The Use of "Marathon" Problems as Effective Vehicles for the Presentation of General Chemistry Lectures James H. Burness The Pennsylvania State University, York Campus, 1031 Edgecomb Ave., York, PA 17403 There has heenmuch discussion in recent years about the need for a systemic change in the nature of the general chemistry course. There have been calls for a drastic restructuring of the content of the course so that it is more relevant, more interestin~,and less of' an introductory physical chemistry course. Despite any changes that might bc -made in the curriculum. however. it is likelv that the - ~ ~ general chemistry course oithe future will still cover a lot of material-that's the nature of the beast, so to speak. Furthermore, the fact that chemistry is an experimental and quantitative science dictates that our students will be required to solve many problems in the course. Whether the oroblems are concerned with the Clausius-Clapeyron equation or the stoichiometry of an important industrial reaction is irrelevant. The mainstream general chemistry students will always have to have good problem-solving skills and understand chemical concepts, models, and principles. Even if the course content is changed, the material will still have to be presented to the students in a way that meets these needs. Is the typical general chemistry lecture the best way to accomplish this? There is a feeling among many chemical educators that things could indeed be done differentlv "~and more effectivelv. Consider some of the common characteristics of the a;chetypal general chemistry lecture. The class is usuallv " laree. - The ~rofessorlectures and the students take notes, a practice-that provides for little instructor-student interaction. The lecture notes and sample problems often duplicate text material. Example problems worked in class are usually the type that demonstrate how to solve a narrowly defined problem. As a result, it is dinicult for students in the class to develop good problem-solving skills. ~
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The Nature of Problem-Solving Much has been written about the nature of problem-solving and its importance in the general chemistry course. Woods ( I ) emphasizes some of the following facts about problem-solving: Many students can recall procedures for solving one type of problem, but this is not problem-solving; likewise, having students see many examples and solve many problems does not help to develop problem-solvingskills. Prablem-solving should be taught in a discipline-specific context and should include applications to real-world prablems. The types of problems chosen by instructors usually focus on knowledge and comprehension-not an application,analysis and synthesis.
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A number of papers in this Journal have echoed similar concerns and have cited experimental evidence supporting these ideas. Lythcott (2)maintains that students can follow rules for solving problems without understanding the chemistry, and stresses that we need to re-think what 'Tnls paper was presented as pan ot a sesslon on 'Allernat ves lo Conferenceon the Freshman Chem~stry-eclLre' at the 1 l l h B~enn~al s t 1990 Cnem~calEoLcatlon. ned n At.anra, Ga. A ~ g ~5--9,
problem-solving is, what purpose it serves in freshman chemistry, and how more students can be enabled to become more successful problem-solvers. The author also states that the problem of students performing well with a woefully inadequate knowledge of chemistry is a result of presenting the student with a '%ere is a sample problem and here is how you do it" approach. Such an approach leaves the students not only with a set of rules that typically work only for uncomplicated problems, but it also leaves them with a lack of essential chemical knowledge. This brings to mind the all-too-familiar student lament, "I can do the sample (or homework) problems, but the ones on the test are too hard." The need to re-think the meaning of problem-solving is underscored by the results of a study by Nurrenbern and Pickering (3).They showed that students have much better success answering traditional questions (for which simple problem-solving algorithms have been taught) than conceptual problems. Their results demonstrate that teaching students how to solve chemistry problems is not the same as teaching the students about chemistry and the nature of matter. Sawrey ( 4 ) extended the Nurrenbern~Pickering study to a larger, more uniform group of students and reached the same conclusions. In a follow-up to this topic, Pickering (5) showed that changes in teaching emphasis can alter the relative success rate of conceptual versus computational chemisby understanding. Kean et al. (6) stress the importance ofteaching students to develop problem-solving algorithms to solve problems-but with the goal of having the students extend the problem-solving skills to solve harder problems. Pestel (8)feels current general chemistry texts contain too many sample problems with worked-out solutions, a situation that encourages mimicry and discourages learning. She also reiterates Woods' point that no matter how many exercises we expect the students to do, doing the exercises will not make the students problem-solvers. Perhaps our emphasis on using dimensional analysis as a problem-solving technique contributes to our students' belief that they understand chemistry if they can solve many limited-scope problems. Students memorize the rules for canceling units, apply them to problems, and get the right answer. Doesn't this mean that they understand chemistry? Lythcott (2)contends that dimensional analysis becomes an algorithm for getting the correct answer without necessarily fostering understanding of the concepts. Brooks (8)says that a good deal of what we teach in the general chemistry course is mechanical. Repeated use of the dimensional analysis approach (sometimes a t the exclusion of other problem-solving methods) can certainly lead students to agree with that comment and to feel that chemistry has no life of its own. Navidi and Baker (9)feel that the benefit of using dimensional analysis to teach students how to improve the percentage of correct nurnerical test answers may be an illusory benefit without an accompanying improvement in their understanding of the subject matter. Volume 68 Number 11 November 1991
