Research: Science and Education
Chemical Education Research
Following the Development of the Bonding Concept Using Knowledge Space Theory Mare Taagepera,* Ramesh Arasasingham, Frank Potter, Arash Soroudi, and Giang Lam Department of Chemistry, University of California Irvine, Irvine, CA 92697-2025; *
[email protected] Background Students are introduced to the bonding concept in high school chemistry. The concept is reintroduced in general chemistry and again in organic chemistry. How does the student’s level of understanding develop through the numerous chemistry courses? The bonding concept contains some of the characteristics of difficult concepts as analyzed by Herron: it involves a theoretical model requiring that students interpret observations that cannot be experienced directly; and it assumes that students can make logical inferences (1). The development of students’ understanding of a concept is generally not tracked through a sequence of courses using the same test, which would make it possible to measure knowledge changes during the learning process. We obtained the results of 2395 tests from 993 students in general and organic chemistry and analyzed the simple percentage of correct answers and the most often occurring incorrect answers. The connectivity of these responses, or the students’ cognitive organization of the material, was established using the knowledge space theory (KST) developed by Falmagne et al. (2) and used by Taagepera et al. (3, 4 ) to map the students’ thinking patterns in learning science. We are looking for structures or patterns, since it is known that experts differ from novices by noticing meaningful patterns of information (5, p 31). Students need to develop some logical connections if their learning will go beyond sets of isolated facts. These connections cannot be found by simply examining the percentage of correct answers on any test, particularly if the test is not designed to follow conceptual development. In other words, answering a selection of questions correctly on a test does not necessarily mean that there is a logical framework or understanding of the material. Other ways to measure conceptual change involving patterns include use of qualitative and quantitative differences in concept maps (6 ) and ordered-tree techniques that measure “closeness” of topics (7, 8). KST provides the overall organizational pattern of conceptual knowledge, assuming some hierarchy of knowledge is required for correct responses, and is thus complementary to other techniques. It has been shown that effective comprehension and thinking require a coherent understanding of the organizing principle (5, p 227). Our fundamental organizing principle providing the hierarchical scheme is based on the electron density distribution models used by Shusterman and Shusterman (9), but was modified by asking students to make predictions on electron density distributions in molecules from electronegativities. From electron density distributions, they can predict the bond polarities and the expected intermolecular
756
forces, which in turn lead to predictions of specific physical properties. If a student makes a prediction of physical properties that contradicts the electron density analysis, that student most likely does not have a fundamental understanding of all the necessary underlying principles. The hierarchical scheme then indicates which principles are not understood well enough. There are studies in physics that show that when students approach problems using a hierarchical analysis, their performance improves (10). The tendency for instructors is to assume that the underlying principles are in place and that we are seeing more than algorithmic or superficial memory on our examinations. However, as many other authors have also observed, this simple assumption is often not the case (e.g., 11). Students may know the principles but not understand or use their logical connections when responding. KST helps us analyze for this behavior. In fact, it has been stated that there would be more concern about students’ mastery of chemistry if tests were given to probe for depth of understanding (12). Research Design The experimental group was primarily biology majors enrolled in the regular general and organic chemistry courses at the University of California, Irvine. The test was developed by the research group, composed of UCI faculty and students who had taken general and organic chemistry. The test consisted of 15 questions, which contained a hierarchical order of difficulty as determined by experts (the research group) using electron densities as the organizing principle. The test questions and acceptable answers are given in Appendix 1. (Note that the numerical order of the questions does not correspond directly to the hierarchical order.) The test was scored in a binary fashion: each question was graded as either right or wrong. For example, in a question requiring justification, if the higher boiling point for ethanol was correctly predicted but the description of its intermolecular forces was incorrect, then the question was marked wrong. Results Student tests were analyzed by looking at the simple percentage of correct responses and by applying KST to look for the connectivity in responses. The most commonly occurring misconceptions were also analyzed. The tests were administered nine times as shown in Table 1. The academic-year of 30 weeks is divided into three quarters (General Chemistry: CHEM 1A, 1B, 1C and Organic Chemistry: 51A, 51B, 51C), which are usually taken sequentially.
