========================================================================= Date: Wed, 12 Jun 1996 07:43:01 EDT From: Donald Rosenthal Organization: Clarkson University Subject: DR- BEGIN DISCUSSION OF PAPER 2 CHEMCONF '96 New Initiatives in Chemical Education An On-Line Symposium, June 3 to July 19, 1996 Sponsored by the American Chemical Society's Division of Chemical Education Organized by: Donald Rosenthal, Department of Chemistry, Clarkson University, and Tom O'Haver, Department of Chemistry and Biochemistry, The University of Maryland at College Park. It is Wednesday, June 12, 1996. I wish to thank Jerry A. Bell and Andrew Ahlgren for submitting their paper, and both of them and many of you for the stimulating discussion. Discussion of Paper 1 is now over. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ There will be additional time for General Discussion between July 15 and July 19. >From 8 AM Eastern Daylight Saving Time (EDST) today until 8 AM EDST on Friday, June 14 you have an opportunity to discuss Paper 2: "The Role of Representation in Problem Solving in Chemistry" by George M. Bodner and Daniel S. Domin Your discussion and questions should be sent to: CHEMCONF@UMDD.UMD.EDU or CHEMCONF@UMDD.BITNET In order to insure that this On-Line symposium functions smoothly PLEASE READ THESE BRIEF INSTRUCTIONS CAREFULLY. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The SUBJECT LINE can be useful in keeping track of various discussion threads. For example: P2 - GJ - D - JS - Problem Solving P2 indicates the message pertains to Paper 1. GJ are the initials of the sender - George Jones D - JS identifies discussion (or an answer) of a question from JS A brief (less than 40 character) description of the content or discussion thread. Please do not append or include a long quotation from the paper or a previous question or discussion message. Quote only a few lines and place a ">" at the beginning of each quoted line. CHEMCONF IS NOT TO BE USED FOR SENDING GENERAL MESSAGES OR EXTRANEOUS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ QUESTIONS. ^^^^^^^^^ Be courteous to others in your responses and your e-mail practices. Please make your comments and questions carefully reasoned and succinct. Send one long message rather than several short messages. (Let's try to maximize Quality/Quantity.) If you wish to sign off, change your mail options, retrieve files, etc. remember to send such request to: LISTSERV@UMDD.UMD.EDU or LISTSERV@UMDD.BITNET and NOT CHEMCONF. (Listserv commands were provided when you signed on and are available on the World Wide Web.) Thomas O'Haver (University of Maryland, Phone: (301) 405-1831 e-mail: to2@umail.umd.edu), symposium co-chair, is managing the CHEMCONF Listserv and the World Wide Web. Please contact Professor O'Haver about Internet problems. Donald Rosenthal Symposium Co-Chair and Chair, Committee on Computers in Chemical Education Clarkson University Phone: 315-265-9242 E-mail: ROSEN1@CLVM.CLARKSON.EDU ========================================================================= Date: Wed, 12 Jun 1996 07:46:10 EDT From: Donald Rosenthal Organization: Clarkson University Subject: Response of George Bodner to P2-DR-SQ-Problems > P2 - DR - SQ - Problems Requiring Mathematics and Those Which Do Not > Most of the examples you discussed in your paper did not require much > mathematics other than simple arithmetic. > Many students can solve a problem once it is formulated in > mathematical terms. Where they have difficulty is in transforming > a verbal problem and/or simple data to a mathematical equation. > 1. Does your research provide any insight or techniques which might help > such students? ----- The examples in our paper were deliberately chosen because they don't require mathematics. Far too much attention in the research literature has focused on mathematical problem solving, as if that was the only kind of problem solving that occurs. We have therefore devoted a considerable amount of attention to non-mathematical problems the interpretation of spectra, predicting the product of an inorganic reaction, and so on. We have also worked with mathematical problems, however, such as multiple-choice stoichiometry questions, The first paper we published in this area [J. Res. Sci. Teach., 23, 727-737 (1986)] dealt with your observation that students can often" solve a problem once it is formulated in mathematical terms," but "they have difficulty transforming a verbal problem and/or simple data to a mathematical equation or equations." In our JRST paper, we described this in terms of two fundamental aspects of the early stages of problem solving: DISEMBEDDING relevant information from the statement of the problem and RESTRUCTURING this information, to transform it into a problem the students can begin to understand. Our research suggested that students who are good at these tasks in one domain are often good at these tasks in another domain. (In our case, the spatial domain and the domain of chemistry problem solving.) Our data, combined with other research in the field, suggests that once a student correctly UNDERSTANDS the problem -- once they have built an adequate representation of the problem -- most of the "problem solving" is over. They still might not get to the correct answer because they lack content knowledge -- such as what is a Michael addition reaction, or what is the correct formula for MgCl2. They also might not get to the correct answer because they lack certain cognitive skills, as noted in Dudley Herron's early papers. But, for many students, once they understand the problem, the problem is well along toward its solution. Thus, we have rejected Polya's model of problem solving, which suggests that one understands the problem; devises a plan; carries the plan; etc. In the preface to "General Chemistry, 2nd Edition, by Bodner and Pardue, John Wiley & Sons," a model of problem solving is described that is based on the assumption that we don't really understand a problem until we have an answer to the problem. -------------------------------------------------------------------- 2. You raise the fundamental question when you ask: How can we help students? Or, > how can students be taught to develop valid > (and useful) internal representation methods to solve problems > such as those cited in our paper? I have a lecture that I have been asked to give many times on the ACS lecture tour that is entitled: "Problem Solving: The Difference Between What We Do and What We Tell People to Do." I am convinced that a significant aspect of our failure to foster problem solving is the difference between what we do when we solve tasks that are problems for us and what we do when we work routine exercises for the students in our courses. Gil Haight used to say: Our problem is that all of our professors are A students and so few of our students are A students. At first glance, it seems obvious to assign a course to someone who is a subject matter expert in that field. But, all too often, this means that we have an individual "teaching" students how to approach tasks that are problems for the students but have been routine exercises for 20 years to the instructor. To illustrate the difference between teaching problem solving and what we often do in class, let me cite an experience from my graduate work. I had completed all of the coursework for a Ph.D. in inorganic, but could satisfy the requirements in organic as well by taking one more course -- natural product synthesis. The lectures in that course were brilliant, and I thought I understood them. But I got 7 out of 100 points on the mid-term, and 30 out of 300 points on the final exam. (My score of 37 out of 400 turned out to be one of the highest B's in the course.) The problem was simple: The exams dealt with organic SYNTHESIS, but the lectures dealt with organic REACTIONS. A knowledge of organic reactions is necessary but by no means sufficient for organic synthesis, which deals with the notion of how reactions might be put together to get to the desired product. Thus, the exams asked us to do something that had never been discussed in class -- designing a sequence of reactions that could convert four-carbon starting materials into a target molecule. If this was an isolated example of the phenomenon, that would be one thing. But I am convinced it is not. They show the student steps in the problem-solving process that are necessary to get to the solution of the problem, but not how these steps are brought together to solve a novel problem. They fall into the trap of assuming that information that is obvious to them will be obvious to their students as well. I have found that the more explicit I am about WHY I do certain things during the solution of a problem, instead of WHAT I do when solving the problem, the better students do in my course. --------------------------------------------------------------------------- ========================================================================= Date: Wed, 12 Jun 1996 07:49:20 EDT From: Donald Rosenthal Organization: Clarkson University Subject: Response of George Bodner to P2-BR-SQ Representations vs. > Subject: P2-BR-SQ - Representations vs. Manipulatives > > 1. What is the volume of an object of density = 5 g/mL and of a > mass = 2 g? what is the representation? Is it: d = m/v followed > by the rearrangement to solve for v (v = m/d)? > What is the representation for a solution involving dimensional analysis? ------- What is the representation for a simple problem? I know what the external representation looks like, it is often an equation such as d = m/v followed by scribbling that deals with the particular example. Or it is just the scribbling relevant to the example, without an external equation -- because the equation is so familiar to the individual that it doesn't need to be written down. When dimensional analysis is used, the external representation looks the way we have seen it look so many times on exam papers. The important question is: What is the INTERNAL representation of this information? That is a much more interesting question, and more difficult to answer. We get quite a bit of understanding, however, by detailed analysis of interviews with students who write the external representations described above. ----------------------------------------------------------------------- > 2. Are "representations" the same as these "manipulatives" or are > they just "pictures" or "images"? > If so, how does an equation (PV = nRT) qualify? > Bert Ramsay, Chemical Concepts Corporation, c3@BizServe.com -------- Are representations the same as manipulatives? No, they aren't. Manipulatives play an important role in students' learning. Dudley Herron used a very similar activity to the one you described in his remedial course at Purdue 20 years ago. He also used activities such as measuring the mass and volume of various pieces of glass as a manipulative to get students to recognize the value of calculating the ratio of these quantities. Manipulatives might be thought of as a device that makes one's internal representation more powerful by making it more likely to lead to a correct answer to a question. Students whose internal representation of density corresponds solely to some image of the relationship we express by