George F. Atkinson University of Waterloo Waterloo, Ontario, Canoda
Network Analysis and Explicit Complementary planning tools
In a paper presented in thrs Journal, the steps in preparing a critical path analysis of an undergraduate chemistry curriculum were ably set forth ( I ) . It is noted there that the specifications of what we want the student to know a t graduation is advantageous if not essential to this form of curriculum review and revision, and that the ACS Division of Chemical Education Curriculum Committee is moving toward specifying an appropriate curriculum in terms of behavioral objectives. Since the previous publication, various subcommittees of the ACS Curriculum Committee have reported, and a general discussion of performance objectives, reflecting the deliberations of the committee, has been presented by Young (Z), who includes a useful bibliography. Not all instructors favor behavioral definitions of curriculum objectives, and the overenthusiasm of early advocates is generating some backlash (31, which is reflected in the recent well-balanced review and bibliography hy Geis (4). In the light of the developments since 1970, i t may be time to reexamine the possibilities available in critical path methods, and some ways of capitalizing on this new tool. In approaching this task, it is assumed that in most institutions, chemical education will continue to be based on a mixture of ideas and probably on a mixed strategy, not exclusively modularized, or self-paced, or otherwise committed to a single approach. To maximize the advantages of network planning, the capabilities and requirements of the various individualized modes of instruction must be recognized and considered a s alternatives to traditional lecture courses. A number of these are clearly summarized by Goldschmid and Goldschmid (5) in a recent monograph. The earlier exposition of critical path methods ( I ) has shown how useful approaches can be made to some forms of curriculum improvement such as elimination of unnecessary repetition, optimum placement of prerequisites, and demonstration of the later relevance of ancillary subjects. On the other hand, the authors retain the notion of uniform course length and in the end, suggest collecting topics used as critical path jobs into conventional semester courses. Completion of a topic thus continues to be related to expenditure of coverage time, rather than to demonstration of learning achievement by the student. Moreover, the entries used in generating the critical path are entirely knowledge packages. If these are further specified to set out the changes in knowledge, skills, and attitudes expected in each, it will be useful both in rendering explicit what we are trying to do in a curriculum, and in recognizing the kind (possibly in terms of Bloom's domains) and level (possibly in terms of Bloom's taxonomic levels) of learning we are requiring of a student a t any time. Variable Module Length A most useful step toward maximizing the benefits of operationally defined learning goals and critical path organization of curricula is the acceptance of variable length modules as publicly identified steps in the final curriculum. If this is done, it becomes feasible to define each module by asking a series of questions such as these 324
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Journal of Chemical Educatron
1) What knowledge and skills are necessary to begin this module?
What additional knowledge and skills and attitudes will be helpful though not absolutely necessary? (Together, these set the enabling objeetiues for the module, which should he distinguished from catalog-number prerequisites. In practice, prerequisites tend to describe what the student had been presented with at the end of some previous semester; whereas enabling objectives are things he must he able to do or to recall at the beginning of the learning module under development.) 2) What differences in knawledge, skills and attitudes are to be brought about in this module? (This establishes the terminal objectives for the module and thus the learning which is to take place during a student's work with the module. Note that since these are learning objectives, their focus is on the student and not on the instructor.) 3) How can achievement of these differences be demonstrated? (This sets criteria for completion of the module. The word "demonstrated" draws attention to the fact that the learning achievement must be communicable-and preferably must he communicated by-thelearner.) 4) Is any future module dependent on attainment of some particular competence within this module? (This suggests whether student achievement in the module should he evaluated at least in part by criterion-referenced testing. For instance: Is a pass-fail standard to be applied as a driving test? Is a pass standard to he made the key to admission to some further work, like requiring swimming ability of those wishing to learn canoeing? If not, will normative testing suffice, like marking on a bell curve?) 5) Is there same body of important knawledge specially suited to heine the content vehicle for the higher levels of learning desired in this madule (e.g., sugar chemistry as a vehicle for teaching stereisomerism)? 