SPRING 2006 WORKSHOPS
ON SCIENCE LITERACY
(Originally published in Educational Philosophy and Theory, (20)2. 1988. 42-52)
Department of Biological Sciences
Hunter College of The City University of New York
695 Park Avenue, New York, N.Y. 10021
Science illiteracy is a serious problem. At one level it affects nations; because large parts of their populations are not adequately prepared, they cannot train enough technically proficient people to satisfy their economic and defense needs. More basically it affects people; those who are science illiterate are often deprived of the ability to understand the increasingly technological world, to make informed decisions regarding their health and their environment, to choose careers in remunerative technological fields and, in many ways, to think clearly. In contemporary society, general literacy is needed by a people to be able to communicate, and receive communication, about the state of their lives. Today these communications are as likely to deal with specifically scientific subject matter as any other. Thus to be truly literate today requires - indeed implies - that one also be science literate.
Science literacy, defined in general terms as the ability to "understand", requires the functional ability to interpret or "read between the lines". In practice, beyond familiarity with certain facts and conclusions of science, the science-literate person must have both a cognitive level that supports reasoning skills, and language skills that permit making and expressing distinctions. I suggest that the acquisition of these cognitive and language skills requires certain life experiences that can be incorporated into science curricula at different levels. I also suggest that appreciation of the process of science can be enhanced by studying the development of critical concepts in an historical context rather than emphasizing current beliefs.
The definition of science literacy
In his Rede Lecture, published as "The Two Cultures and the Scientific Revolution" (1959), C. P. Snow established himself as an authority on the subject of science 'illiteracy' as a problem facing those who are otherwise well educated. He characterized these two cultures as the arts and the sciences, and concluded that there was little traffic between them. Moreover, he suggested that this dichotomy severely limited the ways in which government (largely staffed by "arts" graduates) could cope with the increasing number of essentially technological problems with which it was faced.
Beyond the criticism of his country's educational system, Snow's essay has a more general relevance. In the first edition he suggested that there was one truly general and significant concept of science with which the non-scientist should be familiar - the second law of thermodynamics. Five years and ten reprintings later, Snow provided "A Second Look" in which he exhibited a change of mind. Instead of "entropy", he decided that the one crucial concept that should be in the working vocabulary of every non-scientist should be what he referred to as "molecular biology". Today we would more specifically refer to his concern as the "central dogma of molecular biology", often summarized as "DNA makes RNA makes protein."
The threat and promise of the genetic engineering technology that has grown out of this new area of science may warrant the replacement of one intellectual tour de force by another. But what would that say of the "literacy" of the earlier generation of non-scientists who had assiduously taken Snow at his word and mastered the second law? Would they be cast aside by the tide of events and again find themselves among the illiterates? This doesn't seem quite fair. Perhaps inadvertently Snow has performed a second service: beyond noting the existence of two cultures, he has shown us that science literacy cannot be based on, or scientific illiteracy remedied by, the acquisition of a specific body of knowledge. No one who tries to define or enumerate what might be the specific topics to be included in a course for non-science majors will find much common ground if more than two or three experts are consulted. They may well agree on the pressing need to create a better informed citizenry, but the way in which this is to be done founders in the absence of a common understanding of what "better informed" is
If we are talking ultimately about literacy -- even if only of the science variety -- this lack of agreement should not surprise us. For example, we may wish that fully literate adults had "read" Shakespeare, but it is not at all clear what this means. Does it mean simply to have "gone through" all the plays (and sonnets), or to have "mastered" (understood? appreciated?) only a few? If the latter, which? And if the former, how many otherwise intelligent, informed and well-read people would have to be deemed illiterate? The problem, of course, is that while in a homogeneous and relatively static society literacy may be equated with common knowledge and the ability to read, and that, while a prescription for achieving it may be made and in time fulfilled, in a heterogeneous, intellectually expanding society such an approach is doomed to failure.
