view from my classroom Final Analysis-Rethinking
edited bv FRANK CARDUL~ Niles Township High School 9800 Lawler
Skokie, IL 60077
an Age-old Practice
Robert Becker
Kirkwood High School, Kirkwood, MO 63122 Final Exams The very mention of final exams evokes strong feelings of fear and anxiety in our students. And for those of us who have graduated into the real world, the memories of finals are hardly fond ones! A final exam is, after all, a very stressful way to bring closure to what might otherwise be a very wonderful and positive year of learning, cooperation, and discovery. As teachers, we cannot help but feel uneasy, and, indeed, somewhat guilty, watching our students sweat their way through the chemistry final exam: isolated, quiet, without any access to information other than what they managed to cram into their heads the night before. Throughout the course, the students have been encouraged to work together in a very open, sharing, and cooperative way, teaching each other in labs, on homework assignments, and during classroom discussions, when new concepts and equations were being introduced. Why would they then be required to take a final exam with a format diametrically opposed to everything we have been preaching and practicing all year? On the other hand, there is definite value in having students bring together what they have learned during the year and apply it in a comprehensive and meaningful way. Furthermore, handson lab work always has been a major emphasis during the year. Should it not be emphasized similarly on the final exam? Yet how can a single teacher possibly set up 25 to 30 isolated lab stations and supervise them while proctoring the rest of the exam? These dilemmas have left me in a quandary since my very first year of teaching. About three vears ago, - . however, I hit uoon an idea that resolves some bf these issues-an open-book, open-notes, group-work, lab-practical final exam.' Although none of these concepts is by itself new, I use what I believe to be some different twists and innovations that have made the activity especially effective and v a l u a b l e s o much so that I cannot see mvself ever eoine back to the traditional exam system. The ;her chem;stG teachers in my department have all tried this approach and have liked i t a lot. My conviction and their positive feedback a r e what have prompted this article. Why open-book, open-notes? Chemistry is not about memorization, although that may be the impression many people have, owing to their beloved high school chemistry teacher who made them memorize the entire periodic table! The fact is, reference charts and books always will be available; so why invent contrived, high-anxiety situations where these tools are not available to students just when 'Althouoh orouo work (AKA:coooerative learninol is nothino new. esoeciall;in"a liborator; class sich as chemistLthere has-been ,. ~, ~,~~~~~~ very lillle wrinen abo4 I n rnrs Journal Mosl art c es reference0 Jnoer cooperative eoLcal on penatned lo cooperalton oelween n s l b s uons (1) An c es re aten lo exams are plentdJI, oLr mosl f o c ~on defining exam content rather than overhauling the exam format (2,3).
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they need them the most? Instead, let us emphasize the access, understanding, and application of information, not simply the retention. To be sure, most of my students do end up memorizing, for example, that there are 6.02 x loz3particles in a mole, but this is invariably the result of repeated mention, discussion and application throughout the year. If 20 years down the road, I should run into one of these students on the street-one who has become, lets say, a top-notch computer programmer, and if during the course of normal conversation, i t becomes obvious t h a t her recollection of Avogadro's number is not what it used to be, do I consider myself a failure a s a teacher? Was the time she spent in my classroom a waste? Of course not. But one would hope that if she ever needed to recover this information, she would know where to go to find it, and be able, if necessary, to reteach herself how to apply it. I n the long run, isn't this what we really expect out of our students anyway? Isn't t h i s what education and empowerment are really all about? So why not have our final exams based on these same expectations? One other benefit of this format of testing is that when the students know from the start that their year-end exam is to be open-notes, they are much more likely to take good notes and to keep them well organized, along with their quizzes and