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475 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 some- thing about gravitational forces, resist ve forces of air resistance and fi icti on, 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 diction to worry about, no rubbing, and no faction." 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 fliction 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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476 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM to hold Them down." The students said dhey knew tills because dhey had heard from The media dhat in space Things are weightless. Indeed, dhey 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 Tom these external "authorities." ffwe realty want to know u *at students are to inking, we need to ask then and then be quiet and listen respectfully to u *at they say. ffwe are genuinely interested and do not evaluate, we can learn fron/ our students. What good is having my students know the quantitative relation or equa- tion for gravitational force if dhey 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 dhat dhey separate the effects of gravity from Those of air While many physical science books focus on The constancy of gravitational acceleration, most students know dhat all things do not fall widh 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. l earning is an active process. We need to acknowledge students'attempts to make sense of their experiences and bed 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 dhat will lead to The reasonable conclusion dhat force can be exerted by anydhing 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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GU DED INDU BY N THE SC ENCE CEASSFDDM 477 Tetl< hers questions can model the sorts of questions students might ask them selves when conductSngtersonal inquiry Research and best practice suggest that, if we are really clever and care- ful, students will come more naturally to the conceptual ideas and processes we want them to team. 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 re- search 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 aware- ness. 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 buoy- ancy, 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 GRAVllY AND ITS EFFECTS Part A: What Gravity Is Not Getting the Unit Started Finding OutAbout Students'lnitial Ideas Teachers need to u n co ad ition n TV respect students'capacStSesfor learn ing complex ideas, and students need to learn to respect the teacher as an instructional leader Teachers wSII need to earn that respect through their actions as a respectful guide to learning.

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478 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM For students to understand the following lessons, we need to establish some prerequisite knowledge and dispositions during earlier lessons stu- dents 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 trust- ing that the teacher will help guide them to the big ideas. This should prob- ably 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. Identif,uing PreconceptionsWhat Would Happen If . . . ? Tea< hers need to knou students' initial and developing conceptions. Students need to Kate their initial ideas brought to a conscious le.uel 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 ques- tions 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 asso- ciated with Figure 11-1, - Vacuum inside a bell jar Nature and Effects of Gravity Diagnostic Question Scale reading = 10.0 Ibs <~\~N Glass dome with ~L~ air removed Scale reading = Ibs FIGURE 1 1 1 A diognoshc queshon lo use oi he beginning of his unit

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GU DED INDU BY N THE SC ENCE CEASSFDDM 479 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 led under the glass dome. What would happen to the scale reading with no air under the domes 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 7 And briefly explain how you decid em 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 tem pted to say HI 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 widh slightly greater force in the upward direction, The result being a very slight increase in the scale reading for The vacuous envi- ronmenta "best answer" at this time. This question may be more about understanding buoyancy Than under- standing gravity. However, part of understanding the effects of gravity is learning what effects are not due to gravity. .~udenh nerd opporf unit /es f o explore /he relof ionships among /deai

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480 HO W STUDENTS LEARN: SC ENCE N THE C ASSFOOM Gravitational force is an interaction between any two objects that have mass. In dais case, the gravitational force is an interaction between the ob ect on the scale and the earth as the o h e- object. Many students believe gravity is an interaction between the object and the surrounding air Thus, tills has become a first preconception to address in instruction. If teachers fail to address dais 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 dhat attempt to identify students' preconceptions simply by asking students to write down what They know about X. In our expenence, 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 spe- cific 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 discus- sions what situations elicit the more interesting responses with respect to The content at hand. A Benchmark Lesson' TWeighing in a Vacuum In discussion following The posing of this question, I encourage stu- dents to share Their answers and rationales. Because I am interested in get- ting students' thinking out in the open, I ask that odher students not com- ment or offer counter arguments at This point, but just listen to The speaker's argument. 1, 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 Widh encouragement and support on my part, some students volunteer to share their answers. Some suggest The scale will go to zero "widh 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 down- ward air won't be down much and The scale reading won't go down much," Some students suggest dhat The scale reading will increase (slightly or sub- stantially) "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 odhers suggest dhat the scale reading should stay the same "because air doesn't do anything. The weight is by gravity not by air pres- sure." And odhers agree that the scale reading will not change, "but air is pushing on the ob ea. 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 dhat 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 cnti-