Journal of Chemical Education • Vol. 79 No. 6 June 2002 • JChemEd.chem.wisc.edu
Research: Science and Education 100 Chem 1B Post Chem 1C
90
Chem 51A Pre Chem 51A Post 80
Percent Correct Answers
70
Figure 1. Results for student tracking.
60
50
40
30
20
10
0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Question Number
hydrogen bond and a polar covalent bond in the acetic acid dimer, which was presented in a drawing. Question 7 also proved to be difficult, as the students had trouble identifying the hydrogen bonded to oxygen in ethanol as the most electron deficient. Most of the students did reasonably well on the electronegativity, electron density, and polarity questions 1–6.1 Students who took the test multiple times may have recognized the questions, but since the answers were never discussed explicitly, a correct answer would still indicate some learning on the students’ part. A dedicated effort was made in lecture during CHEM 51A, F 1999, and CHEM 1B, W 2000, to constantly refer back to electron densities, and explicit questions about electron densities also appeared on examinations. These questions were not the same as the ones on this test. The posttest showed significant gains, ~20% on average in both courses. The gains were smaller (~10%) in CHEM 51B, where there is less emphasis on bonding topics. As noted earlier in the pretest, the lowest scores were for questions 10 and 12, which required visualization and depiction of intermolecular forces (H bonding) at the microscopic level. This was somewhat surprising and clearly required further attention.
Most sections of the sequence are offered during each of the quarters: Fall (F), Winter (W), and Spring (S). Pretests refer to tests given before the bonding concept was formally introduced and posttests were given after teaching the concept. We did not give pretests and posttests in every class, particularly if the concept was not formally presented. The results need to be interpreted with some caution, since the pretests and posttests were not always taken by exactly the same students. Our initial intent was to validate the KST methodology in real-life teaching situations. As seen in Table 1, students had the greatest difficulty with questions 10 (av = 36%) and 12 (av = 40%), where they were asked to draw pictures at the microscopic level indicating hydrogen bonding. (Here the average percentage of correct responses was used to determine the general difficulty of the questions.) Visualization at the microscopic level has been identified as a difficulty by various authors (1, pp 186–188; 13, 14). This is particularly disturbing because abstractions in terms of trends or equations make little sense if the students cannot “see” molecules at the microscopic level. Next came questions 13 and 14, which simply asked students to identify a
Table 1. Percentage of Correct Responses to Questions Class
Test
n
1B, W'99
Post
1B, S'99
Correct Responses to the 15 Questions (%) 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
157
85
81
91
92
75
72
42
85
64
14
71
29
49
59
70
Post
173
88
68
84
93
73
57
57
67
68
34
50
39
40
47
54
1B, W'00
Pre Post
464 426
97 98
81 92
90 95
88 92
77 87
72 85
53 72
82 99
82 96
12 63
58 86
18 44
39 66
53 71
31 70
1C, S'99
Post
103
94
96
91
89
85
70
50
84
78
17
74
34
48
59
80
51A, F'99
Pre Post
244 293
95 97
71 91
86 96
70 94
64 74
57 88
62 77
68 90
66 85
14 56
45 61
19 63
44 78
48 71
37 54
51B, W'99 Pre Post
315 220
98 96
98 98
92 92
95 77
87 84
84 92
34 60
87 93
52 83
44 66
55 69
53 59
72 83
77 80
57 57
Average
—
94
86
90
88
78
74
56
84
75
36
63
40
58
63
57
JChemEd.chem.wisc.edu • Vol. 79 No. 6 June 2002 • Journal of Chemical Education
757
Research: Science and Education
At the end of the quarter the greatest gains were obtained for questions 10 and 12, as shown on the posttest. Evidently, once the students start to focus on microscopic representation, they master it quickly. If one assumes that the knowledge about bonding obtained in high school is reflected in the CHEM 1B pretest (W 2000) before the treatment of chemical bonding in general chemistry, then the problem of visualization at the microscopic level starts early—in high school. This is not surprising, since in spite of the material on bonding and even some pictures on Hbonded molecular systems in the high school textbooks, there seems to be little emphasis in the exercise section on having students draw the pictorial representations themselves or analyze trends in terms of intermolecular forces and relate these to the placement of atoms in the intramolecular bond. This is also true of most general chemistry textbooks. Some textbooks rely heavily on memorizing definitions related to 20 different topics in the chapter and on doing algorithmic problems. Under these circumstances it will be difficult for the student to develop conceptual understanding, which would circumvent having to study the same topic over and over again at a superficial level year after year. Twenty-four students took the test 4 times as they progressed from the second quarter of the general