quiz revisions. They begin to see their notetaking not a s a quick-fur means of memorization, hut as the creation of a useful database, one they may keep even after the exam is over! Why group-work? The main benefit of group-work is, of course, its emphasis on cooperation. My exam is written to cover a wide variety of topics and a t a wide variety of difflculty levels. By design, it is far too long for any one individual to complete. Consequently, students realize it is in everyone's best interest to work together, dividing the tasks according to each student's expertise, working in pairs or individually on different parts of the exam, then bringing it all together and criticallv reviewine and revisine one another: work. To watch &dents wo;king together this wav on their last dav of class: the challenge. the oroblemS a l k g , the frustration, the high-fives (i% notAkidding) and the groans, and above all else-the sense of teamwork, of collective and individual accomplishment. . . it never fails to amaze and move me, a s do many of their dialogues (Hey guys, we've got to find this thing's density. That's easy: mass over volume, go weigh it. I know, I already did, but how can I find the volume of this thing? Did you try water displacement? I can't, we weren't given one of those cylinder things. How about length times width times height. . . is there a ruler? Oh yeah. . . Should I use centimeters or inches? Centimeters, definitely. But wait, it's not rectangular. . . Hmm. . .I. Group-work is great; it is hard to argue otherwise. But how does one establish who should be in which group? Alphabetically? Randomly?'.By different learning styles? Let
them choose their own groups? I wrestled with this issue for a long time before deciding on a grouping strategy that is perhaps somewhat unconventional (and if I lose you with this, I am sorry, but I am convinced it is the most effective wav). On their final exam.. mv " students are erouned homogeneously, not heterogeneously. That is, they are ranked bv their a a d e s . and the tov fifth of the class is uut together i s one Goup, the next fift'h together as the second group, and so on, so that students are grouped together with others of like achievement. Note the use of the word achievement rather t h a n ability. This is a distinction worth emphasizing with students-after all, their grade in chemistry is determined by their achievement, not their ability. Either way, a stude& rank is certainl; no reflection on his or her character or worth a s a human being. Most advocates and practitioners of collaborative learning emphasize mixed-achievement grouping, and in many situations that method is desirable. But in the context of a time-limited final exam, homogeneous grouping seems more appropriate. In mixed-level grouping, many students feel cheated or taken advantage of. The low-performing students often feel condescended to. and thev" a r m e that ~ anything they contribute probably kill bring down their erouv's - . score. The hieher-uerformine students. on the other hand, feel it is easier ahd faster f& them to db a problem themselves than to try to teach someone else how to do it. With such a large portion of their grade riding on the exam, it is hard to argue otherwise. Like-achievement grouping solves many of these issues. The students see each other as veers. and when erouvs . are posted, the students' names within each group are arranged alphabetically, so the individuals never reallv know hoGtheycompare to-their group-mates, only that they are considered on a n equal achievement level. All students work equally hard, bkcause they all feel ownership and responsibility for their moups After all. this . performance. . grouping system more closely approximates real-lifesituations. Teachers working i n committees, construction workers teaming together-to erect a structure, scientists collaborating on a research project: they are all more likely to find themselves working among peers of similar performance records. There always will be some degree of variation within the group, of course, and a wide variety of interests and fields of expertise, no doubt, but those individuals would not have gotten where they were unless they had all proven themselves to some common level. Fine, you say, but this homogeneous grouping system just sets up the low-achieving students for more lowachievement. If thev are erouved . toeether with others with equally poor track records, their groups grade is almost predetermined to be a low one. Why should they even