6) How many modes of instruction are appropriate to the module? (Consider: private reading, slide-tape or text-tape package, C.A.I., laboratory wark, supervised problems sessions, seminars, lectures, ETV, ete.) 7) Is this module particularly complementary to, or on the other hand likely to create conflict with, any other module? (Hence, consider encouraging or avoiding near-simultaneous work on both, but remember that conflict of ideas is not always to be avoided.) 8) Does this madule contribute to suitable amounts of redundancy and to reinforcement of some important previous learning by providing (preferablyat aperiodic intervals) for review? Out of such questioning, one module may emerge as a do-it-yourself operation, possihly phrased officially as, "Candidates will prepare themselves for a test on inorganic nomenclature as covered in Doe's programmed text." Or, "Candidates must demonstrate their ability to translate four printed pages of technical literature in German into acceptable English in 2 hr using Patterson's dictionary." Another module may be described as, "Ten lectures will he presented on carbonium ion chemistry. There will he a 2-hr written test, and four out of six questions must be answeied correctly before proceeding to any modules beyond node 17 of the network diagram." Or, "Ten unknown minerals and ceramics will be analyzed for a t least three constituents each. An average grade of 7/10 must be obtained on eight unknowns." The most difficult aspect of variable module length is administrative arrangements. The problems of converting various evaluation methods applied to widely varying amounts of learning into semester-hours of credit is cer-
tainlv nontrivial. One wssihle solution is to beein hv. sen" . arating the two aspects of evaluation: evaluation as a feedback device. and thus Dart of the mechanism for learning; and evduation as an administrative device, recording.steps . of progress toward a demee. This distinction has been made by rickso on (6). ~ h & ,attached to each module may be a scheme for evaluation aimed at showing the student and sometimes the instructor the progress made in achieving the terminal objectives. The impact of this upon administrative arrangements is cumulative and long-term. It assists in answering questions like: How long should be allowed in the critical path for completion of the module? How often should the module he offered? Is there a trend which needs to he investigated toward more or less success in meeting part of the terminal objectives? If the modular pathways to a degree are laid out in a critical path network, one solution to the recording of degree progress for administrative purposes is discovered. The network nodes of maximum connectedness (where the greatest numhers of enabling units converge and/or the greatest numhers of next choices diverge) may he identified and labelled as milestones of p~ogress.~ If desired, these points may he made the locations of formal examinine. In whatever form. thev will be the occasion of formal reports to the registrar's iffice about the progress of the student. If the re~ortinedoes not involve holdine formal examinations, then the node is free of time const~aints.If formal examinations are involved, then a decision on how often to offer examinations is required, and the node hecomes attainable at that interval (say monthly, quarterly, or half-yearly). Regardless of whether the node is marked by a set of essay-type examinations, or by a listing of achievements as varied as a pass-fail on some lah or calculation skill, a letter grade on an essay, and a percentage mark on a multiple-choice test, its significance is that access to a new group of modules is thus gained, and a stage of progress towards the degree is recorded. The advantage of requiring some overall examination a t the chosen nodes is that this will encourage a drawing together of material covered in different modules, and a review of the woods as well as the trees of the student's program. Performance on such an internative examination mav be valuable evidence for academic~~ounsellin~ on future Ehoices or career amhitions, providing insizhts not revealed by the list of modules completed. While the adoption of variable module length should make it possible to avoid padding on the one hand or truncation on the other of some logical unit of work, i t does not guarantee the generation of acceptable modules on the first try. The successive approximations approach outlined by MacKenzie et al. (7) will still he necessary, hut may be undertaken more efficiently. For modules not tied to set lectures, it should be possible to introduce revised material a t any time to be used by the next students to undertake that task, rather than waiting for the annual offering to come round again. If revision of content or review of rate of student progress brings about a change in the estimated time requirement, this does not demand simultaneous compensating adjustment in the length of treatment of other topics to make a course come out to semester or vear leneth. In view of Tmiillo's comment (11 that the use"of criti&l path methods rdduced the required time for offerine a ree ex is tine curriculum bv 23% without introducing vaGabG module 'iength, i t need not he feared that the net effect of adjustments in modules will he a greater time requirement for a degree. Published Critical Path Network The previous presentation of critical path ( I ) does not explicitly recommend publication of the network diagram. There seem to he several reasons why such publication (in the university catalog, for instance) would be advantageous.
