Meta Tasks for Organizing Prevenient Knowledge In Organic

Small numbers of mental operations, or meta tasks, can mobilize the knowledge students bring to a learning task. Often students do not understand the ...
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Research: Science & Education

Meta Tasks for Organizing Prevenient Knowledge in Organic Chemistry K. R. Fountain Department of Chemistry, Truman State University, Kirksville, MO 63501

One can insert the words in brackets into the statement below, made by the late chess grandmaster Samuel Reschevsky, to get an equivalent description of high-level problem solving in organic chemistry (1): I discovered I had the happy faculty of being able to spot weak and strong points in a position [organic synthesis] merely by a glance at its contour. …I could go on to the next step and enhance my strong points [probability of success], while surveying my weak ones [discarding improbable routes]…. …chess logic [organic logic] is the perception of weak and strong points on the board [in the synthesis] or projecting a few moves [steps] from possibility to reality.

Recent papers in this Journal point to the importance of describing small numbers of simple operations prescribed for attacking mechanistic problems in organic chemistry (2), and of an active learning role for meaningful learning (3). This paper develops a sequence of metatasks, a group of simple operations that relate to the sorts of analytical processes involved in “point count chess” (1). In point count chess the contours of the position are assigned a value calculus, based on the values of the pieces for trading purposes. This calculus allows assessment of a position for planning strategy and tactics. Important terms are defined in the glossary. Using the point count a player can estimate that if a certain number of positional features on the board that are favorable to the player (or unfavorable to the opponent) could be obtained, a pawn could be sacrificed to obtain the position. (A similar process occurs in assessing the values of bridge hands.) Note that this language is esoteric to those who think playing chess means you know how the pieces move. The analogy is very close for students of organic chemistry. The tasks in the chess game could be applied by those initiates who have read Point Count Chess. These kinds of tasks go beyond the correct answers to how the pieces move. (A knight moves once like a bishop and once like a rook is correct knowledge but is not playing chess. However, a knight deep in enemy territory, well supported by pawns, makes a master’s mouth water.) Our beginning students know several moves and are mostly satisfied with these correct answers. We need to steer them into situations where the correct answers lead to tasks that can develop the knowledge necessary to solve problems. These tasks cause students to become aware of the contours of a problem before actually selecting a pathway toward the final solution. They provide preliminary activity that organizes what students already know and project potential approaches to problem solving. The awareness of metatasks provides a background for thinking about the solutions of organic chemical problems and promotes a kind of sober play. This play is described by Reif (4) as a prerequisite for expert problem solving. The logic of expert behavior in solv-

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ing organic chemistry problems is much like that of grandmaster-level chess. That level of chess play involves fantasy, assessment, and synthesis. In contrast, most teaching of organic chemistry seems to involve merely teaching how the pieces move. A reformation of such teaching is important if reform of the chemistry curriculum is to occur. I (with others) have pointed to the importance of this play-and-pleasure aspect of teaching organic chemistry by allowing for a formative activity (5). Although students possess much prevenient knowledge from previous classes and experiences, a simple learning task such as filling in concept maps seems to totally stop them. The usual excuse is “There is nothing to put in the little circles until you teach us something.” Clearly, in such cases, the “happy faculty” written about by Reschevsky is not present. This fact indicates that not much learning has occurred—mere fact-gathering has. It is necessary to reinstitute for students both a spirit of play and an ability to organize what is already known as they begin their organic chemistry. The system of metatasks plus the formative material discussed in this paper, applied within an active learning milieu, supplies students with both sober play and organization abilities. The Learning System This section describes the entire learning system (engine) used by several professors at Truman State University (Fig. 1). Such an active learning system is certainly not unique to organic chemistry, but is similar to what Johnson et al. describe as typical of cooperative classrooms (6). Figure 1 shows the flow of information throughout the class. Metatasks supply a constant background for play and organization of tacit knowledge elicited in formative material. Focal awareness is developed by the experiential learning in the classroom. In this experience the teacher presents his/her discovery about what the text says about an entity, allowing indwelling of his/her skill by students by exposing it. The important coherence with any theory under discussion is established inside the “base group” by discussion. Base groups are groups of students having a stable membership charged with providing each member of the group with encouragement, assistance, and the support needed for progress in the class. The base groups feed back information from the summative (i.e., evaluative) portions of the course. The major responsibilities of the base group are (i) to master and implement the concepts, body of knowledge (facts), and theories of the class; (ii) to ensure that all members of the base group master and appropriately implement these features; and (iii) to ensure that all class members master and appropriately implement these features also. Base groups are expected to maintain relationships with the entire class and to work to support mastery-level achievement by the entire class (6). They are the units that define