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try a t all? Here's the catch, and the concept that really makes this whole project fly. To compensate for the various achievement levels of their group mates, each group is graded on a separate curve, in comvarison to those erouos in the other chemistry sections of the same level. 1nothkr words, a low-achieving group five is comvared onlv to other group fives from the oiher sections of the same co&e. The other groups are judged likewise. If a group scores the highest for their level, they generally earn a n A, regardless of that groups track record coming into the exam. This greatly motivates the lower-achieving students, for they realize they have a s much chance of getting a n A on their final exam a s does anyone else in theclass,but also it motivates the higher-achieving students who might otherwise be slacking off and e x ~ e c t i u eto breeze through the u final. They realize they are now be& compared to the topachieving students from the other sections. and thev will have to work equally hard to earn their A. l'f students who have been placed in a top group argue it is unfair that they should have a tougher grading curve than the others, they are reminded that they have been given the advantage of being to work with and receive help from group-mates ~ ~ able ~ who have a better track-record than others. Not using separate curves to compensate for this would be unfair. Most students perceive this system a s a n equitable and le~ - --~ ..o .. f eitimate an-aneement. All students have eaual chances acing the exam; all students have equal chances of failing. The rationale for including lab activities on a chemistrv -" final exam is self-explanatory and really quite consistent with the entire philosophy described above. Rather than asking essay questions of the type "How would you determine. . ." or "What measurements would you take to. . ." why not just have the students do the labs, not hypothetically, but hands-on, the way . thev. have been doine labs all Often space andlor time limitations prevent;eal labs from being incorporated into a final exam, but with the students working in groups and with the utilization of microscale lab techniques (some of which will be illustrated below), it possible to include a s many a s six or seven separate lab activities comprising 20-25% of a n hour-and-ahalf final exam. The exam itself is comprised of 30 questions, each worth four points, regardless of the degree of difficult Below are some sample questions taken from past exams. ~
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1. What is the correct name for FeF3? (Answer: iron(II1) fluoride) This is just simple, straightforward nomenclature, especially because the students have books and notes available. Still, some will forget to specify iron(III), and some
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Robert Becker is generally regarded as one of the most creative and popular chemical demonstrators in the country. A native of St. Louis. MO. Bob received his B.A. in Bioloav and his Masters Education ,~ ~ ~ -in ~ - ~ - from -, from Yale Universitv in 1983. Washinaton Universitv in 1990. After teachina in Greenwich Cnnnertic~~t for six venm hn moved Gack to St. LO& withhis wife, Kathy and his two daughters,Jenna and Amariah. He has taught at Kirkwood High School for the past five years. Becker currently teaches a first year general chemistry course and a second year Advanced Placement course. He also coordinates achemistry outreach program in which high school students travel out to the local elementaw schools and conduct demonstrationsand ,% 1 I- lab activities with 4th wade students. Becker has developed and published several unusual demonstrations and micro-scale lab experiments in Chem 13News, the JournalofChemicalEducation, the Chemmunicator, the Octet Gazeffe,Chemunity News, and the Science Teacher He also has conducted approximately eighty work-shops and presentations across the US and Canada. His hobbies include cycling, camping, windsurfing, gardening, and of course, chemistry. Becker received the 1992Catalyst Award, given by the Chemical Manufacturers Association, and a regional American Chemical Society award in 1994. ~
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will spell the cation flouride [sic]. (Even my dentist makes this mistake, seriously, and I scold him with the same mnemonic device I use on my students: U 0 it to yourself to know how to spell fluoride.) 2. What is the p H of 0.00725 MHCl solution? (Answer: 2.140) Again, rather straightforward if they know how to apply the concept of logarithms to pH problems.
