Then things would just drift off the table. The weight and string and cart would all just float away.” I was tempted to say, “No, don’t think like that.” I suppressed that urge and instead asked in a nonevaluative tone, “Okay, so you say things would just float away. How do you know that?” They suggested, “You know, like in space. There is no air, and things just drift around. They aren’t held down, because there is no air
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How Students Learn: History, Mathematics, and Science in the Classroom to hold them down.” The students said they knew this because they had heard from the media that in space things are weightless. Indeed, they had seen pictures of astronauts just “floating” around. They had also been told that there is no air in space, and they put the two (no air and weightless) together. But they had no first-hand experiences to relate to what they knew from these external “authorities.” If we really want to know what students are thinking, we need to ask them and then be quiet and listen respectfully to what they say. If we are genuinely interested and do not evaluate, we can learn from our students. What good is having my students know the quantitative relation or equation for gravitational force if they lack a qualitative understanding of force and the concepts related to the nature of gravity and its effects? They should be able to separate the effects of gravity from the effects of the surrounding air. Later, they should be able to explain the phenomena of falling bodies, which requires that they separate the effects of gravity from those of air. While many physical science books focus on the constancy of gravitational acceleration, most students know that all things do not fall with the same acceleration. They know that a rock reaches the floor before a flat sheet of paper, for example. Not addressing the more common situation of objects falling differently denies the students’ common experiences and is part of the reason “school science” may not seem relevant to them. So, we need to separate the effects of air from those of gravity. Learning is an active process. We need to acknowledge students’ attempts to make sense of their experiences and help them confront inconsistencies in their sense making. Even more fundamental, I want my students to understand and be able to apply the concept of force as an interaction between objects in real-life situations. They should have first-hand experiences that will lead to the reasonable conclusion that force can be exerted by anything touching an object, and also that forces can exist as “actions at a distance” (i.e., without touching the object, forces might be exerted through the mechanisms of gravity, electrostatic force, and magnetic force). I also want my students to understand the nature of scientific practice. They should be able to interpret or explain common phenomena and design simple experiments to test their ideas. In short, I want them to have the skills necessary to inquire about the world around them, to ask and answer their own questions, and to know what questions they need to ask themselves in the process of thinking about a problematic situation.
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How Students Learn: History, Mathematics, and Science in the Classroom Teachers’ questions can model the sorts of questions students might ask themselves when conducting personal inquiry. Research and best practice suggest that, if we are really clever and careful, students will come more naturally to the conceptual ideas and processes we want them to learn. Being clever means incorporating what we have come to understand about how students learn. This chapter describes a series of activities from which the experience of teachers and researchers demonstrates students do learn about the meaning of force and about the nature and processes of science. It also explains how the specific activities and teaching strategies delineated here relate to what we know from research on how people learn, as reflected in the three guiding principles set forth in Chapter 1 with regard to students’ prior knowledge, the need to develop deep understanding, and the development of metacognitive awareness. We attempt to give the reader a sense of what it means to implement curriculum that supports these principles. It is our hope that researchers will see that we have built upon their work in designing these activities and creating the learning environment. We want teachers to get a sense of what it means to teach in such an environment. We also want readers to get an idea of what it is like to be a learner. The following unit could come before one on forces to explain motion (i.e., Newton’s Laws). By the end of this unit, students should have arrived at a qualitative understanding of force as applied in contexts involving buoyancy, gravitation, magnetics, and electrostatics. The activities involved are designed to motivate and develop a sense of the interrelationships between ideas and events. The expected outcome includes qualitative understanding of ideas, not necessarily formulas. THE UNIT: THE NATURE OF GRAVITY AND ITS EFFECTS Part A: What Gravity Is Not Getting the Unit Started: Finding Out About Students’ Initial Ideas Teachers need to unconditionally respect students’ capacities for learning complex ideas, and students need to learn to respect the teacher as an instructional leader. Teachers will need to earn that respect through their actions as a respectful guide to learning.
