A COMPLEX WEB

For those of you who have never stood in front of a class of students to teach something, I thought you might want to consider what goes into preparing for the challenges a teacher faces when doing his/her job. I'm not going to address the grading of student work products – such as reading essays or going over mathematical operations – or dealing with discipline problems or parent concerns or complaints or demands from the administration. I don't list these concerns as unreasonable elements of the job, but just to put into context what I'll be describing in this posting. What I want to focus on here is the actual teaching act and what goes into performing that act so that it might be successful or at least acceptable with a reasonable level of probability.

To do this, I will borrow from a media selection model that I was taught many years ago. In trying to help an educator choose the right media for a given lesson, I believe that model addresses the factors that either make a lesson a good one or a not so good one. The thing is, for much of this, it turns out to be a guessing game, particularly toward the beginning of the year. We can improve on this, but more on this aspect later. The factors are the complexity of the subject matter, the sophistication of the students, the motivation of the students, and the abstraction level of the materials used – the media. Let me describe each of these.

Complexity levels are determined by how abstract the content is. Of course, complexity is a continuous type variable, but it has an obtuse quality. That is, it's not as if you can put a meter on it and measure complexity. But one can compare things roughly and say that's more complex than that other thing. And if we use the measure of abstraction we can, again roughly, say there are categories of abstraction. The great educational psychologist, Jerome Bruner, gives us a sort of mental measuring stick by which to gauge abstraction. This wasn't his intent; his conception is more a way to describe different representations of material or content. But I will borrow his terms and say that a teacher can think of the content he/she is about to teach and how he/she observes it, mentally. Does the content represent itself as words, verbal explanations, equations, or the like? If so, we can measure this content as being symbolic and this is the highest level of abstraction. If the content is seen as something one can observe happening but not as something one would personally engage in, either because one is not interested, skilled, or otherwise it is not “doable,” then one can measure this abstraction as iconic. Going to the movies and taking in a story that one can see visually is an example of this level of abstraction. Then there is the least abstract level, “enactive,” and that is content one can think of as something in which one can participate such as in playing a game. So by using Bruner's terminology, we can say a unit of content can be of a symbolic, iconic, or enactive level of abstraction.

Now I hope you can see that further complicating a teacher's calculations is that before him/her is a significant variation among students in how content will be perceived in terms of its abstract quality. For some a given content is symbolic while others will see it as either iconic or enactive. For example, a student can see quantum physics, even though it is represented by symbolic figures and diagrams as something he/she can “do” – enactive. That is, complexity is in the eyes of the beholder and in a given class, views of complexity will vary and this poses a source of challenge for the teacher. An attempt at tracking students according to ability levels is meant to address this problem, but it has introduced other problems in its stead – a topic for another posting. My point here is that we can categorize the cognitive presentation that content has for a student in relation to its abstraction level for that student. By using Bruner's terminology, we can compare where the student is with how the content is represented. The obvious aim is to match both; that is, if we have an iconic cognitive view of the content, then we should use iconic materials including the verbal descriptions and explanations the teacher uses.

It is tempting to extend Bruner's terms to describe levels of student sophistication – the next factor – but by doing so, we imprudently narrow how we conceptualize the student. Not only does sophistication of the student refer to how abstract the student can think, but also how universally he/she thinks. This is related to abstraction, but it includes more than abstraction. The question is: how readily can the student grasp the universality of truth and beauty? Does the student merely see truth and beauty in terms of him/herself or in terms of the family, the community, the nation, the world? We can also refer to universality in terms of time. The more universal a student can see and define truth and beauty in ever more expanding realms, the more sophisticated the student is. So sophistication or maturity determines how the student will not only see or be able to understand content, but how the content will be seen in terms of importance. Unfortunately, I don't have categories here. A teacher can be aware that this concern is important and try to gauge where his/her students are. As I alluded to above, the teacher becomes more proficient as the school year advances and he/she gets to know the students more thoroughly. The more the teacher knows and understands the students, the more he/she will come to understand how sophisticated they are.

I will say that social conditions in a school will probably set parameters on this variable. A school has a culture that reflects the culture of a community. That culture will have social norms and the norms go a long way in providing the context in which student sophistication will be developed. While this does not preclude a particular student defying that context and having the student either be more or less sophisticated than the mean, for the most part, the culture will affect the range of sophistication.

Related to how universal a student thinks and feels is his/her motivation is our third factor. There is a link between these aspects. For motivation, I'll use David Riesman's terms: tradition directed, inner directed, and other directed. Again, I am taking license; Riesman had other meanings for these terms. To these terms, I will add the term, principle directed. Again these levels are related to the other concerns, but particularly to maturity. As one begins life, there is a battle within oneself between tradition directed motivation – the views of good and evil one attains from one's parents and family – and inner directed motivation – the drive to seek what one wants which is fairly self-centered during our early years. As we become more social with friends and the bureaucratic world of school and other formal settings, one learns and strives to meet the expectations of others – other directed. Here, a church experience can be highly instrumental. Life experiences bring a lot of what our motivations are based on into question. These challenges usually have their effect and a person seeks to find out what one regards as principled behavior. This can extend from how we view and deal with job related expectations to more abstract realities such as our motivations regarding equality or liberty. Even the more mature criminals adopt a “creed” to their nefarious thinking. Of course, not everyone goes through all of these developments. If one is born in a remote village with little diversity among one's neighbors and a life experience that repeats itself year after year, tradition directed motivations will have a strong effect on how one behaves and sees the world. The musical, Fiddler on the Roof, comes to mind.

I will not add much for the last variable. The materials a teacher uses should be chosen with these other variables in mind. I already pointed out that the terms Bruner uses were meant to describe how content could be represented. Of course, representation relies on materials: textbooks, films, simulations, artifacts, drawings, and the like. Another model that complements Bruner is something called Dale's Cone of Experience. The “cone,” in its visual representation, is a triangle that ascends from a wide base, representing the highest amount of reality presented or the least level of abstraction. The bottom of the triangle contains such enactive representations as simulations or role playing materials or activities. The middle levels of the cone contain materials that one observes or views. They usually portray lifelike images such as in a film or sounds such as in a radio production of a drama. Notice that as one goes up the triangle, the width of it lessens and this represents lesser amounts of reality and, therefore, the material at the mid-range of the triangle is of an iconic level of abstraction. The upper part of the triangle, the part with the least width, contains materials that are at the least levels of depicted reality and, therefore, of the most abstraction. Here we have symbolic representations as written text or mathematical equations. Ironically, the more abstract levels of representation tend to relate to more universal content – math equations work the same wherever you go.

Do teachers think of all this? My experience tells me they don't. Most are not even aware of these variables. Heck; I didn't think about all of this on a daily basis. But I believe that being aware of these concerns helped me be as good a teacher as I could be. Knowing and using these ideas don't guarantee success; a teacher could be dynamite in using these ideas and lack the social skills to be effective in the classroom. But I do believe the above are important concerns and I wish more teachers were at least cognizant of their determinant power on good teaching.