chemistry course (CHEM 1B, W 1999, pretest) to the end of the first quarter of organic chemistry (CHEM 51A, F 1999, posttest). The results for these students are shown in Figure 1. (A much larger number took the test more than one time, but these are not included, so as to keep the population constant.) In general, the scores improved as students progressed in their studies (as was also noted by Birk and Kuntz [15]), to where, at the end of the first quarter of organic chemistry, an acceptable mastery of knowledge was attained, ranging from 98% correct for question 1 to 68% correct for question 14. There is a noticeable drop in the scores from Chem 1C, S 1999, to Chem 51A, F 1999, in 10 of the 15 questions. This indicates that the students forgot quite a bit over the summer. However, one might assume that if the bonding concepts were understood they would not easily be forgotten (16 ). The questions most commonly forgotten between 1C, S 1999, and 51A, F 1999, include questions 4 (relative electronegativities of C, H, and O) and 5 (polar nature of water). As expected, some of the more difficult questions (10–15) were the last to be answered correctly, most commonly in the 4th quarter. Analysis of the Data: Building the Knowledge Structure Using the Chi-Square Analysis The methodology used to determine the knowledge structure and obtain the critical learning pathways has been described in previous publications (3, 4). The formal mathematical details of knowledge space theory are presented in the book Knowledge Spaces by Doignon and Falmagne (2). A simplified version of the knowledge structure calculation is available on the Internet (17). A brief overview is given below. Knowledge space theory (KST) depends upon collecting student data from a set of questions reflecting different levels of conceptual development. A response state is defined by the set of questions correctly answered by the student. Response state [1,2,5] means that the student correctly answered questions 1, 2, and 5 only. We tally the populations of all the occupied response states achieved by the students. Theoretically, for the 758
15-question test 215 or 32,768 response states are possible. For a 300-student class a maximum of 300 response states are possible; typically, 75 to 200 are observed. The more focused (structured) the learning, the fewer response states will represent the entire class. Some of these occupied response states will eventually be part of the desired knowledge structure representing the students as a whole. The knowledge structure is obtained by finding a χ2 fit to 15–30 response states that represent the student responses under the severe restriction that each must have a predecessor state and a successor state in the final network; that is, the structure has to be well graded (one must be able to progress one question at a time along each learning pathway from one state to the next beginning from the null state and ending with correct answers to all questions). The cognitive organization or connectivity of the material can then be determined. Trial response states are selected from the most highly populated response states; lucky-guess parameters and careless-error parameters for each question are estimated. The χ2 value is minimized by a trial-and-error process. Finally, the two or three most probable learning pathways are identified as the critical learning pathways consisting of response states that best define the class and now become representative knowledge states. It is possible that some of the most populated response states will not appear on the critical learning pathway. This is an indication of the fact that answering a selection of questions correctly on a test does not necessarily mean that there is a logical framework or true comprehension of the material. Once the most probable pathway is determined, it is possible to compare each individual student’s performance to overall class performance as well as to expert performance. Data Analysis Optimization of two of the nine test sets (CHEM 1B, W 1999, and CHEM 1C, S 1999) gave a well-defined knowledge structure, and a third set (CHEM 51A, F 1999) gave a partial fit to the first 10 problems. This is in contrast to our analysis of the organic chemistry test reported previously, where a fit was found for 8 of the 10 test sets (3). It is also in contrast to our observation of results on a test on the stoichiometry concept, where a knowledge structure was obtained for both the pretests and the posttests for approximately 475 students (unpublished results). A fit providing a knowledge structure is possible under two conditions related to the number and nature of the states: a small number of response states must be present in comparison to the number of students taking the test, and the response states must have precursor and successor states; in other words, the students must use logical thinking in responding. If 300 students have 300 response states, then there is little likelihood of an organized structure or pattern of understanding. The results on the bonding test indicate that the understanding of the bonding concept is a lot more diffuse than that for stoichiometry, probably owing to the relative length and quality of coverage in the classroom. Examination of high school textbooks shows that the coverage of stoichiometry is more extensive than that of bonding. Spending enough time to learn complex subject matter is one necessary condition for transference. Transference, or application to new situations, is possible only if the material is