Journal of Chemical Education • Vol. 74 No. 3 March 1997

Research: Science & Education production bonuses. In each learning task (experiential learning) an attempt is made to organize prevenient knowledge by mobilizing tacit understanding through formative quizzes. Subsequent application of metatasks organizes the conversion of tacit knowledge into prevenient knowledge for application to the specific learning task. Formative Experiences Formative periods are talkative, almost interactive, opening the mind and psyche to the game. Information about their questions is always elicited from the students. Pointing back to a previous experience (e.g., general chem topics) is often used. Usually a formative session in class ends with the question “Now where did the information you used to solve this problem come from?” If the instructor is adept at eliciting information from students the answer is usually “From us!” Student knowledge is then praised. “Good for you!” All scoring points in such a course are not of equal value. Points assigned to this phase are equivalent to “Monopoly” money. Correction is, of course, supplied as rigorous answers.

Examples of Formative Quiz Questions (Further examples are provided in the syllabus available from the author on request.) These are all from Solomons, T. W. G.; Organic Chemistry, 5th ed.; Wiley: New York. 1. Consider Table 1…and read all of this section. Recast the notion of structure theory so as to account for the differences in the properties of the compounds in Table 1. Make this recasting in the form of a positive statement about structure theory. Acceptable answer: The way atoms are connected determines the measured values of their properties. 2. Consider the molecules BF3, CH 4, and NH3 in Lewis structure terms. Two rules seem to be very important in making Lewis structures: (i) electrons are paired in stable molecules; (ii) each element except H needs to acquire eight electrons around it for saturation of valence. Which of these two rules is the stronger rule? How can the violations be

Figure 1. An active learning engine.

explained for the weaker rule? Acceptable answer: The rule of pairing is the stronger rule because in each case each electron occurred in a pair and none as single electrons. Exceptions occur when there are not sufficient electrons around a central atom to both pair and form an octet, or where an atom has too many electrons to share with atoms having only one electron to share. In these cases an octet is still maintained. (Hypervalent cases are considered later.) The Metatasks These are organizing operations designed to generate approaches to problem solving. They are much like the intermediate inclusive concepts described by Novak and Gowin in a hierarchical learning scheme (7). They represent activities, perhaps done subconsciously, by an organic chemist who is playing with a problem before deciding on a route to explore. They organize prevenient knowledge. The metatasks for this paper are: Table 1. Properties of Ethyl Alcohol and Dimethyl Ether Ethyl alcohol C2H6O

Dimethyl ether C2H6O

Boiling point (°C)

78.5

{24.9

Melting point (°C)