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Alternatives to the Freshman Chemistry Lecture For many years, I taught my general chemistry course (typically between 80 and 120 students) using the standard lecture annroach. Althoueh student evaluations were auite positive, I often had the Feeling that things were not going as well as they could. It became apparent that students were not coming to class prepared; they had not read the appropriate sections of the textbookbefore the lecture. Why should they, when I was giving them complete notes for the course? I would often ask auestions about something I had just said and often got blank stares as aresponse; I realized that my students were so busy writingdownnotes that they hadn't even heard what I had said. One of my students said (via the student evaluation) that I had a bionic left arm (I'm left-handed.) After more than a few of these hints, I decided that it was time to restructure the way I was doing things in the lecture. I felt much of what Lagowski has stated recently (10, 111, viz. that education involves the interaction between student and instructor: that lecturing - is not teaching, nor is listening learning; that student participation in lectures should be increased; and that chemistry exams are filled with "... minutiae, which involve important ideas and wncents. hut still. individuallv. onlv .. remesent . pieces of what Ge call chemistry". There have been a number of papers on alternative approaches to the general chemistry lecture. Kolz and Snyder (12) discussed many of the problems associated with the lecture approach and they used brief lecture problems to "break up" the monotony ofthe lecture. Freilich (13)thought that the conceptual and computational aspects of the eeneral chemistm wurse are different enoueh that they sgould be presen&d during two different semesters and should be assigned different grades. Steiner (14) described the approach of having students work on group problems that were of a difficulty level such that any one student probably couldn't solve the problem and used this technique in an organic chemistry course. Pavelich (15) discussed some of the taxonomies ofthinking mentioned by Woods (1) and stressed that students must understand and work with the material rather than simply memorizing it. He suggested various ways that the instructor can create situations that force the students to think at a higher level than that required during a traditional lecture. Genyea (16) used qualitative problems in a preparatory chemistry course because they force the student to think about the nhvsical content of the ~roblem.He also used seauence&e problems to illustraie how a complex problem cbuld be broken un into smaller arts for which the answer could be more easily obtained. 1; a paper that suggests some variations on the lecture auuroach. Brooks (17) reiterated that .. ~tudentscannot process what you say and simultaneously take notes(I81.Hc suggests that m e ofthe best ways to get the students to thinkisto give them a chance to reason out loud and to hear the instructor reason out loud, and he anexcellent way stresses that problem-solvingsessi~~nsare to accomplish tlus and tomake the thrust ofthe instruction active rakher than passive. This paper describes an alternative approach to the general chemistry lecture that uses many of the ideas mentioned above. The a ~ ~ r o a cish meant to be used as a replacement for many, but not all, of the lectures in the tv~icallvlarge sections of the general chemistry course &signed for science and enginee%ng students. .A
The "Marathon" Problem Approach A "marathon" problem is a long, comprehensive, and dimcult problem that ties together many of the topics in a chanter and that is solved toeether hv the instructor and thestudents. The problems Govide Aehicle for introducing the chapter material, exploring alternative problem-
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Journal of Chemical Education
solving approaches, promoting instructor-student interaction during the lecture, seeing how the many concepts and topics in the chapter are interrelated and, most importantly, developing problem-solving skills in the students. The general approach is the following: 1. Cover some of the basic cnncrpts of the chapter in the first oneor t w o l~ctureranddefine neededtcl-rns Handout t h t marathon prbblem and ask itudsntr to thlnk abuut it a n d to try and get started on it. 2. During subsequent class meetings, salve the problem by asking the class for ideas. Where is the student's solution "headed? If a quantity is needed, how will it be obtained? Identifv alternative a~oroaches. .. ldenufy irrelevant dote. As the problem 19 being aolved,dwur.indrrowly defined proble&olving appriaches. If it reouires mare than one lecture to solve the ~roblem (thisis usually the case), encourage students to workan it between lectures. Encourage out-af-classgroup interaction, 3. Use the last lectureb) for the chapter ta cover material that was not part ofthemarathon problem or to summarizethe