Journal of Chemical Education • Vol. 79 No. 6 June 2002 • JChemEd.chem.wisc.edu
Research: Science and Education
understood. The other necessary conditions in2 3 4 5 6 7 13 14 10 8 9 11 12 15 Q Φ 1 clude using the time wisely by having students Hypothetical Expert Pathway monitor their own learning with feedback and evaluation of strategies; learning in a variety of contexts for flexible transfer; and being able to extract underlying themes and principles (5, pp 235–237). 3 4 7 13 12 Figure 2 presents three critical learning 11 14 10 2 15 6 5 8 9 Q Φ 1 pathways: one represents the experts, who base their reasoning on electron densities, and the 4 3 13 12 7 other two represent novices (students) in Chem Most Common Student Pathway for Chem 1B, W 1999 1B, W 1999, and Chem 1C, S 1999. The critical learning pathway for the experts was obtained from a hypothetical hierarchical sequencing determined by our research group; the 3 4 novice/student critical learning pathways were obtained from actual student data indicating the 2 5 6 8 13 14 9 12 15 10 7 11 Q Φ 1 most probable sequence of response states in the 4 3 knowledge structure. The critical learning pathway represented here is indicated by the sequence Most Common Student Pathway for Chem 1C, S 1999 of obtaining correct responses. The knowledge structure for Chem 1C, S 1999, from which Figure 2. Comparison of expert and novice (student) critical learning pathways. the critical learning pathway was obtained is The critical learning pathway is shown in the order in which correct answers to given in Appendix 2. questions are obtained; Φ is the null state (no correct answers) and Q is the state where all answers are correct. The complete knowledge structure of CHEM 1C, There are a number of ways of constructS 1999, is given in Appendix 2. ing expert pathways: by difficulty relationships, by the skills needed, or by task analysis between methanol molecules. (18). We chose our hierarchy primarily on the basis of the Questions 8 and 9 have the next level of difficulty in difficulty relationship. An expert would be expected to (i) know the expert pathway. They require knowledge of electronegarelative electronegativities, (ii) understand the resulting placetivities, polarity of molecules, and the various intermolecular ment of electrons in a bond and be able to visualize this at a forces and their relative strengths. In question 11, a basic microscopic level, (iii) predict electron density distributions understanding of boiling is also essential: students are expected and polarities, (iv) predict type of intermolecular forces and to know that boiling requires overcoming intermolecular from these (v) properties such as states of matter and soluforces. Question 12 requires additional knowledge about bility and be able to visualize molecular systems, and then miscibility. Using similar reasoning, students should know (vi) compare various molecular systems. that since water and methanol are polar, their polarities would A number of possible hierarchies exist. If one combines funenable the formation of intermolecular attractions: formation damental understanding with system complexity ranging from of hydrogen bonds between water and methanol. Finally, one atom to a molecular system, a possible hypothetical hierarquestion 15 requires the comparison of three molecular systems chy is the one depicted for the expert structure in Figure 2. and a knowledge of what determines the state of a molecular A specific hierarchical analysis is given below. According system at room temperature. to the expert pathway, answering questions 1, 2, 3, and 4 Both student critical learning pathways differ from the correctly requires knowledge of relative electronegativities. possible expert pathway in two major areas: the understanding Ordering the atoms present in order of increasing electrothat H atoms have different electron densities depending on negativity is sufficient information to allow students to correctly whether they are bonded to O or C (question 7), and the answer questions 2 and 3 on electron density distributions. ability to visualize H-bonded systems at the microscopic level, Using this reasoning, students should be able to identify the particularly in question 10. The student response states electron density distributions in the H2O molecule (question indicate a much later acquisition of these ideas than would 5) and the methanol molecule (questions 6 and 7) and asbe predicted from the expert pathway. On the other hand, certain that they are polar molecules. In question 