{117.3

{138

Displaces hydrogen

No reaction

Property

Reaction with sodium

1. Locate the electrons. This usually involves Lewis structures, at least at first. Molecular orbitals rapidly come into play as the remainder of the metatasks are installed. The explicit connection of the role of electrons with every other part of organic chemistry alerts students to the necessity to learn structure. Later, two subtasks are appended under this major one: (i) distribution of electrons in a bond (electronegativity and resonance arguments apply), and (ii) discussion about the energies of electrons in σ and π bonds deals with availability of electrons toward electron demand. 2. Organize the space around the atom. This involves both application of the general chemistry valence shell electron pair repulsion (VSEPR) theory and use of antibonding MOs. Students come to look on a molecule as a collection of quantum spaces, either occupied or unoccupied (potentially occupied) by electrons. This point is tightly connected to the way most modern organic chemists view molecules. Additionally, it alerts students to view all molecules as potentially reactive. The experience gained in discussion of the reactivity or inertness of atoms in general chemistry applies to molecules too. This congruence of earlier material when applied in such an active fashion so early in the organic chemistry course rapidly encourages students to begin thinking of how other facets of their prevenient knowledge could apply. This experience teaches students to expect electrons to move from one quantum space in one molecule toward another quantum space in a different molecule. The early notions of acid–base chemistry are amended to show that (i) transfer of two groups between pairs of electrons is the most fundamental event occurring in acid–base chemistry and (ii) every bond is also a potential site of reaction through its antibonding MO. 3. Find out where electrons are likely to go. This notion is presented first in terms of Lewis acid–base theory. It is then expanded to interaction of electron pairs with

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Research: Science & Education antibonding MOs. 4. Put the electrons where you expect them to go. This task begins the play part of the learning process. 5. Consider energy changes (usually enthalpy). Which direction does the energy go, up or down? How does structure affect the energy? Are there special features present that affect energy? 6. Consider underlying principles. Are there positive charges on electronegative elements? Are there separations of unlike charges? Are the same charges close together (Coulomb’s law types)? Are valency rules violated? 7. Interpret the results of the process. Do they make sense from what you understand from your studies? 8. Are there known analogies? What other things we have learned are similar to the present possibility? In a telling exchange, a student described these tasks early in their usage as “something to do while awaiting inspiration”. Actually, for beginning students, these tasks organize approaches to understanding much of organic chemistry. The presentations of several examples of their applications occur in the next few sections. Applications of the Metatasks Examples from both early in the class and later on are provided from acid–base chemistry and reactivity considerations. The format is (i) statement of the problem, (ii) expected student applications of metatasks, (iii) expected student reasoning. My commentary is in square brackets. First, consider the molecules BF3 and CH3NH 2. Write a reaction predicting their reactivity. Task 1. Locate electrons. [This H H task introduces at an early stage F F N the notion that one prospers best B by drawing out the details. NOTE: H C H F The authors of most textbooks tacH itly assume that students do this. Most beginning organic students do not or cannot!] [Once this task Figure 2. Placement of is accomplished a small reward electrons. ensues. We can now start to play with the problem.] (See Figure 2.) Distribute the electrons within bonds in the molecule. (Where will electrons likely go?) Each B–F bond is polarized toward F. [The prevenient knowledge comes from application of electronegativity arguments. The act of arguing is important. Most students beginning organic chemistry do not understand that this form of argument is central to most organic problems (5).] This would leave the B atom quite electron poor. The bonds are all σ bonds, except for lone pairs on F. The lone pairs are not very available because they are on the most electronegative element. Task 2. Organize the space around the atoms. The B atom is sp2 hybridized, thus planar (Fig. 3). It possesses an empty p orbital. F

H B

F

F

Figure 3. Organization of space around the BF3 molecule.

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H C

H

N H H

Figure 4. Organization of space and location of electrons in CH3NH2.

The CH3NH 2 is sp3 hybridized in C and N. Extra electrons are on N in an atomic orbital (Fig. 4). These electrons are more available than the σ orbitals, so this is the site of the reaction. Task 3. Find where the electrons are likely to go. The most available electron pair likely inserts into the most available space. So, N:→B. Task 4. Put the electrons where they are likely to go. F

F

B F H C H

H

N

H

H

Figure 5. Successful application of metatask 4.

