Writing as Problem Solving

If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.
Rene Descartes (1596 - 1650)

This July I’m one of the faculty members at the Educause Learning Technology Leadership Program in Madison. There is a lot of planning that goes into this thing. A couple of week ago I learned that in the opening session we will be doing something on Interaction Styles based on the Myers-Briggs Typology. This triggered a memory (I learned about Myers-Briggs at the Frye Institute a few years back) and much curiosity about my type, INTP. I did more than my usual amount of Web surfing on the subject and read many descriptions of this type. I found this site where you can take a test to determine your own type, took the test for myself, and confirmed my INTP classification. I was pulled in more and more by the seeming high accuracy in which these descriptions identified me. I had a friend who is an economist take that test; he proved to be an EFTJ, almost the exact opposite of me, and yet the description for that type fit him quite well.

Some of those descriptions for INTP actually use the expression “Absent Minded Professor” and most of them describe the type as “Architect” meaning somebody who builds theoretical constructs to address problems. If you are a regular reader of this blog, ask yourself how many of the posts provide a theoretical argument for a structure aimed at addressing a certain problem. I believe I’m doing that all the time. The descriptions talk about INTPs having a need to make connections between the theoretical constructs and a wide range of experience. I believe I’m doing that too. And the descriptions talk about the fundamental motivation – creating understanding of reality out of complexity. That’s right on the button.

In the process of my Web surfing about INTP, I found Richard Feynman’s Noble Prize address. It so well matched what I wanted to write about that I’m leading off with it. But, to be truthful, I didn’t understand the physics in it. Some of the little points – positrons can be thought of as electrons moving backward in time – yes, I got those. But on the big picture physics issues with which Feynman was grappling – no, that was over my head. I thought it was a great essay nonetheless and I’m going to highlight what it was about it that I found so intriguing and that I think is worth trying to emulate in our writing.

The essay as whole is a recounting of Feynman’s discoveries that were the basis for his Nobel Prize and in choosing my title for this post, slightly inaccurate but I hope you’ll forgive the imprecision, I’m referring to this type of recounting. We might distinguish between introspection coupled with happenstance that produces the original spark of idea and reflection on that thought experience that produces the narrative, the recounting that I’ve referred to. For me writing doesn’t really help with the spark, though it does help remarkably on pushing the idea further and refining it. But that’s not enough to get me to the keyboard. I need an idea for a story. That’s where the recounting comes in.

Feynman’s style is matter of fact, almost reportorial. He doesn’t embellish his discoveries nor does he shun his misperceptions, of which there were many. He falls in love with his own ideas just as one falls in love with a woman, and indeed he uses that metaphor early on in the piece. The passion in pursuit of the idea is love; there is no doubt about it. The essay has an aspect of symphonic music that starts in a minor key and builds slowly. By the middle of the piece there is a strong sense of crescendo. So many ideas are seemingly tying together. It is hard to contain the sense of excitement, on the verge of an important discovery. And interspersed are nuggets of perception such as this one, which make the reader feel they are getting the same sense of the beauty of the ideas that spurred Feynman in his pursuits.

A thing like the inverse square law is just right to be represented by the solution of Poisson's equation, which, therefore, is a very different way to say the same thing that doesn't look at all like the way you said it before. I don't know what it means, that nature chooses these curious forms, but maybe that is a way of defining simplicity. Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.

Another aspect of the essay that is delightful and something that we really need to talk about more is the importance of guessing in discovery. Guessing is mentioned quietly at first, then it comes front and center. But equal attention is given to the time spent on verification, careful checking of the equations to make sure the calculations were correct. Guessing and verification are two parts of the discovery process that must go together. One must abandon belief in an idea when it can't be reconciled with observation or other known theory. But one may persist in trying to save an idea from abandonment by seeing whether a suitable modification or an alternative perspective can bring about such a reconciliation. There is learning in this too, thought it might very well come with the emotional baggage of feeling jilted by a lover.

And he makes a big thing about “artificial mental constructs,” what we first fall in love with when we pursue an idea, that turn out to be less important in our understanding when we have a more mature view and that may be outright wrong, but were critical for moving down the path of discovery. This too is something we need to talk about. Feynman notes there is great risk in taking a non conventional approach to thinking about a physics problem; there is a likelihood that it will lead nowhere. But by taking a non-orthodox approach, one of the individual’s own making, there is likely deeper learning about the ideas at stake, and there is the possibility of new perceptions from the unique point of view.

* * * * *

The rest of us won’t be Feynman’s. Our discoveries will not be as fundamental nor as profound and we very likely won’t be able to make a career out of them. But we can embrace his style in telling our own stories, producing interesting narratives in the process and using those as a way to promote the ideas that we do come up with for the consideration of others. Here’s one from me, another byproduct of the infatuation with my Myers-Briggs type, INTP.

I was unsure of the reliability of what I read after doing the initial INTP search in Google, so I did another Google search (INTP .edu) thinking I’d find a more credible listing if it were at a .edu page. The third response is to this site at Murray State pertaining to the first year experience. It appears that at Murray State they take the Myers-Briggs inventory seriously as a way for the students to identify themselves and come to a greater sense of self-understanding. That was interesting in itself but my attention turned elsewhere. I became taken with the first bullet under “Playing” where it says that lectures may very well be a source of entertainment. This rather innocuous observation became the stimulus for my problem solving.