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How Students Learn: History, Mathematics, and Science in the Classroom For students to understand the following lessons, we need to establish some prerequisite knowledge and dispositions during earlier lessons. Students will need to understand that measurements of a single quantity may vary depending on three factors: the object being measured, the instrument being used, and the person using the instrument. The teacher needs to have enough experience with the class so that the students are confident that the class will achieve resolution over time. Thus, this unit comes about a month or so into the school year. Students need to persevere in learning and trusting that the teacher will help guide them to the big ideas. This should probably not be the students’ first experience with guided inquiry. While the set of experiences in Part A below takes a week or more to resolve, prior initial experiences with guided inquiry may take a class period or two, depending on the students’ tolerance for ambiguity. Identifying Preconceptions: What Would Happen If …? Teachers need to know students’ initial and developing conceptions. Students need to have their initial ideas brought to a conscious level. One way to find out about students’ preconceptions for a particular unit is to ask them to give, in writing, their best answers to one or more questions related to the unit. At the beginning of this unit on the nature of gravity and its effects, the teacher poses the following situation and questions associated with Figure 11-1. FIGURE 11-1 A diagnostic question to use at the beginning of this unit.
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How Students Learn: History, Mathematics, and Science in the Classroom Nature and Effects of Gravity, Diagnostic Question 1: Predict the scale reading under the glass dome with air removed. In the diagram with question 1, we have a large frame and a big spring scale, similar to what you might see at the local market. Suppose we put something on the scale and the scale reading is 10.0 lb. Now suppose we put a large glass dome over the scale, frame and all, and seal all the way around the base of the dome. Then, we take a large vacuum pump and evacuate all the air out from under the dome. We allow all the air to escape through the pump, so there is no air left under the glass dome. What would happen to the scale reading with no air under the dome? You may not be able to give a really precise answer, but say what you think would happen to the scale reading, whether it would increase, decrease, or stay exactly the same and if you think there will be a change, about how much? And briefly explain how you decided. I will not grade you on whether your answer is correct. I just want to know your ideas about this situation at this time. We are just at the beginning of the unit. What I care most about is that you give a good honest best attempt to answer at this point in time. I know that some of you may be tempted to say “I don’t know,” but just give your best answer at this time. I’m pretty sure most all of you can come up with an answer and, most importantly, some rationale to support that answer. Just give me your best answer and reasoning at this point in time. We will be working to investigate this question over the next few days. When asked, more than half of students cite answers that suggest they believe air only presses down. Half of those suggest that the scale reading would go to zero in the vacuous environment. About a third of introductory students believe that the surrounding air has absolutely no effect on the scale reading regardless of the precision of the scale. Most of the rest believe that air only pushes up on the object and that it does so with a strong force. Typically, only about one student in a class will suggest that the air pushes up and down but with slightly greater force in the upward direction, the result being a very slight increase in the scale reading for the vacuous environment—a “best answer” at this time. This question may be more about understanding buoyancy than understanding gravity. However, part of understanding the effects of gravity is learning what effects are not due to gravity. Students need opportunities to explore the relationships among ideas.
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How Students Learn: History, Mathematics, and Science in the Classroom Gravitational force is an interaction between any two objects that have mass. In this case, the gravitational force is an interaction between the object on the scale and the earth as the other object. Many students believe gravity is an interaction between the object and the surrounding air. Thus, this has become a first preconception to address in instruction. If teachers fail to address this idea, we know from experience that students will likely not change their basic conceptual understanding, and teachers will obtain the poor results described earlier. In contrast with the above question, we have seen curricula that attempt to identify