Everyone Wants to be a Model Teacher Part II: Patterns and the Organization of Ideas C. L. Schrader Dover High School. Dover, OH 44622 The first part of this article (J. CHEM. EDUC., 61, 1001 (1984)) emphasized my motives for carrying out model activities with my students. In it I described several of the activities I use with mv students to develon a sound understanding for the diffeiences between observations and inferences. In this second article in the series. I will exnand upon the techniques and share with the reade; activities that L s e to heln students to learn to recognize - patterns and to create modeis to explain patterns. Test Tube Observatlons One week after the completion of the candle activity, the students are asked to record observations for four racks of seven test tubes, without touching them. Students are given a lab sheet that contains drawings of the test tubes and their labels with space provided for them to record their observations within the test tubes. The test tubes contain aqueous solutions of the following salts:
which are arranged in random order. Students are given 20 min to complete this activity, after which the class as a whole discusses the observations chat were made. Emphasis is again put on distinguishing observations from inferences. A typical exchange between students might he, "I observed that some of the test tubes contain blue liquid." The other objects, "You don't know that the test tubes contain a liauid without handling them. The test tubes may have been painted so they appear to contain a liquid, or the test tube may contain a blue gelatin-like material." I ask how can we tell which one of these plaus~blealternative inferences is correct? The response, "Take a test tube and shake it then remove the stopper and look inside." indicates that the students know that questions of this type are answered by doing experiments. Note that in this and in vrevious exercises, I habituallv ask students for alternative hGotheses. One of the charac&stics of formal reasoning is that one systematically considers all possibilities. This requires practice. Furthermore, it is impossible to consider all possibilities in situations that are unfamiliar. In this simple experiment, however, students are able to consider other possibilities, because they have all the factual knowledge necessary to do so. Once the observation part is completed, and i t has been determined that the test lubes contain liquids, I ask the sttidmtstoreport any patternsthat they noticed in theirobervations. natterns test tubes with nickel ~ ~ Several ~ ~ such ~ as. "The ~ in them are green," are suggested. The students have just finished memorizine the svmhols for the elements and are pleased to recall t h a r ~isi the symbol for nickel. If no student challenees this observation. I ask how it is known that those test tubks have nickel in thkm. I next ask for other olausible inferences. A student will suggest, "You put green food coloring in several test tubes and nut Ni on the label of those. blue food colorine in other test Lubes and Cu on the lahel of those, etc." Another student said, ~
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"You filled the test tube with some colored liquids you bought and then put Cu on the label of all the ones that were blue." Other inferences typically include, "You bought magic labels and when the labels are put on a test tube, the color changes, one label causes ereen. another lahel causes blue color. etc.." or, .'You houghtyhe tist tubes like this, and even yo" don;[ know which of the hvootheses sueeeited are true." (This is a very thoughtful and-perceptive &ment.) Magic Label Model The maeic label exolanation which erew out of the ~revious exchange &ads to di~cussionof the way our cultural a'ttitudes shaoe our vercevtions. Because we live in a scientificallv and terhnolog~call.vhriented society, we tend to believe thatihere is a . vhssi(.al or scientific exvlanation for "mapical occur. rences." Despite the fact that my students say they do not believe in magir, many of them are interested in ur believe in ghosts and ESP. "Science, Good, Had, and Hogus" by Cardner (1)is an excellent analysis of science and pseudoscience and includes chapters analyzing ESP, psychic phenomena, and talking animals. The accomplishments of a sufficiently advanced technology would appear to us to be magical, because if they do not appear to be magical then we can imagine some scientific explanation for them. In science fiction, accepted scientific laws may apnear to be violated. For examole. on Star Trek. the Enterorise ioutinely travels many times the speed of light. I t is noipossible for a material obiect to travel faster than the soeed of light if Einstein's specii theory of relativity is correct. 6aptain Kirk and his crew often encounter sentient beines who have extraordinary power. I compare these apparent s,iolations of natural 1nu.sto the discovwv of radionrtivits at the turn of thr century. Scientists were astonished when radioactive substances were found to produce enormous amounts of energy with no detectable mass change or observable chemical reaction. I particularly like to mention that Kurt Vonuegut, Jr.'s idea of ice-9 crystals in "Cat's Cradle" ( 2 )arose from a discussion of work his brother was doing on seeding supercooled liquids with tiny pure crystals. I consider this tie with science fiction and the reference to Star Trek and "Cat's Cradle" important because i t helps students realize that the logical operations utilized in science t o make sense of physical observations can be used in the analysis of events in their everyday lives. A common criticism of science instruction is that students see no relationshio between what they are taught in chemistry and what the; exnerience outside the classroom. Here is one nlace where i t is easy to make connections. A Final Step
In the final step of this activity, the students are asked to evaluate the explanations offered to determine which one is correct. The reasons they give for their choices can be very revealing. One student said, "I think the test tubes with Ni on the label contain nickel, because nickel is a chemical and this is a chemistry class." Another student remarked, "I think you want to trick us, so you put a green liquid in some test tubes and put Ni on all those labels?
