The Name's the Game in Problem Solving Janet N. Ryan Math-Science Specialist, Southern Arkansas Unlversity-El Dorado, El Dorado. AR 71730
Trying to help students develop an approach to problem solving is probably the most frustrating aspect of teaching introductory science or math courses. Every year many hooks and articles are written and millions of cubic meters of air are expended in this effort, with questionable success. Working on a one-to-one basis through our Special Services Project, I've observed many times that students who may be unable even to start setting up a chemistry (or algebra) problem on their own will suddenly work correctly through the entire procedure as soon as I mention the specific type of problem with which they are dealing. Pointing out that two temperatures in a Gas Law exercise generally indicate a "Before-and-After'' problem rather than "Find-theUnknown", or distinguishing between the difference of squares and difference of cubes in an exercise on factoring, provides the key necessary to start the solution process. Initially recognizing the pattern or type of problem and then applying an appropriate name to it appear to he essential for accessing memory and therefore to be preliminary steps in the problem-solving process. Support for the idea that a name is necessary for recall comes from a recent report by Hart, Berndt, and Caramazza ( 1 ) on a natient recovering from stroke. Resultant brain damage dppeared to he restricted 11, un inability to name or cnt~eorizeindividual fruits and veeetables, while the ability to name and classify items from other grbups was not iipaired. However, when he was aiven the name of a particular fruit or vegetable, he could correctly identify, categorize, and describe its properties. Commentina on this report, Marshall ( 2 )says, ". . this knowledge coula only be accessed by the names of exemplars, names that the patient cannot himself elicit with normal facility. I t is as if the name is the key to knowledge . . .." I think these observations are relevant to chemistry students' attempts to sdve problems. The ability of a single term to call un a chunk of information or an entire orocedure f r m long-wrtn mLmury is wniistt:nt with rtlgnitive themy. Cwnirive theor\, rind its a r d i c a t i m 11) urd)lem iolvinr ha\.e been reviewed iecently b;'~rederiksen (3). Eylon an2 Reif ( 4 ) have shown that, when material is organized hierarchically-under headings and subheadings that become progressively more specific to the task-student performance improves. Thus, the name may serve as a heading to retrieve information essential to solving the prohlem at hand. The name by which a particular prohlem is identified and
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labeled should be used consistently in order to provide a familiar heading for searching through memory for relevant information. However, the name does not have to he rigorously accurate. In fact, "Before-and-After" seems to be easier for students to remember and use than either General Gas Law or Charles's Law, probably because it is more descriptive. Carroll (5) has found in linguistic studies that names that are descriptive of the action or procedure are learned more readily and used with fewer errors. In many cases being able to name the type of prohlem under consideration amounts to recognizing verbally the pattern that it represents. Larkin, McDermott, Simon, and Simon ( 6 )report that, based on research with chess masters, pattern recognition permits recall of appropriate strategies that are stored in memory. Indeed, this act of recognition and recall occurs so rapidly that it appears intuitive. The authors suggest that a similar process accounts for the apparent ease with which an expert solves problems in physics, rapidly selecting appropriate facts, formulas, and procedures. Furthermore, the process of recognizing and naming substeps may be important in solving complex problems. Frazer and Sleet (7) report that approximately half of the students who could solve all the individual substeps of a chemistry prohlem could not apply these skills to solving a problem which incorporated them. They suggest that the unsuccessful students had overburdened their working memory capacity and were unable to recognize all the substeps. Johnstone (8) reached a similar conclusion by analyzing the number of pieces of information needed to solve chemistry questions. I have noticed that encouraging students t o name and write down individual suhsteps as they recognize them improves their performance on more complex problems. Rather than being unwilling Or unable to start because they can't see their way through the entire procedure, they start by writing down whatever they do recognize, then look for another identifiable step. The initial identification of substepsdoes not need to he in the same sequence as the solution will ultimately require. I tell students that trying to solve a chemistry problem is like crossing a brook by tossing out stepping stones. You want to cross sequentially from step to step, but you can toss out the stones in any order. Similarly, as you start working on a problem, write down what you see as you recognize it, then arrange the steps in some logical order. This list of substeps
corresponds to what Larkin et al. ( 6 )call "external memory" and helps reduce the load on short-term memory. The difficulty in trying to help students learn to perform the initial steps of recognition and identification is that often we are not consciously aware of them in our own approach to problem solving. Reif (9) points out that the initial description of a problem is done automatically by experts and is an essential part of the solution process; it is also a process which students tend to perform incompletely. As any bird watcher knows, i t is much easier to identify a bird in the field if you know its key characteristics. Likewise, many chemistry problems provide clues to facilitate pattern recognition. For example, a problem that asks "how much" and gives starting amounts for two reactants is most likely a limiting-reagent stoichiometry problem, a t least in part. Perhaps we ought to put more emphasis on helping students identify and name the type of problem they are dealing with as they read through it, before they begin to define terms or look for appropriate formulas. There is some evidence that teaching students (adults as well as children) when and how to select and use particular procedures is beneficial (10,II). Driver (12) points out that teachers need
to educate students to perceive relevant facts and patterns, whether it is in solving problems or making observations in the laboratory. Although class time is very limited, particularly in introductorv chemistrv courses where there are so manv. touics . to w w r , ll,vlieve investing a few minutes in This effort as r w h we of r)rohlem is cwered will help srudrnts imurove their p&foriance and efficiency. I t may also give them a skill which they can apply in many situations outside of chemistry class. Literature Cited
a.
L. Hart,d., Jr.;Borndt, S.;Cararnseza. A. Nature 1985.316.439 2. Manhdl. J. C. Nature 1985.d16. 388.
3. Frederiksen, N. R w Edm Rer. 1984.54(3),363. 4. Eylnn. B.: Reii, F. Cognition andinstruction 1984.1.5. 5. Carmll..l. M. What's i n n Name? An Esrov in the Pavchoioev o f R r f e r m c e :Freeman: 8. Larkin, J.:McDormntt, J.;Simon, D.P.;Sirnon,H. A.Scbnre 1'380,208,1335 7. Fmrer, M. J.: Sleet, R. J. Eur. J , Sci. Educ. 1984.6.141. 8. Johnstone, A. H . J . C h e m . Educ. 1984.61.847.
Edue.
9. Reif F. J . Chem. 1983.60.948. 10. Schuenfeld, A. H. Am. Math. Mon,
1980.87.794.
P.Arith. Teoch. 1985.33, 19. 12. Driver. R.T h e Pupiias Scienlin:Open University Milton Keynes. England, 1983: pp 11. Havel.
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