Experience in student counselling, and studies of student and even faculty opinion (such as (8)) indicate that tabulated listing of program requirements and alternatives, or of sample outworkings of core plus electives programs, are not an effective form of communication. To supplement or replace such lists hy a network diagram would be a valid experiment. In particular, such a diagram should he able to clarify for the student the patterns of prerequisites. If it cannot, possibly the state prerequisites need review. I t should make much clearer to the student that certain topics (and hence modules) such as nomenclature rules hinge on private effort, and might profitably he undertaken using a conventional or programmed text during a vacation, or in the early days of a semester before assignments begin to come due. Overall, the published network should encourage individually paced learning, and also provide due warning of topics seen by the faculty to he heavily dependent on lectures so that students can plan to clear the decks of other more flexibly scheduled matters when such lectures approach. Also, the student will receive encouragement through following his progress over shorter time intervals, and should find his attention drawn more often to impending decisions to he made instead of having these pile up into yearly crises a t the very times when academic advisors are trying to help everyone at once. This sort of idealized program flexibility is not likely to he achieved quickly or easily in most colleges, and may not even be thought desirable in many places. It does, however, offer an alternative line of thought about various aspects of undergraduate programs. Simpler Forms of Network-Based Planning Large schemes such as those proposed above are not the only ways in which network diagrams can be useful. Nor is it always necessary to use the typical critical path diagram in which arrows represent jobs and nodes represent events (of no time duration). Tmjillo (1) begins with the construction of such a diagram, in which the graphics are purely topological and metrics (such as times) are added as notations; hut derives eventually a more familiar block diagram on a time base (Figures 4 and 5, respectively, in reference ( I ) ) . Lowe (9) using examples of maintainence work in chemical plants, which are themselves iuteresting, shows how to follow the reverse path from a simple schedule on a time base to a critical path network. Battershy (10) presents a more formal treatment of various network planning techniques, including the use of connectivity inatrix notation instead of graph notation for the network, and Roy's method of potentials using node diagrams. In this last system, nodes represent jobs (or in our academic projects, courses) and arrows represent sequence requirements. It will he apparent that the Roy method lends itself to the analysis of course prerequisites. We have recently applied this method to reviewing the prerequisite relationships created by a substantial revision of course offerings. The Roy diagram was first drawn on a time base showing every course occurring as soon as possihle. The diagram was then redrawn showine the term in which each course was normally to be taken: These diagrams appear as Figures 1and 2. Interesting findines included the followine. Although it is obvious common sense to use prerequisites as soon as possible after they have been completed, this was done in only 22 of 50 cases. Delays in other cases are shown in Table I. It also becomes simple to determine the proportion of courses in each subdiscipline, and, overall, which are terminal (i.e., are not prerequisite for any further course), and to determine the length of the "chain" of courses leading to each terminal course. The former information is readily derived from Figures 1 and 2 if desired, and the Volume 5 1 , Number 5. May 1974 / 325
Figure 1. Prerequisite network for a Chemistry program showing sequence requirements only. Subdiscipline symbols: Y, polymer; P, physical: T, theoretical; 0, organic: 8 , biological: A, analytical: and I, inorganic.
