Metaphor, Model, and Theory in Education Research
by Nathan Dickmeyer - 1989
The concepts of metaphor, model, and theory are defined and used to show how social science research in general, and education research in particular, has differed from Popper's description of natural science research. (Source: ERIC)
To improve our understanding of education research methods and perhaps lend some context to the patchwork of styles and world views that now exists in the educational research community, I would like to examine three important conceptsmetaphor, model, and theoryand use them to suggest a metaview that accommodates many different forms of contemporary research. Each of these terms relates to a portion of the knowledge building that goes on in the social sciences, especially education research. Understanding these concepts should help us weave together and make better sense of the processes and limitations of education research. This article will also attempt to shift our focus from the particular paradigms and world views that we use to structure education research to a broader world view or meta-paradigm incorporating many views. Using the three key concepts of metaphor, model, and theory in research, I hope to show how social science research in general and education research in particular has differed from Poppers description of natural science research (especially physics). In doing so, I will have to describe some of the limits of social science research. Nevertheless, I shall develop the concept of doing good social science research in a way that does not condemn much of what is currently being done.
WHAT IS A METAPHOR?
A metaphor is a characterization of a phenomenon in familiar terms. To be effective in promoting understanding of the phenomenon in question, the familiar terms must be graphic, visible, and physical in our scale of the world. To characterize teaching as pouring knowledge into the empty vessel of a student is to describe the phenomenon in physical terms at a very handy size. In our imagination, we can see ourselves physically doing teaching in this way. Metaphoric characterizations bear no real physical resemblance to the process being described, except in the most limited sense. A student is not a vessel; knowledge is not a liquid. Nevertheless, we can act on these metaphors in reasonable ways. We can acknowledge, for example, that a teacher has something to give to a student. To the extent that the metaphor emphasizes a key characteristic of the system; and to the extent we can manage that key characteristic, metaphors are extremely helpful to our understanding of the phenomenon.
Metaphors are often hortative, too. The associations tied to particular characterizations of the system can have emotional overtones that influence how we develop research and policy. To call our schools factories that produce educated students as products is to sound an alarm for many education researchers. That students are undifferentiated and dehumanized is part of the metaphor, even if the intent of the metaphor-maker is to highlight the constructive process of development in students.
Metaphors are often reassuring. When we really do not know how learning takes place, the vision of a student receiving knowledge in liquid form calms us. Our purposes as educators become clearer and more firm: We pour. Without some sort of vision like this, we may have difficulty grasping the importance of what we do.
Metaphors are nonquantitative at their root. Their truth is difficult to measure at best. We seldom outline what the key characteristic is that we are attempting to highlight with a metaphor. We seldom rank the merits of competing metaphors and judge winners. To do so would undermine many of their purposes. We use metaphors to grasp intellectually systems that operate in ways quite mysterious to us, like learning. We may be able to move beyond metaphors, but we really cannot subvert them to quantitative analysis. They highlight and make graphic some simplified component of the real system. Although one metaphor may better model some part of a system or emphasize a more significant piece of a system, any metaphor has merit if it makes an aspect of a system more clear.
Metaphors are thus an important first step in understanding a complex system. We reduce the complexity to one or two key and important features. We then find a physical system that exhibits those few key features, and we draw the analogy. Our understanding is broadened because our powers to observe are increased. When we can focus on a few key features, we can then begin to see in greater detail how a system is operating. If learning is like having a liquid poured in, we can ask, if we pour faster, does learning increase? If it does, then we know a little more about the system.
The major limitation of metaphors is in their inherent simplification. Out of many interacting factors available in a system as complex as learning, we choose to highlight only a few with a metaphor. As a result we do not get a complete picture. Even if we use a dozen metaphors, each in turn ignores some factors that, through interaction, limit our ability to comprehend the system and predict the effect of any intervention. Yet, designing interventions is one of the primary uses of a metaphor.
The set of rules that describes how we will use a metaphor is in a limited sense a paradigm. We start with a metaphor and then we develop rules about how to work within the metaphor. If we define our world in terms of a metaphor, our research can focus on the questions raised by that metaphor and, in fact, because we focus on an extreme simplification of the system under study, our methods of study are quite simple. We look for cause and effect resemblances between our metaphor and the system being described. As we take a metaphor and begin to build a paradigm, we build a world view that starts to make questions of how we should do research more rigorous. Then we begin to bridge the gap between metaphor and model.
WHAT IS A MODEL?
