In the Classroom
General Education and General Chemistry—Redux Leslie S. Forster Department of Chemistry, University of Arizona, Tucson, AZ 85721;
[email protected] Spearheaded by a committee report from Harvard (1), the general education movement was invigorated at the end of World War II, although the movement has lost momentum in the intervening half-century. Educational reform is cyclic; Harvard has issued a new report aimed at revitalizing the liberal education component of the undergraduate curriculum, with an emphasis on general education in science (2, 3). The report identifies three groups of students in introductory science courses: “science majors, those preparing for medical school, and those whose interests lie outside science” (3), and suggests that courses be designed to serve the needs of all three groups at the same time. Few post-secondary institutions are selective enough to make this a viable approach. Instead, the more conventional separation of beginning chemistry courses into two groups, one for science and engineering majors and the other for nonscience majors will persist. In 1955 I wrote a paper with the same title (4) as this paper: in the former paper I suggested a number of general education topics that were appropriate in an introductory chemistry course designed for science and engineering majors. It was tacitly assumed that chemistry courses for technical majors necessarily expose students to the general education aspects of science. I now feel that a more explicit approach is necessary and that the general chemistry course is a suitable vehicle for addressing certain general education issues. General chemistry texts usually define “the scientific method” in a misleading way, and include historical vignettes as recognition that a science course should contain more than technical content. Many instructors treat this material as optional and do not formally present general education topics. Ideally, we should describe how various sciences actually operate and provide students with a basis for evaluating knowledge claims in the media. This goal is far too ambitious. The scientific enterprise is so complex that any attempt to unambiguously characterize fully the many facets is doomed to fail (5). Time constraints dictate that more modest goals must be pursued, such as: What attributes separate the natural sciences from other intellectual pursuits; How are theory and experiment interrelated; How is consensus reached in science. The Varieties of Science I once thought it possible to formulate a clear-cut criterion to differentiate science from other areas of knowledge. Experience has shown that no agreement on this distinction can be expected. However, we can discuss the multiple connotations of the terms “science” and “scientific”. In this way differences between the sciences will emerge. Consider these exemplars of terminological diversity: (1) “quantum mechanics is a scientific theory”; (2) “DNA evidence in a criminal trial can be scientifically justified”; (3) “the opinion poll was scientific”; (4) “the efficacy of the drug was established by a scientific study”; (5) “evolution is a scientific fact”; (6) “scientific creationism is an alternative to Darwinian evolution”; (7) “economics is ‘the dismal science’”. A starting point for the semantic discussion is to categorize the various areas of knowledge. One way to do this is shown in Figure 1. This scheme is neither complete nor unambiguous. Any classifica614
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tion is necessarily imprecise with ill-defined boundaries. Many disciplines fall on the borderline between categories. In particular, a problem arises in distinguishing the natural from the social sciences. Most natural scientists are realists in the sense that they only believe in phenomena that are not subject to human emotions or behavior. Both economics and physics can be formulated in mathematical form, but physical phenomena are assumed to be rooted in the external world whereas economic behavior can be changed by intentional human actions. Psychology includes the natural scientific components cognition and perception in addition to emotional and psychiatric features. Sociology and political science results are highly sensitive to the behavior of individuals and groups. Many aspects of medicine also fall on the borderline. Diagnoses based on laboratory tests are not the same as those that depend on the subjective experience and skill of the physician. The natural sciences can be further divided into historical and experimental categories. Both types are empirical and involve a theoretical framework but they differ in the way that conclusions are validated. Historical sciences, by definition, involve unique events that must be analyzed by a network of inferences. The essence of an experimental science is the possibility of controlling the conditions under which the phenomena appear. There is no possibility of replicating the events in either evolution or cosmology. Observations can be repeated, but the events that gave rise to the observations cannot. Some geological interpretations are subject to experimental test but most are not. The great power of an experimental science lies in the requirement that putative phenomena must be reproducible in order to find widespread acceptance. Reproducibility is a necessary but not sufficient condition for validity, as evidenced by the ill-fated polywater claim that attracted the attention of a significant group of experimental and theoretical researchers for nearly ten years (6). The anomalous properties of water in narrow glass and quartz capillaries were reproduced by different research groups. Skepticism persisted and it was finally shown that the unusual behavior was due to dissolved impurities. An account of the “anomalous water” history reveals much about the way that the scientific enterprise actually works to eliminate spurious knowledge claims. Even a brief summary of this history would be instructive. The more recent claim of cold fusion has not met the requirement for reproducibility and is not widely accepted, although proponents still remain. If there is any validity to the phenomenon of nuclear fusion at ambient temperatures,
Natural Sciences Historical Experimental Geology
Biology
Evolution
Chemistry
Cosmology
Physics
Social Sciences Economics
Religion Intelligent
Political Science
Design
Sociology
Scientific
Psychology
Creationism
Medicine
Figure 1. A proposed distinction between some areas of knowledge.