Table 1. Delay in Use of Prerequisites*
Terms of delay
1
2
"unavoidable" (Fig. 1) "normal"
4
1
3
4
11 12 4 I
Entries are number of given length of delay. Table 2. Length of "Chain" up to Every Terminal Courses
Length of chain No. of occurrences
2 3 4 5 6 7 8 1 1 5 1 4 1 1 2
a Entries include the terminal course. The critical (longest) path to each terminal course is used.
latter is collected and presented in Table 2. In view of recent public queries in various jurisdictions about possible shortening of undergraduate degree programs, it is interesting to note that even without any adjustments, very few of the sequences of courses in this program could not be accommodated in a 3-yr (6-term) program. However, the excentions include biochemical courses of meat interest to tire many students interested in heal& sciences, and these cannot be liahtlv tampered with without risking. appreciable enrollment'ios~es. After redundant statements of requirements were eliminated, there are found to be only five courses with genuine multiple prerequisites of which three represent the only subdisciplinary crosslinkages-to theoretical in each case. In constructing this network, a t least one clearly erroneous prerequisite was found. The key courses in the development of subdisciplinary areas stand out clearly because of their maximum connectedness. Such courses command special attention in allocating teaching duties, and in monitoring student performance. The extent of the proliferation of terminal courses, and the scarcitv of disci~line-linkina courses was - or intemative brought into sharp focus. Such discoveries about a program change on which a committee had worked conscientiously for almost two 326
/ Journal of Chemical Education
.................\............a ......... m Figure 2. Prerequisite network for a chemistry program showing "normal" pattern of taking courses (dotted liner show delays i n using prerequisites).
years indicate the benefits to be gained from even very simple applications of network analysis. For comparison, we analyzed Trujillo's network, developed on a l-wk instead of a l-term time unit, and found only a total of four delays in using prerequisites: one each of 5 and 15 wk, and two of 30 wk. This is at least a beginning of evidence for greater efficiencies when network techniques are used from the beginning of a revision operation. Possibly one of the most important general points about a momam which the use of network planning reveals is whether it is drawn together by certain-integrative courses near graduation, or whether it diversifies into many unrelatedsuecialities. The common tendencv to consider letting every faculty member "do his own thing" as an elective for the senior classes may easily create an unrecognized and unplanned drift to the latter situation. In the light of departmental objectives, this may be acceptable. If it is not, its recognition is the necessary first step to planning a more integrative program termination, such as that displayed by Tmjillo. Another useful outcome from network planning is the clarification of the place of each course in the program. This simplifies decisions on course and topic objectives and on time allocations to topics in the course. Lilerature Cited ( 1 ) Tmiillo drl Rio. J. J.. Vawas. R. C., and Taylor T. E.. J. CHEM. EDUC., I 548 , (1970). (2) Young, J.A.. J. CHEM.EDUC.. 49. W (19721. 13) Woike, R.L., J. CHEM. EDUC.. 50,99119731. 141 Geir, G. L., "Eahaviorai Objeetiver:' An ERIC Paper. ERIC Clcaringhoui~on Media andTeehnoiogy, Stanford. California94306, April 1972. (51 Goldschmid. B. and M . L., "Individualizing I n s f r u ~ i a nin Higher Education: A Review." Center far Learning & Development, McGiil Univemity, Montreal, r,."L."" q"="-%,
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I61 nickson, S. C., "Grading
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Re~earchonLearnioeandTeachiip,University of Michigan. Ann &br. 1911. Ersot. M.. and H. C.. 'Tea~hineand Lesrninr. hhn-
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1970. Chapter XI. 18) Laurence, S. A,. "Amietim of Firat-Year University Student.." prpaenfed sf OntarioEdvcstionalResearch Cauneil Cooference Toronta 1970. 191 Lowe. C. W.. "Critical Path Analy& by Bar Chan." Business PublicstionsLtd..
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(10) Bsttenby. A.. "Network Analysis lor Planning snd Scheduling," 3rd Ed. JohnWiiey& Sons. NewYork, 1970.