A model is another simplification of a complex system, but it is one that lends itself to a more careful study of the systems operation. Models usually have a numbereven hundredsof variables that are explicitly a part of the simplification. Models, however, are often derived from a beginning metaphor of the human system under study. Models are improvable, but not really disprovable, since by definition they are simplifications of reality. No model is completely true; some aspects of the real system have been ignored.
Within human systems we must deal with billions of variables at the least. The predictable working of any human event rests on innumerable previous human and other natural and unnatural events, from the kind of breakfast a mother had while expecting a babys birth to the musing of an early Greek philosopher. If we are studying learning, all these events may, in a strictly causal fashion, have a role in our ability to predict an outcome. We may, however, choose to simplify the situation by using a model and look only at certain variables. We know that some variables will have a greater impact than others. In this way we might hope to better understand a system like learning and to better predict the effect of an intervention.
We may want to look at the kind of training received by the teacher, the discipline in the school, or the nutritional level of the child. Our model may take any number of these areas and find any number of measurable aspects of the system that might help us predict some other (or included) phenomenon, like test scores or attitude toward learning. Although we may be operating under some broad metaphor, like the filling of a vessel, or the staged accomplishment of competencies (a ladder), we no longer rely on the visualness of our construction to determine our research. We rely on discovering a larger number of key variables with varying degrees of measurability that allow us to look more closely at isolated aspects of a system, and occasionally, with some flaws, at the system as a whole.
Models are a step removed from metaphors because models are built to allow us to manipulate and test changes in a simplified system. Models are sets of relationships between variables that in some way characterize a complex system. We choose the variables for a number of reasons. Some variables are chosen because we think that we can manipulate them within the real system. For example, we may think that we can control the training of teachers. For that reason it makes sense to build some models with the training methods of teachers as an important variable, because, if we learn something, we can do something. Some variables are chosen simply because we can measure them, although we may not be able to change them. Measuring the racial composition of a school is more straightforward than changing it. Not all variables chosen in this way lead to models with exciting results.
Models work best in truly complex systems. Modeling of an accounting system, where the transactions and accounts are finite and known, is less pleasing than modeling learning, where the variables appear nearly infinite and largely unknown, By definition, there are many models of any one system, each based on a particular choice of variables and perhaps on differing ways of characterizing the relationships among the variables. Since each is a simplification, like metaphors, there is no one perfect or best model. One may be more easily quantifiable than another. One may have more interesting variables, but no one is correct.
Lave and March offer some guidance for evaluating models.1 Their standards are truth, beauty, and justice. A model is good if the derived predictions are true. A model is beautiful if the predictions and the process of building the model are interesting, where the beauty of the effort leads to real understanding of the system. The concept of justice is more difficult to grasp because our ideas of truth hamper our understanding of justice. Truth within the confines of a paradigm may not be complete truth. All models are simplifications, and the choice of what to include and what to leave out easily influences the range of predictions available from the model. Two models may be perfectly true in their predictions, but only because their predictions are limited and our ability to measure certain variables is also restricted. One model, however, may rest on gender or racial differences. The truth of the model may reflect the simplification more than the direct cause and effect supposedly modeled. Taking into account all societal influences is nearly impossible and gender or racial differences may be only artifacts. If policy interventions are developed that unfairly discriminate, then the model simply is not just.
WHAT IS A SCIENTIFIC THEORY?
I shall locate this discussion within Karl Poppers highly influential notion of science. A theory is a very narrow proposal on the workings of a system. A theory may be disproved by a critical experiment.2 The system is described in positive terms at the most detailed level possible.
I wish to avoid the colloquial notion that theory means anything hypothesized. In the natural sciences, the use of theory proper is recent. Einstein is Poppers hero, with physics theories often stated in disprovable, mathematical terms. Within Einsteins theory was the conclusion that light should bend under the influence of gravity. Tested during an eclipse, the theory held up.3
Theories may begin with models, but in the end must not be simplifications in terms of any known phenomena. Current physics theories must weather experimental tests of their predictions in all realms from the subatomic to the cosmological. There is at least one very difficult limit to constructing physics theory (besides the necessity that the theory have testable predictions): Heisenbergs Uncertainty Principle. We cannot precisely establish a particles momentum and position simultaneously. This principle causes few problems until we get to atomic dimensions when precision takes on a scale larger than the particles themselves. At that point we really do not know where things are and where they are goingprecisely.
So far, physics has accommodated this limitation with statistical descriptions. Particles travel with probabilistic velocities from probable locations. Unfortunately, it is at this point that physics slips from theory into modeling. We cannot disprove that an electron was at a certain point with a certain velocity. We can only test a probability. The flaw, of course, is our ability to measure. We cannot measure the velocity of an electron without changing its position. The limit of measurability is the limit of theory. Without measurability we cannot fully test theory. We can only see whether our simplified model stays within statistical bounds.