the equation "d = m/v" are less likely to get to the answer of a complex density calculation than those whose presentation is richer because it evokes schema that help the student recognize why density would be a useful quantity to describe a substance. I hope these comments help. ========================================================================= Date: Wed, 12 Jun 1996 07:51:31 EDT From: Donald Rosenthal Organization: Clarkson University Subject: Response of George Bodner to P2-CTB-SQ Spacial Ability > Subject: P2-CTB-SQ-spacial ability vs problem solving > Bodner and Domin have presented in paper #2 evidence that appears > to correlate spacial ability with problem solving abilities. > Is spacial ability something that can be taught or is it innate? > If the former, what can we be doing in our classes to improve this > ability? If the latter, should we go to the extreme of making > "evidence of spacial ability" a prerequisite for our courses? (i.e. > Is it *possible* to elevate an unsuccessful problem solver to a > successful one?) > > Chris Bailey There is no doubt that there is a correlation between spatial ability and problem solving in several content domains, including both general and organic chemistry. The key might be the fact that what we ask students to do when solving problems in chemistry is something that is also required in tests of spatial ability -- namely, to find or DISEMBED relevant information and to RESTRUCTURE this information, or transform it into something that we "understand." That doesn't mean that training in spatial tasks will automatically transfer to enhanced problem- solving ability. There is no evidence of this, although it can't hurt. All it suggests is that people who are good at one of these tasks are more likely to be good at the other. Spatial ability is probably an innate skill, although it can be enhanced through training. I scored at the 99th percentile on the pilot's portion of the AFOQT -- the Air Force Officers Qualifying Test -- in 1965 because many of the tasks on this portion of the exam involved my ability to manipulate mental images of three-dimensional object sophomore organic. There is no doubt in my mind that a test of spatial ability might be useful in an organic course, to identify students who might have difficulty with certain components of the course. It is equally likely that students who have poor spatial skills might benefit from being tutored in this area while taking organic courses. But I wouldn't make a test of spatial ability a prerequisite for any course. This is the difference between Binet's original notion of an IQ test and the sins of Galton, who translated this test into English. Binet wanted a test to help diagnose students who might need help; Galton wanted to use this test to screen immigrants into the U.S., to "protect" the native population. I feel somewhat queasy about putting the label of "successful" versus "unsuccessful problem solver" on an individual. I can only measure their ability (or lack thereof) within a given context. That doesn't mean that students who are poor problem solvers in my course might not excel in someone else's, within a different problem solving domain. I am convinced, however, that I can improve the problem-solving skills of any student who enrolls in my course by paying attention, during lecture, to what we do when we solve problems. If these comments generate new questions, please send them to me. ========================================================================= Date: Wed, 12 Jun 1996 08:57:24 -0400 From: George Long >I am convinced that they TRY to use our representations to duplicate our >explanations. I am equally convinced from my experience with organic >chemistry they the representations they use have very different meanings for >them then they do for us. > This all sounds similar to linguistics. Has any correlation ever been made between the work of the people that explore how languages are created, and how people learn languages (e.g. Noam Chomsky's work) and How people learn the "Language" of chemistry, i.e. our representations ?? Do you think that if we adjust our representations to make problems easier for beginning students, it will make it more difficult for them to become experts? **************************************************************************** George R Long, Ph.D. Department of Chemistry Indiana University of Pennsylvania Indiana, PA 15705 grlong@grove.iup.edu 412-357-2575 Our lives are merely trees of possibilities - Marc Bolan **************************************************************************** ========================================================================= Date: Wed, 12 Jun 1996 09:58:27 -0400 From: JBELL Subject: The PURPOSE(s) of grades COMMENT FROM BELL AND AHLGREN The brief discussion of grading techniques has taken place in the absence of any clearly defined PURPOSE for the grades. There has been a tacit understanding that we all know what the purpose is and that we are all reading from the same page. But the very statement that there is _a_ "purpose" for the grades, is misleading. There are many purposes. Purposes include advising those who want to know (e.g., employers, subsequent course instructors, graduate schools, parents, the student herself) how the student stacks up against her peers; judging the success of the program; judging the skill of the instructor; motivating students (before the fact) to study; rewarding students (after the fact) having tried hard (or punishing them for not); and, of course, advising students on how close they come to what someone has decided they should be able to learn. Perhaps there could be a conference on just this topic. The foci of such a conference could be (a) filling out the list of purposes, (b) filling out the list of testing/grading methods, and (c) checking the cells (A-F?) in a purposes-by-methods table for which methods serve which purposes how well. ========================================================================= Date: Wed, 12 Jun 1996 10:16:49 -0400 From: JBELL Subject: Re: P1 - BT - reduced coverage Brian Tissue wrote: ... Continuing with the analogy from the paper of a mind as paths in a forest, broad coverage produces many paths. When students or graduates encounter new material later in their careers, they have relevant paths, although faint, to help them effectively construct new knowledge and understanding. AHLGREN AND BELL: The notion of faint paths needs to incorporate the notion of "threshold" and "half-life." How lightly can it be trod and leave a trace? How faint can it be and survive 6 months later? ========================================================================= Date: Wed, 12 Jun 1996 09:32:50 -0400 From: JBELL Subject: Re: P2 comment on Volland questions Do you think the models we use create a bias in the minds of our students? Do you believe students use our models and representations to duplicate our explanations in the same way they use problem algorithms? COMMENT FROM A. AHLGREN: Yes, bias is the purpose of instruction: to affect the way that the student interprets the world. (The alchemists are still doing their part to induce a different bias.) We should try to be aware of what the intended biases are -- and what some unintended ones may be as well. Yes, students will likely imitate our explanations at first. In some schemes of "conceptual-change" teaching, that is a deliberate step. First the teacher demonstrates how the explanation works. Then the students attempt to use that kind of explanation in a variety of contexts. It is in choosing those contexts that we hope to induce students' understanding -- and with still other contexts to test their understanding. I once participated in a study at the University of Minnesota in which introductory chemistry students were located six months after the final examination and given the exam again (plus some new questions). Over half could still figure the % of Fe in FeO, but only a fifth could answer the new question of what the % of cream would be in a mixture made from 100g coffee and 25g cream. (Coffee and cream weren't in the periodic table?) So about a third could perform the algorithm without understanding it any more (if ever). Perhaps the coffee & cream example would have helped students to understand in the first place -- but then we would have needed another context to test them. It is a different issue whether the student believes in the truth of the explanation, or whether she believes the explanation to be better than her own previous way of explaining. But science doesn't seek to compel belief. We hope to be able to show students that a scientific explanation is rewardingly successful in accounting for phenomena. But the reward has to be to them, and they inevitably get to decide whether it is worth the effort to learn -- or to give up their alternative beliefs. ========================================================================= Date: Wed, 12 Jun 1996 12:10:58 -0500 From: "Dr. David Ritter" Subject: p2-role of representations Bodner and Domin present an interesting analysis of the role os representations in problem solving. I, too, have been puzzled by responses that students give to "relatively easy" questions that I put on exams "to build the students' confidence." I would like to know if the evidence supports the conclusion that I draw from the paper: if the skills used by the successful students are taught, then the rate of success will increase. Let me briefly give an example to illustrate my concern that this may not necessarily be true. For the last four years I have included a question on the final exam in my Chemical Literature course. Students were given a page from Current Contents and asked What are the initials of the Chen from Los Alamos lab? I was as convinced as GMB that this would be an easy question, and should therefore "build the students' confidence." (the reference showed "Chen KY" at Los Alamos lab and I expected the answer KYC) In 1993 everyone missed the answer, only writing down the first two initials. I was certain that my teaching was at fault, and that I could remedy this the next year. So in 1994, in the last week before the final exam, we studied initials. I picked a student's name from the class, wrote it on the board, and wrote out the initials, pointing out to the class how this is done. The class performance rose to 50% success rate. I was still not satisfied with this result, and again searched for a way to improve my teaching. In 1995 I covered initials more extensively in the first two weeks of the semester, performance dropped to 40% correct responses. I took this as proof of the need for a last week review. Therefore, in 1996 I began earlier in the semester and covered initials early on by using an overhead transparency with the names of six Nobel laureates and reciting the initials of each together with the class. I told them that the question would be on the exam. We repeated this exercise several times throughout the semester, and reviewed it during the last week. Performance rose to 70% correct. I had expected better, and thus can only conclude that something must still be lacking in my teaching. I wonder whether including the use of representations will help my students overcome