students’ preconceptions simply by asking students to write down what they know about X. In our experience, this question is so generic that students tend not to pay much attention to it and simply “do the assignment” by writing anything. Instead, preinstruction questions should be more specific to a context, but open up the issues of the discipline as related to that context. These sorts of questions are not easy to create and typically evolve out of several iterations of teaching a unit and finding out through discussions what situations elicit the more interesting responses with respect to the content at hand. A Benchmark Lesson1: Weighing in a Vacuum In discussion following the posing of this question, I encourage students to share their answers and rationales. Because I am interested in getting students’ thinking out in the open, I ask that other students not comment or offer counter arguments at this point, but just listen to the speaker’s argument. I, in turn, listen carefully to the sorts of thinking exhibited by the students. I know this will faciliate my helping the class move forward later. With encouragement and support on my part, some students volunteer to share their answers. Some suggest the scale will go to zero “with no air to hold the object down.” Others suggest, “The scale reading will not go to zero but will go down some because gravity is still down and the weight of the air pushes down too, but since air doesn’t weigh very much, the downward air won’t be down much and the scale reading won’t go down much.” Some students suggest that the scale reading will increase (slightly or substantially) “because there is no air to hold the object up. It’s about buoyancy. The air is like water. Water pushes up and so does air. No air, there is no buoyancy.” Still others suggest that the scale reading should stay the same “because air doesn’t do anything. The weight is by gravity not by air pressure.” And others agree that the scale reading will not change, “but air is pushing on the object. It pushes up and down equally on the object, so there shouldn’t be any change.” By now several students have usually chimed in to say that one or another of the ideas made sense to them. The ideas are now “owned” by several class members, so we can discuss and even criti-
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How Students Learn: History, Mathematics, and Science in the Classroom cize the ideas without criticizing a particular person. It is important to be supportive of free expression of ideas while at the same time being critical of ideas. Students are more likely to share their thinking in a climate where others express genuine interest in what they have to say. Waiting until one student has completely expressed his or her idea fosters deeper thinking on that speaker’s part. Asking speakers critical questions to clarify what they are saying or to help them give more complete answers and explanations fosters their own engagement and learning. With most of their initial thinking having been expressed, I encourage students to share potentially contradictory arguments in light of the candidate explanations. Students might suggest, “When they vacuum pack peanuts, they take the air away and the weight doesn’t go to zero”; or “The weight of the column of air above an object pushes down on the object”; or “Air acts like water and when you lift a rock in water it seems lighter than lifting it out of water, so air would help hold the object up”; or “But, I read where being on the bottom of the ocean is like having an elephant standing on your head, so air must push down if it acts like water”; or “Air is just around things. It doesn’t push on things at all, unless there is a wind.” Some students begin to say they are getting more confused, for many of these observations and arguments sound good and reasonable. Once arguments pro and con for most of the ideas have been expressed, it is time to begin resolving issues. Thus far, we have been freely expressing ideas, but I want students to know that science is not based simply on opinion. We can achieve some resolution by appealing to nature; indeed, our inferences should be consistent with our observations of nature. I ask, “Sounds like a lot of good arguments and experiences suggested here, so how can we get an answer? Should we just vote on which should be the right answer and explanation?” Typically, several of the students suggest, “No, we can try it and see what happens. Do you have one of those vacuum things? Can we do the experiment?” I just happen to have a bell jar and vacuum pump set up in the back room. First, I briefly demonstrate what happens when a slightly inflated balloon (about 2 inches in diameter) is placed under the bell jar and the pump is turned on: the balloon gets larger. I ask the students to explain this result. The students (high school age at least) usually are able to articulate that I did not add air to the balloon, but the air outside the balloon (within the bell jar) was evacuated, so the air in the balloon was freer to expand the balloon.