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GU DED INDU FY N THE SC ENCE CEASSFDDM 481 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 hkely to share their thinking in a climate where others express gen nine interest in what they have to say Waiting u nti/ 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 orto hey them give more complete answers and explanationsfosters their own engagement and learning. Widh most of their initial thinking having been expressed, I encourage students to share potentially contradictory arguments in light of The candi- date explanations. Students might suggest, "When They vacuum pack pea- nuts, 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 ob ect"; 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 L)o you have one of those vacuum things? Can we do The experiments" I just happen to have a bell jar and vacuum pump set up in The back room. First, I bnedy demonstrate what happens when a slightly indated 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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482 HO W STUDENTS LEARN: SC ENCE N THE C ASSFOOM Attention is extremely important to learn ing. 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 moti- vated and engaged. "How many drink The scale reading will increase?" Hands go up. "t)ecrease?" Many hands go up. "t)ecrease 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 con- clude about The effects of air on The scale reading?" Some students suggest, "Air doesn't do anydhing." Sometimes to get past this response, I need to prime The discussion of implications of The results by asking, "t)o 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 summanz- ing obserr able results a nd the conclusions general iced 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? t)id we learn anydhing?" Aldhough a few students suggest, "We didn't learn anything," o he- s 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: "Conclu- sions are different from results. Conclusions are about The meaning of The

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GU DED INDU BY N THE SC ENCE CEASSFDDM 433 results, about making sense of what we observed so, what can we con- clude? What do These results tell us about The effects of The air?" Widh some additional discussion among The students, and possibly some additional clan- f~cation 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 appal ently gravity is not caused by air pressure pressing things down." Actit try A I Activity Al is a simple worksheet asking students to review their an- swers to questions about their initial ideas, o her 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 an- swers with each o he- in groups and to add a page of corrections to their own answers before handing in their oliginal 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 penod. In showing That gravity is not caused by air pressure, we have generated questions about the effects of the sur- rounding air Students now want to know the answer to the original ques- tion. 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 stu- dents 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 L)oing 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 expenences. To deepen students' understanding of The effects of surrounding fluids Then, we now engage in several elaboration activities wherein students have opportu- nities to test various hypotheses that came up in the benchmark discussion. Revisiting ideas in new contexts kelps organize then in a rick conceptual framework and facilitates application across contexts.

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484 HO W STUDENTS LEARN: SC ENCE N THE C ASSFOOM Opportunitiesfor 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 stu- dents 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. Eilaboratlon 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 studentsfreedom to explore maygive 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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GU DED INDU BY N THE SC ENCE CEASSFDDM 455 This was such a nice example of suggesting and testing alternative ex- planations Blat 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, o he- students have tested the stickiness hypodhesis by using a rigid plastic glass widh a tiny (~1 mm) hole in the bottom. When dhey fill The glass, put on the card, and invert The glass, dhey put Their finger over The hole. When dhey move their finger off The hole, The water and card fall. They conclude dhat 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 tenta- tive 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 dhat it makes sense that the air pushes up and are more convinced after dhey see The various directions in which air pushes in the odher activities. ELaboradon 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 dhat 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 Flat 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 dhat cylinder The farther down one pushes the small cylinder, thus compressing The air I commend these students for their careful observation and suggest dhat odher 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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504 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM Sometimes, there are emergent goals that need to be addressed before returning to the primary instructional goal For exa mple, teach ing about ti e content may need to moue to the background of the instruction while teach ing about the processes of science are brought to tbeforeground, et en 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 fairtest. Student 4 Oh yeah. Teacher OK. Why not, Chris7 Why isn't it a fair tests Hang in there Tommy Student 11.1 think we areabouttoclearthisup. Iwill haveyou 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 saying7 Student 3 You gotta keep things constant. Like change only one thing and keep otherthings constant. Student 4 Oh yeah, like we did before, make a fair test. OK, Tommy7 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 la few students are saying ~variables~l. Yeah, we have to keep all the variables the same except one. Teacher But, does that help you, Tommy7 Student 1 Not really What's it got to do with this experi- ment7 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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GU DED INDU FY N THE SC ENCE CEASSFDDM 505 the distance changes the scale reading. Otherwise, if we change other things too, we will not know whether it is distance or some- thing 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 happened7 Student 3 Well, we didn't keep the otherthings, vari- ables, 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. IAt 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.l Now can we tell if varying the distance affects the forces Yeah. It does. Student 2 Teacher How does distance affect force, Tommy7 Which way does it got The smaller the dis- tance . . . Student 1 The smaller the distance, the bigger the force. Does it get smaller if the distance gets bigger7 Teacher Good question. Let's try it. 11 increase the distance, and the scale reading is lower I So, what can we conclude now7 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 force7 Student 1 Would we change the paper clips or keep them the same7 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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506 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM Student 1 is that right7 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 orwhat 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. Right7 Teacher Yes, good. Now suppose you wanted to see if the strength of the magnet affected the force. What would you do7 Student 1 Change the magnet and see if the force changed. Teacher What would you do about the other variables7 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 l let them go ahead with the apparatus and see what they can find out, which I charge them with demonstrating later forthe rest of us. Meanwhile, I continue with Tommy and anyone else who admits to needing some help here.l 411 students can learn, hut some need more assistance than others, and some need more challenge than others. Teacher Student 1 Teacher Student 1 So, Tommy. What are the factors that we want to investigate here7 See if bigger magnets have a bigger force. OK. Anything else7 See if more paper clips makes the force reading bigger