3. How many structural isomers of C5H12O are there? (Answer: 14) This question is considerablv more involved than either of.the tkst two. It twts theirhhility to draw d i d itructural formulns, rc!cormize whirh are isomers and which :ire repeats, and to exhaust all possible arrangements for the alcohols a s well a s for the ethers-hopefully in a systematic way. Partial credit usually is awarded based on how close the answer is: 14 = 4 pts; 13 or 15 = 3 pts; 12 or 16 = 2 pts; 11or 17 = 1pt. 4. How much KC1 can dissolve in 6 5 g of water a t 83 "C? (Answer: 34 g) The solubility curves are in their textbooks, and they should know where to find them. Answering this question requires the application of several skills: 1. interpreting a solubility curve and interpolating to 83 "C; 2. setting up a proportion (or unit analysis) to adjust for the given 65 g of water, since the curves are all per 100 g of
tacular flower-like symmetry with brilliant colors (Fig. 2). Each lab station contains these two Dens ~ l u asn extraneous third pen, so the students must krst ietermine which two pens to use before they can begin to replicate the pattern. 7. Obtain from the instructor a set offiue solutions (A, B, C, D, E1. Observe them and how they react with one another on the provided spot plate. Return the set of solutions along with the cleaned spot plate a n d obtain a second set of solutions (1,2,3, 4, 51, identical to the first set, only in scrambled order: Determine which number corresponds to which lette,: WARNING: Safety goggles must be worn at all times. Also, once you return the first set, you may not get it back. This is similar to a lab done a t the beginning of the year (actually, on the very first day while seated right in their desks!). What makes this lab esneciallv convenient and easy to conduct is that it has been microscaled-and plsstirized! The five solutions must trr di.itinrmiahahl(! hv the , reactions they have with one another (such as: 1M H C ~1 M Pb(N0dz. 1M NaHCOn. 1M KI. and 1M HNOn). Thev are placed in cut-off thin-ktem pipets, which a; housed in audio cassette boxes-a technique learned a t a workshop given by microscale pioneer Tom Russo. A few half-bulbs from a slightly larger pipet are wedged into the cassette slot to serve a s holding cups for the solution pipets. The spot plate is a small rectangle of stiff acetate from a n over-head transparency, which can be slipped into the box behind the bulbs (See Fig. 3). Clean up involves ~
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water; 3. reporting their answer with correct units and to the appropriate number of significant figures.
5. How many protons are there all together in a molecule of octane? (Answer: 66) Although they have never had a question like this during the school year (and, indeed, it is a rather unusual question), they have studied molecules and atoms, organic nomenclature, and the concept of atomic number and subatomic particles. This question requires them to pull all those concepts together. 6. Taped to the board is a flower-like pattern made by radial chromatography, a technique you explored earlier in the year: Using only the materials a t your lab station, reproduce the flower pattern a s precisely a s possible. You haue only sixpieces offilterpaper; so use them wisely. Staple your best attempt to this sheet.
Early in the year, the students do a n open-ended radial chromatography activity a s a take-home lab with their parents. For anyone unfamiliar with this technique, see the December 92 issue of this Journal (4). I t is quite effective to use two black pens: A (vis-a-vis) and B (Expresso) and spot the paper in a n AABAAB. . . pattern of dots in a circle (See Fig. 1 below). The chromatogram has a spec-
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acetate spot plate half-bulb holding cup
Figure 3. Set-up for question 7. just a wipe of a paper towel! 8. Use the volumetric flask prouided to make up a 1.35 M solution ofNa2S04. Bring it to the instructor for a molarity check; you must be within 3% to receiue full credit.
A beaker of sodium sulfate and a plastic spoon are located a t the center lab station beside the electronic balance. An open cardboard box on its side serves a s a windshieldlprivacy-booth around the sides and hack of the scale, so groups are not tempted to copy what they may see another group do. Like the other lab activities, this evaluation is completely authentic and outcome-based. The molarity is checked a s they hand it in by comparing its density to that of a standard 1.35 M NazS04 solution. This can be done by massing a precise 10.00-mL portion of the solution or by transferring the solution into a cylinder and testing it with a sensitive hydrometer (with a mark drawn right a t the target density). The hydrometer is certainly more dramatic, and a reliable and sensitive one can be made easily by placing some mercury in a thin-stem pipet and sealing the opening with some hot-melt glue. The amount of mercury can he determined easily by trial and
error. Once t h e pipet floats with its stem approximately half-way submerged, seal it and mark it. 9. Determine the density of object X.