Human systems present a parallel situation. Theory is possible up to our limit of measurement. Unfortunately, unlike physical systems, everything interesting is past the limit. Any anthropologist will tell you that each measurement and each inquiry will change a human system. We are also appropriately limited by the right of privacy. We will never know everything about anyone.
As social scientists we also cope by using statistical predictions. We have a notion of randomness and can ferret out patterns that seem to reflect some earlier cause or intervention. Let us take the most simple kind of prediction and try to make a theorysomething from the rational-man paradigm: Man evaluates situations and seeks to avoid pain. Even with that simple attempt at a theory most readers would not take long to think of a critical experiment that would invalidate the theory.
Is it statistically true? Yes, to the extent that we would believe that normal behavior follows this pattern and is significantly different from random. All that nonrandomness means, however, is that the factors that cause us to avoid pain are more likely to appear than the factors that cause us not to avoid pain. The pattern that we do see, the expression of these behavior-toward-pain factors, would very rarely happen if we were indifferent toward pain. Do we have enough to make a theory? No, because we do not know all the factors. We might predict correctly most of the time, but we would be wrong some of the time. Can we do a lifetime of research and find all the factors? No, because of the limit of measurability. Can we build a pretty good model? Maybe.
The differences between my definitions of theory and model are slight. Theories are predictions based on certainty: This is the way the world works; If this occurs, then this will occur. A theory lasts until it fails a critical test. Then we find that we must measure some factors at a more detailed level of magnitude. A model, however, lasts until its predictions appear absurd, and sometimes longer. Each lasts until something more must be taken into account. Variables can be added to models; theories can take on extra terms. The critical differences between the two are how they are tested and how they are used. Models are tested with limited designs on truth, beauty, and justice. Theories stand until disproved. Models are used to explore systems so that at some point a theory might be built. Theories capture our knowledge as perfected.
Thus, both social sciences and quantum mechanics are made more of models than of theories. We never predict precisely within either one. Both, however, have served us well. Within our positivist/rationalist thinking, we wish that both would reduce to theoriesthat we did not have to predict either a persons behavior or an electrons positions with probabilitiesbut we do, and we will for a long, long time.
For a quick look at how these conceptions of metaphor, model, and theory fit current research, I went through the major articles in a recent issue of the Teachers College Record, The styles of analysis used in each article can be roughly lit into three (actually only two) of the categories above.
In The Emergence of the Teachers Voice, Joseph P. McDonald provides us with a powerful metaphor for examining schools: the teachers voice. He also aptly describes how shifts in metaphors of school process have implied different models for education research, although the models are not fully developed in the article. He uses the term theoretical assertions to stand for metaphorical amplifications that can lead to a model of the classroom and thus to further education research. He adds other metaphors to characterize actions in the classroom: riding herd on secondary effects; channeling a fast and fluid stream of largely unpredictable events.4
The last is very suggestive of further research that might lead to a model. What are the events? What does a teacher do to channel the events? What skills need to be developed in teaching to allow the fast reactions necessary to channel the fluid? Does effective channeling improve learning?
James W. Garrison, in Democracy, Scientific Knowledge, and Teacher Empowerment, begins with the metaphor Knowledge is power. In the best flexible paradigm sense, Garrison examines education research done within each of several metaphors. He reviews research done within metaphors like the behavioristic teacher and the personalistic teacher. The research that he cites indicates that more extensive models have been developed within each metaphor complete with variables and predicted outcomes. Garrison then looks for new ways to view teaching in order to generate new models.5
Robert E. Floden and Christopher M. Clark in Preparing Teachers for Uncertainty begin fairly quickly with model development. A classroom can be modeled (based on the metaphor) as a collection of information flows. For them the most important set of variables measures the uncertainty of the information flows.6
In Peering at History through Different Lenses Suzanne M. Wilson and Samuel S. Wineburg also model the classroom as a collection of information flows. For them, however, the critical variables are the quality and extent of prior socializations.7
Aaron M. Pallas, in School Climate in American High Schools, develops a model closest to the definition developed above. He has many variables that he measures, and he looks for associations. He does avoid defining causes and effects exactly, because he wants to use the model to develop better descriptions of the phenomena he has measured. In the article he discusses the truth of the model that he has built and shows that school climate does indeed influence a number of things. The findings are presented not as a result, but as a step toward developing a better model.8
Robert J. Sternberg and Marie Martin develop a number of strong metaphors in When Teaching Does Not Work: What Goes Wrong? They discuss the fit of intellectual styles. Fit is a strong physical concept. They list intellectual styles as legislative, executive, and judicial. Once again the metaphor is graphic and helps us sort out some basic characteristics. A great deal of simplification, however, has occurred.9
Although the term theory is used in many of the articles, none pretends to present a theory of the type I describe above (perhaps I should call it grand theory or unifying theory). None seems to operate under a description of how learning takes place at any level of detail. All choose a metaphor to describe the phenomenon of interest, although contrasting metaphors are often developed to add more views of the same phenomenon. Occasionally the metaphors are taken further and variables are measured and correlated with other variables. The metaphors evolve into models. No author presented a critical test to determine the truth of a metaphor or model. We would expect critical tests only of theories.
