FEBRUARY, 1955
103
It would have been far worse if the student had misplaced the extremes in the group, since less comprehension of the properties of the compounds, the theory of acidity, or other essential knowledge would have been indicated. That is, 4, 2, 3, 1 is worse than 1, 3, 2, 4, although both receive the same credit by Mr. MacKenzie's method. In the second example, a student has shown flagrant ignorance in listing 1butene as the highest boiling compound, but would be penalized the same amount for the much less serious error of listing n-butane as the lowest boiling comTo the Editor: pound. It is well to consider the amount of displaceThe readily apparent inequities in the scoring method ment and relative positioning in errors in proper place presented by Scott MacKenzie in "Proper place prob- problems, as well as the mere fact that error has been lems," THIS JOURNAL, 31, 428-9 (1954), lead me committed. This can be achieved simply by the followt o offer a method I have found both indicative of ing method. Each item in the answer is allotted a point value the student's grasp of the subject and simple to use. The statistical method presented by Mr. Mac- equal to the number of items (four in Mr. MacKenzie's Kenzie ignores relative positioning of answers, and first example, six in his second, 48 in the example of the states). Two points are removed from this value for each unit or position the student's item is displaced TABLE 1 from its proper position: Seoring of Answers to Four-part Proper Place Problem Item
1 2 3 4
Correct
HF HIO NHs CHI
Ezarnole 1 Ezamole 2
4 4 4 4 0
HF NHI HzO CHI
4 2 2 4
CH, -2 NAa 2 H?O 2 HF -2 0
Exomale .?
H20 2 NHa 2 CHc 2 HF -2
KO.items in list No. position^ displaced Score for item
4
6
0 1 2 3 1 2 0 -2
0 1 2 3 4 5 6 4 2 0 -2 - 4
To give credit for relative placementof some items, one point is added to the total .score for each item in Total 0 7 16 12 a series longer than two items placed in correct relaPer cent 100 75 0 44 tive positions, but not in correct absolute positions. The scores can then he placed on a per cent basis, neglects near misses. In a series correctly placed and the computed per cent of any nominal score for 1, 2, 3, 4, should a student answer 4, 1, 2, 3, he would the question taken. Examples hased on Mr. Macreceive no credit at all by this method, for all four Kenzie's first list are given in Table 1, those hased answers are out of their places. Surely the fact that on the second list in Table 2. I n each table, Example the student put 1, 2, 3 in correct relative order shows 1 is the order cited by him. Example 2 is the worst some knowledge. A student who, asked to list the possible answer, reversal of order. states in the order that they entered the United States, It may be admitted that this method does not lists Arizona first, but follows this with the rest from adequately recognize the greater difficulty of longer Delaware through New Mexico in proper order, surely lists, but the experienced teacher is likely to reserve shows knowledge far greater than chance. Yet this long series for more mature students. These should method would give him no credit, because all of the be as capable of solving them as neophytes are the states would be listed out of their proper places! I n shorter ones. This is no worse than expecting advanced the first example cited by Mr. MacKenzie, a student mathematics students to solve problems involving has placed the weakest and strongest acids in their calculus, but requiring only simple arithmetic of gradeproper positions, but inverted the intermediate two. school pupils. Series
3
TABLE 2 Scoring of Answers to Six-part Proper PIace Pmblem ILem
1 2 3 4 5 6
Ser~es Total Per cent
Cowed
Acetic acid I-Propanol Acetone Methyl formate Butane 1-Butene
6
6 6
6 6 6 0 -
36 100
Ezample 1
Ezample 2
Ezample 3
Example 4
1-Butene -4 6 I-hapanol Acetic acid 2 Methyl formatte 6 Acetone 2 Butane 4 0 16 44
1-Butene -4 Butane 0 Methyl formate 4 Acetone 4 1-Propanal 0 Acetic acid -4 0
Acetic acid 6 Acetone 4 Methyl formate 4 1-Butene 2 Butanc 6 I-Propanal -2
Acetic acid 6 Acetone 4 Methyl formate 4 Butane 4 1-Butene 4 I-Propanol -2
-
.-
0 0
20 56
0
4
24 67
JOURNAL OF CHEMICAL EDUCATION
104
It may also be admitted that this method carries no guarantee of absolute justice; for example, the worst possible arrangement of proper place items is reverse order, yet, where consistent, this surely means knowledge of some sort, perhaps perfect knowledge of the material, but incorrect reading of the problem. Student answers a t best involve a depee of uncertainty of motives, conditions, and personal errors that only omniscience or mind reading could fathom. The teacher's good judgment is required in every individual evaluation. Statistics and other mathematical systems are no substitute for this. I believe, however, that this method is more help to judgment than the statistical method presented by Mr. MacKenzie. Perhaps a combination or compromise between these methods could be effected. I should be interested to see what might be evolved.