this hurdle, and if so how to do it. I am considering using a multimedia approach because of the success others have described in the literature. I appologize for the length of this, but want to communicate the problem. Is there anyone else out there with a similar situation? Is it possible that there are other significant factors in student success rates that may mask the relatinships to teaching methodologies? David Ritter Department of Chemistry Southeast Missouri State University c617scc@semovm.semo.edu ========================================================================= Date: Wed, 12 Jun 1996 16:28:49 EDT From: Richard Potts Organization: University of Michigan-Dearborn Subject: P2-RP-D-CTB-Spacial Ability Whether or not spacial ability can be taught or is innate, it can be enhanced through training. In General Chemistry we encounter many students who lack this ability, and are then faced with the task of teaching it. I highly recommend that students receive some training in spacial ability while they are in high school. I am not advocating high school chemistry teachers shoulder the task, but that students be strongly advised to take a drafting (mechanical drawing) course. This course requires the student to take a three dimensional object and draw it on a two dimenional page in several different perspectives. This mental process is the same as needed for chemistry as well as math and physics. What better practice for students with real objects to develope spacial ability which will be of great value in dealing with the abstract in several disciplines as they continue their education. I feel a drafting course should be considered a required core course. ========================================================================= Date: Wed, 12 Jun 1996 16:42:10 -0400 From: "Richard O. Pendarvis" Subject: P2 - Dimensional Analysis and/or Representations One of the concerns I have always had about the widespread use of dimensional analysis is that I wonder if it does not inhibit the development of internal representations of physical problems. It is possible for the students to chain together the correct series of numbers without having to conceptualize what the problem is about. Even if it does not inhibit the development of the ability to internally represent physical phenomenonon, it does not encourage the development of this ability. Some years ago, Dr.Howard Williams of the University of Southern Mississippi developed and I believe presented a concept of "tabularizing" problems [representing problems with a table] which I find helps students to understand how the quantities in a problem fit together as a whole. This implies that it does a better job of helping them to develop an internal representation of the physical phenomenon. - - ____ | | _ | | Organic Chemistry / \ |_| | | || CAI Programming / \ | | / \ || Pizza / \ / \ | | _||_ Star Trek (_________) (_____) |______| _/____\_ Doberman Pinschers --------------------------------------------------------------------------- | Richard Pendarvis, Ph.D. P.O. Box 1388 | | Associate Professor of Chemistry Ocala, FL 32608 | | Central Florida Community College EMAIL: afn02809@freenet.ufl.edu | --------------------------------------------------------------------------- ========================================================================= Date: Wed, 12 Jun 1996 16:54:22 EST From: Rich Taylor Subject: DR- BEGIN DISCUSSION OF PAPER 2 Colleagues: As I read both papers 1 and 2, I was struck by some similar themes. I echo some previous ideas, but perhaps restate them. For years I have told students that learning chemistry is like learning a foreign language (not always helpful, they have similar problems in language classes). What the papers seem to be discussing is a problem of 'fluency,' a level of comfort in dealing with the commerce in the subject, rather than mastery of rules and vocabulary. I agree with the authors that no degree of algorithmic problem solving skills can directly lead to the ability to confront novel problems which require better symbolic understanding of the particulate nature of chemistry. It is unfortunate to note one is called to teach less content while at the same time noting that there is substantial overlap in coverage between high school and freshman chemistry. Since the particulate nature of the topic is so effectively dealt with in organic courses, should there be further experimentation in teaching freshman organic courses? Questions of coverage in courses including majors versus non-majors courses might also come into play. I'll close with a minor quibble on the problem shown in figure 5. As all have certainly noted by now, there are diastereomers which increase the number of products. How to deal with such questions before they are brought up in the course is a topic for another day. -- Richard T. Taylor Associate Professor of Chemistry Chemistry Department Miami University Oxford, OH 45056 513-529-2826 taylorrt@muohio.edu ========================================================================= Date: Wed, 12 Jun 1996 17:04:50 EST From: George Bodner Subject: Bob Bruner's question Response to Bob Bruner's question: Isn't it true that successful problem solvers "recognize" whether their solution and therefore their representation worked? I am not convinced that most of the students we have interviewed "know" whether they have been successful or not on the kinds of problems we give them. I know that good problem solvers are more likely to check their work when they are working on novel problems -- but almost never check their work when they "solve" routine exercises. I know that bad problem solvers are less likely to do this. But I also know that unsuccessful problem solvers are often trapped by the representations they construct when they choose a representation that is not very powerful or when they choose a representation that is misleading. My favorite example is the prediction of the products of the reaction between methylcyclopentane and bromine. The students who got the "wrong" answer -- predicting three products instead of four -- might have "checked" their work for ever, without realizing that they got the wrong answer because they didn't (or couldn't) recognize the fact that a bromine radical could also attack at the C(1) carbon atom. I am not convinced that students got the wrong answer in the SOCl2 reaction because they didn't take time to balance the equation. (Organic chemists seldom write balanced equations for reactions unless they are using these reactions as the basis for a discussion of the mechanism of a reaction.) Bob presents another approach to getting the right answer to the SOCl2 reaction -- "knowing" what this reagent does with carboxylic acids. But that reinforces students perception that the only route to success in organic chemistry is memorization -- that it is impossible to solve tasks they encounter in this course by any form of "problem solving." I believe that it IS relevant that unsuccessful problem solvers only try one representation because those who are successful are less likely to get trapped in the first representation they encounter. I am convinced that one of the things that differentiates between students who are successful (in general) from those who are not is their ability to move from one representation to another, or even from one representational system to another. ========================================================================= Date: Wed, 12 Jun 1996 17:05:30 EST From: George Bodner Subject: Jerry Bell's question Jerry Bell raised the question: What sort of research results do we have on the issue of the inability of many organic students to distinguish between the functionality of a species and the "inert" remainder of the molecule. I don't have answers, but I have some ideas. I am interested in understanding the process by which chemists look at a molecule and recognize the important information. Craig Bowen looked into some of this in his work on how graduate students "do" organic synthesis. Let me give you an example that might focus our discussion. One evening last year, I walked into the office to find a couple of my undergraduates struggling with a homework problem from Phil Fuch's organic course. Phil asked them to design a synthesis for a compound I will label 1,1-dideutero-4,4-diphenylcyclohexane. But he didn't give them that name, he gave them the structure. The students were "good" students, who had been working on this problem for several hours. Their attention was focused on the bottom of the molecule, where there were two large phenyl groups attached to a single carbon atom. They couldn't think of any way to use their understanding of aromatic chemistry to introduce these phenyl groups. And these groups were obviously interfering with progress toward the answer to the problem. I asked them to think about a simpler molecule: 1,1-dideutero- cyclohexane. Could they put that together? They immediately started talking about the notion of how to introduce a pair of deuteriums onto a single carbon atom and concluded that they knew of one way to achieve this. Could they close a ring to form the intermediate that would have to be reduced to make the dideutero compound? Yes, they figured they could do this. Could they assemble the molecule that would be the starting material for this reaction? Yes, they figured they could. The key to the problem was turning their attention from the "bottom" of the molecule, where they weren't being very successful (or imaginative) to the "top." It was recognizing the site of the "action" in the synthesis. This example, coupled with Craig Bowen's results in his M.S. thesis, worries me because it suggests that one of the key differences between successful and less successful problem solvers in the domain of organic synthesis might be something known as the "chess players syndrome." There has been quite a bit of research on problem solving among chess players. Some of this work has clearly shown that the approach a good chess player -- a master, but not a grand master -- takes to the game is not all that different from the approach of a good beginning player. They don't think all that many more moves ahead. But they have an ability to recognize the "center of action" in a chess board. (If you have them look at a chess board, turn their back for a moment, and then look at the board again, they immediately recognize changes you make in the position of a player that is in the "center of action," whereas they don't recognize changes you make in the position of peripheral players. Note, of course, that the center of action does not necessarily correspond with the center of the board. Nor does the periphery necessarily correspond to either side of the board.) The primary difference between the very good expert chess player and the good amateur chess player has been described as nothing more than 50,000 hours of practice, playing chess. They see a particular pattern of chess pieces and say to themselves, "Oh, that's like ...," and they know how to proceed. What does this mean for those who teach organic chemistry? Perhaps it means that they have to spend more time in class specifically talking about organic synthesis. How do they recognize the "center of action" in a