When this discussion is completed and I begin to move to a new topic, a t least one student will ask, "Which explanation is correct?" I don't answer the question directly, but rather explain that if scientists have two explanations which are equal in accounting for experimental results they choose the one that makes the most successful predictions. If both are still equal, we use Occam's Razor, which means the explanation which is simplest or which requires the fewest assumptions is chosen. I t should he kept in mind that the purpose of such activities is to develop the habits of thought upon which more complex analysis will be built. Although this exercise may seem trivial, it requires the student to be creative and to consider all possibilities. "If.. . , then . . . , therefore" reasoning is required to connect the observations to the inferences. Extending Information to Subsequent Experiences Two experiments that are related to the colored liquids are also carried out. In the first experiment, students are required to prepare enough of a solution of a given salt to fd two 250-ml stock bottles. (Among the solutions prepared are NiC12, Ni(N03)~.CoCIz, CoSOq, and Co(NO&.) These solutions will be saved for use later in the year in a qualitative analysis unit on unknowns. Prior to this activity, the students have learned the definition of molarity. They must apply this definition t o carry out this preparation. This activity offers students concrete experiences in: 1. estimating the volume of solution in milliliters needed to fill the stock bottles, 2. calculating and measuring out ut specific number of moles of the aolute, and 3. observing the process of dissolving this solute in enough water to make the desired volume of solution.
After preparation of the solution each student is asked to observe and discuss other solutions with tbeir classmates. 1nvariahly.a student will state, "All thesolutionscontaining nickel are green, and all those containing cobalt are red. Does that orove that the chemiral exidanation iscorrect'!" Of course i t doks not, but this observation does show the need and usefulness of a chemical exnlanation. In the second experiment, five carbonates including copper (11) carbonate and nickel(ll) carbonate are each reacted with four different acids. he students learn that each reaction produces bubbles of a gas that, after being passed through lime water, is identified as carbon dioxide. In the reaction with sulfuric acid, a t least one student will comment that the solution above the remaining nickel(I1) carbonate is green. This must mean that the chemical reactions produced water, carbon dioxide, and a solution containing n&kel\ll) auliute which is green-the same color as [he liquid in the test rube labeled N&o~.This provides an opportunity to discuss the importance of relating information from one experiment to another. In fact. one of the limitations of artificial intellicence (thinkine cornp&) is the difficulty of programming ;he re&niti& of these subtle relationshios. 1)ouelas Hofswdter. in his recent book, "Goedel, Escher a i d ~ a c h y Eternal ~n ~ h d e Braid" n (3)explores this theme in exquisite detail. ~
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Martln the Martian As an additional example of model-building which begins with concrete observations, recognition of patterns and an assumption of the underlying cause of the pattern, the fable of "Martin the Martian" is read. The fable of Martin the Martian first appeared in the CHEM Study (4) materials as an illustration of making observations, collecting data, searching for regularities and proposing a model to explain the observed patterns. This model also can he used to make predictions. Martin is not familiar with burning, but observes that tree limbs, fence
posts, and wooden poles burn while rocks, glass marbles, and cement blocks do not burn. From this data, he deduces that burnability is determined hy shape and that cylindrical objects burn. L'sinn this model, he then ndlects iron pipe, soda bottles, and a car axle while rejecting a wooden door and a box of newspapers. During the long, cold night which follows he revises his model to: wooden objects burn. Seating Arrangements On the fust day of the school year, the students were seated alphabetically, according to tbeir last name, then first name and initial. Students are also asked to fill out a questionnaire including the typical personal descriptors of name, address, phone, social security number, height, weight, hair and eye color, and grade in school. I also request some unusual information including shoe size, names and ages of siblings and parent, family car type, favorite element, color, car, sport, soft drink,gum, movie, sport hero, and book. Two weeks after the class has read the fahle of "Martin the Martian." I assign new seats to each student. I ask them what model was usedin the former seatine arraneement. Nearly everyone knows they were hut I require greater precision in the seated alpha'betical~~, statement. Thereare four rows withsixstudents ineach row and they must state that the students are seated alphabetically according to last name, the first name and initial beginning in front and