Task 5. Consider energy [in this case, enthalpy]. If this reaction actually does go it is in the same direction as forming a covalent bond between two atoms. Bond formation is usually quite favorable if valency considerations are met. If the reaction goes, probably the energy of the system (CH3 NH2 and BF 3) decreases. It would be an exothermic reaction. [If this kind of exchange of information occurs as part of a formative quiz, the question of the reality of the reaction would exist. The formative quiz questions given above would lead students to the knowledge that the reaction occurs.] Task 6. Consider underlying principles. Would two oppositely charged atoms be stable together? The distribution N+–B{ results from logical thinking about the role of electron donation. Task 7. Interpret the results of the process. A covalent bond forms. Opposite charges are located next to each other. Energy is probably lowered. Similar items are known from the textbook. Something similar occurs from general chemistry. Task 8. Are there known analogies? Reactivity between atoms concerns transfer of electrons from specific regions on atoms to specific regions between atoms. Reaction 1 completes the process. {

+

BF3 + NH3 → F 3B– NH3 Reaction 1

A more sophisticated application from deep in the second semester appears with the reaction 2.

O

H2SO4 conc.

?

Task 1 Locate the electrons. Lone pairs are on O in both the acid and the ketone. The π electrons of the C=O group are held less tightly than the σ electrons in the C=O. They are polarized toward O. Task 2 Organize the space around the atoms in question. The H–O groups of sulfuric acid are likely to have σ* orbitals that are low-lying. The π* orbitals also deserve consideration, but transfer of electron density to them is not likely from H2SO4.

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Research: Science & Education Task 3 Find out where the electrons are likely to go. Either the lone pairs or the π bonds in the C=O group must act as a base. The lone pair is most likely because these electrons are less bonded than the π electrons. Task 4 Put the electrons where you expect them to go. (Reaction 3.)

+ HOSO3H O

+

+

–OSO H 3

O H

Tasks 5 & 6. Consider energy and underlying principles. Now what should we do? To progress further we need to decide what to do with electrons. If worry about energy is to be next we can decide only that the protonation occurs, from the definition of a strong acid. Resonance allows us to place charge on the C atom, as below, and is a special underlying principle. [Application of tasks 5 & 6 ] The energy task is thus done. Task 7. Interpret the results of the process. The process makes sense from acid–base theory.

C

O

C H

terial. Pondering this caused me to wonder if it results from lack of a common paradigm between fields. To truly reform the teaching of chemistry we must get at fundamental aspects of learning. A chemist’s knowledge of content is simply not useful in creating educational reform. We are thus cut off from the very understanding we need to reform— fundamental knowledge of the act of learning, discovery, and recognition of problems. An attempt to bridge the perception gap, inherent in such a situation, is to project the elementary aspects of knowing, creating knowledge, and discovery into a particle simile understandable by chemists. The tacit understanding of Nature (in the Polanyi sense) of most chemists is a particle model. The modification of this particle understanding by claims of the Copenhagen interpretation of quantum mechanics (9) seems to not bother many chemists because it leaves the major uses of the tacit model intact. The astonishing claims of the Copenhagen school are thus quietly subsumed under the continued usefulness of the tacit model without much fuss. Something similar could occur with the claims of educational theory, especially the more esoteric (to chemists) features, if we could understand learning in a sense similar to properties of quarks in an elementary particle and the exchange of information between them. I propose a particle simile in which the elementary act of learning is a gnoson (Greek gnosis = knowledge + on = particle). A gnoson would have the structure suggested in Figure 6.