problem-solvingapproaches used. The basic idea is to replace wasted lecture activity with valuable time for instructor-student interaction. Why work through one or more sample exercises during the lecture if they are essentially the same as the ones in the textbook except for the numbers? Why waste time writing definitions on the board when thev are in the text? The marathon problem still provides a mechanism for covering these tonics. but it does so in a wav that forces the students to thindand that allows them tosee a variety of problemsolving approaches. The approach will be illustrated by describing two marathon problems and discussing the conc e ~ t addressed s bv each of the uroblems. it should he notkd that since H marathon problem covers a large portion of the material in a chapter, its use could depend somewhat on the textbook used for a given course (we use the second edition of Zumdahl (19)). Most of the general chemistry texts are similar enough, however, that many of the problems can likely be used with little or no modification. ~~
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Sample "Marathon" Problems Example 1 The frst marathon problem to be considered is used for the first chapter, which covers introductory material: A cylindrical bar of gold that is 1.5 in. high and 0.25 in. in diameter has a mass of 23.1984 g, as determined with an analyticalbalance. An empty graduated cylinder is weighed on a triple-beambalance and has a mass of 73.41 g. After pouring a smallamauntofaliquidintothegraduatedcylinder, the mass is 79.16 g. When the gold cylinder is placedinside the graduated cylinder (the liquid covers the top of the gold cylinder), the volume indicated on the graduated cylinder is 8.5 mL. Assume that the temperatures of the gold bar and the liquid are 86 "F. If the density of the liquid decreases by approximately 1% for each 10 "C rise in temperature (over the range 0-50 'C) , determine (a) the density of gold at 86 "F. (b) the density of the liquid at 40DF.
Note: Parts (a)and (b)can be answered independently Notice that this problem covers SI units, unit conversions, significant figures and uncertainty in measurements, temperature conversions, and density. Note also that dimensional analysis can be applied to small suh-sections of the problem, but cannot be used as a general
approach to the problem as a whole. The problem forces students to think about the physical set-up and to make a mental picture of what is happening. The importance of making drawings or mental pictures of chemical situations has already been pointed out (20).The problem also forces students to differentiate between multiple measurements of a given type. For example, it is not uncommon for a student to quickly suggest that the density of gold be determined by dividing the mass by the volume. When the student is asked which mass and volume should he used, however. he or she is oRen not sure. There are masses for the graduated cyhnder, the gold cylinder, and the liquid. It is s u r ~ r i s i n ghow manv studettts thtnk that the volume of the cylinder is 8 . 5 m ~ . The discussion of temperature conversions and the temperature dependence ofthe density usually provides some surprises for the students. Most students believe that ifthe deniitv decreases bv 1% for each 10 "C rise in tem~erature. ~~~~~~-~ then it follows t h a t i t must increase by 1% for each 10 drop in temperature. I t takes a little convincing to get them to realize that the percentage increase is equal to the oercentaee decrease onlv if the oercentaees are small. which is why wecan maketheassumption for this problem. One student rot d o interested in this idea that he derived the correct relationship between the two quantities (d = i l ( l + (i1100)).where d and i represent percentage decrease and increase, respectively. Heblotted percentage decrease versus percentage increase using Lotus 1-2-3 and could graphically see that the values are essentially the same if they were approximately 2% or less, but differed significantly a t higher percentages. The class was very interested in this graph because a student, not the instructor, had worked it out. Most students want to wnvert the Fahrenheit temperatures to Celsius, but a few have the insight to see that the temperature dependence of the density can also be expressed as a 1% drop for each 18 "F rise in temperature. Some students suggest that the difference in Fahrenheit temoeratures (86 - 40 = 46 "F) be used to determine the diffe'rence in Celsius temperatures, but then incorrectly convert 46 "F to degrees Celsius using the normal temperature conversion formula. Many of them don't realize that the 32 "F term should not be used. The nice thing about this approach is that there is time to discuss all of these issues a n d still cover all of the topics in the chapter. I t is invaluable for students to see the reasoning used by the instructor and other students. Furthermore, the importance of them seeing that the problem can be solved by a large number of approaches rather than a single mechanical approach (dimensional analysis rears its ugly head again) cannot be overemphasized. The instructor must guide the discussion, asking why a student wants to do a certain calculation and what the next step will be. Pains must be taken to involve as many students in the discussion a s possible, but the students are usually more eager to participate than to sit back passively taking notes from someone who has a bionic l e e arm. ~~~
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Note: The answers to the problem are (a) 19 g/cm3; (b) 0.80 g1mL.
