Lewis Structure Skills: Taxonomy and Difficulty Levels Joseph A. Brady and John N. Milbury-Steen Officeof Academic Computing and lnst~ctionalTechnology, University of Delaware, Newark. DE 19716 John L. Burmeister Department of Chemistry and Biochemistry, University of Delaware, Newark, DE 19716 Although the ability todraw Lewis structures is crucial for predicting a molecule's shape and reactivity, no adequate computerized lessons were nationally available. Therefore, the Office of Academic Computing and Instructional Technology at the University of Delaware, with the help of the Department of Chemistry and Biochemistry, committed itself to developing an intelligent tutoring system. An early prototype collected considerable data about student performance, which revealed the relative difficulty of the required skills. Although this discussion is about the data, not the prototvne.. the followine comments will describe how the data were obtained. The user drew a two-dimensional picture of the molecule or complex ion using a mouse to place or delete atoms, bonds, and electrons. On-line help was available: a periodic table, a summary of steps for completing the structure, a scratch sheet for calculating the valence electron pool, and information about electronegativity. The user could request a correctness evaluation at any time. Otherwise, the evaluator did not intervene spontaneously, except if the wrong atom became defined as central. The editor's evaluator did not consider formal charee nor the correctness of aneles between bonds. If the stru>ure was incorrect, the evaluitor identified the basic error, suppressing a cascade of related but subordinate errors. It would say, for example: "The indicated 0 atom has an incomplete outer shell." The correct answer was available to the student on request after three evaluations with errors. The user was not asked to predict the shapes of species. Data were collected in the fall of 1986. The student volunteers had had a lecture on drawing Lewis structures and had done homework or a lab exercise but had not practiced long euoueh to become adeot. The students were from honors . chemistry sections, physical sciences, engineering, and nursine. and no one maior was nredominant. Each student action was written to a file, and the resulting archives captured the et'lorts of 47 students at work on a orohlem set of 51 struc729 times, tures. They collectively solved ~ e d i structures s an averaee of 15.5 ner student. Two students did only three one stident worked 50. The average student worked for an hour. Henceforth, any of the 51 structures in the problem set will be called a "problem", and any of the 729 times the students correctly solved a problem will be called a "solution".
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The Dlfflculty ofthe Overall Task The first auestion the nroiect asked was whether the task 65%of the solutions were as a whole was difficult. fn correct the first time the evaluator was called: 85% bv the second time. A more detailed report is given in Table 1: One concludes that students do not find the task especially diffiResented at the Tenth Biennial Conference on Chemical Education. Purdue University, West Lafayene, IN, August 3, 1988.
Table 1. Tha Dlnlcully d the Overall Task Evaluator Calls' 1 2 3 4
Solutions
Percent
476 139 53 29 32 729
65 19 8
4
4 100
-
more man 4 Totals
'me number of times It was necessar, for ms sNdent to call theevaluator bemre the was correct ~ t d e m solution .~ Table 2. Problem
Easy Problems
% cwect, First Evaluation' 100 100 94 93 93 90 88 88 87 87 85
HF PC16 801'-
PFB-
SnCbNH.+ CHI AIC14i
wlo SF8
NHS-
~kill~~eq~lrsd~ 3.7
.
1,s 1,4. 11 I , 5, 11 1. 5. 11 I, 5. 7. 12 1.5.7 1.5.11 1-10 1.5 1. 7. 10, 11
'The percent of the time a solvtion was correct on the first request for evaluation. "For the numsrical mdea. see Table 2.