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How Students Learn: History, Mathematics, and Science in the Classroom Attention is extremely important to learning. We hang a weight on the spring scale, put it under the jar, and seal the edges, and I ask students to “place their bets.” This keeps students motivated and engaged. “How many think the scale reading will increase?” Hands go up. “Decrease?” Many hands go up. “Decrease to zero?” A few hands go up. “Stay exactly the same?” Several hands go up. I start the pump. It is important to give students opportunities to apply (without being told, if possible) ideas learned earlier. The result surprises many students. The scale reading does not appear to change at all. Some students give a high five. I ask, “What can we conclude about the effects of air on the scale reading?” Some students suggest, “Air doesn’t do anything.” Sometimes to get past this response, I need to prime the discussion of implications of the results by asking, “Do we know air has absolutely no effect?” A few students are quick to say, “We don’t know that it has absolutely no effect. We just know it doesn’t have enough effect to make a difference.” I ask, “Why do you say that?” They respond, “Remember about measurements, there is always some plus or minus to it. It could be a tiny bit more than it was. It could be a tiny bit less, or it might be exactly the same. We can’t tell for sure. Maybe if we had a really, really accurate scale we could tell.” I also want the students to see that conclusions are different from results, so I often guide them carefully to discuss each. “First, what were the actual results of the experiment? What did happen? What did we observe?” Students agree that there was no observable change in the scale reading. “Those were the results. We observed no apparent change in the scale reading.” Students should be provided opportunities to differentiate between summarizing observable results and the conclusions generalized from those results. Because I want students to understand the role of experimentation in science, I press them for a conclusion: “So, what do we know from this experiment? Did we learn anything?” Although a few students suggest, “We didn’t learn anything,” others are quick to point out, “There can’t be any big changes. We know that the air doesn’t have a big effect.” At this point, it appears students have had sufficient experience talking about the ideas, so I may try to clarify the distinction between results and conclusions: “Conclusions are different from results. Conclusions are about the meaning of the
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How Students Learn: History, Mathematics, and Science in the Classroom results, about making sense of what we observed. So, what can we conclude? What do these results tell us about the effects of the air?” With some additional discussion among the students, and possibly some additional clarification of the difference between results and conclusions, most students are ready to believe the following summary of their comments: “If the air has any effect on the scale reading, it is not very large. And apparently gravity is not caused by air pressure pressing things down.” Activity A1 Activity A1 is a simple worksheet asking students to review their answers to questions about their initial ideas, other ideas that have come out in discussion, and the results and conclusions from the preceding benchmark lesson. Typically, I hand this summary sheet out as homework and collect it at the beginning of the next class. By reviewing what students have written, I can identify related issues that need to be discussed further with certain students. Alternatively, I may ask students to check and discuss their answers with each other in groups and to add a page of corrections to their own answers before handing in their original responses. One purpose of this activity is to encourage students to monitor their own learning. Students need opportunities to learn to monitor their own learning. Progressing from the preinstruction question through the benchmark discussion takes about one class period. In showing that gravity is not caused by air pressure, we have generated questions about the effects of the surrounding air. Students now want to know the answer to the original question. I used to end the investigations of the surrounding air at this point and move on to investigating factors affecting gravity, but I discovered that students slipped back to believing that air pressed only down or only up. Therefore, we redesigned the curriculum activities to include more time for investigation into the effects of surrounding fluids. Doing so also allows us to incorporate some critical introductory experiences with qualitative ideas about forces on objects. This experience helps lay the groundwork for the later unit on forces, when we will revisit these ideas and experiences. To deepen students’ understanding of the effects of surrounding fluids then, we now engage in several elaboration activities wherein students have opportunities to test various hypotheses that came up in the benchmark discussion. Revisiting ideas in new contexts helps organize them in a rich conceptual framework and facilitates application across contexts.
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How Students Learn: History, Mathematics, and Science in the Classroom Opportunities for Students to Suggest and Test Related Hypotheses In the benchmark lesson, several ideas were raised that need further testing. Some students suggested air only pushed up, others that air only pushed down, still others that air pushed equally or did not push at all. Some suggested that air was like water; others contested that idea. Each of the following activities is intended to give students opportunities to test these ideas in several contexts, recognizable from their everyday world. That is, each activity could easily be repeated at home; in fact, some students may have already done them. One goal of my class is for students to leave seeing the world differently. Groups of three or four students each are assigned to “major” in one of the elaboration activities and then to get around also to investigating each of the other activities more briefly. In every case, they are asked to keep the original bell jar experiment in mind: “How does this activity help us understand the bell jar situation?” With respect to the activity in which they are majoring, they will also be expected to present their results and conclusions to the class. Elaboration Activity A2: The Inverted Glass of Water. This activity was derived from a trick sometimes done at parties. A glass of water with a plastic card over the opening is inverted. If this is done carefully, the water stays in the glass. Students are asked to do the activity and see what they can learn about the directions in which air and water can push. They are also given the opportunity to explore the system and see what else they can learn. Allowing students freedom to explore may give teachers opportunities to learn. Teachers need to allow themselves to learn. My purpose here is to help students see that air can apparently push upward (on the card) sufficiently to support the card and the water. That is usually one conclusion reached by some students. Early in my use of the activity, however, I was surprised by a student who emptied the water and placed the card over the open end of the inverted glass and concluded, “It’s the stickiness of water that holds the card to the glass.” For a moment I was taken aback, but fortunately other students came to my rescue. They said, “At first we thought it might be because the card just stuck to the wet glass, but then we loaded the card with pennies to see how many pennies the card would hold to the empty glass. We found it would only hold about three pennies before the card would drop off. The water we had in the glass weighs a lot more than three pennies. Stickiness might help, but it is not the main reason the card stays on. The main reason must be the air below the card.”