7, students the most complex question (15) appears earlier than expected must recognize from electron density distributions that the from conceptual development. This was especially noticeable in hydrogen atom attached to oxygen bears a partial positive CHEM 1B, W 1999, where the states of CH4, H2O, and NaCl charge, while the other three hydrogen atoms attached to at room temperature had just been covered in lecture. It is poscarbon bear no partial positive charges. sible that these substances are part of every student’s daily expeThe next level of difficulty in the expert pathway comes rience and therefore even the scientific rationale is better retained from questions 13 and 14. These require knowledge at two as observed in the students’ justification for the answer. levels. Knowledge of electronegativities is required to determine Besides following the general trends in the class, indithat the molecule is polar and to realize that the polarities vidual students’ understanding of a concept can be analyzed. result in intermolecular forces that lead to hydrogen-bonding Falmagne has done this successfully, for instance, in the Irvine, interactions. Next comes question 10, which requires molecuCA, Unified School District, where individual student response lar-level representation of the hydrogen-bonding interactions JChemEd.chem.wisc.edu • Vol. 79 No. 6 June 2002 • Journal of Chemical Education
759
Research: Science and Education
states are available weekly for following students’ progress in mathematics and beginning algebra (19). In this study, a response state of [8] would indicate that the student had somehow memorized or guessed that methanol had stronger intermolecular forces that ethane. If the student understood that the stronger intermolecular forces came about because of hydrogen bonding, which in turn was brought about by electrons being closer to O than H, then he or she would have been in a response state [1,2,3,4,5,6,7,8]. Common Misconceptions Misconceptions exist at all levels: (i) understanding the definition of electronegativity; (ii) applying the concept of electronegativity to predict bond dipoles; (iii) predicting intermolecular forces; and (iv) applying intermolecular forces to predict physical properties. A special category is the visualization of molecular systems at the microscopic level. Question 2 addresses the notion that an atom in a chemical bond with the greater electronegativity will have more electrons closer to it or higher electron density. The problem asks (diagrammatically) whether bonding electron pairs in H2O, will more likely be closer to oxygen, closer to hydrogen, or directly between the two. This problem is very similar to the one used by Peterson and Treagust (20) and also by Birk and Kuntz (15). A significant number of students answered that electrons will spend most of their time directly between O and H in a water molecule. This misconception seems to arise because most general and organic chemistry textbooks indicate that the electrons will indeed be found halfway between O and H. This happens because when teaching Lewis structures, textbooks often leave electron density considerations for later. Since the Lewis structures provide merely an accounting of electrons, the actual placement (closer to one atom or in the middle) after electronegativities have been introduced is never incorporated into the structure. The problem occurs because students tend to take simple models literally (21). It was surprising to find that in the beginning of the organic course (Chem 51A, F 1999, pretest) ~30% of the students placed the electrons in the middle of the oxygen–hydrogen bond (question 2). It will be very difficult for students who “do not know where the electrons are” to understand functional group chemistry. A common misconception of college chemistry students relates to the inability to distinguish between electron density distribution in H atoms in different chemical environments in a molecule (question 7). No distinction is made between hydrogen atoms bonded to carbon and those bonded to oxygen. This makes it difficult for the student to understand acidities of various hydrogen atoms and the related phenomenon of hydrogen bonding. The confusion becomes obvious in drawings of molecular systems at the microscopic level, where the hydrogen bond is to be designated by a dotted line. See Figure 3 for some examples of student work. The most common misconceptions were in fact found in questions 10 and 12, which depend on the student’s answer to question 7. This is troublesome because if the students cannot visualize molecules in a beaker, there is no basis for memorizing abstract trends for various physical properties. In question 10, students often displayed very little true understanding of intermolecular interactions. They did such things as draw hydrogen bonds from the methanol oxygen 760
H
H
H O C H
H
H O C H
H
H O C
H
H
H H O C H
H
H H
H O
H H O C H
H
H O
H
Figure 3. Typical student answers to (top) question 10 and (bottom) question 12 indicating misconceptions.