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In the Classroom
it is up to the supporters to demonstrate the effect under conditions that can be reproduced. Reproducibility in studies with living systems must involve a statistical analysis; the conclusions in these studies are more difficult to validate.
A Case History—Theory versus Experiment Isolated events are of only limited interest in the experimental sciences. At the lowest level of a science is the search for generalizations. The development of the gas laws, especially Boyle’s law, illustrates how quantitative generalizations are made (7). Boyle used a closed-ended J-shaped manometer in which the volume of trapped gas is reduced as the pressure increases. This can be demonstrated and sufficient data collected during a class period to show how an empirical law is formulated. According to his own account Boyle did not recognize the inverse proportionality of pressure and volume, but a reader of his paper did. In order to appreciate the creativity involved in this experiment, the students must place themselves in the mind of someone in the mid-17th century where the properties of gases were only dimly recognized. Boyle made no attempt to control the temperature and it is interesting to speculate the difficulty that would have resulted if the pressure was very sensitive to temperature. It took more than another century after Boyle’s law was enunciated for the promulgation of a second empirical law, Charles’s law, which was initially stated as the change in volume is proportional to the change in temperature on any arbitrary temperature scale. This provides an opportunity to distinguish a linear relationship from proportionality between volume and temperature, which only obtains with the introduction of the absolute temperature scale. Incidentally, it took another half-century to develop the Kelvin scale and the concept of absolute zero. A qualitative demonstration of gas effusion through a pinhole is rationalized with Graham’s law. Empirical laws are closely related to direct experience. At this point the intuitive nature of the inductive leap to the kinetic–molecular theory can be discussed and contrasted to the empirical laws. Daniel Bernoulli suggested such a theory in 1738 but it was not until 1850 that Maxwell developed the modern kinetic–molecular theory of gases and introduced the notion of a velocity distribution. The power of theory to unify Boyle, Charles, and Graham’s laws can then be demonstrated by a commercially available two-dimensional molecular motion model (8). This account demonstrates the use of the hypothetico-deductive method as one way to validate experience and to connect apparently dissimilar empirical laws. It must be pointed out that this method, though widely used in physics, is less applicable in chemistry and biology. Even though experience provides the bedrock of all science, empiricism is not enough to describe modern science. Theories play an essential, but often misunderstood, role. In favorable cases, theory can predict results deductively, but often is only a means of organizing disparate phenomena into coherent knowledge. Much of chemistry relies on quantum mechanical ideas such as atomic and molecular orbitals but the use of these concepts does not depend on a deductive procedure (9). Rather, approximate and pictorial models are used. What would chemistry be like if some kind of periodic table were not available? The power of the orbital model to explain periodicity can then be described. The use of models in chemistry is a difficult point to discuss at the general chemistry level. We all use models that are only loosely justified www.JCE.DivCHED.org
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by fundamental theories, but that work well enough to guide our thinking and to make interpolations from experience that masquerade as predictions. The use of complex instrumentation to collect “facts” involves a theoretical interpretation of the observations. There is a continuous interplay between the direct observations and theory and the conclusions are often tenuous. The entire area of synthetic chemistry is based on experience and theoretical guidelines, but is also an art.