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How Students Learn: History, Mathematics, and Science in the Classroom This was such a nice example of suggesting and testing alternative explanations that I now bring up the possibility of the stickiness being all that is needed if this idea does not come up in the group presentation. More recently, other students have tested the stickiness hypothesis by using a rigid plastic glass with a tiny (~1 mm) hole in the bottom. When they fill the glass, put on the card, and invert the glass, they put their finger over the hole. When they move their finger off the hole, the water and card fall. They conclude that the air rushing in the hole pushes down on the water and that the air pushing from under the card is not providing sufficient support. I now make sure I have plastic cups available in case I need to “seed” the discussion. After making these observations, students are ready to draw the tentative conclusion that the upward push by the air on the card must be what is supporting most of the weight of the water on the card. They note the water must push down on the card, and since the stickiness of the water is not enough to hold the card, there must be a big push up by the air. This conclusion is reached more easily by more mature students than by middle-level students. The latter need help making sense of this argument. Most are willing to say tentatively that it makes sense that the air pushes up and are more convinced after they see the various directions in which air pushes in the other activities. Elaboration Activity A3: Inverted Cylinder in a Cylinder of Water. This activity was derived from some students describing observations they had made while hand-washing dishes. They had observed what happened when an inverted glass was submerged in a dishpan of water. In activity A3, a narrow cylinder (e.g., 100 ml graduated cylinder) is inverted and floated in a larger cylinder (e.g., 500 ml graduated cylinder) of water. Again, students are asked to see what they can learn about the directions that air and water can push. I want students to see that air and water can push up and down, and that the deeper one goes in a fluid, the greater is the push in any direction. While doing this activity, students observe that the farther down one pushes the floating cylinder, the more difficult it is to push. Thus, they conclude that the water is pushing upward on the air in the small cylinder, and the push is greater the deeper one goes. Typically, some students cite as additional evidence the observation that the water level in the small cylinder rises within that cylinder the farther down one pushes the small cylinder, thus compressing the air. I commend these students for their careful observation and suggest that other students observe what happens to the level of the water in the inner cylinder. The more the air is compressed, the harder the water must be pushing upward on the air to compress it, and the more the compressed air must be pushing upward on the inside of the small cylinder.
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How Students Learn: History, Mathematics, and Science in the Classroom Sometimes, there are emergent goals that need to be addressed before returning to the primary instructional goal. For example, teaching about the content may need to move to the background of the instruction while teaching about the processes of science are brought to the foreground, even though both are always present. Student 2 See, it’s what I thought, less paper clips makes it stronger. Student 3 No it’s what I said. Smaller distance makes it bigger. Student 4 We got too many things happening. Student 1 I’m getting lost. Student 3 It’s like we studied before about making fair tests. This isn’t a fair test. Student 4 Oh yeah. Teacher OK. Why not, Chris? Why isn’t it a fair test? Hang in there Tommy [Student 1]. I think we are about to clear this up. I will have you decide when the argument and results of the experiments make sense to you. The rest of you need to talk to Tommy to convince him of what you are saying. Chris, you were saying? Student 3 You gotta keep things constant. Like change only one thing and keep other things constant. Student 4 Oh yeah, like we did before, make a fair test. OK, Tommy? Student 1 No, I don’t remember anything about a fair test. Student 4 It’s like when we said we have to keep all the things [a few students are saying “variables”]. Yeah, we have to keep all the variables the same except one. Teacher But, does that help you, Tommy? Student 1 Not really. What’s it got to do with this experiment? That was something we did before when we were studying other stuff. Student 3 In this experiment we have to keep the number of paper clips the same and the strong magnet the same and change the distance. Only change the distance, if we want to see whether