to another methanol molecule’s methyl hydrogens (Fig. 3). In question 12, even when the hydrogen bond was drawn correctly between the oxygen of one molecule and the hydrogens of the other, the nonacidic hydrogen on the carbon was used. This shows a lack of understanding of varying electron densities of non-equivalent hydrogen atoms. Other misconceptions also appeared quite commonly. For example, some students drew hydrogen bonds as one would usually write covalent bonds; that is, they drew solid lines. The confusion of a hydrogen bond with a covalent bond is also obvious in answers to question 13. In question 12, another common misconception was that ethane should be more soluble than methanol in water because the intermolecular forces in ethane are weaker than those of methanol. The reasoning was that water will more easily be able to break apart the weaker intermolecular forces in ethane, and thus ethane will dissolve more easily in water than methanol! Conclusions Whereas our last study in organic chemistry indicated that we need to spend more time showing students how to build connections around an organizing theme, this research indicates that not only do we need more time for making the connections, we also need more time to teach the factual material of a fundamental aspect of chemistry—bonding. The students’ knowledge is superficial and does not seem to be transferable: they cannot make inferences. Application of KST indicated a weak logic structure in 6 of the 9 sets analyzed. The students seem to have some disconnected information, which can be easily forgotten. However, the analysis itself can be used as a remedy, since it helps us to assess the students’ cognitive organization of knowledge and therefore enables us to teach with greater insight by going back to the basic principles of bonding with special emphasis on visualizing molecular phenomena at the microscopic level. KST also helps us in organizing the course materials and writing good examinations by emphasizing conceptual development and leaving out disconnected bits of information. The following remedies might apply to dealing with the most common misconceptions. In discussing Lewis structures, it must be pointed out that electrons are in the middle of the bond only when the atoms are of equal electronegativity (in simple situations). Otherwise the electrons will be closer to the more electronegative atom, and the more electronegative atom will have the higher electron density. This is becoming easier as more colorful electron density maps become available (22) and are actually used in textbooks (e.g., Bruice, 23). This “where are the electrons?” method will likely lead to fewer misconceptions of the kind described above.
Journal of Chemical Education • Vol. 79 No. 6 June 2002 • JChemEd.chem.wisc.edu
Research: Science and Education
The Lewis structure problem is related to one where the students assume that all H atoms in molecules have the same electron density, regardless of what other atom they are bonded to. Again, some direct confrontation might be useful here. It becomes very clear when students study 1H NMR that they still have trouble relating the different shifts to electron densities around H in cases where there is no anisotropy. The misconception on electron densities around H also leads to not recognizing electron-deficient H’s that bring about hydrogen bonding. The hydrogen bond is also often mistaken for a regular covalent bond. In teaching, we might have to repeat that the hydrogen bond is not a covalent bond, it is a much weaker interaction. It has even been suggested that we stop calling the weak interaction hydrogen bonding and call it the hydrogen interaction instead! Another approach might be to ask students to visualize what the behavior of a molecular system would be if the hydrogen bonds were indeed covalent bonds (1, pp 186–188). The inability to visualize molecular phenomena at the microscopic level derives from the fact that these depictions are not emphasized enough in coursework or textbooks, starting with high school chemistry. It is assumed that the students can visualize a beaker of water molecules at the microscopic level, which this study and others indicate is clearly not the case. Yet when shown the pictures as indicated in this study or a demonstration or videotape (24 ), the students acquire the knowledge readily. Acknowledgments We would like to thank the students in our research group who corrected tests, analyzed the data, and shared their insights with us: Mohammad Anwar, Nicole Batard, Ai Bui, David Chiu, Henry Liu, Stacy Lonjers, Jenivi Marucut, Amana Rafique, Susanne Spano, and Patrick Wong. Note 1. In the case of CHEM 51B, W 1999, there is a discrepancy between the pretest and the posttest answers to question 4, where the students were supposed to list C, H, and O in order of increasing electronegativity. On the pretest 95% of the students answered correctly, whereas on the posttest only 77% did. One possible explanation is that since the emphasis during this quarter was on the chemistry of the carbonyl group (which was visualized as having a partial positive charge on carbon and a partial negative charge on oxygen), the students might have now confused the ordering of absolute electronegativities of C and H.