Thus one of my beliefs stands in this rather simple test. True theories are unavailable in the social sciencesor at least they are not referred to in this issue of the Record.
IMPLICATIONS FOR EDUCATION RESEARCH
Implied above is the proposition that the hypothesis testing that we do as part of education research is really model building, not theory building or theory discovering. Hypothesis testing allows us to see whether one set of variables is associated in any way with another set of variables. Our criteria for testing any association rests on our ability to discriminate between random association (one variable or set of variables is not dominant in a sea of variables causing a change in another set of variables), and nonrandom association (some sort of detectable causal change or influence exists).
Once we establish the existence of a nonrandom association, then we can put these variables into a model. We do not say that we have discovered how learning takes place. We still have no theory. We may have pinned down a relationship with policy implications, but more importantly, we have a framework in which to place another set of variables in order to increase our understanding of interactions. If we are lucky, we may have two or three models with which to view the situation.
Still, simply establishing a nonrandom relationship does not identify a useful model. We may have a case for a possible model, but there are other tests:
1. What have other models shown?
2. Is this model interesting? What are the predictions that go beyond the primary prediction?
3. Is it just?
4. Does it suggest other models not yet developed?
We must shift our focus from developing a model and proving its truth to a strategy of continuously developing, testing, discarding, and amplifying models. Models are ways of seeing the world. Testing their truth is part of using them to focus our attention on parts of the education world.
Any piece of education research must begin with a review of the models that have been developed about the situation. The researcher should show what has been learned from each model. Then, either an existing model should be further tested or expanded and tested, or a new model should be presented and tested to shed light on the subject from a different direction. A simple review of untested metaphors is less useful.
Robert Birnbaums most recent book, How Colleges Work, is an excellent example of attempting to learn as much as possible from a collection of models aimed at a single social system. In his study of colleges and their efforts at governing themselves (a kind of institutional learning), he examines the governing process within a series of metaphors: the Collegial Institution, the Bureaucratic Institution, the Political Institution,-the Anarchical Institution, and the Cybernetic Institution. Although the models are not fully developed in the text, Birnbaum does rely on some model-testing research done by his co-workers. In the end, he uses not so much the truth)) of the models to improve policymaking as the increased sophistication that his readers develop as they understand the relations of each of the important variables within the models.10
Perhaps this article should be called a positivists apology for the state of social science research. The article works within a positivist view of the world. Real events determine other real events, like learning. The apology is for not being able to know or measure the real events in a truly meaningful way.
The physical world has had more successes. Lasers and their applications were developed from first principles. What we might do with schools if we knew a few first principles about learning! Not everything in the physical world is like laser development, however. We still build bridges using rules of thumb. They still sometimes fall down. We cannot model or predict the outcomes of all the variables. We overengineer; we inspect. With bridges we even know a lot about first principles, although we have far to go before we can transfer our knowledge of interatomic forces to sheer stress predictions in randomly aligned crystal structures. In education we face a system much more complex than a bridge, even with its uncountable numbers of misaligned atoms. In both cases, however, we seek to build models that tell us more about the systems.
Thus, our research orientation, even within the positivist framework, cannot be to seek theory-certaintythe complete explanation of learning. We must use Lee Shulmans interpretive orientation11 to view our research. We must learn to admire the complexity of our social world and strive to grasp increasing numbers of dimensions and interactions. To do this we must use multiple lenses to help us examine the world with models to make us ever more sophisticated observers. In the end, however, we require another process, often called intuition, to integrate the many views we have seen in our examination.
The conflicting paradigms within the qualitative and quantitative research camps have appropriate places in the search for social science understanding. Building on each and integrating what we learn remains a challenge.