The Importance of a Strong Confrontation in anInquiry Model of Teaching

Kenneth Collins20 Stuyvesant Oval, New York, New York 10009

The inquiry model of teaching, which has been used recently atPurdue University for some research, is based on an initial confronta-tion that involves the students with the material. This confrontationcould be generated by an interesting film, a problem, or simply astatement that engages the students. Following the confrontation, thestudents ask questions and the teacher supplies information so thatthe students can answer their own questions. He also uses appropriateprompts and cues to help the students progress. As the students ad-vance, they learn new material at their own rate and in a way thatmakes sense to them. The discussion is also guided so that the studentrealizes the heuristics involved in his learning.

It seems reasonable that a strong confrontation, one that deeplyinvolved the students, would be more effective than a weak confron-tation, one that only mildly involved the students. We tested this hy-pothesis by using a high school freshman accelerated geometry classas our population. Sixteen out of the thirty students volunteered forthe program and they were randomly distributed into two groups.The groups were checked, using school records, for differences in IQand mathematics grades, but they were very close since the class wasquite homogeneous. Each group participated in four sessions, lasting45 minutes each. The material was the analysis of logic problems.Hopefully each group would learn to analyze problems by developingvalid laws of implication and by using other acceptable techniques,such as set theory. Another desired goal was that the students wouldlearn the relationships between the different methods they used andhow to apply each appropriately to solve various logic problems. Eachsession was introduced with a problem that was logically incorrect.The experimental group analyzed a problem whose conclusion ser-iously challenged their beliefs and values whereas the control groupanalyzed a problem whose logical structure was identical but whosecontent was very mild. The problems lead to discussions of logicalprinciples and incorrect methods of implication. The students wouldanalyze the problems from different points of view, often using settheory, until they were satisfied that they understood why the argu-ment was not valid. They examined how to attack the problem, try-ing to generalize their efforts to other cases, and what logical princi-ples were involved. Each group used the same inquiry model and de-veloped their own logic symbolism and analysis. They both arrived at

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an attack of logic problems using correct laws of implication and settheory. They also analyzed the relationship between the two pointsof view and developed a system for manipulating the symbols of eachmethod.The experimental group was able to do this in 20% less time than

the control group. This was due mainly to the speed and vigor withwhich they attacked the confrontation problem and the fundamentallogical principles on which the problem was based. It was also inter-esting to note that the class participation in the experimental groupwas considerably high. By the fourth session, the entire class spenthalf the time arguing at the board while the teacher sat in a chair andwatched, making occasional remarks.Both groups were able to state the heuristics by the completion of

the program. At the end of the fourth session, a test consisting of eightlogic problems was given to both groups. An example of two of theseproblems follows:

Given the following three statements as premises:(1) If John takes the train, then John misses his date if the train is

late.(2) If John doesn’t get the job, then (a) John feels downcast and

(b) should go home.(3) John shouldn’t go home, if John misses his date and he feels

downcast.is it valid to conclude that:

1. If John takes the train, then John does get the job, if the trainlate?

2. If John doesn’t miss his date, then John shouldn’t go home andhe doesn’t get the job?

The first conclusion is valid while the second one is not. As can beseen, the problems were not unduly easy. Half of the problem had avalid conclusion. The means for the experimental and control groupswere six and five respectively. A test showed that the experimentalgroup did significantly better (p<.01) than the control group.The results were better than anticipated and one possible explana-

tion is that despite the attempted impartiality of the teacher, theremay have been a preference for the experimental group. Anotherpossible explanation is that the confrontation for the experimentalgroup generated cognitive dissonance in each student that had to beresolved. This encouraged a hard attack on the problems an aggresiveanalysis for flaws. It is interesting to note that the experimental groupdid far better than the control group with the test problems that werelogically incorrect. The students used were from accelerated classes,which might be more receptive to this procedure than would be truein general. Perhaps if more than four sessions were used, the difference

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between the two groups^ scores would have decreased and becomenonsignificant. Finally, the effectiveness of the strong confrontation,and indeed the inquiry model itself, maybe severly diluted if the classsize is substantially increased. These arguments will have to be an-swered with a larger experiment involving student groups of variousIQ levels. However, the first attempt to verify the importance of astrong confrontation did give us very promising results.

BIBLIOGRAPHY1’ J. Burner, Process of Education, 1961.2 A. Foshay, "A Modest Proposal," Educational Leadership, 1961.3’ G. Miller, "Teacher and Inquiry," Educational Leadership, 1966.4 J. Suchman, "The Elementary School Training Program in Scientific In-

quiry," The Science Teacher, 1960.[5] J. Suchman, "Learning through Inquiry," The Merrill Palmer Quarterly of

Behavior and Development, 1961.

FIVE MILLION EARTH MODELS CALCULATED;ONLY SIX SURVIVE

Scientists "playing dice" with the structure of earth have won the game atodds of about a million to one. Their results show that this planet7s structure isvery likely to be much more complex�and of different proportions�than mostgeophysicists have thought.

Five million models of the earth were calculated by a computer; only sixsurvive when tested against what is actually known about the earth.That the earth has three main divisions�a central core, an intervening mantle

and a very thin crust�has been known for a long time.Some 300 years ago Isaac Newton noted that the average density of the earth

was five to six times that of water. Since the rocks on earth’s crust are onlyabout three times as dense as water, the case for heavier material inside wascinched.During the last 60 years, scientists have not only found layers within these

divisions but have also learned to estimate the depths of these internal layerswith increasing confidence.However, the computer models of the earth’s structure indicate the previously

assumed dimensions for the core and mantle, and the layers within them, couldwell be off by many miles.

Previously all known earth models based on observation were founded on cer-tain assumptions, such as a chemically homogeneous mantle below 600 miles anda relationship between the velocities of earthquake waves and internal chemicalcomposition based on laboratory test of minerals and rocks.These assumptions are not necessarily true of the real earth, Dr. Frank Press

of Massachusetts Institute of Technology believes on the basis of the five millioncomputer models. His calculations were made using what is known mathemati-cally as the Monte Carlo method; that is, the various figures were fed into thecomputer on a completely random basis, as when dice are thrown, and the re-sulting mathematical model then tested to see how closely it resembled the realearth.Of the six that passed this examination, all had a larger core than is usually

assumed for the earth, with the outer, fluid core consistent with an alloy of ironand 15 to 25% silicon. The inner, solid core, Dr. Press believes, has a compositionconsistent with an alloy of iron and 20 to 50% nickel.The mantle is not the same throughout. And the transition zone between the

deep and upper mantle shows large density fluctuations one of the most surpris-ing results of the computer calculations.