synthesis? How do they work backwards? Perhaps the instructor needs to be take advantage of the philosophy known as the reflective practitioner -- someone who reflects intensely on their own practices, in order to improve them or to be better able to communicate them to others. Let me know what you think about these ideas. ========================================================================= Date: Wed, 12 Jun 1996 19:09:07 EDT From: Ascanio DiPippo Subject: Re: Paper #1: What are Students Lerning? Students aren't interested in learning; only in getting a diploma WoO ========================================================================= Date: Wed, 12 Jun 1996 19:13:27 EDT From: Ascanio DiPippo Subject: Re: Grading Systems Why complicate it; use the Harvard and other private school system. A = average B = fail C = I paid 25 K for this degree and I will have my lawyer contact you. WoO ========================================================================= Date: Wed, 12 Jun 1996 19:32:14 -0700 From: Bob Bruner Subject: P2 - comment on density representation I often add to a "simple" density calculation problem a part b of the general form "What is the density of half a bar?" (I even suggest that they try calculating it, if it isn't obvious.) Yet, Many who do the part a calculation, either "blindly" using the formula or using very clear dimensional analysis, miss part b. This is clearly an example of students relying on formulas or algorithms without understanding. The question is what we can do about it. The concept of an intensive property has escaped them. This had made me very conscious of aiming the lab activity at demonstrating the intensive nature of d, not simply measuring it. A density lab should include a graph of m vs v for a series of samples (different volumes of a liquid serves the purpose), and then a prediction. Bob Bruner Contra Costa College bbruner@uclink4.berkeley.edu ========================================================================= Date: Wed, 12 Jun 1996 19:32:19 -0700 From: Bob Bruner Subject: P2 comment - abuse of dimensional analysis Richard O. Pendarvis message excerpt... >One of the concerns I have always had about the widespread use of >dimensional analysis is that I wonder if it does not inhibit the development >of internal representations of physical problems. It is possible for the >students to chain together the correct series of numbers without having to >conceptualize what the problem is about. I am a strong advocate of dimensional analysis. One of its _virtues_ is that it can help a student work out a path, even in unfamiliar territory. That is, it can help guide you through a problem you don't _quite_ understand. Yes, it can be abused. I think that it is our responsibility to use d.a. as a complement to other problem solving tools -- to show why/how it helps. Bob Bruner UC Berkeley Extension & Contra Costa College bbruner@uclink4.berkeley.edu ========================================================================= Date: Thu, 13 Jun 1996 13:09:30 +1000 From: Rowan Hollingworth Subject: P2 - RH - D - Teaching Learning & Problem Solving Thanks to Bodner and Domin for putting into place one more piece of the jigsaw puzzle, that makes up our current picture of the processes of understanding concepts and solving problems in chemisty. It is vital that we use the results of research, such as this, to assist students in their struggles to grasp chemical concepts and then apply them in solving problems. I agree with Theresa Zielinski - P1 - TJZ, D, More is less etc, who said > I think that instruction on learning how to learn needs to be embedded >into >the chemical curriculum along with technology. In our first year chemistry courses, I have given a series of additional tutorials, entitled "Learning Chemistry Effectively." In these, I have tried to make expicit to students the findings of current (and older) educational research as a rationale for approaching their studies in certain ways and using certain techniques to enhance their understanding of chemical concepts and their abilities to solve chemical problems. Knowing the explicit reason why it will be effective to take a certain approach is also important. It seems to me that our students fall into three groups. First, those who, through their own efforts, intuition or past teaching, already use some effective learning techniques; second those who, if shown techniques will go ahead and use them and third those who, for whatever reason, are not prepared to put in the hard effort involved in coming to grips with chemical concepts, even when shown effective learning and problem solving methods. The first two groups, (a majority of our students), I am sure do benefit by being exposed to these results of eductional research, as it gives them a concrete rationale for applying effective techniques in their studies. At the risk of leaving less time for chemistry content, we do need to spend more time with students teaching them how to learn and how to solve problems. Clearly the ideas presented by Bodner and Domin are best presented by us as chemists, as we possess the backgound knowledge to apply their findings in different areas of chemistry with relevant examples. Feed back during my tutorials showed students are most concerned that discussion of study techniques and the learning process always relates directly back to specific chemical examples. (Our students are rather reluctant to attend general tutorials on academic study skills, as they tend to feel it wastes their time, because they fail to see direct application to their studies in chemical poblem solving for instance.) Dr Rowan W Hollingowrth Dept of Chemistry, University of New England, Armidale NSW, AUSTRALIA Email: rholling@metz.une.edu.au ========================================================================= Date: Wed, 12 Jun 1996 22:22:28 +0000 Reply-To: lljones@bentley.UnivNorthCo.EDU Comments: Authenticated sender is From: "Loretta L. Jones" Subject: Re: Jerry Bell's question George Bodner wrote: > This example, coupled with Craig Bowen's results in his M.S. > thesis, worries me because it suggests that one of the key > differences between successful and less successful problem solvers > in the domain of organic synthesis might be something known as > the "chess players syndrome." I like the notion of the chess players syndrome and feel that it applies far beyond organic synthesis reactions. The primary > difference between the very good expert chess player and the good > amateur chess player has been described as nothing more than > 50,000 hours of practice, playing chess. They see a particular > pattern of chess pieces and say to themselves, "Oh, that's like ...," > and they know how to proceed. This is what we all wish for our students, for them to learn the patterns and find their way among them. Last year I asked my students to prepare problem-solving strategies for the stoichiometry material we had just covered in a general chemistry course. They were to bring the strategies to the exam, they could use them during the exam, then they turned them in to be graded along with the exam. This was an oddly invigorating assignment for the students, who descended upon the teaching assistants and tutors for help. The second time I made this assignment, I allowed students to put examples on their strategy sheets and that is what many of the sheets consisted of---only examples, no actual strategies. The students told me that they solve homework exercises that way---by finding an appropriate example and applying the same approach. The examples served as patterns for them to follow. Now for the humbling experience. I gave a group quiz, without strategy sheets, to see if the patterns had been learned. I expect you can predict the outcome. They got lost amidst the representations: Is it this type of problem or that? Do we write it this way or that? Does it make a difference how we write it out? Except in certain groups that functioned like Olympic teams, the concern was not with what we were to find out and how, but with which learned algorithm would give the correct answer. > Perhaps the instructor needs to be take advantage of > the philosophy known as the reflective practitioner -- someone who > reflects intensely on their own practices, in order to improve them > or to be better able to communicate them to others. This is a key, I think. In the book Blue Highways, by William Least Heat Moon, the author travels to New Harmony, Indiana, to visit the site of a utopian community settled many years ago. An artifact left by the idealists was a labyrinth, grown up into a tall maze of hedges. One turns and twists and goes down many blind alleys before reaching the center. The maze is supposed to represent the search for God. After starting through the maze, Moon looked down and noticed that a trail had been worn in the dirt that led directly to the center, with no false turns or retracing. Immediately he lost interest in the maze, because the meaning and enjoyment had been all in the finding of the way. It seems to me that successful learning, the kind of learning that changes lives and stays with us for many years, is the kind that results from finding one's way through the maze. The more prescriptive our directions to students, the more shallow their learning may become. Perhaps the reflective instructor can best reach students by sharing stories of paths trodden and mazes solved, to inspire students to find their own solutions. Groups help, too, as students find allies in their struggle. Loretta L. Jones Department of Chemistry and Biochemistry University of Northern Colorado Greeley, CO 80639 lljones@bentley.univnorthco.edu ------------------------------ Date: Thu, 13 Jun 1996 07:03:03 EDT From: Donald Rosenthal Subject: P2-DR- Teaching Students Problem Solving P2-DR-Discussion of Teaching Problem Solving to Students In response to P2-DR-SQ you stated: > ... a significant aspect of our failure to foster problem solving > is the difference between what we do when we solve tasks that are > problems for us and what we de when we work routine exercises for > the students in our courses. > > Gil Haight used to say: Our problem is that all of our professors are > A students and so few of our students are A students. > > I have found that the more explicit I am about WHY I do certain things > during the solution of a problem, instead of WHAT I do when solving the > problem, the better students do in my course. These comments lead to some questions: 1. Is the course instructor (an A student) necessarily best in a position to teach problem solving to the students? Many Universities courses have recitation sections taught by graduate students and it is in these recitation sections where homework problems are discussed. Very often the students, who are taking the course, are asked to put problems on the board and each student explains the problem to the rest of the class. Another recent trend is to use cooperative (or collaborative) learning and have students work together in groups to solve problems. Some teachers when working with students on a one-to-one (or group) basis will explain how the problem should be worked. Other instructors will try to have the student explain how he has attempted to solve the problem and try to HELP the student get to the correct solution. 