this, but it is true and emphasizes that this criticism of method A is largely manufactured. It is interesting to consider method B as a possible alternate method. For several answers it does appear more equitable, but my objections to this method are twofold. First, it is much more generous (and thus appears more equitable). By method B a student has an expectancy over double that by method A . Items 3 4 5 6
Expectancy, method A 17% 16% 16% 16%
Ezpecfancy, method B 47% 35% 377j
...
Thus, in comparing the two systems, one must not confuse generosity with equity. A second objection to method B is, I feel, much more fundamental. It assumes that the grader knows with absolute certainty, on seeing any answer, the knowledge held by the student. Thus in the sequence 5 , 2 , 1 , 3 , 4 the grader says, in effect, "The student knows 2, has a good notion of 3 and 4, is poor on 1 and badly off on 5 ; he deserves 28 per cent." This is sheer guesswork. By method A the grader always asks, in effect, "Has the T o the Editor: student written an answer which, o n the basis of probThe communication of Mr. L. 0. Smith expressed ability, enables me to feel that he knows something of the certain criticisms of a method of grading proper place question?" One must say "no" in reference to the problems which was recently proposed. I desire to above sequence. answer these criticisms and t o deny that the alternate I shall continue to consider .with interest alternate proposal is as good or better. I n what. follows, the methods. Method A may ultimately give way to a original proposal will be referred to as method A , while more advantageous system. I do not feel that method B the alternate will be method B. . . IS that system. Smith states that method A "ignores relative positioning of answers and neglects near misses." Quite true; but this fact should not be considered as a fault of method A but one of its main assets. For if a student does not know one pair of items in a list of four, he might write 4, 2, 3, 1 or 1, 3, 2, 4 or some such com'Those wishing to apply method B to higher lists o m calculate bination. Why should lack of knowledge of one pair the expectanciea. The set indicated has 720 answers to be be worse than lack of knowledge of another just be- graded, added, and averaged. cause one pair happens to involve the end items? That property of method A which is most frequently criticized is also discussed by Smith. It is illustrated T o the Editor: by the sequence 6, 1, 2, 3 , 4 , 5. He points out correctly Proper order problems of the type, "Arrange in dethat by method A the student would receive 0. This creasing order: 3/6, 3/3, 0.1, '/g, 1 / ~are '' often posed in argument appears damning a t first sight, but it is, I feel, chemistry to test the knowledge of the relative orders of artificial and highly contrived. It makes two assump- some property such as melting point, acidity, activity, tions: first that the student knows well 1 , 2 , 3 , 4 , 5 but etc. Grading is simple as long as full credit is given is totally ignorant of 6 ; this might be true but is usually only for the perfect answer and any mistake reduces not in questions in chemistry; I have never encountered credit to zero. However, if it is desired to assign partial such a mistake in grading lists longer than four items. credit to incorrect answers, the rational procedure ma'y Second, i t assumes that the student, bright enough t o not be obvious. MacKenzie (THISJOURNAL, 31, 428 know 1,2, 3,4, 5 and totally ignorant of 6, then has not (1954)) has proposed a procedure which has been enough sense to place the unknown in the middle of criticized by Smith, who offers a substitute approach. the list so that, by a n y system of grading, hesuffers less1 I would like t o present an analysis of the basic premises A third point should be made in refutation: Students involved and some consequences with respect to grading generally remember best the highsandlows(thestrongest and the meaning of this type of problem. acid, the most densely populated state, the longest Let us first distinguish between proper order and rocket flight, etc.), and this is probably the chief reason proper place problems. The former asks for the relative that arrangements such as 6, 1, 2, 3, 4, 5 are almost positions of items, as in the above sample; the latter never seen. I feel that there is no particular merit in asks for the position of each item in a series, for ex-