A Case History—Resolving a Controversy One characteristic of a natural science is the impetus to remove disagreements in either facts or conclusions. Prior to 1936 Avogadro’s number (NA ) was listed in chemistry texts as 6.06 × 1023, a difference of greater than 0.5% compared to the current value. The events that led to a revision in the value of a fundamental constant provide insight into the selfcorrecting character of the scientific enterprise. In 1913 Milliken had determined the charge on the electron by the oil-drop method; this value, combined with the known amount of charge required to electrolytically deposit a mole of a mono-valent ion, led to NA = 6.06 × 1023 (10). The socalled grating constant method of evaluating Avogadro’s number, an alternative way of determining NA, can be described in connection with the unit cell concept. NA can be obtained if the X-ray analysis provides the unit cell volume and the number of molecules in the unit cell. These quantities coupled with the crystal density yielded 6.02 × 1023 for NA (11). A discrepancy between the two values had been known since 1925 and the difference was large enough to stimulate research on the source. The oil-drop result depended on the viscosity of air. Once this viscosity was redetermined in 1935, both the oil-drop and grating constant results were in agreement (12). This story illustrates the value of approaching a problem in different ways. Another facet of Milliken’s work stirred controversy: he used only a fraction of the data collected and has been subjected to the charge of data manipulation. Fortunately his notebooks have survived showing there were good reasons for rejecting many data points (13). The skill and judgment of a good experimentalist enters into the evaluation of the results: the rejection of bad data is the hallmark of science. This illustrates the subjective aspect of science, dispelling notions that science proceeds by a well-defined “method” that distinguishes it from other intellectual endeavors. Statistics and Statistical Theories Statistical reasoning is used in science in two different ways. Both kinetic–molecular theory and quantum mechanics apply to collections of particles and are statistical in an a priori sense, as shown with the kinetic–molecular theory model described above. Gas pressure is only defined in terms of multiple collisions with the walls. Demonstration of the statistical nature of quantum mechanics is more difficult. A two-slit diffraction pattern can be exhibited with a HeNe laser and parallel scratches in an exposed photographic film. It can be stated—but not demonstrated at this level—that reducing the laser intensity to allow only one photon to strike the film will result in one small spot, not a diffraction pattern. Accumulation of many such spots produces the same diffraction pattern as many photons in a more intense beam (this experiment has actually been performed). The individual photons know where to go, but only in a statistical sense, a nonintuitive result. In contrast to a statistical theory, empirical or inferential statis-
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tics in the natural and social sciences are used differently. Public opinion polling and medical statistics illustrate this difference. Both forms of empirical statistics rely on an adequate sample from a large population. If the sample is not representative of the population the results will not be reliable. Medical statistics range from epidemiological (e.g., correlations between diet or environment and disease onset), to controlled clinical trials. A drug is considered effective if there is a statistically significant difference in a parameter such as blood pressure or cholesterol level between the parameter in treated and untreated populations. The minimum improvement for clinical significance is established arbitrarily. In many cases, the criterion for efficacy is a subjective report by the patient. The variability of the human organism seldom leads to straightforward interpretations of such statistical studies. The Theory of Evolution—A Continuing Controversy Although no formal criteria exist to answer the question What is science?, a discussion of the alternatives to Darwinian evolution reveals important differences between the natural sciences and religion. The pressure to include these anti-evolution views in public school science curricula and textbooks has been ongoing for many years. Discussion of radioactive decay provides a natural bridge to evolution. Radioactive dating as a tool for estimating the ages of geologic formations depends on the constancy of the decay time. Uncertainties arise from sample contamination, but the concordance of dates from a number of samples by different radioactive decay series imparts confidence in the results. Challenge to the four-billion-year age of the earth by self-styled scientific creationists (adherents of Old Testament chronology), requires denying the validity of the dating assumptions. Incidentally, 14C dates are subject to error because the rate of 14C production in the upper atmosphere