O H

Resonance in a protonated carbon

Task 8. Are there known analogies? Alcohols and ethers protonate the same way (lone pairs). The present process is likely due to resonance stability of the oxo cation. What does the cation then do? If it can get a pair of electrons from the benzene ring, cyclization is possible. Apply task 1 again. There are two choices. Application of task 5 here allows choice of 6 ring formation rather than 5 ring at the ipso position. Application of task 6 reveals no special underlying principles other than resonance to worry about. Task 7 allows interpretation of the ring closure to be a type of Friedel-Crafts reaction. Analogies are known from the study of the Friedel-Crafts reaction. This type of instruction fails occasionally when students become content with simple answers. In the ring closure example just cited, trivial answers occur when students are content merely with protonation of the C=O group. This kind of failure can be taken care of by a policy that distinguishes simple solubility from actual acidcatalyzed reaction. Careful planning with a fully developed set of specifications for each unit heads off most of the simple answer troubles (5). Discussion Applications of the metatasks are similar to what occurs as a scientist discovers a new elementary particle. To get students involved in their own learning we must guide them to a discovery of how knowledge is constructed in our field. Experience shows that chemistry professors read neither much scientific philosophy nor much educational ma-

Figure 6. Suggested structure of a gnoson.

By analogy with the posited structure of a proton, which chemists seem to have no trouble with, the gnoson has the following characteristics. The quarklike particles within the gnoson are mediated in various ways by the exchange of the virtual photons coherence, focal awareness, and integration. The mediations shown in the figure are only one set of various ways to bring about the conversion of a question or problem to new knowledge. Occasionally this transformation occurs with emission of jets of high energy photons. These photons have been known to penetrate psyches with production of endocharm. The relationship of the gnoson idea to metatasks is simply that the metatasks promote focal awareness of the problematic nature of what we know. Chemists use these metatasks when they do these kinds of actions, but they are so used to doing it they have subsumed this knowledge into a tacit basis for action. Many students have no such basis with which to mobilize their thinking to begin work on a problem. The awareness of avenues for problem attack become clearer when coherence and integration between prevenient knowledge, tacit skill, or knowledge occurs as it

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Research: Science & Education bears on the question. To learn is a two- or three-phase process. In the first phase, a gnoson must be captured or generated. This capture or generation is the responsibility of the Intelligent Quantum Teacher (to make the particle simile complete with the Copenhagen interpretation). The Teacher organizes the experiment in such a way that the necessary capture of the gnoson can occur. Polanyi would say an “indwelling of the TEACHER’s art would occur” (10, p 17). The concept of indwelling includes interiorization of the indwelt entity. Interiorization is an act to identify with the teaching in question in such a way as to rely on it for understanding the nature of what is learned. At Truman State University, several professors believe that the formative material mobilizes students’ tacit knowledge by asking them interpretive questions about what they have read in the text. In the context of base groups, such interpretive activity exposes an individual learner to the learning styles (tacit knowledge) of all who partake in the group, thus allowing an indwelling. In this sense Polanyi points out that chess players replay the games of grandmasters to “indwell them”, to see what the grandmaster had in mind when he made the brilliant queen sacrifice. Active learning requires students to indwell a learning moment, to capture their own gnoson. The teacher’s role is to teach them how to capture gnosons, and to organize the classroom environment to do so. In the second phase, the tacit understanding must be organized into prevenient knowledge. Some scheme of playing with both tacit understanding and that knowledge required to solve the problem must occur. The metatasks lead students to play in a general manner with what they already understand about the general topics going into the problem solutions. This play also enables them to see the problem as a problem more deeply. Polanyi clearly points out the difficulty with noting a problem except in terms of tacit understanding (10, pp 75–80). Yet, looking forward before the event (of discovery), the act of discovery appears personal and indeterminate. It starts with the solitary intimations of a problem, of bits and pieces here and there which seem to offer clues to something hidden. They look like fragments of a yet unknown coherent whole. This tentative vision must turn into personal obsession; for a problem that does not worry us is no problem: there is no drive to it, it does not exist. This obsession, which spurs and guides us, is about something that no one can tell: its content is undefinable, indeterminate, strictly personal. Indeed, the process by which it will be brought to light will be acknowledged as a discovery precisely because it could not have been achieved by any persistence in applying explicit rules to given facts.