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How Students Learn: History, Mathematics, and Science in the Classroom the distance changes the scale reading. Otherwise, if we change other things too, we will not know whether it is distance or something else that made it bigger. To become learners, independent of authority, students need opportunities to make sense of experiences and formulate rational arguments. Student 1 OK. So, what happened? Student 3 Well, we didn’t keep the other things, variables, the same. So, we need to do that to find out what happens. Teacher Good, to find out whether that one variable, for example the distance, affects how big the magnetic force is. [At this point, because the apparatus is difficult to control, I demonstrate what does happen when we keep the big magnet and the number of paper clips the same and just decrease the distance between the magnet and paper clips. The scale reading rises.] Now can we tell if varying the distance affects the force? Student 2 Yeah. It does. Teacher How does distance affect force, Tommy? Which way does it go? The smaller the distance … Student 1 The smaller the distance, the bigger the force. Does it get smaller if the distance gets bigger? Teacher Good question. Let’s try it. [I increase the distance, and the scale reading is lower.] So, what can we conclude now? Student 1 The bigger the distance the smaller the scale, and the smaller the distance, the bigger the force scale. Teacher Good. Now, what do we need to do to test whether the number of paper clips makes a difference in the force? Student 1 Would we change the paper clips or keep them the same? Student 2 If you want to test the paper clips, you change the number of paper clips and see if that changes the force.
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How Students Learn: History, Mathematics, and Science in the Classroom Student 1 Is that right? Oh! Oh! I get it. So to see if one thing affects the other thing, you change the one thing and see what happens to the other. The teacher’s questions to clarify students’ statements help the students become clearer about what they know. Teacher That’s sounding like you’ve got the idea of fair test or what is sometimes called “controlling variables,” but could you say it again and say what you mean by the word “thing,” which you used several times. Student 1 OK. To see if paper clips affect the scale, the force, you change the number of paper clips and see if the force changes. Right? Teacher Yes, good. Now suppose you wanted to see if the strength of the magnet affected the force. What would you do? Student 1 Change the magnet and see if the force changed. Teacher What would you do about the other variables? Student 2 I’d keep … [At this point I interrupt to let Tommy (Student 1) continue his thinking. Meanwhile, other students are getting restless, so I let them go ahead with the apparatus and see what they can find out, which I charge them with demonstrating later for the rest of us. Meanwhile, I continue with Tommy and anyone else who admits to needing some help here.] All students can learn, but some need more assistance than others, and some need more challenge than others. Teacher So, Tommy. What are the factors that we want to investigate here? Student 1 See if bigger magnets have a bigger force. Teacher OK. Anything else? Student 1 See if more paper clips makes the force reading bigger.
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How Students Learn: History, Mathematics, and Science in the Classroom Student 5 And see if distance makes the force bigger or smaller. Student 1 We already saw that one. Teacher If we changed the number of paper clips and we changed the magnet, would we know whether one of these affected the force? Student 6 Not if we changed both. If we changed both, one or both might be changing the force. Teacher So, what do we need to do, Tommy? Student 1 Oh, do we need to only change one thing, like change the strength of magnet we use and don’t change the paper clips? Student 6 And we’d need to keep the distance the same too right, else that might be changing the force too? Teacher Good. So, we think that strength of magnet, the number of paper clips, and the distance might all change the magnetic force. So we just change one of those variables at a time and keep the others constant and see if the force changes and in what direction. Assuming all the students are familiar with the equipment, sometimes it is more important to help some students focus on the argument while others wrestle with the details of manipulating the equipment. In a while, I bring the whole class together. I help the students summarize the ideas they have developed and how the controlled experiments helped test those ideas. The group that had the challenge to test factors demonstrates the apparatus and the procedures they used to obtain the following results: The more paper clips, the higher the scale reading (keeping magnet and distance constant). The stronger the magnet, the higher the scale reading (keeping number of paper clips and distance of separation constant). The greater the distance of separation, the lower the scale reading (keeping number of paper clips and strength of the magnet constant).