2. What do you think of these techniques? ---------------------------------------------------------------------- I remember reading many years ago that most mathematicians after proving a theorem, then develop a very well organized and logical solution for publication. This published solution gives very little insight into how the theorem was actually proven. This seems to be similar to what you are saying about how many instructors operate - they present well organized and logical solutions which do not give students very much insight. ---------------------------------------------------------------------- Many problems can be solved in more than one way. 3. Is it worthwhile presenting more than one way of solving a problem? ====================================================================== ------------------------------ Date: Thu, 13 Jun 1996 09:24:56 -0400 From: Stacey Lowery Bretz Subject: P2 - SLB - What to tell the students? Bodner and Domin mention that students' reactions to questions such as those in paper 2 typically involved crying "unfair." What I wish to know is what Bodner and others __tell__ students both before and after exams to help them recognize that developing the skills of disembedding and restructuring are indeed "fair" expectations on our part as instructors. I find it challenging to discuss with students such metacognitive issues when such discussions typically elicit comments such as "I didn't sign up to take a psych course." It seems to me the real challenge here is to help students come to understand that what can be most interesting now and of most value later on the job is learning how to "find one's way through the maze" as opposed to assembling a collection of loosely related algorithms (see Loretta Jones' last message). I'd be interested in hearing from others regarding their reflective instruction practices. <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Stacey Lowery Bretz ph: (313) 593-5157 Assistant Professor of Chemistry fax: (313) 593-4937 University of Michigan-Dearborn email: slbretz@umich.edu Department of Natural Sciences 4901 Evergreen Road Dearborn, MI 48128-1491 "The most important single factor influencing learning is what the learner already knows. Ascertain this and teach her accordingly." ---David Ausubel ------------------------------ Date: Thu, 13 Jun 1996 09:22:48 -0400 From: "Jeff Davis (CHE)" Subject: P1 and P2, WHEN can students gain these skills? Both of the first two papers have dealt with provocative insights that revolve around students being able to relate problems to the real world and their ability to construct and use representations that make them effective problem solvers. Someone mentioned that it is not surprising that college students have these difficulties because they are all still at the concrete level of cognitive skills. This, of course, puts a completely different spin on what science instruction ought to be aimed for in K-12, the main effort of Project 2061 as I see it. Nearly all interactions between college and HS teachers revolve around course content and external representations and skills using these representations. It has been a while since I was engrossed in Piaget when Dudley was championing the cause but I don't recall from my reading that any of the research indicated that one can't move beyond the concrete stage before you are 18 years old. Am I wrong? Given both the science literacy needs and the technology needs of society it would appear that perhaps the most valuable service chemistry faculty could render would be not only to better understand this problem from the standpoint of helping our own students understand chemistry better but also to provide a mechanism by which all the other kinds of students in the university, including all those prospective K-12 teachers out there, also not only understand how chemistry and science works but also how to convey this understanding to their own students. To what extent are these kinds of concerns being addressed from this specific direction (attention to developing internal representations and connections with more familiar real objects) either in actual university classrooms or in the schools? Jeff Davis Prof. and Chair Dept. of Chemistry Univ. of South Florida ------------------------------ Date: Thu, 13 Jun 1996 09:29:00 EDT From: to2 Subject: Discussion archives for Paper 2 available Archives of yesterday's discussion of Paper 2 are now available. Click on "Discussion of Paper 2" on the ChemConf home page. Discussion archives will be updated daily. I thought you all might like to know that there are currently 923 subscribers to the conference, representing 51 countries! We are especially glad to have such international participation. Tom ------------------------------------------------------------------------- Tom O'Haver Professor of Analytical Chemistry University of Maryland Department of Chemistry and Biochemistry College Park, MD 20742 Maryland Collaborative for Teacher Preparation (301) 405-1831 to2@umail.umd.edu FAX: (301) 314-9121 http://www.wam.umd.edu/~toh ------------------------------ Date: Thu, 13 Jun 1996 09:45:47 -0400 From: "Patricia S.Hill" Subject: Re: CHEMCONF Digest - 11 Jun 1996 to 12 Jun 1996 In response to the question of whether spatial visualization skill develop- ment can be taught and whether it will improve problem-solving skills. Sheryl Marlor at Michigan Technological University has developed a course in 3-D spatial visualization which includes a text and lab manual. The course is designed for freshman engineering students and initial results seem to support the idea that teaching these skills will improve problem solving skills. This was an NSF-funded project. The workbook includes examples of 3-D skills needed in organic chemistry. Patricia S. Hill Associate Professor of Chemistry Millersville University Millersville, PA 17551 ps_hill@daffy.millersv.edu ------------------------------ Date: Thu, 13 Jun 1996 11:27:04 -0400 From: Maureen Scharberg Subject: Re: P1 and P2, WHEN can students gain these skills? In reference to the above question, 50% of the students enrolled in physical science classes at the college level are not at Piaget's level of formal thinking. Reference: Pallrand, G.J. (1979) "The transition to formal thought". Journal of Research in Science Teaching, Volume 11, No. 1. pages 67-77. >From my observations of my students in my introductory chemistry course, I would agree with this statistic. Thus, to accomodate the variety of students in my class, I provide many modes of learning and teaching chemistry, which integrates both the macroscopic and microscopic phenomena of chemistry in individual and group learning environments. #@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@ Maureen Scharberg Department of Chemistry San Jose State University San Jose, CA 95192-0101 phone:(408) 924-4966 fax: (408) 924-4945 email: scharbrg@sjsuvm1.sjsu.edu "To see what everybody else has seen, and think what nobody else has thought." Albert Szent-Gyorgyi ------------------------------ Date: Thu, 13 Jun 1996 10:31:46 CST From: "James A. Carroll" Subject: P2 d "Fair" is efficient Noting that students complained that the question was not "fair" struck of chord with me. I have been bothered by that comment on student evaluations of teaching, and have had trouble learning what fosters that opinion. The paper never returns to discuss this perception. I have a suggestion on which I'd like comment. Students who have completed a full college-prep secondary program can be presumed to be efficient "problem" solvers. They've learned to play the education game. Most of their homework drills and school experiences have involved building knowledge, comprehension, and application skills. Homework and test questions have largely required response at these levels. [Or is solution of an elementary algebra problem an analytical skill when one is inexperienced?] Students who learned to be "successful" problem solvers may even have been at a disadvantage because they worked too slowly on items that were drill to the instructor, many of which the instructor expected the students to know as "routine exercise". The bulk of the end-of-chapter questions in a general chemistry (or organic?) text involve drill, expanding the students' repertoire of exercises that can be done routinely. Sample exercises in the text and worked problems in study guides reinforce the notion that everything can - should - be worked out as an application of some rule or equation. Our texts do not help convince students that "problem" solving is important to work on. Though my students and I work "problems" in class, such exercise in chemistry and problem solving is slow, so the number of problems worked tends to be low. When "problems" and "routine exercises" show up on tests, novice students - those who have not synthesized "successful" and efficient skills - have to choose how to approach the problem. The only flag that student's have is the point credit. (I give more credit to "problems" because they involve more mental steps - I was giving time for the restructuring emperically.) On the bromination question, students who choose to be efficient used the information most readily available to get an answer that has involved some application of symmetry. They've done what they're generally asked to do, and applied their knowledge correctly, yet their answer was wrong. I suggest that's what fosters the feeling that the question wasn't "fair". Most college students have learned to be efficient problem solvers during secondary education, only to learn that their chemistry instructor is rewarding "successful" problem solving. What's the current expression corresponding to "bummer"? The discord between efficient and "successful" is resolved with practice as individuals learn to apply the efficient tools of assessing the task ("problem" or "routine exercise") early and developing alternate structures rapidly, and the "successful" tools of using complementary models (pictorial or equation) and checking their work. Jim Carroll Phone (402) 554-3639 Chemistry Department Dept (402) 554-2651 University of Nebraska at Omaha FAX (402) 554-3888 Omaha, NE 68182-0109 ------------------------------ Date: Thu, 13 Jun 1996 10:38:25 EST From: George Bodner Subject: Don Rosenthal asks a series of questions that might be phrased as follows. Is the course instructor in the best position to teach problem solving to the students? What is the role of the recitation section taught by graduate students? What is the role of cooperative (or collaborative) learning in problem solving? Is it worthwhile presenting more than one way to solve a problem? A close friend (who will not be named, to protect the "innocent") once said: "Physical chemistry is too important to be taught by a physical chemist." (Organic chemistry is too important to be taught be an organic chemist, and so on.) Our work suggests that the course instructor is not inherently in the best position to teach problem solving. But, by carefully reflecting on what they do when they face novel situations, and differentiating between these practices and what they do when they work routine exercises, they can become the best individual