Must we then give up the notion of striving to pass on the ideal of literacy? No. Although we may argue about the criteria for "full" literacy, we can usually agree about some necessary attributes of this, what we might call "lesser" literacy. People are clearly illiterate if they cannot "spell out" a simple text (which assumes only one method of reading). And they are probably also illiterate if they can only spell out a text; those who cannot interpret a text so as to follow the instructions needed to fill out forms or take driver's license tests are called "functional illiterates".
The distinction that is being made here relates to a broader set of levels of expertise. Among scientists, for example, we may acknowledge degrees of competence that will characterize practitioners in a specialized area and lesser degrees of knowledge that non-experts may bring to nearby or distant fields. Independent of detailed knowledge, however, scientists often have the ability to understand what a colleague has written. This is because, regardless of field, there is a similarity in the approach taken by scientists to their problems, including the way they identify and try to solve them, as well as the way they communicate their solutions. Depending on the amount of jargon or reference to specific findings in the scientific literature that is included in this text, a scientist's writing may also by appreciated by anyone else familiar with these habits of scientific thought and writing.
This approach to the meaning of "science" literacy clearly goes beyond the simple ability to plough through a text word by word. With science, as with other college level courses, we are dealing with understanding concepts as opposed to understanding directions. This is why, at the college level, we are concerned with more than just functional literacy. We expect our students to get more than the plot out of a text, and we are dissatisfied if they cannot in some way "read between the lines" to interpret what is in front of them. I believe that to some extent these interpretive skills are expected even of entering students; as work in our various disciplines proceeds we try to sharpen and refine them. For example, if they are reading about human activities, we expect them to be able to infer motives into what they read and, beyond that, to justify their inferences on the basis of related "facts" supplied by their text. Similarly, in history we are not content with a repetition of isolated facts, or even of the story. We expect that understanding involves an appreciation of relatedness that goes beyond chronology and includes geography and social interactions as well.
This realization has been used by Don Nix (personal communication) at IBM to develop a strategy for teaching reading comprehension at a grade school level. Part of his approach involves questioning. In addition to asking students to answer questions requiring the ability to recall what has been read, he has incorporated questions whose answers require interpretation based on understanding. He points out, however, that the inferences we expect students to draw are often grounded in culture as well as in content. For example, the significance of a "three and two" count on a batter in a baseball game can be appreciated by a child, but lost on someone unfamiliar with the game. Both culture and content, of course, reflect different kinds of experience: a child brought up in an ascetic environment will not know what to infer from an open display of emotion, and a person used to a pine forest would find references to the fall colors of New England puzzling.
Does this give us any additional insight into the immediate goals to be pursued in the quest for a means to achieve science literacy? I think it does. It implies that we cannot content ourselves with following the approach often taken in courses in which the conclusions of the discipline are enumerated. Beyond that -- preferably prior to -- it is critical to present a meaningful discussion of the phenomena that must be accounted for. This must then be followed by an elaboration of the rules of inference that are characteristic of the discipline in question. And these rules, in turn, must then be applied to demonstrate how some of the major conclusions have been reached. Ultimately, literacy in an area comes from the general ability to follow the reasoning in that area, not simply from the detailed familiarity with the specific material that has been read.
Cognitive development and science literacy
Now, if it is not subject matter that makes science different, we should be able to ask what can provide a focus for enhancing science literacy. Specifically are there specific thought processes that are necessary to science? The answer is yes, but note that the criterion is necessity, not uniqueness. The most easily accessible term for these thought processes was introduced by the Swiss developmental psychologist Jean Piaget: it is "formal operational". Piaget suggested that the "formal operational" developmental stage followed the "pre-operational" and "concrete operational" stages of cognitive development, and that these stages were not only sequential, but were age-dependent as well, to be completed somewhere in one's teens.
The "concrete" stage is characterized by an emphasis on well-definable objects and the "formal" stage by an ability to abstract. Some of the varieties of abstraction have been described as the isolation and control of variables, combinatorial reasoning, correlational reasoning, probabilistic reasoning, and proportional reasoning. Only the last of these is strictly quantitative; the others are clearly applicable to a number of disciplines.