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Teacher GU DED INDU FY N THE SC ENCE CEASSFDDM 507 Student 5 And see if distance makes the force bigger or smaller. Student 1 We al ready 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 force7 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, Tommy7 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 clips7 Student 6 And we'd need to keep the distance the same too right, else that might be changing the force toot Good. So,wethinkthatstrength 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 u ire tee equipment, sometimes it 15 more important to Rep some studentsfocus on tbe argument agile others wrestle wits tee details of manipulating tee equipment In a while, I bring the whole class together I help the students sur ma- nze the ideas they have developed and how the controlled experiments helped test those ideas. The group that had the challenge to test factors demor strates 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 num- ber 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 constanO.

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508 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM Students need assistance in differentiating between results and conclusions. Results are specific to the experiment, we ite concl usions general ice 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 Feces. Building a Bridgefrom Understanding Magnetic Action at a Distance to Understanding GravitationalAction at a Distance Analogies can help bndgefrom the known to the unknown am 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 differ- ences. 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. Iron ~ /EQrt h FIGURE 1 1 6 Diagramming an analog be veen magnetism and gravity

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GU DED INDU FY N THE SC ENCE CEASSFDDM 509 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 knewthat. Teacher Student 8 Student 1 Student 3 Teacher ISo the students appearto recognize the analogous situations. Now comes the difficult part.l From our previous experiments you know on what factors the magnetic force depends. Right7 IThere 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 magnetisms Student 2 Oh. Maybe it depends on the separation distances Maybe on the mass of the thing, 'cuz that would be like the number of paper clips. Maybe on the strength of the magnet. No, there is no magnet in the gravity situation. OK. Hang on. Tommy IStudent 11. there is no magnet in this situation Pointing to the gravitational easel, but what might be similar to the strength of the magnet7 Student 1 The strength of the earth7 To build deep understanding of ideas, students need opportunities to transfer tlbe ideas across contexts. Tea< hers need to check on this transfer of knowl- edge to new situations

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510 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM 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, evi- denced 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 sur- rounding 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 gravita- tional 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 be- tween 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 phenom- ena 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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GU DED INDU FY N THE SC ENCE CEASSFDDM 511 Activities in these subunits are more consistent with what is presently sug- gested in cunicula, so they are not described here. But students' preconcep- tions, such as "heavier falls faster," need to be addressed. More mature stu- dents 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 favors affecting air resistance. Explaining Motion of Projectiles Next investigations, especially for older students, can involve under- standing 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 addi- tional investigations into The nature and effects of gravity will build a stron- ger 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 odher teachers, researchers, and curriculum developers. The sequence of activities described is not The only one that could foster learning of The main ideas dhat have been The focus here. Likewise, The dialogues presented are just examples of the many conversations dhat might take place. Teaching and learning are complex activities dhat spawn multiple problems suggesting multiple solu- tions. 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 teach- ers are using. But dlis chapter has not been just about activities dhat 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, cur- nculum, and teaching act as a system consistent widh The principles of How People Learn. We have tried to give the reader The flavor of what it means to teach in a way dhat is student-centered, knowledge-centered, and assess- ment-centered. By looking at The teacher's decision making, we have at- tempted 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 encour- aged to question each odher by asking, "What do you mean by dhat?" "How

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512 HOW STUDENTS LEARN: SC ENCE N THE C ASSFOOM 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 fommative 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. Leaming experiences need to develop from first-hand, concrete expen- ences to the more distant or abstract. Ideas develop from experiences, and technical terms develop from the ideas and operations that are rooted in those expenences. 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 understand- ing 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. Teach- ers can model the sorts of questions that the students will later ask them- selves. 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 stu- dents 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 phe- nomena 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 mOIliTOIillg their own learning, Finally, teachers also need the freedom to learn in their classroomsto learn about both learning and about teaching. NOTES I 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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GU DED INDU FY N THE SC ENCE CEASSFDDM 513 2. The computer-based Dia~,moser assessment system described is available on the web through www.FACET nnovations.com. Thus, it is accessible to teach- ers and students anytime from a computer with web access and appropriate browser The concept and program were developed by the authors, hiinst en and Kraus, Earl Hunt, and colleagues at the University of Washington, FACET Immovations, Talana Inc., and surrounding school districts. It inc udes sets of questions for students, reports for teachers, and suggested lessons to address problematic facets of thinking.

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