cult. The task may be inherently straightforward. class instruction may be effective, or co&enG from the prototype may be helpful. Certainly, any student who cannot solve a nrohlem after one or twoerror messaees is flounderine. Students erred significantly more iften on the first-problem presented in the session than on succeeding ones. This is probably due to awkwardness in adjusting to the program. However. student ~erformanceon the second problem in the session was consistent with the overall .werag&. (Readers who want to try to duplicate these findings may obtain a copy of the data-collecting program by writing to one of the authors, Joseph Brady, enclosing a formatted 5%in. disk. The program requires an IBM PC with a mouse and a CGA graphics card. Also, since the data files that are generated consist of nothing more than X and Y coordinates of where the mouse was clicked, a data file interpreter is necessary and will be furnished.) A
The Dlfflculty of lndlvldual Problems The second issue the project wanted to investigate was the students' decree of success on individual nroblems. In the prototype, each of the 51 problems in the problem set had been labelled "easy", "medium", or "hard", but this had been done intuitively, and this lahelling was not empirically confirmed. In Tables 3, 4, and 5 the problems are Volume 67
Number 6 June 1990
49 1
lab*
Problem
a.
Average Problem
% Conect. First Evalwtimb
Tabb 4.
SkillsReq~ired~
Robiem
Hard Problems
% Carect. First Evalwtion"
SkIlisReq~ired~
-mi$ percent mlgM be aniflcially low because this problem was sometimes given as the first One 1" 6BS8b. ame percent of ms urns a solutlon was c a r r m on me fir* requesl f a evaluation. =For me numerical codes. see Table 2.
Table 5. m e Dmlculty of lndlvldual Skllls mi8 percent m i g be ~ anificlally low because this problem was smtlmss given as me fir~tOW In me session. first request for evaluation. percem of thetims a wlvtion was m c t on =FOTthe numerical c a d s , see Table 2.
Robiem DiffIcuRp easy average hard
Skill O i f f i ~ ~ l t y
Central Atom Skills
classified by actual, observed difficulty as measured by the percentage of students who solved the problem correctly on the first call to the evaluator. At this stage of the analysis, the project had not analyzed the skill factors that predict the level of difficulty, so the third column of those tables did not yet exist. Some easy problems, such as HF were solved correctly on the first try all of the time, while other problems such as FN02, were rarely correct. The next task was to explain the difficulty level of each problem in terms of the skills required in solving it. A Taxonomv ot Skllls
Table 2 summarizes the skills that the project proposed as ~redictorsof the difficultv of each problem. (The study had humbered them before grouping them logically.) The abilitv to choose the central atom consists of several cases. In species of three atoms or more, the central atom is the one and only atom type of which there is one instance (unique central case, skill 1).This is really adisguised appeal to symmetry, since often the central atom is of one type and the peripherals are all of other types. This rule will not work, however, for HOI, since each of the three atoms has one instance in the molecule. In the ambiguous case (skill 6),the most electropositive atom is chosen as the central one. The appeal to electropositivity is the most generally applicable way of choosing the central atom, but students typically prefer using the uniqueness rule to the rule that requires them to compare electronegativities. A chart of electronegativities might not be readily available, and estimating relative electronegativities from the periodic table is difficult for beginning students. Species with only two atoms do not, of course, have a well-defined central atom, and this is the trivial case (skill 3). The skill analysis assumes that the abilities required to connect the peripheral atoms to the central one, and to complete the outer shells of the peripherals are mechanical and relatively unimportant. The crucial skill group, which the project has called the "adjustment skills", refers to deciding how to complete the outer shell of the central atom. In some cases the central atom follows the octet rule. Sometimes simply connecting the structure and filling the 492
Journal of Chemical Education
easy easy average-bard
1. Unique 3. Trivial 6. Ambigwus Ad]usbnem Skills
hard average-hard emy-average
2. OW 4. Promote 5. Trivial 8. Ex~essIve 9. Deficlem 10. octet
weraga-had hard BaSy-Bverage
Counting Skills 11. Anion 12. Cation
45
9
39 9
19 0
easy easy
36
4
8
easy
Miscellaneous Skill
7. H "duet" a
Percemap of problems of mi8 dinicuW exhibiting this skill.