from the teacher's left to right. We agree that all suhsequent seating arrangement will be made in the same way, e.g., from the teacher's left to right and from the front to back. I then challenge the student to find the model used in the current seating arrangement. I usually use something simple like arranging them according to their age or from shortest to tallest. Students are more successful.if they can look around the room and get immediate clues. Once the model has been discovered, I ask how i t was arrived at. A typical reply might be "I looked around the room and noticed that the shortest people were in front." Observations of students'heights and orderine of students accordine" to heieht from shortest to tallest corresponds to collecting and ordering data. Two weeks later, 1 again assign the students new seats,still using a simple scheme, such as numericully according to the last four dieits ot'their tclephnne numher. I use the personal profile sheet I collected the first day to generate these models. Since there are no immediate visual clues, the students must collect data and look for a pattern. Students are given up to 20 min of class time to collect data. If a t the end of that time they have not found the model, they are encouraged to continue to generate and test models of their own. In the case of the new seating arrangement, the model is not readily apparent, so students must collect data a t random initially and usually over a small range. A student may ask students nearby for their telephone numbers and try to discern a pattern. If the telephone numbers for several students show a pattern, the student will extend the range of data. Occasionallv. a student will find a model that works for all but one or two Eases. I have students ask those who do not fit the model to cbanee their seats to make the model work. In a class discussion, I tell the w r y i g f the medical research scientist who colored the skin of the mice to ret the data he needed so his research project would get addkonal funds, but who subsequently was exposed as a fraud (I). I also recommend they read C. P. Snow's hook, "The Search," which is a fictional account of a similar occurrence (5).Many other seating models have been used including age of oldest sibling, total age of all siblings, the sum of the last four digits of their telephone numh&, in order of the wavelength ut Their fawrite ahir, and alphahetirally according to thrir mothers' muiden names. Sclentlflc Attitude The seating arrangement activity presents a good opportunity to discuss a list of scientific attitudes written by Nay ,Volume 61
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and Crocker ( 6 )that includes objectivity, open-mindedness, honestv. - . resaect . for exoerimental facts. willineness to chanee opinion, skepticism, a questioning attitude, sekcriticism, tKe belief that the universe is not capricious, and the power of logical reasoning. Scientists believe that the truth will emerge so that no one can maintain a fraud indefinitely. A different approach to the same problem is for the student to assert that an error was made in assigning the seats. Perhaps there is an anomaly, or the data are incorrect. This is similar to Mendeleev's placing of elements in the periodic chart according to their chemical properties and not their atomic weight. Mendeleev assumed the atomic weights were inaccurate and that when better measuremenh were available the order of the atomic weights would agree with his placement of the chart. Anomalies do, in fact, occur because some students write down their telephone or social security number incorrectlv or chance their favorite color. This exercise als; provides some useful social interactions among stu(lents. The data-collecting process allows students
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t o obtain information about each other and generates discussion. This activity is repeated once each six weeks and the class can earn extra credit as a -aroua . bv. finding the correct seating model. Doing this as a group project can &ow students that science is a human endeavor and sharing of data and comparing theories are important parts of the-process. The development of computer chips or new drugs is not done by single individuals but involve many people and we all share the rewards. In each of thwe modeling exercises I give students 15 to 20 min of class time to formulate models and to collect data to test the model. Llterature Clted (1) Gardner, Martin. "Science: Gmd.Bad and Bagus,"Avon Boob, New York, 1981. (2) Vonncgut, Kurt, Cradle." Holt Rmehput, Winaton. Inc., N m York, 190.
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(3) Hofstsdter. Dough, R.. "Doedei, Escber and Bath: A" Eternal Golden Braid."Basic Books, Inc.,New York, 1979. (4) Perry,R W..Steiner, L. E.,TeUefacn.R. L., and Dcetz. P. M..''Chemistry.~ental Foundstians"(a Chem Study Revision), Prentice Hall, pp, 7-8.1970. (5) Snow.C. P.."The Search? Peneuin Puhii8hins Co.,~~ 1975. (6) Nay,M. A,, and ~roeker.'~. ~ . , k v e n t o of w the Affective Attributes of Scientists,.' "Science Educstion."pp.6 1 4 2 , Jan.-Mar., 1970. v~
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