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How Students Learn: History, Mathematics, and Science in the Classroom Students need assistance in differentiating between results and conclusions. Results are specific to the experiment, while conclusions generalize across situations. From these results we conclude that the magnetic force grows larger with more magnetic “stuff” (paper clips containing iron), with a stronger magnet, or with closer distance of separation between the big magnet and the iron pieces. Building a Bridge from Understanding Magnetic Action at a Distance to Understanding Gravitational Action at a Distance Analogies can help bridge from the known to the unknown and from the concrete to the abstract. I now illustrate two situations on the front board. One is something like the situation we have just investigated, with a large magnet pulling on an iron object and stretching a spring scale. Since this diagram is a bit different from the previous one, I ask students to discuss the similarities and differences. When they appear to see that the situations just seem to be different representations of the same conclusions we drew, I move on to the second diagram. It looks like the first, except that a large sphere represents the earth, and the object is anything that has mass (see Figure 11-6). The spring scale is the same. I ask students how this situation is similar and different from the weighing of a fish depicted in Figure 11-4. FIGURE 11-6 Diagramming an analogy between magnetism and gravity.
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How Students Learn: History, Mathematics, and Science in the Classroom Student 5 Oh, it’s like, the earth pulls on the object like the magnet pulls on the piece of iron. Student 7 They are both actions at a distance. Student 4 So what. We already knew that. [So the students appear to recognize the analogous situations. Now comes the difficult part.] Teacher From our previous experiments you know on what factors the magnetic force depends. Right? [There is a chorus of “yes,” but I don’t trust it because we now have a different diagram, and I want to know if the students are transferring what they know about the previous situation. Students recite the list: “how much iron,” “how big (strong) the magnet is,” “how far apart they are.” Now reasonably assured, I move on.] Teacher What are some possible factors on which gravitational force might depend, if it acts similarly to magnetism? Student 2 Oh. Maybe it depends on the separation distance? Student 8 Maybe on the mass of the thing, ‘cuz that would be like the number of paper clips. Student 1 Maybe on the strength of the magnet. Student 3 No, there is no magnet in the gravity situation. Teacher OK. Hang on. Tommy [Student 1], there is no magnet in this situation [pointing to the gravitational case], but what might be similar to the strength of the magnet? Student 1 The strength of the earth? To build deep understanding of ideas, students need opportunities to transfer the ideas across contexts. Teachers need to check on this transfer of knowledge to new situations.
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How Students Learn: History, Mathematics, and Science in the Classroom Teacher It is kind of like the strength of the earth isn’t it. Just like the magnetic force depends on how big and strong the magnet is, the gravitational force might depend on how big, how much mass there is in the earth. Just like the more magnet we have, the bigger the force; the more mass the earth has, the bigger the force. I cannot easily show you, with experiments, on what factors the gravity force depends. But by what is called an “analogy,” we can make a good guess at the factors gravity depends on. If gravity action at a distance acts like magnetic action at a distance, it should depend on how much there is of each of the two objects interacting and on how big the separation distance is. By careful experiments with sensitive apparatus like the Cavendish torsion balance we saw before, scientists have verified that the guesses we just made work out in experiments. That is, the gravity force, evidenced by the spring scale reading, would be smaller if the mass of the earth were smaller, if the mass of the ball being held near the earth were of less mass, or if the ball were placed farther away from the earth. Parts C and D: What Are the Effects of Gravity? Explaining Falling Bodies Part A was about “what gravity is not.” That is, the effects of the surrounding fluid are not the cause of weight or gravity. But we ended up seeing that fluids such as air and water can have an effect on scale readings when we attempt to weigh objects. Part B was about the nature of gravitational force being one of the actions at a distance. And by analogy we concluded that the magnitude of the gravitational force depends on the masses of the two interacting objects and on the separation distance between them. Investigations into the nature of forces could stop here or could continue and focus on gaining a better understanding of the effects of gravity. Subsequent investigations in my classes involve explaining the phenomena of falling bodies. Part of a rich understanding of falling bodies is to understand the effects of air (or fluid) resistance as well those of gravity.