While the general distinctions introduced by Piaget are convenient as the basis for discussion, many of his details have been subject to considerable criticism. By now we realize that not all people reach the formal operational stage by their teens, and in fact many people seem never to reach it. Unfortunately for our quest for science literacy, much of science is formal operational, and much of the traditional college-level instruction in science accepts this implicitly, making no attempt to adopt a teaching strategy that will help the unprepared students over the obvious hurdles. Because most nascent scientists do become formal operational by their teens, if not earlier, courses designed at this level can very well succeed, not only for nascent scientists but also for the larger group of student who reach this level of cognitive ability. Only when such courses are required of all students does one see the beginning of trouble.
The need to include science as part of a general education for all students need not be rehearsed here. (see Arons 1985). What we must address, however, is the nature of the courses that provide the science. If not all students are equally prepared to cope with the formal aspects of science, it is also the case that, even among those who are prepared, there is a large variance involving the general and specific information levels which a teacher can assume, which includes misinformation as well as lack of information. And somewhere between the areas of cognitive readiness and adequacy of information is a gray region involving preconceptions of the nature of science, which are often misconceptions. But simple awareness of these problems is not in itself a solution.
Overinterpreting Piaget's general conclusion regarding the age at which people generally move into the formal operational stage of reasoning to the point where it is made a law leads some people to assert that those who are not formal operational by the time they reach college never will be. This is far from the case.
In the first place, many studies (see Chiappetta 1976) have shown that the age at which people achieve formal operational thinking is greatly variable, and that Piaget's original sample was not representative. For over a decade now, it has been known that most students entering college function at a concrete operational stage or at an intermediate, "transitional" stage (Herron 1975, Beistel 1975). Moreover, studies of the reasoning practices of students have shown that even some who are formal operational on sample problems "revert" to concrete approaches when confronted with content-oriented material. That is, while these students know how to reason, they don't do it "under pressure".
Beyond this, however, there are by now numerous findings related to factors associated with the failure to achieve formal reasoning, the relationship between both propositional logic and numerical maturity and formal reasoning ability, and the teachability of formal reasoning. Lawson (1985) who has undertaken an extensive review of research on formal reasoning in science, presents a number of general conclusions that have a bearing on these issues. For the purposes of this essay the conclusion that can be drawn from Lawson is that, given the need to teach science to a large population, and the fact that much of this population is not prepared to accept science in the terms in which it has traditionally been taught, the terms must be altered. However, because the basis of science lies in large part in reasoning processes, we cannot simply replace that reasoning by simplified statements of facts or conclusions; that would be a denial of science as a process, as a uniquely human activity. On the other hand, the hope presented in Lawson's conclusions is that properly designed courses can in fact result in the teaching/learning of formal reasoning. This must be a primary goal in achieving a more science-literate society.
Education for science literacy must confront issues of science
But the teaching and learning of formal reasoning cannot be the only goals. The history of science abounds with what we now see as "wrong" conclusions. Sometimes those conclusions are not in accord with newly discovered facts. Sometimes they no longer pass muster -- not because Aristotle or Ptolemy, or Copernicus or Newton, or Lamarck or Cuvier lacked formal reasoning ability but because the way in which we choose to interpret observations is to a large extent determined by a world-view that exists prior to the act of observation or the attempt at analysis. In a formal sense this world-view is our metaphysics, or more generally our metascience. We approach experience with limitations: in some cases with preconceptions; in other cases with pigeonholes in which to file the experience in others. If the preconceptions are misconceptions, or the pigeonholes are inappropriate, we are bound to have trouble.
For example, the Greeks had at their disposal the same technological abilities that Galileo did; they could determine length as accurately as necessary, and they could use a water-clock to measure time. (Galileo reports his ability to measure time intervals to "a tenth of a pulse beat", which is approximately equal to the reaction time inherent in any human-interfaced timing procedure.) Nevertheless, they did not even attempt the dissection of motion in the modern sense. Presumably this was because they believed understanding to be the result of an intellectual process, not the study of specific ("accidental") observations that they realized were liable to some sort of error. More recently, we are told that the difficulty in accepting the conclusion that DNA was the carrier of genetic information lay partly in the strong belief that the variety of nucleic acids was inadequate to the task; compared to proteins they were just too "simple". The "simplicity" was in the naive concept (from today's vantage point) that complexity of task required complexity of structure. The insight that overcame this block was the realization that information for structural complexity could be carried in coded form.
Carey (1986) notes that "to understand something, one must integrate it with already existing knowledge schemata" -- the preconceptions and pigeonholes mentioned above. She points out that many students do not understand what they are taught precisely because in the attempt to integrate the new material they force their interpretations of it to agree with their misconceptions. In test situations they may be able to give "right" answers, but these are often generated by rote. This is demonstrated when probing questions test for understanding. The psychologist is interested in understanding the phenomenon of understanding. The science educator, on the other hand, is more interested in developing pragmatic ways of assisting the student to surmount the barrier caused by misconceptions.
One approach to this challenge is to consider the notion that the difficulties experienced by today's student in assimilating increasingly sophisticated concepts into a world-view based on limited experience is similar to the difficulties confronted by the scientists who developed these newer points of view. Why, for instance, should we accept the notion that the earth moves about the sun, when "it is clear" that it is the sun that rises and sets? No amount of looking at the sun or the stars will give the flash of insight resulting in our current idea. The specific question of how we know that the earth orbits the sun can be answered by following the history of the concept; that is, by following what scientists of the day were actually thinking at different points in time. This historical approach might enable our students to overcome critical problems regarding their approach to the outside world. Just as significantly, it provides a (hi)story which connects concepts that at first might appear to be unrelated.
The stories that can be used as the bases of concept development can form most of a term's work or only a lecture. In an interdisciplinary course, Foundations of Science, currently being developed at Hunter College, we have spent two thirds of a semester developing the idea that the earth moves around the sun. At the beginning, when only observations were being considered, some "well informed" students found it difficult to say that the celestial sphere rotated around the earth since they knew better. Several weeks later, after we "disproved" the early Greek attempts to attribute diurnal variations in the heavens to rotation of the earth by such evidence as the absence of strong winds, we then raised the Copernican approach. One student asked in disbelief, "But does the earth really move?" In a similar vein, when the phenomenon of the Magdeburg hemispheres was demonstrated in class and students were asked to account for their inability to separate them, one student mused: "Maybe it's the pressure of the air. ... But no, it couldn't be that strong". Our observation is that naive students are not prepared to accept current understanding, even of such basic and long-standing "truths" as the motion of the earth and the pressure of atmosphere, without deliberate repetition of the development of these concepts.
Granted, this observation has been made before. Wandersee (1985) has asked the question "Can the history of science help science educators anticipate students' misconceptions?" He concludes that [while] "students do not merely recapitulate the history of science in learning ... it is evident that the misconceptions of the past can be found in the conceptual frameworks of today's students". Our goal must be to teach students not only what we know, but also how we know it. But this means getting beyond particular experiments or observations to the thought processes that have gone into their interpretation. Wandersee quotes Stephen Toulmin in this regard: "There is only one way of seeing one's own spectacles clearly: that is to take them off. It is impossible to focus both on them and through them at the same time".
In principle there is no reason why isolated examples of scientific achievement may not be used as illustrative of the process of science. In many ways this is what has always been done, with the hope that the process will be properly inferred as the content of the example is assimilated. However, the use of a sequence of related achievements, which naturally hang together as a (hi)story, provides a number of advantages. In the first place each part of the story becomes more meaningful as it relates to a larger picture. Beyond that, however, the use of "stories" demonstrates that the scientific process is in general sequential and incremental. But perhaps most important, since most stories of the development of major scientific ideas show that these ideas change in the process of being refined, the use of such major themes illustrates the nature of scientific "truth" as being temporary and subject to revision, not final and unalterable.
Science literacy implies the ability to use and understand language
The foregoing considerations have been based on the perspective of a college teacher. That is, from one who teaches students who have gone through most of their developmental processes. Indeed, if you question some of them they will indicate that what they have yet to learn are facts, not ways of learning, let alone ways of knowing. To get over this hurdle, we can move backwards. We can consider what might be provided in a preventive sense to students of a younger age, at an earlier stage of their educations. Consider, first, the role of language in science, aware that the cognitive levels discussed above do not reside only in the mind. They are reflected in the way the world is perceived and in the language used to question, describe, analyze, and explain the world. Nor are those cognitive levels the result only of an intrinsic developmental process. Most likely they are also the result of a variety of experiences -- with the world and the people in it -- that in sum may be called life.
Many people who are "science illiterate" are not so much lacking the specific vocabulary of science as they are a working knowledge of certain aspects of everyday language that, in a refined form, appear as the syntax of science. I believe that these aspects are characterized by the extensive use of words which refer to abstract relationships, and by connective words which in context express such relationships. (One reason for the current identification of science illiteracy as a problem may relate directly to changes in science during the twentieth century. In all fields, modern science is associated with a decreased emphasis on dealing primarily with obvious things in obvious relationships to each other and an increasing concern with more subtle, and often indirect and statistical relationships among invisible entities. This change in emphasis has been accompanied by a change in language.)
The abstract nature of the language of science represents no more than a continued development of language skills, and a large part of our population develops them as a normal part of their intellectual growth, quite possibly in a manner largely independent of schooling. [This observation has previously been made by Davis, cited in Miller (1983, 33)] As students, such people are able to master scientific concepts to the degree that they wish to apply themselves to the task, or indeed to such other complex matter as might be found in economics, business, law or politics. Other students, however, have not mastered these aspects of language -- indeed may have had little or no exposure to them -- and to the extent that they are confronted with science as an abstract system they become lost. To avoid that, the content of science is often presented at a simplified level and much of the abstraction needed to express these relationships is abandoned. The baby is thrown out with the bath water. Huggins and Adams (1980) make much the same point. In discussing the problem of syntactic complexity they note "... decomposing complex sentences into simple sentences may change meaning". This leaves a series of "facts" -- declarative, didactic sentences that can be memorized but do not adequately convey either the goal of the scientific enterprise or the achievement of science. While this approach may have been designed to accommodate a population with poorly developed language skills, all students whose exposure to science is limited to instruction in these minimalist terms develop into the "science illiterates" whose presence is now being so decried.
Language follows from experience
If science illiteracy is considered to be an instructional problem, one solution is to find ways to develop more sophisticated language skills in the science teaching methodology. To do so will require the identification of those aspects of language that are used extensively or differently in a science context and those concepts in the introductory science curriculum that are most likely to be mislearned by students because they lack adequately developed language skills. Since it is likely that language follows experience (Arons 1983), it would also be appropriate to re-create those "pre-scientific" experiences (such as building, classifying, and playing with devices that demonstrate sequential events and causality) in exercises that are at an interest level appropriate to the age involved.
The point is that, in talking about a variety of scientific phenomena, one is often tempted to use some sort of metaphor or reference to an assumed experience. In discussing molecular structure, for instance, and the fact that the interactions between molecules suggest that there are different kinds of bonds between atoms, it is convenient to mention such construction toys as Tinkertoy, Lego, Erector Sets, and many of a more recent vintage. For students who have not grown up with these toys as part of their environment such references are of no use. At a more sophisticated level it is similar to the classic explanations of thermodynamic cycles in terms of steam engines. To a 19th century population familiar with steam technology this might be a suitable teaching device. But today such references would themselves have to be explained before they would be of any use. Clearly, it is incumbent upon the teacher to develop the language of science, including common references, in terms of common experiences, and to take pains to provide these experiences to as great an extent as possible.
At the same time, it is crucial that in the interests of promoting understanding the evaluation and testing aspects of an introductory course must go beyond the customary reliance on rote memory. Such testing merely emphasizes the relationships between words as symbols devoid of conceptual references. It does not get at either the relationships between concepts or the association between words and concepts. Morgenstern and Renner (1984) observe that "approximately 90 per cent of the items analyzed from all [standardized science] tests required only recall".
The existence of linguistic deficiencies among college students
The idea that linguistic deficiencies of a particular sort are a major cause of science illiteracy is based on an analysis of my experience of teaching an introductory college course in biology to hundreds of students at a time. While each of the events to be noted is by itself inconclusive, the entire set of experiences becomes persuasive. Retrospectively, the first clue may have been the frequently voiced student criticism that the test questions were "tricky". Attempts to explain particular verbal constructions to students by appealing to such notions as "precision" or "making distinctions appropriate to a college course" were seen as so much sophistry; from the students' point of view the questions were tricky and only that.
Additional anecdotal support for this idea comes from repeated incorrect answers to questions asked in class, or in essay format on exams, the correct answers to which required students to provide a sequence of steps. Descriptions of many biological phenomena are of just such a nature, where "understanding" means mastery of a sequence such as "A then B then C then D ...". If, for example, the letters represent stages in growth there is an obvious increase in complexity inherent in the process. Thus either omission or interchange of events signal a lack of understanding. Subsequent discussion with students often showed that they really thought that the entire process was essentially equal to the sum of its parts, independent of order. It was as though in reading or hearing "then" the student was understanding "and". Now in a sense "then" does include "and"; that is, if a process involves a sequence of events ("A then B ...") it is certainly true that it consists of the set of those events ("A and B ..."). But the sequential relationship is more restrictive, hence more precise, and it is this distinction that many students apparently fail to grasp.
The strongest evidence for the idea that linguistic sophistication is needed to understand science comes from work initiated with the support of an NSF CAUSE award to R. Grant and E. Shahn of the Department of Biological Sciences at Hunter College. We hoped to improve student performance in an introductory biology course by establishing a supplementary instructional facility which would provide a number of services. One of these would enable students to take, ad lib., "diagnostic" tests designed to show their level of mastery of a large number of concepts in the course. The diagnosis was based on the student's answers to six true/false questions dealing with each concept, and the tests were so structured that the questions for a given concept were separated from each other.
Throughout the initial set of questions there were a number of the form "A because B". During one summer when the system was still being tested a student came to discuss several tests with close to 150 questions. She was concerned only with the questions whose correct answers she couldn't understand, and three of her problem questions were of this form. Her confusion was expressed with the question, "But A and B are both true. How can "A because B" be false?" Our subsequent discussion only confirmed the supposition that she had interpreted "because" to mean "and".
Further analysis dealt specifically with the possibility that there was widespread misunderstanding of the meaning of "because". Six true/false questions were devised which were all of the form "A because B", and which were all unrelated to biology, for example, "Japanese cars are small because they use less gasoline". In each case the answer was false, because either "A" and "B" were unrelated or the true statement should have been of the inverted form, "B because A". Too many students still answer some of them incorrectly, indicating that there is indeed a serious problem.
Generalizing from these two examples, it seems that students often misread conjunctions so that they mean "and". Often "and" is also part of the meaning of "because", but not the entire meaning. When encountered as explanations of "true" observations in terms of other information which is also "true", statements of the form "A because B" do refer to situations in which "A" is true and "B" is true (e.g., "The streets are wet because it's raining") but what is meant is more than this. While a thorough grammatical study has not been performed, there is nevertheless enough matter here to provide fertile ground for speculation.
I have tested the validity of this notion in a nonsystematic manner in a junior-level course in Molecular Biology. In answer to essay questions students had considerable freedom in choosing how they structured their responses. More than 15 per cent of the papers included statements in which the word "because" appeared and was misused, in some cases repeatedly. These were not situations in which the wrong "explanation" was provided; rather, the nature of the causal relationship that was indicated by syntax was totally inappropriate or teleological. This misuse of "because" is thus not a problem that is limited to children or to naive freshmen. In this last case it showed up among a large part of a class of students who had successfully completed four or more years of science courses.
The problem under discussion is not simply one of logic. While there are similarities between scientific inference and explanation on the one hand and logical operations on the other, they are not identical. "Causality", for instance, is not the same as "logical implication". To see this, consider a statement of the form "A because B" and try to analyze it as "A implies B" or "B implies A". In some sense "A because B" includes the idea of precedence; B happens (or exists) before A. That is one difference. But there is a point of view which is more subtle. If "A because B" means that every time B happens A will follow, then one may say that it is equivalent to "B implies A". But if you observe A you will know that B has happened, so in a different sense "A implies B." It thus seems that "because" may be interpreted as implication in both directions, or that it doesn't properly refer to implication at all.
To cope with these obvious problems, I do not suggest that students be confronted with linguistic paradoxes (although these are often extremely stimulating) or to make them masters of logic. I do suggest that the development of the ability to understand what is said about science requires the ability to follow processes which are fundamental to understanding the world of science as well as to cope with the language used to describe these processes and express their relationships to each other. This, in turn, may require exposure to specific experiences that illustrate certain properties -- such as sequence and causality -- that scientists have found to be recurrent in their view of the world.
Language and cognition are related
The relationship between language and cognition is supported by research in reading theory and the development of those cognitive abilities needed for achieving competency in science. Huggins and Adams (1980) relating complexity of syntax to difficulty in comprehension, note that children have problems coping with complex sentences. They also note that syntactic analysis cannot successfully proceed in a content-free fashion; that is, account must be taken of the meaning or deep structure of sentences as well as the more ambiguous surface structure. Lawson, Lawson and Lawson (1984) suggest that "a necessary ... condition for the acquisition of proportional reasoning during adolescence is the prior internalization of key linguistic elements of argumentation". Proportional reasoning is frequently used as a necessary aspect of science literacy in the sense that its lack is considered a mark of science illiteracy. From this one may conclude that introductory science instruction must explicitly take account of aspects of formal reasoning.
The reason for the close association between proportional reasoning and science literacy is clear from some simple examples. The early applications of geometry/trigonometry to determining the heights of structures by measuring the lengths of their shadows, and using the length of the shadow of an object of known height, is a non-trivial example of this kind of reasoning. Another is the realization that if doubling a given force accelerates twice as much mass to a given velocity, tripling the force will have this effect on three times the mass. Note that this is reasoning applied to experiment, it is not the result of pure thought. If it were, one could just as well suggest that doubling a force would accelerate a given mass to twice the velocity. But that is not the way the world is. The reasoning processes at play here are the same as those that are needed to solve the problem: "If a chicken and a half can lay an egg and a half in a day and a half, how many eggs can a chicken lay in a week?" The solution is not found by observing that this is the same as "A chicken can lay an egg in a day".
Literacy as ability to understand differs from literacy as "knowledge"
The significance of the concept of science literacy posited here may be better appreciated if viewed against the goals that have been set for science education in the past. There is really no long-standing tradition in this area. Public secondary education in the U.S. is barely a century old, and initially science was not a required part of the curriculum; in many locales it still isn't required. As science was included in the course of study, changes in emphasis, content, and approach occurred in a rather rapid and haphazard manner. Against this background there has been a continual debate regarding goals.
Past approaches to science literacy
For many years "science" was considered to be the body of facts -- the information -- discovered by and thus initially the property of scientists. Added to this was the "philosophical content", a discussion of some version of what was called the scientific method. The emphasis was thus usually on what was different about science compared to the student's daily life, from the points of view of both the subject matter itself and the approach to the subject matter. Science was considered part of our intellectual heritage and was to be transmitted much as was the history of the Middle Ages. The approach, and for many students the effect, was that there was no necessity to learn (or better, to master) the subject, and that memory was sufficient.
As sciences progressed, and their applications increasingly intruded into the daily lives of students, it was suggested that these newly prominent features themselves should become the focus of instruction. Of course there had always been the hint of relevance in problems, but the increasing use of engines made the simple machines (levers and pulleys) of physics texts and Galileo's day no longer familiar. Similarly, the variety of life forms which had been the center of the study of botany and zoology were no longer part of the life experience of an increasingly urban student population. Thus aerodynamics and the workings of a refrigerator were added to the curriculum, as were the advances in microbiology and their relationship to disease that characterized the development of medicine in the nineteenth and early twentieth centuries.
More recently, additional advances in science and changes in public concern have again altered the curriculum. The realization, for example, that the abstractions of Mendelian genetics (which were in the curriculum 40 years ago) really did have a chemical "explanation" was followed by a rush to include the latest of molecular biological findings -- and jargon -- among the facts to be presented to students. The fact that we interact with our environment in myriad and not always beneficial ways has led to the inclusion of the word 'ecology' in curriculum outlines, if not the complexities of this serious branch of science. And while energy and the law of its conservation have been a central part of any serious study of physics since the early nineteenth century, it required an economic near catastrophe to lead to the acceptance of "energy conservation" (not the same thing by any means) as an appropriate topic for required high school science courses.
A number of less dramatic changes have also influenced what is taught in high schools. The subject matter now includes nutrition, evolution, and aspects of modern reproductive biology that might be included in 'sex education' courses. Changes of approach have also had an impact on curriculum design. A frequent criticism is that students are not prepared for the 'new' content, or approach, or both.
Cognitive and language skills depend on culture and gender as well as age
This posited unpreparedness opens up the whole area of what is appropriate for students of a given age, if it is indeed age that characterizes student readiness. Developmental psychologists and what are now called cognitive scientists are jointly engaged in a healthy debate which does not have well-defined lines, regarding what should (or should not) be done. One point in particular should be made: while Piaget's developmental sequence of cognitive levels may indeed be descriptive of all students, studies have shown that many students, even among those who go on to major in the sciences at college, do not reach the formal operational level characteristic of abstract reasoning by the time they begin their majors (Arons 1983, Karplus et al 1979, Herron 1975, Beistel 1975). Thus the degree of abstraction required by modern science seems to make the emphasis on this aspect of science inappropriate in required high school curricula.
Beyond age alone, both culture (Lawson and Bealer 1984, Karplus et al. 1979) and sex (Benbow and Stanley 1983, De Hernandez, Marek, and Renner 1984) seem to be measurably associated with differences in a variety of cognitive abilities. Benbow and Stanley (1983) rule out some of the more common explanations for this effect of sex-based differences. Current research is thus telling us that the pedagogical innovators of the future must be sensitive to a variety of parameters that some might rather ignore as being irrelevant.
Finally, science education over the past several decades has itself been subject to aspects of the technological advances that, as indicated above, are part of its subject. At one level science courses are taught, with printed material as a major resource, although it is generally recognized that some sort of laboratory experience should be an integral part of such courses. This is because the subject of science is nature, not words, and the meaning of the words used to communicate scientific concepts can be fully appreciated only when one "sees" the reality to which they are supposed to refer.
Recent studies of thinking (Morgenstern and Renner 1984, Johnson-Laird and Wason 1977), reasoning (Lawson, Lawson and Lawson 1984), problem solving (Lochhead, to be published), language in general (Deese 1984) and syntax in particular (Alvermann 1983, Huggins and Adams 1980) are making it increasingly clear that there is a considerable overlap among these areas. Nevertheless, while scientific knowledge is expressed in what may be a sublanguage of its own, or many such sublanguages (Sager 1981), and a developmental sequence of higher-level cognitive skills needed to work with these sublanguages has been essentially agreed upon (Arons 1979), little emphasis has been given to the process by which students acquire the language needed to work with these skills. Huggins and Adams (1980), whose comments on complex sentences have been noted above, go on to observe that these sentences are often the ones that contain subordinate conjunctions -- essentially the problem area I have identified above. But, aside from describing the sources of the difficulties associated with different syntactic constructions, they do no more than "present[s] some evidence that young children have difficulty coping with complex syntax".
What emerges from this consideration, then, is that understanding science today -- being science literate -- requires more than factual knowledge. It requires an ability to relate often strange phenomena to a language framework, and to work with standard language in a sophisticated manner. In addition, in some areas it requires the use of mathematical skills that are fundamentally based on the ideas of proportionality and elementary statistical principles.
I suggest that these fundamentals of science literacy can transcend the changes that have characterized the past several decades. I also suggest that the specific vocabulary of science, the rules of language necessary for concept development, and the fundamentally mathematical reasoning processes can all be developed as generalizations of simple experiences. Thus this approach to a definition of literacy has immediate applications in the sense that it can both drive the creation of curricula at all introductory levels and provide a means of their evaluation.
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