has varied over time. Corrections for this effect have been made by comparison of the radiocarbon dates with those obtained from analyses of tree rings. Dating by the Rb–Sr and other longlived systems is not subject to this uncertainty. The essential point advanced by opponents of evolution is that the supporting evidence is inadequate and that the alternatives are equally scientific. It would not be appropriate to detail all the evidence supporting the basic tenets of evolution theory in a general chemistry course (14). It is sufficient to simply state that evolution postulates that higher organisms, including man, are descended from simpler systems over time without the intervention of a supernatural power. Most biologists support evolution as the only way to understand the various observations, but there are gaps in the overall picture and debate over the theory. To the extent that scientific creationism and intelligent design, the two most prominent alternatives, point out these deficiencies, this criticism falls within the framework of science. It is the essence of natural science that the evidence for any theory is always subject to challenge. There are assertions in many of the sciences that are speculative and subject to revision. The history of cosmology is replete with examples. This problem is most acute in the historical sciences and we should not be surprised if evolutionary theory is modified as new evidence is found. An important tenet of intelligent design is the assumption that organs such as the mammalian eye are too complex to have evolved by random processes, a view that is suggestive, but imprecise. When one looks for positive support for an 616
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alternative explanation within the intelligent design framework it cannot be found. Scientific creationism relies entirely on a literal interpretation of Genesis to explain the appearance of all extant species, clearly a nonscientific approach. Proponents of intelligent design refuse to specify the nature of the “designer”, but insist that it is not materialistic. By any reasonable definition of science, intelligent design falls in the realm of religion. No alternative to evolution yet proposed can be called scientific, in spite of assertions to the contrary. It is unlikely that any discussion of this issue will change the minds of either proponents or opponents of evolution, but each side should understand the basis for their position. Many mainstream religions have found no difficulty reconciling a belief in God with the tenets of evolution. Henry Eyring, an eminent chemist and a devout Mormon, said “in my mind God is behind it whether we evolved or not” (15). Consequently, even in this most contentious area there need not be any conflict between religion and science. Summary The examples given above are merely suggestive. Each instructor will choose general education topics consistent with his or her own background and interests. Although there are no simple criteria that distinguish a natural science from other intellectual pursuits, there are some features that are common to all of the natural sciences. These include a belief in the reality of an external world that does not require non-natural forces to function, skepticism in accepting unusual knowledge claims, and a willingness to change in the light of new evidence. Natural scientists are pragmatic and employ theoretical models that work even if they are only approximations. Some aspects of a natural science are well-established while others are speculative; none, however, are immutable. If general education in science is important for non-scientists it is equally essential for science majors. A reasonable discussion of general education topics can be included in a general chemistry course without sacrificing essential content. Literature Cited 1. General Education in a Free Society; Harvard University Press: Cambridge, MA, 1945. 2. Science 2004, 304, 810. 3. A Report on the Harvard College Curricular Review, April 2004. http://www.fas.harvard.edu/curriculum-review/HCCR_Report.pdf (accessed Jan 2006). 4. Forster, L. S. J. Chem. Educ. 1955, 32, 206–208. 5. Ziman, J. Real Science; Cambridge Univ. Press: Cambridge, 2000. 6. Franks, F. Polywater; MIT Press: Cambridge, MA, 1981. 7. Conant, J. B. Robert Boyle’s Experiments in Pneumatics; Harvard University Press: Cambridge, MA, 1950. 8. Science Kit. http://Sciencekit.com/ (accessed Jan 2006). 9. Scerri, E. R. Sci Educ. 2000, 9, 405–425. 10. Milliken, R. A. Phys. Rev. 1913, 2, 109–143. 11. Beardon, J. A. Phys. Rev. 1935, 48, 385–390. 12. Birge, R. T. Phys. Rev. 1935, 48, 918. 13. Holton, G. Hist. Stud. Phys. Biol. 1978, 9, 166–224; Goodstein, D. Am. Scientist 2001, 89, 54–60. 14. An Evolving Dialogue; J. B. Miller, Ed.; Trinity Press: Harrisburg, PA, 2001. Essays on scientific and theological aspects of the evolution debate, including a description of intelligent design. 15. Eyring, H. Reflections of a Scientist; Deseret Book Co.: Salt Lake City, UT, 1983; pp 53–62.
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