Appendix 1. Developing Conceptual Understanding in Science Research Project Chemical Bonding and Applications
Literature Cited 1. Herron, J. D. The Chemistry Classroom: Formulas for Successful Teaching; American Chemical Society: Washington, DC, 1996; pp 186–187. 2. Doignon, J.-P.; Falmagne, J.-C. Knowledge Spaces; Springer: London, 1999. 3. Taagepera, M.; Noori, S. J. Chem. Educ. 2000, 76, 1224–1229. 4. Taagepera, M.; Potter, F.; Miller, G. E.; Lakshminarayan, K. Int. J. Sci. Educ. 1997, 19, 283–302. 5. Bransford, J. P.; Brown, A. L.; Cocking, R. R. How People Learn: Brain, Mind, Experience, and School; National Academy of Sciences Press: Washington DC, 1999. 6. Basili, P. A.; Sanford, J. P. J. Res. Sci. Teach. 1994, 28, 293–204. 7. Reiman, J. S.; Rueter, H. H. Cognitive Psychol. 1980, 12, 554–581. 8. Nash, J. G.; Liotta, L. J.; Bravaco, R. J. J. Chem. Educ. 2000, 77, 333–337. 9. Shusterman, G. P.; Shusterman A. J. J. Chem. Educ. 1997, 74, 771–776. 10. Eylon, B.S.; Reif, F. Cognition Instruction 1984, 1, 5–44. 11. Nakleh, M. B.; Lowrey, K. A.; Mitchell, R. L. J. Chem. Educ. 1996, 73, 758–762. 12. Moore, J. W. J. Chem. Educ. 1999, 76, 5. 13. Nurrenbern, S. C.; Pickering, M. J. Chem. Educ. 1987, 64, 508–510. 14. Johnstone, A. H. J. Chem. Educ. 1993, 70, 701–705. 15. Birk, J. P.; Kurtz, M. J. J. Chem. Educ. 1999, 76, 124–128. 16. Squire, L. R.; Kandel, E. R. Memory: From Mind to Molecules; Freeman: New York, 1999; p 71. 17. Potter, F. Simplified Version of KSP Analysis; http:// chem.ps.uci.edu/~mtaagepe/KSTBasic.html (accessed Feb 2002). 18. Albert, D.; Lukas, J. Knowledge Spaces: Theories, Empirical Research, and Applications. Erlbaum: Mahwah, NJ, 1999; p 7. 19. Falmagne, J.-C. ALEKS at UC Irvine: A Complete Educational System for Arithmetic and Elementary Algebra; http:// www.aleks.uci.edu (accessed Feb 2002). 20. Peterson, R. F.; Treagust, D. F. J. Chem. Educ. 1989, 66, 459–460. 21. Harrison, A. G.; Treagust, D. Sci. Educ. 2000, 84, 352–381. 22. MacSpartan, version 1.0, and PC Spartan, version 1.0; Wavefunction, Inc., Irvine, CA; http://www.wavefun.com/ (accessed Feb 2002). 23. Bruice, P. Y. Organic Chemistry; Prentice Hall: Upper Saddle River, NJ, 2001. 24. Sanger, M. J.; Phelps, A. J.; Fienhold, J. J. Chem. Educ. 2000, 77, 1517–1520.
(Circle one.)
H
a
b
c
d
e
O
O
O
O
O
H
H
H
H
H
H
H
H
H
(Acceptable answers are given in italic type or as specified in the question)
1. Of the elements H and O, which is more electronegative? H
