Further Studies on Concept Learning versus Problem Solving Miles Pickering Princeton University, Princeton, NJ 08544 Does the ability to solve a problem imply an understanding of the molecular concepts behind the problem? This has been an unquestioned axiom of freshman chemistry teachingfor the past 30 years. Recently a paper by Nurrenbern and Pickering ( I ) raised real questions about whether this axiom is really true. This stndv reoorted that students could solve a mathematical proGemabout gases hut be unable to solve a problem about eases shown in diagram form. Similarly even students able to Live stoichiomethc problems had serious difficulty writing an e ~ u a t i o nfrom diagrams nf molecules. This result is consistent with the workbf Yarrock ( 2 )and Gabel (3). The work reported in the Nurrenbern and Pickering paper generated a great deal of interest (4). The first question raised was the degree of generality of the effect. At least one renlication confirmed the results with a verv different student population ( 5 ) ,and this paper will report another incidental reolication.Theeffect aooears to beauite widesoread .across student populations. But there are still other questions that might he asked, and one of the most important is what happens to the stu~
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254
Journal of Chemical Education
dents when they get to other courses in chemistry, organic for example. Are there two kinds of students, some who possess an ability to do conceptual problems and some who can do mathematical ~ r o h l e m swithout molecular understanding? Is the dilferdnce hetween the groups a difference of ability or just a gap in knowledge? T o resolve some of these questi&s, a group of studenis from Princeton were followed into the sophomore organic course and their performance analyzed. Method
As a part of the first hour test during the second semester, students enrolled in the lower level freshman chemistry course a t Princeton were asked to solve both the gas problems in ref I . One is a conceptual question using diagrams and the other, a traditional gas problem. (The reader may refer to ref 1 or ref 5, which precedes this article, for details.) These students were then followed into organic chemistry the following year, and their grades were analyzed as a function of their success or failure on the conceptual gas problem.
Table 1.
Results
Of the 101 students in the freshman course, all but five could do the traditional numerical gas problem, hut only 38 could do the conceptual gas problem. The success rate for this problem is 3870, similar to the success rates a t other schools listed in Table 1.The students that are successful on - --both questions will he grouped as the "successful" group in this studv. The ones who can do only the traditional question will form the "nonsuccessful" group. The averaee erades on this exam, and for all the nonlahnratory portions of the course grades, are listed in Table 2 for both erouos. The erouo that can do both questions scored statisLicaliy significanily higher than the nnnauccessful eroUD.'l'his was true on both the remainder of the first hour test A d also on the total exam score for the course. By the end of the term, the average difference between the two groups is large enough to affect the letter grade significantly! This result is in accord with that of Sawrey (5). Unfortunatelv for this research proiect, mans students in this course do n i t enter organic chemistry, and so the sample sizes become smaller for the rest of the study. Table 3 lists the average scores for all continuing students in both groups on the oreanic final exam and for the total organic course grade. he group that can successfully do the gas problem does slightly better on the organic final and also in total grade for the organic course. However, the differences are not statistically significant. Previous studies (6)have indicated a verv - .high - correlation between grades in freshman chemistry and grades in organic. Therefore the small effects seen in organic might occur because the students who get the concep&al question right are the better students on averape. T o compensate for this, two matched samples were created. Each student in the successfulgroup was paired with one whose freshman chemistry grade was as similar as possible but who had not solved the conceptual question correctly. Then the organic scores of this matched comparison group were compared with the group under study. The differences then vanish, as shown inTable 4.
--
Results for Tradltlonal versus Conceptual Problems for Several Schools Percentage of nudents successful on succes6fd on both q~estions traditional only
University of Wisconsin-Stout' Unlversltyof CBlifornia. San Diegob
36% 31% 38%
PrincetonC
67% 88% 95%
'Ref 1. 'Ref 5. =PresentstyJy.
Table 2.
Freshman Chemlrtry Scores for Two Student Poo~latlons Successful on conceptual problem D mean
F l r ~ t h o u r t e ~ t r a w ~ c o r e 71.0 66.0 First hourtest excluding conceptml q o e s t h Course total (excluding 467
83.7
38
number of students a
14.55 14.55
Unsuccessful on ~once~tual problem mean rs
-
17.4 17.4
3.02'
85.37
2.75'
55.87 55.87 418
t
95
significant st me p < 0.01level. Table 3.
Organlc Scores for All Contlnulng Students SNdents successful on conceptual problem mean c
Freshman chemlsby Organlc final Orpanic course made
477.7 50.05 63.3
77.6 18.4 13.2
Omer f
studems mean o
429.7 45.51 58.05
value
72.6 17.3 12.2
2.17' 0.86 1.42
Dlscusslon
From the beginning, the major question has been whether the ability to do the conceptual questions was due to some special ability or due to specific knowledge. This study shows that, if students are matched for freshman grade, there will be no difference in their ability to perform in organic, whether or not they can do the conceptual gas question. This argues strongly that the difficulty with the conceptual question is the lack of some specific factual knowledge about gases, not some arcane ability difference. Other data support this view. The remarkably similar results on the conceptual question from school to school (as shown in Table 1) seem to argue that the kind of student population is unimportant, certainly not true if ability is the governing factor. There is a pronounced trend in ability to do the traditional gas question. For example, comparing the success rate on the traditional question a t Princeton with tbat of the University of Wisconsin-Stout gives a ,y2 of 26, aienificant a t D < 0.001. This ~resumablvreflectsthe underI$ng differen'ce in math aptitude. The other niece of suooortine data is that, yes, it is ~ o s s i hle to teach students tb'solve>roblems o f t h e conc~ptual tvoe. -. Data from a course a t the University of Minnesota designed for nonscience majors where concepts rather than problems were emphasized showed that, out of 21 students, about 17 could solve a conceptual problem, even thoughonly four could solve a traditional stoichiometric problem (7). This isexactly the reverseof the present study. I t argues that teaching emphasis can adjust the relative success rate. Thus. the available data seem to areue not that there are two tydes of students, but rather two distinct educational goals. Both goals (or neither goal) may be achieved, or one
Table I Scores for Matched ComDarlson GrouDs SUCC~~~~UI Comparison coup Students mean o. mean (T Freshman chemlsny Organic final Organic course
477.7 48.8 62.1
77.6 17.8 12.26
476.6 48.0 64.3
78.33 11.8 10.3
and not the other. The goals show different patterns of correlation with student population, and changes in teachinp.emphasis can alter the relative success rate. Presumahlv instructor and textbook emohasis has caused students todirect their efforts toward problem solving. But the abilitv to solve a orohlem. while desirable in itself, does not seemto imply m&h real "nderstanding of microscopic reality, and i t is this understanding tbat is a t the heart of chemical science. The instructor is thus presented with a choice as to which goalis to be achieved. Amain point of this research is to help the educational community become conscious of this choice so that the decision can be made intelligently. Literature Clted Nurrenbern, S.:Pickering, M. J. Chem. Educ. 1987.64.508. Yarrwk. W. L. J.Re%ScL T e m h 1985.22,449. Gabel, D.i.;Samuel.K.V.;H u m , D.J. Chzrn.Educ. 1987.64.685 Froiiieh.M. 9.J. Chem. Educ. 1988.65.442. 5 . Sarrey, 6. J. J . Chrm.Educ. 1990.87.252. 6. Rirpe. J.;Pickering,M. J Cham. Educ. 1985.6% 313.
1. 2. 3. 4.
7 . Wilson. A . private mmrnuniestion,1987.
Volume 67
Number 3 March 1990
255