Object X can he anything you choose, but it should be the same for each group. Last year, right triangle blocks were used. W e had done L x W x H volume calculations for rectangular solids i n various situations throughout the year, b u t we had never dealt w i t h triangular solids. Many groups solved this problem correctly, either by carrying over what they had learned i n math or by just recognizing the shape to be exactly half of a rectangular solid. 10. At the lnh stotion you u.rl/ find solutions G , H,uud I\: .M~nsuwout 10 drops of G i n f oa test tuhr, and measure out 8 drops o f H and 2 drops of W into a small beaker: Pour the test tube into the beake,: swirl u i ~ o r o u.s .hfor 3 5 s, then ohwror for o whrlr. Rlnw out and&kr dry thr Iesl luhv nnd beoker: and thrn t n to determine u hat proportions of G, H, and W will cause the final solutionto change colorsprecisely 30.0 s after they are mixed. Credit will be awarded based on how close you come as timed by the instructor (see table). You may practice as many times as you like, but you will be allowed only three attempts i n front of the instructor Only your last attempt will count. period 20-40 23-37 2&34 2832
credit (pts)
(5)
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G and H are two clock reactants ( I use G = NazSzOsHC1-starch, H = KI08, though any clock reactants will do). T h e concentration should be dilute enough so that straight equivolume mixing of G and H changes from colorless to dark blue i n 6-10 s. W , of course, is water. My students do not cover kinetics i n their first year of chemistry, so this entire activity is completely new and open-ended to them. I f they have learned t h e principles of the scientific method, however, and i f they approach the problem i n a systematic manner, they usually succeed. Exam Logistics
1. Students are told about the exam format early i n the year:
This encourages good note taking, not just for the sake of t h e individual, but so they may be an asset to their group.
2. A week or so before the final exam, the students are told who their group-mates will be. They also aregiven some time during class t o get into their groups and discuss strategies-who will take what units to review and become the group's 'expert" on that unit. Most groups see that collectively they have most, i f not all. of the bases covered. and t h e individuals see that they will be able to contribute constructively to the group effort and be evaluated on their streneths, rather than on their weaknesses.
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3. On the day of the exam, desks are armnged into five small, inwardly-facing rings spread out amund the roomusually one in each of the four corners and one in the center: Each ring of desks has a nearby lah-station with all the necessary supplies. I f lab benches are not a part o f the classroom, movable tables or carts work just as well, with jugs of water and wash basins taking the place o f sinks.
Figure 4. Method for curving the grades.
4. The students come i n and sit i n their assignedgroups. Each group is handed a folder containing five copies of the final: four of which have DO NOT WRITE ON THIS T E S T written all over t h e m w i t h a bright highlighter marker. T h e fifth is t h e copy upon which they are to put their names and write their answers. [ I t is wise to mark t h e folder and each test copy with t h e groups number t o avoid mix-ups when they turn them back in.] Any work done on separate scrap paper must be transferred neatly onto t h e main copy i f i t is t o be counted. 5. The students work for the allotted time period-ne and a half hours, i n my school's case. W h e n the time is up, they turn their folders back in-all five copies, with t h e one t o be graded on top. One can confirm at a glance that all copies of the test have been returned. T h e n t h e top copy i s simply removed from each folder and replaced with a new one. The students also are instructed t o leave their lab stations just the way they found them-minus, of course, any depleted chemicals.
6. There are, of course, many ways of curving the grades. The simplest would be to have the highest score at each leuel be the denominator for that leuel. For example, with five chemistry sections taking t h e exam, i f the group one raw scores were 54,84,70,79, and 46 out of a possible 120, the 84 would serve as the deuominator for each of these five groups, and their curved grades would be 64% D, 100% A, 83% B, 94% A, and 55% F, respectively. Presumably, the group two raw scores would all be somewhat lower, with a high of say, 77; this would then serve as t h e denominator for curving each of the level two groups. Likewise for all the other levels. But what i f some group two just happens to do extraordinarily well-say 87-outscoring even t h e best level one group? Is it fair t o apply this denominator (87)to each o f t h e other group two scores, effectively giving level two a tougher curve than level one? And what i f ,on the other hand, all the level two groups do very poorly-say 32,34,31,32, and 33-is it fair to use 34 as t h e denominator, thereby giving each of these groups an A? T h e fact that a small number of data points may deviate quite dramatically from t h e norm i s something with which the students are well familiar, as is the solution to this situation: apply a best fit line. Simply plot the scores for each level, draw a best fit line for the high scores, and then use that lines intercepts as the denominators (See Fig. 4). Literature Cited
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