Much has been said about discovery learning that does not include the sentiments in the previous paragraph. Discovery learning does indeed require us to go “where no man has gone before” in each instance of such learning. At the beginning of learning the tacit dimension is thus all important. A discussion of the effect we believe occurs with using the metatasks includes some features of Polanyi’s philosophical viewpoint of tacit knowledge or tacit learning (10, 11). His views are reflected in at least one major work on educational psychology (8), although I know of no direct connection. Play within the basic framework extended by the metatasks allows students to make choices of the results of their play that should lead to strategies for learning the integrated structure of organic chemistry. Such learning ex-

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presses itself in a real mastery of the subject that allows projection forward to new learning tasks. The more complete the integration into a self-constructed framework the more able one is to project from the present knowledge to future learning. In this experience the teacher presents his or her discovery about what the text says about an entity, allowing indwelling of his or her skill by students by exposing it. The important coherence with a theory is established with the base-group interactions. These groups feed back information from the summative (evaluative) portions of the course. The new knowledge constructed in such groups form the tacit knowledge of a new learning task. This process is demonstrated by Gowin with his “telling questions” and parade of knowledge VEEs (12). Polanyi also points out that we subsume material to the level of skills and that this (newly) tacit knowledge projects us into recognizing a new problem. We cease attending to tacit knowledge (attending from tacit knowledge) to attend to a “distal” knowledge (the new problem) in much the same way a concert pianist ceases to attend to the hands in order to give life to a performance. A second consideration of the use of these metatasks can be related to papers in this Journal (13) and other works on teaching for thinking (14). Reference 13 points out the desirability of continuing the student thinking task in question and answer sessions in class. The metatasks provide a facile way of doing this. One can always ask students “Which metatasks are you applying here?” to aid them in clarifying their problem solving. This strategy points out to students the necessity to analyze how they are solving problems. In this way the metatasks act as a scaffold for building the cognitive processes necessary to problem solving. This notion of a scaffold is captured in the following quote from ref 14. A major organizing concept for the teaching/learning of higher order cognitive strategies is the scaffold…or instructional support. A scaffold is a temporary support provided by the teacher (or another student) to help students bridge the gap between their current abilities and the goal. A scaffold is temporary and adjustable. It is used to help learners “participate at an ever increasing level of competence”… , and it is gradually withdrawn as the learners become more independent.

The philosophy of metatasks agrees with these works conditionally. It is an important difference that the metatasks become tacit knowledge, or parts of skills (i.e., they are not temporary, but are part of the overall knowledge). The efficacy of the metatasks is reflected in Table 2, which compares (largely) the same students from consecutive semesters of organic chemistry. This survey was originally done to ascertain the effects of single features of the course on student attitudes. The data were collected as a set of course features vs. a set of activities, and the students scored each feature in terms of how they felt it helped with each activity. The resultant table of data was used to construct an attitude map (15). The metatasks in Table 2 are one set of the data in Fig. 7 for the first semester. The other data are relevant because Figure 7 shows the relative attitude students show toward the metatasks in relationship to the other course features. (Is metatasking worthwhile compared to the other things we do?) Table 2 represents then a slice across a 3-D surface, such as Figure 7. The view of such a surface is limited in a printed medium, but insight can be gained when it is turned

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Research: Science & Education Table 2. Student Attitudes Toward Metatasks Scorea Attitude

Fall semester mean (SD)

Spring semester mean (SD)

They help me read the textbook

4.3 (3.1)

6.4 (0.8)

They help me prepare for class

4.6 (3.1)

7.8 (1.5)

I understand the lecture better

6.3 (2.8)

8.3 (2.1)

They help in exam preparation

6.3 (2.1)

8.6 (1.1)

They are of no use at all

2.3 (2.4)

2.2 (1.3)

They help me visualize spacial material

5.6 (2.94)