Example2 The following marathon problem is based on Chapter 4 in the Zumdahl text, which covers reactions in aqueous solution. The formate ion, (CH02)-,ia related to the acetate ion and forms ionic salts with many metal ions. Assume that 9.1416 g of M(CHO& (where M represents the atomic symbol for a particular metal) are dissolved in water. When a solution of 0.200 M sodium sulfate is added,a white precipitate forms.The sodium sulfate solution is added until no more precipitate
forms, then a few excess milliliters are added. The precipitate is filtered, washed, and dried. It has a mass of 9.9389 g. The' filtrate is placed aside. A potassium permanganate solution is standardized by dissolving 0.9234 g of sodium oxalate in dilute sulfuric acid, which is then titrated with the potassium permanganate solution. The principal products of the reaction are manganese(I1) ion and carbon dioxide gas. It requires 18.55 mL of the potassium permanganate solution to reach the end point, which is characterized hy the first permanent, but barely perceptible, pink (purple)color of the permanganate ion. The filtrate from the original reaction is diluted by pouring all of it into a 250-mL volumetric flask, diluting to the mark with water, then mixing thoroughly. Then 10.00 mL of this diluted solution is pipetted into a 125-mL Erlenmeyer flask, approximately 25 mL of water is added, and the solution is made basic. What volume of the standard oermaneanate solutmn ~ 1 1 benwded 1 tu tntratethissolutmntorhrrnd pomt7Thr pnrmpal produrls of thc rrncr~onnrr rarhnnate m n and manganese(N1oxide The information in the first paragraph can be used to discuss strong and weak electrolytes, molecular, ionic and net ionic equations, solubility rules, types of chemical reactions in aqueous solution, limiting reagents, and gravimetric analysis. The identity of the metal M can be deduced from this information, and thus the number of moles of formate ion in the filtrate can be calculated. I t is useful to ask students questions such as "Which quantities will determine the answer to the Droblem?" (manv don't rewenize that the concentrarion of the permanganate solution is one of the factors: others think that the conc~ntrationof the formate ion in the filtrate, rather than the number of moles, is important.) The information in the sewnd paragraph is obviously meant to be used to determine the concentration of the potassium permanganate solution. As a n added bonus, however. i t can be used to discuss titrations (in eeneral). end point versus equivalence point, the color changes during the titration, oxidation numbers, redox reactions, and the techniques for balancing a redox reaction by the halfreaction (ion-electron) method. The third paragraph can he used as a springboard for a discussion of dilution, volumetric techniaues. and applving .. . - the half-reaction method to reactions h basic solution.