to teach problem solving strategies because they are often the only individual at the institution who has the insight to provide a broad picture of how experts in that field attack problems they encounter. Graduate students can be a superb resource for improving the problem-solving skills of their students because they are closer to the students in terms of age and experience. But they often lack the insight gained from several years of experience as the instructor in charge of the course about the aspects of the course in which their students need help. Thus, like some computer tutorial programs, they can get the students to spend hours developing skills that will earn them less than 1% of the points necessary to pass a course. There is abundant evidence that individuals working together in groups can solve problems -- and develop better problem-solving skills -- than individuals working alone. All we have to do is look at our practices when we "do" chemistry. All too often, we seem to own two different hats. One we wear when we "do" chemistry, and the other we put on to "teach" chemistry. I am convinced that our students benefit when we approach the learning of chemistry by students the same way we approach the learning of chemistry by chemists. As an example of what I mean, let me note that a number of years ago, the anarchistic model of problem solving in the introduction to the Bodner and Pardue text was presented at a seminar at Purdue. One of my colleagues argued: "You can't possibly expect the students to follow this model when they work problems in your course because this is what I do when I do research." As you might expect, I disagree. I believe that it is important to periodically give the students more than one solution to a problem, to clearly convey to them the notion that there is no "best" way to work the problem. I also believe that is important to make "mistakes" when solving problems in class. (Fortunately, for me this is easy to achieve!) This way, the students have to pay attention to what we are doing, and, more importantly, recognize that problem solving is never linear. It doesn't move directly from the start to the finish of a task. Those of us who work problems for a living -- which is what most chemists seem to do -- often start in the wrong direction, get lost for a period of time in the path toward the solution, start over, etc. The key to our performance is the fact that we are persistent; we keep track of what we have accomplished; we try not to lose sight of the goal; and we routinely ask ourselves: "Have I gotten anywhere?" ------------------------------ Date: Thu, 13 Jun 1996 11:39:53 -0400 From: Maureen Scharberg Subject: Re: P1 and P2--How do we convince our colleagues? After reading and thinking about P1 and P2, how do we convince our colleagues, who are non-members of the chemical education choir, that what they are transmitting as real, 3-D molecules is often being received by students as sticks and symbols? Please note that this question can apply to other areas of chemical education research. Maureen Scharberg #@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@#@ Maureen Scharberg Department of Chemistry San Jose State University San Jose, CA 95192-0101 phone:(408) 924-4966 fax: (408) 924-4945 email: scharbrg@sjsuvm1.sjsu.edu "To see what everybody else has seen, and think what nobody else has thought." Albert Szent-Gyorgyi ------------------------------ Date: Thu, 13 Jun 1996 11:57:20 -0400 From: "Jeff Davis (CHE)" Subject: P2-JD-D-DR-Teaching Students Problem Solving >I remember reading many years ago that most mathematicians after proving >a theorem, then develop a very well organized and logical solution for >publication. This published solution gives very little insight into how >the theorem was actually proven. This seems to be similar to what you are >saying about how many instructors operate - they present well organized >and logical solutions which do not give students very much insight. Unfortunately we can't lay this just at the feet of mathematicians. This is exactly what much of the literature in chemical research has become. Without access to theses and dissertations much of the actual goings-on in chemistry would be lost. Jeff Davis ------------------------------ Date: Thu, 13 Jun 1996 12:43:04 -0400 From: AAHLGREN Subject: Re[2]: P1 and P2--How do we convince our colleagues? Maureen Scharberg wrote: "...how do we convince our colleagues, who are non-members of the chemical education choir, that what they are transmitting as real, 3-D molecules is often being received by students as sticks and symbols?" I think that skeptical colleagues will be convinced only when they discover the phenomenon in their own students, although they may be stimulated to look by reading about research on others'. An article on good student-interview technique -- with lots of chemistry examples -- would be very helpful in preventing interviewers from asking questions in the same, familiar ways that concealed what students were thinking before. John Fackler at Texas A&M told me last week that giving their graduate students the freshman chemistry test was a stunning eye-opener. ------------------------------ Date: Thu, 13 Jun 1996 13:50:07 -0400 From: George Long Subject: Re: P2-JD-D-DR-Teaching Students Problem Solving >>I remember reading many years ago that most mathematicians after proving >>a theorem, then develop a very well organized and logical solution for >>publication. This published solution gives very little insight into how >>the theorem was actually proven. This seems to be similar to what you are >>saying about how many instructors operate - they present well organized >>and logical solutions which do not give students very much insight. > >Unfortunately we can't lay this just at the feet of mathematicians. This >is exactly what much of the literature in chemical research has become. >Without access to theses and dissertations much of the actual goings-on >in chemistry would be lost. > >Jeff Davis > Why should the original way a problem is solved be important? we should not want to reproduce the path someone took to get to an answer. In fact, the point of the literature is to distill research down to the most easily usable form. The whole point of science is to build upon organized Idea's that others have painstakingly developed. > >The bulk of the end-of-chapter questions in a general chemistry (or >organic?) text involve drill, expanding the students' repertoire of >exercises that can be done routinely. Sample exercises in the text >and worked problems in study guides reinforce the notion that >everything can - should - be worked out as an application of some >rule or equation. Isn't this similar to the memorization of vocabulary, etc that one undergoes when they learn a language ? Isn't a large degree of memorization, of rules and algorithms to be expected for a novice in any field. Isn't it a requirement if we expect the students to be effective users of chemical technology. This leads me to question the statement by George Bodner >I am convinced that >our students benefit when we approach the learning of chemistry >by students the same way we approach the learning of chemistry by >chemists. As an example of what I mean, let me note that a >number of years ago, the anarchistic model of problem solving in >the introduction to the Bodner and Pardue text was presented at a >seminar at Purdue. One of my colleagues argued: "You can't >possibly expect the students to follow this model when they work >problems in your course because this is what I do when I do >research." As you might expect, I disagree. The students are just not at the same cognitive level as an experienced and practicing scientist, nor do they have a sufficient background. Our rules and algorithms are designed to simplify a concept (just like an amorphism e.g. a stich in time saves nine)and make doing a task simplier. Certainly no one would argue that students should discover on their own knowledge which took people like Dalton, Lavosier, Gibbs, and hundreds of others 300 (or more) years to determine Lastly, I don't think it is clear where memorization ends, and conceptual understanding begins anyway. Perhaps once one aquires enough memorized facts and algorithms, they will "CONNECT" them to "CONSTRUCT" their conceptual framework ? **************************************************************************** George R Long, Ph.D. Department of Chemistry Indiana University of Pennsylvania Indiana, PA 15705 grlong@grove.iup.edu 412-357-2575 Our lives are merely trees of possibilities - Marc Bolan **************************************************************************** ------------------------------ Date: Thu, 13 Jun 1996 14:05:00 -0400 From: AAHLGREN Subject: Re[2]: P1 and P2, WHEN can students gain these skills? >Scharber wrote: "50% of the students enrolled in physical science classes at the college level are not at Piaget's level of formal thinking. ... Thus, to accommodate the variety of students in my class, I provide many modes of learning and teaching chemistry, which integrates both the macroscopic and microscopic phenomena of chemistry in individual and group learning environments." From my reading of the research, the 50% figure (+or- 15%) is reasonable. Scharberg's two points are telling ones and their conciseness shouldn't underplay their importance for this conference. For example, if half of your students may not be able (among other things) to think proportionally, then density, gas laws, and stoichiometry basically don't make sense to them and they have no choice but to memorize procedures. Unless you want to dismiss these students as unready to learn any worthwhile ideas in chemistry, you have got to figure out what they *can* learn about chemistry--that is still worth their time and yours--and different ways of teaching it. It would be hard to find a better aid in thinking about all this than Dudley Herron's new book, "The Chemistry Classroom: Formulas for Successful Teaching." Its artful title belies a rewardingly reflective presentation of 20 years of analysis and experimentation in these problems. ------------------------------ Date: Thu, 13 Jun 1996 14:18:31 -0400 From: AAHLGREN Subject: Re: P2 d "Fair" is efficient Carroll's assessment of "unfairness" is certainly consistent with what I know of Pat Heller's extensive research on problem-solving in college physics courses at the University of Minnesota. Students who have been successful at running algorisms without understanding become resentful of attempts to help them understand -- after all, they are being forced to give up behavior that has stood them in good stead up till now. If the game is different, different people may be winners. But Carroll may be too optimistic in his closing statement that "The discord between efficient and 'successful' is resolved with practice as individuals learn..." if many (most?) students do *not* learn... ------------------------------ Date: Thu, 13 Jun 1996 13:49:25 -0500 From: "Dr. David Ritter" Subject: Re: Jerry Bell's question I may be missing the point in some recent examples because of my lack of organic skill, so please let me ask a question. >Jerry Bell raised the question: > > What sort of research