7.2 (2.2)

a

Based on a 10-point scale: 1 means completely disagree and 10 means completely agree.

at various angles in the spreadsheet. (I used Microsoft Excel 5.) The trend line corresponding to the metatasks is darkened in Figure 7. The figure shows the relationship between the metatasks and other features in our active learning engine. It indicates that when these metatasks are used as a part of a conscientious effort to promote active learning, they contribute at least as much as the other features used in the course, and perhaps enhance the effectiveness of other features. Statistical analysis would have been desirable for this learning system but was not possible because of the small sample size. We expect to give a full statistical treatment in the future. Meanwhile the features–activities–attitude score data may be taken as Piagetian clinical interviews. The trends in Table 2 indicate that the tasks are valuable to nearly everyone. The low score of 2.3 or 2.2 in the fifth item indicates high levels of satisfaction. Growth in acceptance of these tasks increases from their introduction early in the first semester to late in the two-semester sequence. Some surprises exist. The tasks originally were useful to mediate lecture material. Students report that the tasks find uses outside of lecture. We believe that the increased usefulness of these tasks indicates that they increasingly become part of the tacit learning they bring to new learning tasks. We can conclude that application of the metatasks described in this paper in an active learning system increases the level of student awareness of organizing pathways for problem solving. The overall performance of this class has been extremely good. For a class of 26 students over the entire second semester we have 18 operating at the 75% level on hour exams, and 21 at the 75% level on take-home weekly quizzes. These levels of attainment are unprecedented at NMSU, and they indicate near-mastery levels for these students. While NMSU has been selective in admissions we have not noted this level of success previously. Anecdotal interviews with students find a great level of satisfaction that they are actually learning something. The level of endocharm (5) seems to be greatly enhanced over levels I, for one, have previously observed. Confidence levels are likewise high as measured by the amount of participation in classroom projects and question and answer sessions. An additional index of the performance of the class taught by these methods is the scores on the American Chemical Society (ACS) standardized final exam. The median score on the 1994 version was 49 items correct (raw score), high 65, low 32. Norms were not available at the time

Figure 7. An attitude map of features vs. activities for firstsemester organic chemistry.

of writing. However, the raw scores indicate a high degree of attainment with this method of instruction. Anecdotal stories abound of how the use of metatasking aids in other courses also. Glossary Tacit knowledge (tacit understanding or tacit learning): knowledge that we know so well we take it for granted. Polanyi points to riding a bicycle around a curve (10). This can be done tacitly, or described quantitatively, with rules showing balances of forces etc. The tacit knowledge in this case consists of the learning our body has done without communication to the intellect in a formal way. Prevenient knowledge: knowledge that comes before the learning inherent in a learning task. This simple descriptive term is what I take to summarize the Ausebelian knowledge that is so important in that theory of knowledge construction (2, 7, 8). Gnoson: the elementary “particle of learning”. It is more than the “fact” learned, but less than the entire process. In the simile of an elementary particle (9) a gnoson is a complex particle bounded by past knowledge (or prevenient knowledge, tacit knowledge in Polanyi’s sense (10, 11), and future knowledge. The mediators of a gnoson consist of (i) integration of marginal and tacit knowledge, subliminal clues, or subceptional learning (10, 11); (ii) focal awareness of the object to be learned; and (iii) coherence with a theory or subsumed knowledge. A virtual gnoson is a gnoson having an anti-character to one of its mediators. Examples are (i) anti-integration (failure to integrate) of subceptual learning or tacit clues allows a discovery to not be appreciated; (ii) anti-focal awareness disallows discovery (the importance of focal questions has been discussed by Novak and Gowin [7]); (iii) anti-coherence refuses discovery and attendant knowledge construction, because without connection to what we already know we cannot recognize new knowledge. Formative: materials and activities that are used primarily to induce play or as an advanced organizer for experiential learning. This material must be only lightly evaluated, with a view to aiding formation of concepts and inducing activity. Often credit is given for incorrect answers that display (or indicate) innovative or substantive thought. Focal awareness: being aware of what you are focusing on implies not paying attention to peripheral affairs.