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How Students Learn: History, Mathematics, and Science in the Classroom Activities in these subunits are more consistent with what is presently suggested in curricula, so they are not described here. But students’ preconceptions, such as “heavier falls faster,” need to be addressed. More mature students can also quantify the acceleration of freely falling bodies and arrive at equations describing the motion in free fall. But younger students can gain a qualitative understanding of free fall as speeding up uniformly, and they can gain some understanding of factors affecting air resistance. Explaining Motion of Projectiles Next investigations, especially for older students, can involve understanding the motion of projectiles. Preconceptions, including “horizontal motion slows the vertical fall,” will need to be addressed. Understanding the independence of horizontal and vertical motions is a learning goal. Again those activities are not discussed in detail here. Suffice it to say that additional investigations into the nature and effects of gravity will build a stronger relationship between ideas and increase the likelihood that what is learned will be understood and remembered. SUMMARY In this chapter, we have tried to make real the principles of How People Learn by writing from our experience and the experience of other teachers, researchers, and curriculum developers. The sequence of activities described is not the only one that could foster learning of the main ideas that have been the focus here. Likewise, the dialogues presented are just examples of the many conversations that might take place. Teaching and learning are complex activities that spawn multiple problems suggesting multiple solutions. What we have discussed here is just one set of solutions to exemplify one set of generalizations about how students learn. That having been said, the activities described are ones that real teachers are using. But this chapter has not been just about activities that teachers can take away and use next week. Our main purpose is to give teachers and curriculum developers an idea of what it looks like when assessment, curriculum, and teaching act as a system consistent with the principles of How People Learn. We have tried to give the reader the flavor of what it means to teach in a way that is student-centered, knowledge-centered, and assessment-centered. By looking at the teacher’s decision making, we have attempted to provide a glimpse of what it is like to be a teacher or a learner in a learning community that is respectful of members of the community while at the same time being critical of the ideas they voice. Students are encouraged to question each other by asking, “What do you mean by that?” “How
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How Students Learn: History, Mathematics, and Science in the Classroom do you know?” But they are also guided to listen and allow others in the community to speak and complete their thoughts. Students’ preconceptions are identified and addressed, and subsequent learning is monitored. This means assessment is used primarily for formative learning purposes, when learning is the purpose of the activities in the classroom. By listening to their students, teachers can discern the sorts of experiences that are familiar and helpful in fostering the learning of other students. Learning experiences need to develop from first-hand, concrete experiences to the more distant or abstract. Ideas develop from experiences, and technical terms develop from the ideas and operations that are rooted in those experiences. When terms come first, students just tend to memorize so much technical jargon that it sloughs off in a short while. Students need opportunities to see where ideas come from, and they need to be held responsible for knowing and communicating the origins of their knowledge. The teacher should also allow critical questions to open the Pandora’s box of issues that are critical to the content being taught. The better questions are those that raise issues about the big ideas important to deep understanding of the discipline. Some of the best questions are those that come from students as they interact with phenomena. Students need opportunities to learn to inquire in the discipline. Teachers can model the sorts of questions that the students will later ask themselves. Free inquiry is desirable, but sometimes (e.g., when understanding requires careful attention and logical development) inquiry is best guided, especially when the teacher is responsible for the learning of 30 or more students. But the teacher does not need to tell students the answers; doing so often short-circuits their thinking. Instead, teachers can guide their students with questions—not just factual questions, such as “What did you see?”, but the more important questions that foster student thinking, such as those that ask students to provide explanations or make sense of the phenomena observed. By listening respectfully and critically to their students, teachers can model appropriate actions in a learning community. Through questions, teachers can assist learners in monitoring their own learning. Finally, teachers also need the freedom to learn in their classrooms—to learn about both learning and about teaching. NOTES 1. We use the term “benchmark lesson” to mean a memorable lesson that initiates students’ thinking about the key content issues in the next set of activities.
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How Students Learn: History, Mathematics, and Science in the Classroom 2. The computer-based Diagnoser assessment system described is available on the web through www.FACETInnovations.com. Thus, it is accessible to teachers and students anytime from a computer with web access and appropriate browser. The concept and program were developed by the authors, Minstrell and Kraus, Earl Hunt, and colleagues at the University of Washington, FACET Innovations, Talaria Inc., and surrounding school districts. It includes sets of questions for students, reports for teachers, and suggested lessons to address problematic facets of thinking.
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Representative terms from entire chapter: