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Teaching Introductory Physics
Arnold B Arons
Chapter 13: Critical Thinking
"The simple but difficult arts of paying attention, copying accurately, following an argument, detecting an ambiguity or a false inference, testing guesses by summoning up contrary instances, organizing one's time and one's thought for study -- all of these arts ... cannot be taught in the air but only through the difficulties of a defined subject; they cannot be taught in one course in one year, but must be acquired gradually in dozens of connections." (Jacques Barzun)
"No curricular recommendation, reform, or proposed structure has ever been made without some obeisance [deferential respect] to the generic term 'critical thinking' or one of its synonyms. The flood of reports on education in our schools and colleges that has been unleashed in recent years is no exception; every report, at every level of education, calls for attention to the enhancement of thinking-reasoning capacities in the young. A currently prominent formula is 'higher order thinking skills.' Few of the documents that come to us, however, attempt to supply some degree of specificity -- some operational definition of the concept, with illustrations of what might be done in day-to-day teaching to move toward the enunciated goals.
It is the object of this chapter to try to 'unpack' the term 'critical thinking' -- to list a few simpler, underlying processes of abstract logical reasoning that are common to many disciplines and that can be cultivated and exercised separately in limited contexts accessible to the student. Subsequently, the individual's conscious weaving together of these various modes results in the larger synthesis we might characterize as 'critical thought.' As Barzun points out in the quotation cited above, this can be done only through practice in, preferably, more than one field of subject matter.
To glimpse some of the ways in which effective schooling might enhance students' reasoning capacities, it is instructive to examine a few of the thinking and reasoning processes that underlie analysis and inquiry. These are processes that teachers rarely articulate or point out to students; yet these processes are implicit in many different studies. The following listing is meant to be illustrative; it is neither exhaustive nor prescriptive. Readers are invited to add or elaborate items they have identified for themselves or sense to be more immediately relevant in their own disciplines.
1 Consciously raising questions 'What do we know ... ? How do we know ... ? Why do we accept or believe ... ? What is the evidence for ... ?' when studying some body of material or approaching a problem.
Consider the assertion, which virtually every student and adult will make, that the moon shines by reflected sunlight. How many people are able to describe the simple evidence, available to anyone who can see, that leads to this conclusion (which was, incidentally, perfectly clear to the ancients)? This does not require esoteric intellectual skills; young children can follow and understand; all one need do is lead them to watch the locations of both the sun and moon, not just the moon alone, as a few days go by. Yet for the majority of our population the 'fact' that the moon shines by reflected sunlight is received knowledge, not sustained by understanding.
Exactly the same must be said about the contention that the earth and planets revolve around the sun. The validation and acceptance of this view marked a major turning point in our intellectual history and in our collective view of man's place in the universe. Although the basis on which this view is held is more subtle and complex than that for the illumination of the moon, the 'How do we know ... ?' should be an intrinsic part of general education; it is, for most people, however, received knowledge -- as is also the view that matter is discrete in its structure rather than continuous.
Similar questions should be asked and addressed in other disciplines: How does the historian come to know how the Egyptians, or Babylonians, or Athenians lived? On what basis does the text make these assertions concerning consequences of the revocation of the Edict of Nantes? What is the evidence for the claim that such and such tax and monetary policies promote economic stability? What was the basis for acceptance of the doctrine of separation of church and state in our political system?
Cognitive development researchers [e.g., Anderson (1980); Lawson (1982)] describe two principal classes of knowledge: figurative or declarative on the one hand, and operative or procedural on the other. Declarative knowledge consists of knowing 'facts' (matter is composed of atoms and molecules; animals breathe oxygen and expel carbon dioxide; the United States entered the Second World War after the Japanese attack on Pearl Harbor in December 1941). Operative knowledge involves understanding where the declarative knowledge comes from or what underlies it (What is the evidence that the structure of matter is discrete rather than continuous? What do we mean by the terms 'oxygen' and 'carbon dioxide' and how do we recognize these as different substances? What worldwide political and economic events underlay the American declaration of war?). And operative knowledge also involves the capacity to use, apply, transform, or recognize the relevance of declarative knowledge in new situations.
'Above all things,' says Alfred North Whitehead in a well-known passage on the first page of The Aims of Education, 'we must beware of what I will call 'inert ideas' -- that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations.' And John Gardner once deplored our tendency ... 'to hand our students the cut flowers while forbidding them to see the growing plants.'
Preschool children almost always ask 'How do we know ... ? Why do we believe ... ?' questions until formal education teaches them not to. Most high school and college students then have to be pushed, pulled, and cajoled into posing and examining such questions; they do not do so spontaneously. Rather, our usual pace of assignments and methods of testing all too frequently drive students into memorizing end results, rendering each development inert. Yet given time and encouragement, the habit of inquiry can be cultivated, the skill enhanced, and the satisfaction of understanding conveyed. The effect would be far more pronounced and development far more rapid if this demand were made deliberately and simultaneously in science, humanities, history, and social science courses rather than being left to occur sporadically, if at all, in one course or discipline.
2 Being clearly and explicitly aware of gaps in available information. Recognizing when a conclusion is reached or a decision made in absence of complete information and being able to tolerate the attendant ambiguity and uncertainty. Recognizing when one is taking something on faith without having examined the 'How do we know ...? Why do we believe ...?' questions.
Interesting investigations of cognitive skill and maturity are conducted by administering test questions or problems in which some necessary datum or bit of information has been deliberately omitted, and the question cannot be answered without securing the added information or making some plausible assumption that closes the gap. Most students and many mature adults perform very feebly on these tests. They have had little practice in such analytical thinking and fail to recognize, on their own, that information is missing. If they are told that this is the case, some will identify the gap on reexamining the problem, but many will stil fail to make the specific identification.
In our subject matter courses, regardless of how carefully we try to examine evidence and validate our models and concepts, it will occasionally be necessary to ask students to take something on faith. This is a perfectly reasonable thing to do, but it should never be done without making students aware of what evidence is lacking and exactly what they are taking on faith [Realize that press releases in some disciplines do this as a matter of routine]. Without such care, they do not establish a frame of reference from which to judge their level of knowledge, and they fail to discriminate clearly those instances in which evidence has been provided from those in which it has not.
3 Discriminating between observation and inference, between established fact and subsequent conjecture.
Many students have great trouble making such discriminations even when the situation seems patently obvious to the teacher. They are unused to keeping track of the logical sequence, and they are frequently confused by technical jargon they have previously been exposed to but never clearly understood.
In the case of the source of illumination of the moon cited earlier, for example, students must be made explicitly conscious of the fact that they see the extent of illumination increasing steadily as the angular separation between moon and sun increases, up to full illumination at a separatin of 180 degrees. This direct observation leads, in turn, to the inference that what we are seeing is reflected sunlight.
In working up to the concept of 'oxygen' (without any prior mention of this term at all) with a group of elementary school teachers some years ago, I had them do an experiment in which they heated red, metallic copper in an open crucible and weighed the crucible periodically. What they saw happening, of course, was the copper turning black and the weight of crucible and contents steadily increasing. When I walked around the laboratory and asked what they had observed so far, many answered, 'We observed oxygen combining with the copper.' When I quizzically inquired whether that was what they had actually seen happening, their reaction was one of puzzlement. It took a sequence of Socratic questioning to lead them to state what they had actually seen and to discern the inference that something from the air must be joining the copper to make the increasing amount of black material in the crucible. It had to be brought out explicitly that this 'something from the air' was the substance to which we would eventually give the name 'oxygen.' What they wanted to do was to use the technical jargon they had acquired previously without having formed an awareness of what justified it.
This episode illustrates the importance of exposing students to repeated opportunity to discriminate between observation and inference. One remedial encounter in one subject matter context is not nearly enough, but opportunities are available at almost every turn. Mendel's observations of nearly integral ratios of population members having different color and size characteristics must be separated from inference of the existence of discrete elements controlling inheritance. In the study of literature, analysis of the structure of a novel or a poem must be distinguished from an interpretation of the work. In the study of history, primary historical data or information cited by the historian must be separated from the historian's interpretation of the data.
A powerful exercise once employed by some of my colleagues in history was to give the students a copy of the Code of Hammurabi accompanied by the assignment: 'Write a short paper addressing the following question: From this code of laws, what can you infer about how these people lived and what they held to be of value?' This exercise obviously combines exposure to both processes 1 and 3.
4 Recognizing that words are symbols for ideas and not the ideas themselves. Recognizing the necessity of using only words of prior definition, rooted in shared experience, in forming a new definition and in avoiding being misled by technical jargon.
From the didactic manner in which concepts (particularly scientific concepts) are forced on students in early schooling, it is little wonder that they acquire almost no sense of the process of operational definition and that they come to view concepts as rigid, unchanging entities with only one absolute significance that the initiated automatically 'know' and that the breathless student must acquire in one intuitive gulp. It comes as a revelation and a profound relief to many students when they are allowed to see that concepts evolve; that they go through a sequence of redefinition, sharpening, and refinement; that one starts at crude, initial, intuitive levels and, profiting from insights gained in successive applications, develops the concept to final sophistication.
In my own courses, I indicate from the first day that we will operate under the precept 'idea first and name afterwards' and that scientific terms acquire meaning only through the description of shared experience in words of prior definition. When students try to exhibit erudition (or take refuge from questioning) by name dropping technical terms that have not yet been defined, I and my staff go completely blank and uncomprehending. Students catch on to this game quite quickly. They cease name dropping and begin to recognize, on their own, when they do not understand the meaning of a term. Then they start drifting in to tell us of instances in which they got into trouble in psychology, or sociology, or economics, or political science course by asking for operational meaning of technical terms. It is interesting that this is an aspect of cognitive development to which many students break through relatively quickly and easily. Unfortunately, this is not true of most other modes of abstract logical reasoning.
5 Probing for assumptions (particularly the implicit, unarticulated assumptions) behind a line of reasoning.
In science courses, this is relatively easy to do. Idealizations, approximations, and simplifications lie close to the surface and are quite clearly articulated in most presentations. They are ignored or overlooked by the students, however, principally because explicit recognition and restatement are rarely, if ever, called for on tests or examinations. In history, humanities, and the social sciences, underlying assumptions are frequently more subtle and less clearly articulated; probing for them requires careful and self-conscious attention on the part of instructors and students.
6 Drawing inferences from data, observations, or other evidence and recognizing when firm inferences cannot be drawn. This subsumes a number of processes such as elementary syllogistic reasoning (e.g., dealing with basic propositional, 'if ... then' statements), correlational reasoning, recognizing when relevant variables have or have not been controlled.
Separate from the analysis of another's line of reasoning is the formulation of one's own. 'If ... then' reasoning from data or information must be undertaken without prompting from an external 'authority.' One must be able to discern possible cause-and-effect relations in the face of statistical scatter and uncertainty. One must be aware that failure to control a significant variable vitiates [spoils] the possibility of inferring a cause-and-effect relation. One must be able to discern when two alternative models, explanations, or interpretations are equally valid and cannot be discriminated on logical grounds alone.
As an illustration of the latter situation, I present a case I encounter very frequently in my own teaching. When students in a general education science course begin to respond to assignments leading them to watch events in the sky (diurnal changes in rising, setting and elevation of the sun, waxing and waning of the moon, behavior of the stars and readily visible planets), they immediately expect these naked eye observaitons to allow them to 'see' the 'truth' they have received from authority, namely that the earth and planets revolve around the sun. When they first confront the fact that both the geo- and heliocentric models rationalize the observations equally well and that it is impossible to eliminate one in favor of the other on logical grounds at this level of observation, they are quite incredulous. They are shocked by the realization that either model might be selected provisionally on the basis of convenience, or of aesthetic or religious predilection. In their past experience, there has always been a pat answer. They have never been led to stand back and recognize that one must sometimes defer, either [temporarily] or permanently, to unresolvable alternatives. They have never had to wait patiently until sufficient information and evidence were accumulated to develop an answer to an important question; the answer has always been asserted (for the sake of 'closure') whether the evidence was at hand or not, and the ability to discriminate decidability versus undecidability has never evolved.
An essentially parallel situation arises in the early stages of formation of the concepts of static electricity (see Sections 6.7 and 6.8). Students are very reluctant to accept the fact that, before we know anything about the microscopic constitution of matter and the role of electrical charge at that level, it is impossible to tell from observable (macroscopic) phenomena whether positive charge, negative charge, or both charges are mobile or being displaced. They wish to be told the 'right answer' and fail to comprehend that any one of the three models accounts equally well for what we have observed and predicts equally well in new situations. They want to use the term 'electron' even though they have no idea what it means or what evidence justifies it, and they apply it incorrectly to irrelevant and inappropriate situations.
If attention is explicitly given, experiences such as the ones just outlined can play a powerful role in opening student minds to spontaneous assessment of what they know and what they do not know, of what can be inferred at a given juncture and what cannot.
7 Performing hypothetico-deductive reasoning; that is, given a particular situation, applying relevant knowledge of principles and constraints and visualizing, in the abstract, the plausible outcomes that might result from various changes one can imagine to be imposed on the system.
Opportunities for such thinking abound in almost every course. Yet students are most frequently given very circumscribed [restricted] questions that do not open the door to more imaginative hypothetico-deductive reasoning. The restricted situations are important and provide necessary exercises as starting points, but they should be followed by questions that impel the student to invent possible changes and pursue the plausible consequences.
8 Discriminating between inductive and deductive reasoning; that is, being aware when an argument is being made from the particular to the general [inductive] or from the general to the particular [deductive].
The concepts of 'electric circuit,' 'electric current,' and 'resistance' can be induced from very simple observations made with electric batteries and arrangements of flashlight bulbs. This leads to the inductive construction of a 'model' of operation of an electric circuit. The model then forms the basis for deductive reasoning, that is, predictions of what will happen to brightness of bulbs in new configurations or when changes (such as short circuiting) are imposed on an existing configuation.
Exactly similar thinking can be developed in connection with economic models or processes. Hypothetico-deductive reasoning is intimately involved in virtually all such instances, but one should always be fully conscious of the distinction between the inductive and the deductive modes.
9 Testing one's own line of reasoning and conclusions for internal consistency and thus developing intellectual self-reliance.
The time is long past when we could teach our students all they need to know. The principal function of education -- higher education in particular -- must be to help individuals to their own intellectual feet: To give them conceptual starting points and an awareness of what it means to learn and understand something so that they can continue to read, study, and learn as need and opportuninty arise, without perpetual formal instruction.
To continue genuine learning on one's own (not just accumulating facts) requires the capacity to judge when understanding has been achieved and to draw conclusions and make inferences from acquired knowledge. Inferring, in turn, entails testing one's own thinking, and the results of such thinking, for correctness or at least for internal coherence and consistency. This is, of course, a very sophisticated level of intellectual activity, and students must first be made aware of the process and its importance. Then they need practice and help.
In science courses, they should be required to test and verify results and conclusions by checking that the results make sense in extreme or special cases that can be reasoned out simply and directly. They should be led to solve a problem in alternative ways when that is possible. Such thinking should be conducted in both quantitative and qualitative situations. In the humanities and social sciences, the checks for internal consistency are more subtle, but they are equally important and should be cultivated explicitly. Students should be helped to sense when they can be confident of the soundness, consistency, or plausibility of their own reasoning so that they can consciously dispense with the teacher and cease relying on someone else for the 'right answer.'
10 Developing self-consciousness concerning one's own thinking and reasoning processes.
This is perhaps the highest and most sophisticated reasoning skill, presupposing the others that have been listed. It involves standing back and recognizing the processes one is using, deliberately invoking those most appropriate to the given circumstances, and providing the basis for conscious transfer of reasoning methods from familiar to unfamiliar contexts.
Given such awareness, one can begin to penetrate new situations by asking oneself probing questions and constructing answers. Starting with artificial, idealized, oversimplified versions of the problem, one can gradually penetrate to more realistic and complex versions. In an important sense, this is the mechanism underlying independent research and investigation.
13.3 WHY BOTHER WITH CRITICAL THINKING?
The preceding list of thinking and reasoning processes underlying the broad generic term 'critical thinking' is neither complete nor exhaustive. For illustrative purposes, I have tried to isolate and describe processes and levels of awareness that appear to be bound up with clear thinking and genuine understanding in a wide variety of disciplines and to show a deep commonality in this respect among very different kinds of subject matter. These processes underlie the capacity defined by Jacques Barzun in the quotation that heads this chapter.
Developing these intellectual skills requires extensive, sustained practice. Such practice is not possible in a space devoid of subject matter. It is only through contact with, and immersion in, rich areas of subject matter that interesting and significant experience can be generated. Although it may be possible, in principle, to generate limited aspects of such practice through artificial kinds of exercises and puzzle solving, or even through analysis of scores in sports contests, it seems a waste of time to resort to such sterile channels when all the vital disciplines of our culture lie at our disposal.
Why should we want to cultivate skills such as those I have listed? There are many obvious reasons having to do with quality of life, with professional competence, with the advance of culture and of society in general, but I particularly wish to suggest a socio-political reason: the education of an enlightened democractic citizenry. What capacities characterize such a citizenry?
Justice Learned Hand, the distinguished jurist of the precedeing generation, argued with telling irony that we would be able to preserve civil liberties only so long as we were willing to engage in the 'intolerable labor thought, that most distasteful of all our activities.' John Dewey in Democracy and Education contends that 'The opposite to thoughtful action are routine or capricious behavior. Both refuse to acknowledge responsibility for the future consequences which flow from present action.'
The requirements set by Barzun, Hand, and Dewey can be broken down to more fundamental components. The sophisticated distinction between enlightened and short range self-interest is based on hypothetico-deductive reasoning. Such reasoning is also inevitably involved in visualizing possible outcomes of decisions and policies in economic and political domains.
There is need to discriminate between facts and inferences in the contentions with which one is surrounded. There is the necessity of making tentative judgments or decisions, and it is better that this be done in full awareness of gaps in available information than in an illusion of certainty. There is the highly desirable capacity to ask critical, probing, fruitful questions concerning situations in which one has little or no expertise. There is the need to be explicitly conscious of the limits of one's own knowledge and understanding on a given issue.
Each of these capacities appears on the preceding list, and I believe that each can be cultivated and enhanced, at least to some degree, in the great majority of college students through properly designed experiences embracing a wide variety of subjects.
I hasten to emphasize that these skills alone are not sufficient to assure good citizenship or other desirable qualities of mind and person. Other ingredients are necessary, not the least of which are moral and ethical values, which impose their own constraints on the naked processes of thinking and reasoning. Although values are not disconnected from thinking and reasoning, the educational problems they pose transcend the limits of this short essay and require discussion in their own right.
13.4 EXISTING LEVEL OF CAPACTITY FOR ABSTRACT LOGICAL REASONING
In the United States some investigators have rather belatedly come to realize that much of our science curricular material, and the volume and pace with which we thrust it at our students, are badly mismatched to the existing levels of student intellectual development at virtually every age. I am convinced that the same is true in other disciplines, but the fact is less readily discerned because assignments and tests concentrate on end results and procedures rather than on reasoning and understanding.
I say that 'some' have become aware of this problem because, despite the unequivocal and relentlessly accumulating statistics, many who teach in the schools, colleges, and universities remain unaware of the emerging data; others fail to see any relevance to their own teaching.
Beginning about 1971, investigators began administering elementary tasks in abstract logical reasoning (such as those pioneered by Jean Piaget [see Piaget and Inhelder (1958)] in his studies of the development of abstract reasoning capacity in children) to adolescents and adults of college age and beyond [see, for example, Chiapetta (1976); McKinnon and Renner (1971)]. The tests have centered principally on arithmetical reasoning with ratios or division and on awareness of the necessity of controlling variables in deducing cause-effect relationship.
Although the results vary significantly from one population to another (economically disadvantaged versus economically advantaged; concentrating in science and engineering versus concentrating in humanities or fine arts versus concentrating in the social sciences, etc.), the overall averages have remained essentially unchanged with increasing volume of data since the first small samples were reported in 1971, and, most suggestively, the averages do not change appreciably with increasing age beyond about 12 or 13: Roughly one third of the total number of individuals tested solve the tasks correctly; roughly one third perform incorrectly but show a partial, incipient grasp of the necessity mode of reasoning; the remaining third fail completely. In Piagetian terminology, the first group might be described as using formal patterns of reasoning, the third group as using principally concrete patterns, and the middle group as being in transition between the two modes [Arons and Karplus (1976)].
The weaknesses revealed by these two specific tasks would mean relatively little if they stood by themselves, but, in fact, these weaknesses are closely correlated with weaknesses in other modes of abstract logical reasoning such as discriminating between observation and inference; dealing with elementary syllogisms involving inclusion, exclusion, and serial ordering; recognizing gaps in available information; doing almost any kind of hypothetico-deductive reasoning.
Most of the curricular materials thrust at students in the majority of their courses at secondary and college level implicitly require well-developed reasoning capacity in the modes that have been listed in this discussion. In fact, only a small proportion of the students (less than one third) are ready for such performance. The rest, lacking the steady, supportive help and explicit exercises required, resort, in desperation, to memorization of end results and procedures. Failing to develop the processes underlying critical thinking, they fail to have experience of genuine understanding and come to believe that knowledge is inculcated by teachers and consists of recognizing juxtapositions of arcane vocabulary on multiple choice tests. (Readers familiar with studies of William G. Perry will recognize his first category of intellectual outlook among college students [Perry (1970].)
13.5 CAN CAPACITY FOR ABSTRACT LOGICAL REASONING BE ENHANCED?
In our Physics Education Group at the University of Washington, we have worked intensively for some years with populations of pre- and in-service elementary school teachers and other nonscience majors ranging in age from 18 to over 30. Initially no more than about 10% were using formal patterns of reasoning. By starting with very basic, concrete observations and experiences, forming concepts out of such direct experience, going slowly, allowing students to make and rectify mistakes by confronting contradiction or inconsistency, insisting that they speak and write out their lines of reasoning and explanation, repeating the same modes of reasoning in new contexts days and weeks apart, we have been able to increase the fraction who successfully use abstract patterns of reasoning to perhaps 70 to 90%, depending on the nature of the task.
The most important practical lesson we have learned is that repetition is absolutely essential -- not treading water in the same context until 'mastery' is attained, but in altered and increasingly richer context, with encounters spread out over time. Quick, remedial exercises in artificial situations preceding 'real' course work are virtually useless. One must patiently construct repeated encounters with the same modes of reasoning in regular course work and allow students to benefit from their mistakes. Progress becomes clearly visible in the sense that the percentage of successful students increases with each repetition.
It is still a very long step from the development of specific abstract reasoning processes in one area of subject matter, such as elementary science, to more advanced levels of subject matter in the same area, not to speak of transfer to entirely different areas. What little evidence exists suggests that very little transfer occurs from experience acquired in only one discipline. I myself am strongly convinced, however (mostly by fragmentary, anecdotal evidence, and perhaps some admixture of wishful thinking), that very great progress could be effected if students were simultaneously exposed to such intellectual experience in entirely different disciplines. This is largely a matter of conjecture since an organized experiment at the college level has not really been tried ..."