results do we have on the issue of the > inability of many organic students to distinguish between > the functionality of a species and the "inert" remainder of > the molecule. > >I don't have answers, but I have some ideas. I am interested in >understanding the process by which chemists look at a molecule >and recognize the important information. > >This example, coupled with Craig Bowen's results in his M.S. >thesis, worries me because it suggests that one of the key >differences between successful and less successful problem solvers >in the domain of organic synthesis might be something known as >the "chess players syndrome." > >There has been quite a bit of research on problem solving among >chess players. Some of this work has clearly shown that the >approach a good chess player -- a master, but not a grand master -- >takes to the game is not all that different from the approach of a >good beginning player. >...They see a particular >pattern of chess pieces and say to themselves, "Oh, that's like ...," >and they know how to proceed. > I have always thought that this is the essence of Polya's phase two of problem solving: "Devising a plan." Polya statements to the student: "Do you know a related problem?"; "try to think of a problem having the same or a similar unknown."; "Here is a problem related to yours and solved before. Could you use it?" seem to me to describe the process which both the good and grand master chess players go through. Once the chess player has learned how to recognize where the center of action is, is the primary difference between the good and grand master chess players in the size of their repertory? If the above is true, (to continue the chess metaphor) the first task for us in teaching problem solving concerns getting our students up to the level of the good problem solvers before getting them to the level of grand masters. Thus, to most effectively teach problem solving skills, we should focus on the previous phase (if I may continue with Polya), that of "understanding the problem." We are to teach students to construct "correct GMB's representations for problem solving." Is this the skill that will improve students' ability to find the area of interest of the chessboard (or organic molecule, as it were), and thereby improve success in solving the problem? Is this not what Polya means by "understanding the problem?" David Ritter Department of Chemistry Southeast Missouri State University c617scc@semovm.semo.edu ------------------------------ Date: Thu, 13 Jun 1996 14:44:08 -0400 From: AAHLGREN Subject: Re[2]: P2-JD-D-DR-Teaching Students Problem Solving Long's analogy to learning language is a good one. People do not learn language naturally by memorizing a large vocabulary and only later learning how to put it together. (Computers might be programmed to learn this way, but people don't.) Putting it together begins as soon as there are a few words to relate. Once there are some connections available, then vocabulary can be very useful and words are subsequently memorized as a need for them to make meaning arises. (Yet some language instruction seems to be based on memorizing a great body of terms in the hope they will spontaneously configure themselves into meaningful relationships.) Putting it another way: The activation energies required for configuring ideas in chemistry are too great for spontaneous configurations to occur very often at typical temperatures from merely mingling the reactant ideas, no matter how concentrated they are. Some very precisely tuned enzymes are usually necessary. A few such enzymes may have evolved by chance in really good chemistry teachers and can be passed on. With enough knowledge of the principles and configurations involved, we might be able to design enzymes for the purpose. Again, Herron's new book is a good place to look for clues. ------------------------------ Date: Thu, 13 Jun 1996 16:51:50 -0400 From: Kenn Harding Subject: P2 - KH - D - RT (Foreign Language Analogy) Rich Taylor comments on making an analogy in learning chemistry to learning a foreign language and goes on to suggest that we are talking about 'fluency' rather than 'mastery of rules and vocabulary'. My experience in organic chemistry is reinforced by evidence presented by Bodner that suggests that significant numbers of students have problems with 'vocabulary' long after we assume that we can concentrate on other things. In organic chemistry, the 'foreign language' we are teaching is complicated by: (i) even the linear words in our normal alphabet do not follow normal spelling rules - CH3CH3 and H3CCH3 represent identical structures, CH3CHO represents a simple molecule but CH3COH is a 'spelling error'; (ii) most of our discusssion of organic molecules involves use of symbolic representations (which continue to look like hieroglyphics to many students); (iii) we can (and do) use multiple symbolic representations (i.e. multiple hieroglyphic spellings) for a structure (Lewis structures, Kekule' or line-bond structures, condensed structures, skeletal structures, Newman projections, Fischer projections, wedge-dash structures, chair structures, etc.). I believe many of our students are having 'vocabulary' problems as represented by Bodner's discussion of the structures in Figure 1. I sometimes point out to students that not only are we teaching them a foreign language using arcane symbolic structures, but we are expecting them, in our beginning 'language' course, to solve complex logic problems in this language (analogy, deduction, synthesis). Unfortunately, this does not seem to make them more eager to delve into this subject with enthusiasm. As pointed out by Bodner (see Bodner's 12 June response to question by Jerry Bell), even students that can generate appropriate representations can have a problem in 'decoding' the appropriate component of the structure to use in solving even a simple complete the reaction problem using analogy. An example might come from benzoic acid problem discussed in the paper. The symbolic representation shown in Figure 6 will aid a student in recognizing the carboxylic acid nature of the structure and trigger a recall of acyl substitution chemistry. However, a student who has not learned to generalize the role of SOCl2 (have they tried to memorize complete sentences (reactions) as a set of hieroglyphics?) may instead recognize and concentrate on the aromatic substructure. Now some recollection about SOCl2 producing some type of chlorine substution may result in a chlorobenzoic acid as their answer (perhaps even correctly applying rules about directing effects and generating m-chlorobenzoic acid). This is more likely to occur on a comprehensive final exam where the specific chapters being covered does not aid a student in 'finding' the correct substructure. My conclusion is that we need (a) to spend more time and effort trying to help students gain a better understanding of structures and their representations (hands-on mechanical models or computer-generated representations as in paper 3?) and (b) to be much more cognizant that a student question about a problem may not be whether SOCl2 or HCl is the correct reagent, but how to decipher the symbolic representation in a way that leads the student to consider consider these types of reagents. However, the 12 June comment by David Ritter sounds particularly discouraging. If a 70% correct response is the best rate that can be achieved on such a simple 'disembedding' task, what are our chances of significantly increasing the correct response rates to our synthesis problems in organic courses? Of course, we can sit here and think that the students we have in 'our' classes are not such intractable 'posts' (or are they?). Kenn E. Harding Professor and Graduate Advisor Department of Chemistry Texas A&M University College Station, TX 77840 Phone: 845-5345 or 800-334-1082 FAX: 409-845-2338 TAMU Chemistry WWW Homepage: http://www.chem.tamu.edu/ ------------------------------ Date: Thu, 13 Jun 1996 21:55:55 -0400 From: George Long Subject: Re: Re[2]: P2-JD-D-DR-Teaching Students Problem Solving > > Long's analogy to learning language is a good one. People do not > learn language naturally by memorizing a large vocabulary and only > later learning how to put it together. (Computers might be programmed > to learn this way, but people don't.) Actually, I don't believe computers "learn" this way either - neural net programs start with no prior knowledge of a system, begin to make connections, keep the ones that work, then build more around the successful connections. There is a minimum amount of data required to start. The closer a neural net is to being trained properly, the more easily it can assimilate new data. David Brooks published a good article concerning this a number of years ago in JCE. The success of a neural net is also dependant on the training set it uses to "learn" something. We might infer from this that an appropriate breadth of topics is important, and as has been mentioned in the discussion, different approaches to problems are important. > > Putting it another way: The activation energies required for > configuring ideas in chemistry are too great for spontaneous > configurations to occur very often at typical temperatures from > merely mingling the reactant ideas, no matter how concentrated they > are. Some very precisely tuned enzymes are usually necessary. Great analogy !!! But I would argue that spontaneous configurations do occur all the time - People do learn chemistry, and it is a spontaneous - AHA !! - experience when they finally get a concept To further overuse the neural net analogy, we provide the students with a training set(curriculum), and an associative memory (a pre-organized knowledge base). Perhaps we can motivate them to be active learners, but I don't think it has ever been shown that we can make the connections for the students. **************************************************************************** George R Long, Ph.D. Department of Chemistry Indiana University of Pennsylvania Indiana, PA 15705 grlong@grove.iup.edu 412-357-2575 Our lives are merely trees of possibilities - Marc Bolan **************************************************************************** ------------------------------ Date: Thu, 13 Jun 1996 20:42:25 -0700 From: Bob Bruner Subject: Re: P2-JD-D-DR-Teaching Students Problem Solving >Why should the original way a problem is solved be important? we should not >want to reproduce the path someone took to get to an answer. In fact, the >point of the literature is to distill research down to the most easily >usable form. The whole point of science is to build upon organized Idea's >that others have painstakingly developed. Because the "original way" reflects how scientists really think. And that is one of our goals to teach. (I'm not suggesting we confuse the role of a scientific journal with this, but the point is that the lab notebooks, not the journal article, are real science.) Isn't a large degree of memorization, of rules >and algorithms to be expected for a novice in any field. Isn't it a >requirement if we expect the students to be effective users of chemical >technology. No. Real life is open book. You can look up facts. What you need to learn is what to look up, and what to do with it. Students will learn some facts from repeated usage; with luck repeated usage reflects the more important facts. I've taught chem with open book tests, to emphasize that thinking is more important than memorizing. (The problem with open book tests is that students take it as an excuse to not study. Allowing student-written note sheets serves the same purpose, and is better.) >Our rules >and algorithms are designed to simplify a concept Maybe, but many of our rules have soft edges. (Why do we use a roman numeral in the name of a iron cpd, not a zinc cpd? Hard to make that sound _logical_ to a young student.) Bruner's rules about rules (short version)... 