peripheral octets places all the available valence electrons and at the same time gives the central atom a complete outer shell of eight electrons as a side effect (the trivial case, skill 5). If electrons are left to be placed after connecting the structure and completing the peripheral octets, placing the electrons on the central atom may bring its outer ahell up to eight (the octet case, skill 10). However, the valence shell of the central atom often technicallv violates the octet rule. Several situations mav arise after :he structure is connected and the peripheral octets are filled. Plarine the remaining available electrons on the central atom may give it more ;had eight in its outer shell (the excessive case. skill 8). If the soecies is odd (i.e., has an odd number of electrons in its valence electron pool); the central atom could comdete its outer shell with oulv seven electrons (the odd species case, skill 2). If all of the &oms have been olaced and the central atom still lacks two or four electrons ior a compete octet, then more electrons can be shared by "promoting" bonds from single to double, occasionally from double to triple (the bond-promotion case, skill 4). However, peripheral halides as a rule are not involved in double or triple bonding. If all the peripherals are halides, bond pro-
motion is then suppressed, and the outer shell of the central atom may be lefcwith fewer than eight electrons (deficient case, skill 9). The student must be able to recognize each of these situations as normal. The project, in its analysis of skills, hypothesized that the adjustment skills involved in each nroblem would be the crucial oredietors of difficultv. " The adjustment of the central atom hinges on knowing how many electrons are left to be placed, which in turn requires the student to know how many were originally available. The presence of a charge on the species apparently complicates this calculation (skills 11 and 12). since year after vear students make the same slip: thev subtract the negative charge or add a positive one: students may also have difficulty in remembering that hydrogen completes its outer shell with two electrons, rather than eight (skill I ) . An o~tionalon-line h e l ~permitted the student to enter the &umber of electrons-in the total valence pool. After three incorrect tries, the calculation was shown in detail.
Problems requiring bond promotion (skill 4) are generally hard (seven of them), or average (seven). Two of them were even easy, but these anomalies are explainable. Students may guess that Nz would need more than one bond since there are onlv two atoms. B O P was usuallv called correct. and therefore determined to be easy, because the evaluate; accepted a deficient outer shell on B as well as a resonance arrangement. Of the 239 opportunities in which the evaluator might have found an error with this skill. it did so 90 times (38%). Problems requiring more than eight electrons in the outer shell of the central atom (skill 8) were considered to be of average or hard difficulty, about equally divided. The results are much like skill 4, above. Likewise, problems requiring fewer than eight electrons in the outer shell of the central atom were found to he average or hard. In brief, any adjustment that leaves the central atom with other than eight valence electrons is not easy.
The Difilculty ol lndlvldual Skills The last step in analyzing the data was to determine whether the observed difficulty of the problems was dependent upon their component skills. The results show that the adjustment skills in combination with the skill of choosing an ambiguous central atom are the key factors. Among the easy problems, adjustments that leave the central atom with eight valence electrons predominate. Problems of average difficulty expand the adjustments to hond promotions on resonance structures and to central atoms with more than eight electrons in the outer shell. Hard problems involve bond promotion, odd species, or a deficient outer shell on the central. Hard problems also involve central atoms that are ambiguous. This permits skills themselves to be sorted by difficulty. Among the central atom skills, the ambiguous central case (skill 6 ) was the most difficult. Problems requiring this skill were presented 132 times, and students made errors about one-fourth of the time. Of all the adjustment skills, the odd-species case (skill 2 ) was most difficult. Nitrogen dioxide was drawn correctly at the first evaluation by none ofthesixstudents whoattempted it; chlorine dioxide by onlv two of seven students. There were only two odd species in the problem set. Often the student is not even precalculating the available valence electron pool but is mechanically placing electrons in pairs. Eventually the student will pause to calculate the total valence pool but will often refuse to recognize that an odd number is possible. The odd number presents the principal difficulty. Occasionally the predisposition toward an even number will even cause a mistake in counting.
Conclusion The data confirm the ~roiect'sskill taxonomv. since the : required observed difficulty of a problem depends upon & skills, as the project defined them. The taxonomv then becomes useful&