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Research: Science & Education Focal awareness is Polanyi’s term for differentiating his two basic terms in knowing into proximal and distal terms. Proximal terms are like skills we are not conscious of when we perform. A concert pianist does not concentrate on his fingers, but is focally aware of a host of other items that give life to his performance. Organic chemistry professors are often guilty of saying to students, “Here are all the notes! Why don’t you play brilliantly?” The students responses are often, “Where should we place our fingers?” Whereupon we say, “Forget about your fingers and play the notes!” This is a very good thing for a concert pianist to do. It is correct that we should tell them this, but we should also help them to not worry about their fingers. Experiential learning: consists of presentation of materials and methods to be mastered. Such material is presented as classroom activity consisting of instructor coaching, raising issues, in-class assignments, presentations of textual material, etc. A second branch is the working of weekly take-home quizzes. These quizzes are problems without supplied answers. The weekly quizzes are worked on individually or in base-groups meetings. In-class assignments are always done in base groups. So are the computer exercises (currently all based on HYPERCHEM™) Production bonuses: rewards for groups achieving given levels of scores on unit exams. Each member of the successful groups receives the reward. Each base group can receive the reward. Our current reward is five bonus points for each member of a group that achieves an every-member score of 70% (raw score) on a given hour exam. It is important that nonperformance within these base groups be recognized and confronted. Our basic advice to nonperforming individuals is “Perform or drop the class!”

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Acknowledgment I thank the students of CHEM 329 and CHEM 331 for their diligence and curiosity about learning that made the results so rewarding. Literature Cited 1. Horowitz, R. A.; Mott-Smith, G. Point Count Chess: An Accurate Guide to Winning Chess; Simon and Schuster: New York, 1960. 2. Wentland, S. H. J. Chem. Educ. 1994, 71, 3. 3. Pendly, B. D.; Bretz, R. L.; Novak, J. D. J. Chem. Educ. 1994, 71, 9. 4. Reif, F., J. Chem. Educ. 1983, 60, 948. 5. Afzal, D.; Delaware, D. L.; Fountain, K. R. J. Chem. Educ. 1990, 67, 1011. 6. Johnson, D. W.; Johnson, R. T.; Smith, K. A. Active Learning: Cooperation in the College Classroom; Interaction: Edina, MN; especially p 8:24. 7. Novak, J. D.; Gowin, D. B. Learning How to Learn; Cambridge University: New York, especially Chapter 2 pp 15–20. 8. Ausubel, D. P. Educational Psychology: A Cognitive View; Holt, Rinehart and Winston: New York, 1968. 9. (a) Herbert, N. Quantum Reality; Anchor, Doubleday: New York, 1985; (b) Zukav, G. The Dancing Wu Li Masters; Bantam New Age: New York, 1979. 10. Polanyi, M. The Tacit Dimension; Anchor, Doubleday: Garden City, NY, 1967. 11. Polanyi, M. In Knowing and Being; M. Grene, Ed.; University of Chicago: Chicago, 1969. 12. (a) Gowin, D. B. Educational Theory; 1970, 20, 319–328; (b) Encyclopedia of Educational Research; H. E. Mitzel, Ed.; Free Press: New York, 1982, Vol. 3 pp 1413–1416; as cited in ref 7. 13. Kovacs-Boerger, A. E. J. Chem. Educ. 1994, 71, 302. 14. Rosenshine, B.; Guenther, J. In Teaching for Thinking; Keefe, J. W.; Walberg, H. J., Eds.; Reston, VA, 1992; Chapter 4. 15. Delaware, D. L.; Fountain, K. R. J. Chem. Educ. 1996, 73, 116.

Journal of Chemical Education • Vol. 74 No. 3 March 1997