1. Don't memorize rules without knowing when they apply. 2. Don't worry about exceptions to rules until you understand the rules. 3. Don't worry much about exceptions at all. Originally written in the context of beginning nomenclature, but perhaps more generally useful. I would rather the kids learn chemistry, and learn names while doing chemistry, than memorize names and rules. The ones who aren't going on won't remember them, the ones who are will get plenty of reinforcement. Much of what Harding wrote (Thu, 13 Jun 1996 16:51:50 -0400) I think fits here. >Certainly >no one would argue that students should discover on their own knowledge >which took people like Dalton, Lavosier, Gibbs, and hundreds of others 300 >(or more) years to determine Agreed. And I think we need to be cautious about moves towards teaching by discovery. There is merit, but it is slow, and it is hard to re-create the original environment. We can't teach everythin that way. >Lastly, I don't think it is clear where memorization ends, and conceptual >understanding begins anyway. Perhaps once one acquires enough memorized >facts and algorithms, they will "CONNECT" them to "CONSTRUCT" their >conceptual framework ? Fair point. Bob Bruner UC Berkeley Extension & Contra Costa College bbruner@uclink4.berkeley.edu Date: Thu, 13 Jun 1996 21:27:18 PST From: Christine Pastorek Subject: P2-CP-D-Spacial Ability, 2D and Self Confidence The lack of what I think has been referred to as spatial ability on the part of some students may be rooted in the incomplete 2D communications systems teachers are forced to use. Humans operate in everyday life on 70% visual 3D input. It's no wonder that students have trouble visualizing structures and chemical reactions on a molecular level-we present them in 2D, monotone colors, along with artist's renditions-and say-can't you SEE this...this bond sticks out over here..!? Well we are presenting them a pretty poor external representation of the real thing to begin with. We are crippled because the depth of our communication form has not changed in a l-o-n-g time-we aren't doing things much differently now than when cave dwellers painted on their walls of the hunt and slaughter-or when Egyptians painted images of humans and animals at obtuse angles-boy, those are realistic- blackboards-textbooks-overheads-PC monitors-they force us to tie one dimension behind our backs!! Hopefully we are beginning to peek out of the cave and will soon be routinely using interactive video and virtual reality to convey the live concepts of chemistry. Maybe more students will actually see what it is that we experienced chemists see. Blaming poor performance in chemistry on an absence of spatial abilities might overshadow the fact that some students are just too darn timid and inexperienced to communicate what they know-after all this IS chemistry-the hardest subject in the world-right?-my dental hygienist told me this just yesterday! Most students don't seem to have the self-confidence to "dissemble" and consequently they lose out on the chance to "restructure" (I assume that these are voluntary acts)! They are afraid to make a little mistake, especially in front of their peers. As teachers of problem solving strategies, we chemists need to get our students actively involved and personally responsible for learning the processes of problem solving and how to use them. Throw them in the proverbial swimming pool. Ask students in front of their peers more direct but still open ended questions about what they think about the outcomes and solutions to problems. We need to ask them to restate the question in their words and make suggestions for the consequences for various actions-they need to learn how to make predictions. They need positive reinforcement on decision making -not just more points. I want my students to say: "hey I can figure this out!" They need to hear from us "you have a point here, your plan is a good one" even if their first answer might not be a correct one. Once they experience the rewards of making educated guesses, anticipating the results, exploring other options, they develop the confidence to predict what will happen in new and novel situations...and just maybe we have helped liberate a whole new generation of problem solvers! ------------------------------ ------------------------------ Date: Fri, 14 Jun 1996 10:37:01 MDT From: Reed Howald Subject: Re: P2-RH- Teaching Students Problem Solving Dr. Rosenthal poses some interesting questions. I would like to see some real discussion of how to achieve real success in the teaching of science. It is amazing how we all resist approaching these questions scientifically. We have as a race thousands of years of experience in teaching. In the last 200 years of science teaching we have a vast amount of experimental data on what works and what does not work. There is quantitative data there that has never been examined quantitatively. With computer graded examinations it is now easy to collect information on the student outcomes together with the examination questions and the teaching methods used. Not only is it not being examined, most teachers are throwing the data away. >1. Is the course instructor (an A student) necessarily best in a position > to teach problem solving to the students? No. The course instructor is in a good position to correct misinterpretations, and to provide help when people get stuck. But the best teaching is done by other students. Cooperative education works. The apprenticeship method works, but we don't have enough master teachers for a completely one on one teaching system. >2. What do you think of these techniques? >Many Universities courses have recitation sections taught by graduate >students and it is in these recitation sections where homework problems >are discussed. There are great successes and great failures in this, depending on the quality and training of the graduate student teaching assistants. It should be very easy to assemble quantitative data here documenting the danger in relying on this approach. >Very often the students, who are taking the course, are >asked to put problems on the board and each student explains the problem >to the rest of the class. Even the threat of doing this is an effective teaching technique. One way to ensure that cooperative learning groups are doing their job (to ensure that everyone in the group knows how to solve the problem) is to randomly pick a group member to explain their work to the whole class. >Another recent trend is to use cooperative (or collaborative) learning and >have students work together in groups to solve problems. Cooperative learning works. I generally think that fads in teaching are to be avoided, but this one is too good to ignore. What quantitative data exists demonstrates that it works. You can discount it as due to the placebo effect (any teaching technique the teacher is enthusiastic about will get improved results). But in this particular case cooperative education works so well that I am sure a double blind experiment in cooperative education would show positive results. >Some teachers when working with students on a one-to-one (or group) basis >will explain how the problem should be worked. Other instructors will >try to have the student explain how he has attempted to solve the problem >and try to HELP the student get to the correct solution. The explanation approach can be done in lecture format to a group of 500. The second method works better, and is that used in any apprenticeship situation. One first watches the master do it, but more learning occurs when the master is watching the apprentice work. Again this is so clear that it could be documented quantitatively, but we avoid collecting and looking at the data. >I remember reading many years ago that most mathematicians after proving >a theorem, then develop a very well organized and logical solution for >publication. This published solution gives very little insight into how >the theorem was actually proven. This seems to be similar to what you are >saying about how many instructors operate - they present well organized >and logical solutions which do not give students very much insight. True. The methods we show in lecture are more organized than the way we actually work problems now, and lack the trial of representations that didn't work smoothly that we used when we first worked problems of this type. >Many problems can be solved in more than one way. >3. Is it worthwhile presenting more than one way of solving a problem? Yes. Work a problem two ways in one lecture section and only one in the other. Then include the problem in an exam and you will have quantitative data. I think the results will show that this will show that the extra time spent in class to present it two ways was worthwhile. However an even better use of 5 minutes of class time would be to allow groups of 4 or 5 students time to discuss and tackle this same problem before or instead of presenting one or any solution. Sincerely, Reed Howald Department of Chemistry and Biochemistry Montana State University Bozeman, MT 59717 "uchrh@earth.oscs.montana.edu" ------------------------------ Date: Fri, 14 Jun 1996 14:22:27 -0400 From: James Herron Subject: Jeff Davis's Reference to Piaget I was out of town when Jeff Davis wrote: >It has been a while since I was engrossed in Piaget when >Dudley was championing the cause but I don't recall from my reading that >any of the research indicated that one can't move beyond the concrete >stage before you are 18 years old. Am I wrong? You are not wrong, and some researchers believe that people are capable of sophisticated reasoning at very early ages (pre-school). This is still an active area of research with many unanswered questions. About all that seems to be clearly established is that CERTAIN FORMS of tasks that appear to require reasoning that is used habitually in science can be solved by children who are much younger than the age (12-15) that Piaget identified as the period during which "formal operations reasoning" develops. (These same children ARE NOT successful on other forms of these tests.) I have not the research on these questions during the last couple of years, but I reviewed and discussed much of it when I was preparing the manuscript for Chemistry in the Classroom. (Found in Appendix M of the book.) For those interested in this research, Flavell, Miller, & Miller (1993) Cognitive Development (3rd ed.) Englewood Cliffs, NJ: Prentice-Hall is a good place to start. J. Dudley Herron, Chair Department of Physical Sciences 123 Lappin Hall Morehead State University Morehead, KY 40351-1689