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Note: The answer to the problem is 11.76 mL. Advantages and Disadvantages This method addresses many of the problems associated with a oassive lecture aDDroach and uses a number of the ideas f;lr enhancing pr&lem-solving skills that have already been citedin the literature. I t shares the advantages of dramatically increasing student participation and instructor-student interaction, using lecture time more efficiently, allowingstudents to see int&relationships between chemical concepts, and providing a more relaxed atmosphere in the classroom. I t can be easily used for large sections a s long a s the instructor makes a n attempt to involve a s man;students in the discussion as possible: The instructor spends less time writing notes on the board and more time talking about chemist& and problem-solving. The instructor is much less pressed to "cover the material" using this approach, although i t still gets covered. In fad, there is time left over for more demonstrations or audicvisual supplements. There are, however, some disadvantages. First of all, the marathon problems are difficult to make up, and they seem to be more suited to quantitative types of material than what the students like to call "theory". I have not, for example, been able to think of a good marathon problem for the chapter that covers the topics of atoms, ions, molecules, and nomenclature, nor do I see a good way of using this
Volume 68 Number 11 November 1991
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approach to cover atomic theory. Another disadvantage i s t h a t the approach puts more responsibility on the student to prepare for t h e lecture. (Maybe this is really a n advantage.) A student who wouldn't prepare for the "standard" lecture (where he or she i s "taught" t h e material) will be in worse shape when t h e instructor walks into class and says, "Well, what do you think we should do to solve this problem?" A related problem is that the class notes tend to be less structured. A final, but significant, problem is that some students get disconraged by t h e marathon problems. Although they a r e repeatedly told t h a t t h e purpose of the problem is to provide a cohesive framework for discussing the course material and that they a r e not expected to solve the problem immediately, some students still get frustrated (perhaps because they a r e t h e victims of a "plug and chug" a n d "cancel t h e units" mentality t h a t they cannot overcome.) My experience i s that the majority of students like t h e approach, and t h a t t h e advantages vastly outweigh the disadvantages. They appreciate the relaxed atmosphere and the interaction with other students and with me. I
haven't heard about my bionic left arm since I started using this a ~ ~ r o a cCh o. ~ i e of s the marathon ~ r o b l e m tsh a t have been developed a r e available from t h e iuthor.
Literature Cited 1. Wmds, DonaldR. InNeuDinctions for Twehingondkoming, No. 30; Stice, J. E., Ed.; Jossey Bass: San Frsn&eo. 1987, p. 55. 1990,67,248. 3. Numenhem, S. C.: Piekering. M.J Chem. Edue 1987,64,508 4. Sswrey, B. A. J. Cham. ~ d u 1990.67.253. c 5. Pickerulg,M. J Cham. Educ 1990,67,254. 6. Kean,E.; Middlecamp, C. H.; Scott, D.L. J. Chem. Educ. 1988,65,987. 7. Pestel. B. C. J. C h . Edvc 1988.65.444. 8. ~ m & , 0. W J Chrm. Edue 1987.64.53. 9. Nsndi, M. H.; 0aker.D. J. ChemEduc. 1984,61,5Z. 10. Lagowaki, J. J. J Cham. Edur lSSO,67,811. 11. Lagowaki. J.J.J. Cham. Educ 1988.65.559, 12. Ko1z.M. S.;Snyder, W. R. J. Chom. Ed-. 1982,59,717. 13. FreMch, M.J. Cham. Edge 1988,65,442. 14. Sterner,R. P. J. Cham. Edue 1980.57.433. 15. Pavelieh,M.J. J Chem. Educ 1982.59.721. 16. Genyea. J. J. Cham. Educ lW3,60,478. 17. Bm0ks.D. W. J. ChamEduc 1984.61.858. 18. Lhdeav. P. H.: Norman. 0. A. Humon Informfion Pmssiw. 2nd ed.; Academic
2. Lmcdt,J. J.Cham.Educ
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Startinewith - ~ - - ~ theseatemher 1991issue. the JournalofChemical Education will be aublishedurimadv bvan in-house desktop publishing process. Since papers'suhmitted f&m now on will be scheduled-for forafter chat time, the Journal is requesting that authors prepare their papers in one of the following personal computer formats whenever possible. The electronic text and graphics from papers in these formats can be used directly to produce the typeset version. Do not, however, submit a paper on disk. Wait until the reviewers have accepted the paper, and then send the final version on disk. At the time of acceptance, authors will receive an instruction sheet and form to accompany the disk they submit. Authors should still follow the instructions outlined in the Notice to Authors (last published on page 535 and-536of the June 1991issue) for the original submission of papers. The list below indicates the formats for text and graphics accepted by Ventura Publisher, the Journal's desktop publishing system. We will be using it in the MS-DOS environment, but we have the capacity to translate many Macintosh formats. If a system does not match any of these formats, the text can be saved in ASCII (text) format by man" oroerams and sent in that form. Anv. mestions about formats should be directed to Debora Bittaker at . (mj4ii-i732. While we encourage authors to use the followingformats for preparation oftheir manuscripts, computer compatibility will have no bearing on whether a manuscript is accepted. Papers that are not electronically compatible will be scanned or directly typed into the system. ~~
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