Here is the chain of my thinking. Indeed, I used to go to lectures a lot when I was at Cornell and then as a grad student at Northwestern and here I’m talking about lectures outside the courses I was taking. Lectures were a source of intellectual entertainment. (Nowadays I watch The Charlie Rose Show for this same sort of information.) I know that on occasion in thinking about the debate over whether lectures are a good or bad mode of instruction, I’d mentally note my own predilection for attending them. Then, the not quite syllogism is that if lectures are a good form of entertainment, they must be good for classroom instruction as well and indeed there were many lecture-based classes that I took where I got a lot out of the course. Then I make the simple inference that if lectures were good for me they’d be good for other students as well, naïve egotism as the basis for my thinking. Indeed, one of the really disturbing ideas that has come out as a result of reading about INTP is a questioning of whether my core beliefs about learning are really robust for everyone else, or if instead these ideas only make sense for INTPs. That questioning has left me with a sense of unease. I don’t yet have a good feeling for how to resolve the issues.

Then I recalled a lesson about egotism that I learned from Naomi Miyake, a Japanese scholar (with a degree from the U of I) whom I meet on a trip to Taiwan where we along with other colleagues toured to discuss our early lessons from efforts with learning technology. In her presentation Naomi showed two Mercator projections, one produced in the U.S. the other in Japan. For the logic of such maps, it is completely arbitrary where to chose the latitude line that “cuts” the globe so the map unfolds. Naomi showed us that the U.S. ends up at the center of the map produced in the U.S. while Japan ends up in center of the map produced there. What could be a better demonstration of the universality of our egotism? This made me comfortable in the thought that I could use myself as representative of all INTPs, particularly those who are faculty members.

Summing up where we are now, we have that INTPs like lecture, they tend to be egocentric (which among other things tends to contribute to the belief that their non-INTP students are lazy), and there is a concentration of INTPs among the professoriate. Then throw in for good measure that INTPs typically have a strong streak of stubbornness. Is it any wonder that they are inclined to believe that lecture is a good form of instruction?

Now a little aside for my explanation of why lectures work for INTPs, because others may very well be confused on this point. INTPs live to process their own ideas and they come to know things through their internal processing. When a conclusion has been reached that idea no longer holds interest. The issue arises – where should the INTP next focus his attention? Lectures are fodder for such processing. They point the way to questions that need to be asked, to theories that need to be understood, to ways an argument unfolds. The lecture is an excellent source of intellectual fodder.

In large part for this reason, I’ve never understood why so many others take notes during lectures, particularly when the ideas are available elsewhere, such as in a book or on a Web site. Taking notes seems to interfere with processing. It is a deliberate suspending of thought, with the busy work of recording the ideas as an inferior substitute to thinking about them, a caving in on the critical issue of whether the student is sharp enough to understand what the professor is speaking about. I never much cared for those lectures where a lot of detail was spewed out with that as the main purpose, where the Professor expected the students to take extensive notes to capture that detail. I always preferred lectures that gave the big picture, that tried to convey a mental image of the issues at stake, that constructed a long and thoughtful argument to prove the proposition at hand. And I suppose, if I were to reflect on it, I would have come to the observation that note taking and raising one’s had to ask questions is negatively correlated, because in those type of classes one asked questions that were about the implications of the big picture ideas, and the note takers weren’t focusing on that.

To my knowledge, the research on teaching mode that condemns the lecture in favor of active learning methods, consider this site for example, does essentially nothing to confirm the professor’s own learning and the role of the lecture as intellectual fodder. As an INTP who is well aware of my own learning, if only implicitly, at first blush I’ll likely reject the findings of that literature. Patently, they must be wrong. For you to convince me to abandon lecture in favor of active learning, you need to make a more nuanced argument along the following lines.

1. Typical students are unlike me in their Meyer’s-Brigg typology. Very few are INTPs, who count for only about 1% of the population. Indeed most of our students are probably Extroverts rather than Introverts.

2. Typical students likely don’t process internally like I do. They may find trying that difficult and unrewarding. They may not see relationships across ideas like I do. They will need other ways to draw out those relationships and make them overt.

3. In a hypothetical study where INTP students were separated out from their peers, it should be found that the INTPs did indeed do well in a traditional lecture format. But that same study must show the peers of INTPs did poorly in the lecture framework. The peers did better when the approach embraced group problem solving. This sort of study would confirm my own learning, not deny it.

4. In a different hypothetical study, one that focused longitudinally on career choice, it should be found that INTPs disproportionately enter into doctoral programs upon graduation and among doctoral students INTPs disproportionately enter into academia.

5. In yet a different hypothetical study, student evaluations of teaching should show a correlation between student satisfaction, on the one hand, and the closeness Myers-Briggs type, on the other. In other words, the egotism idea about preferred teaching styles and learning style should be confirmed.

6. It should be found that some INTP faculty do succeed in providing courses that students find satisfying, in spite of the M-B type differentials, but such faculty are not “naturals” as teachers and have to put considerable effort into modifying their approach to be suitable for students.

Points 1 and 2 are garnered from the writings about the Myers-Briggs typology and empirical work done on the MBTI. (Note that this Wikipedia page offers a type breakdown by frequency in the population and disputes that INTP is only 1% of the population.) Points 3 to 6 are my conjectures. They are guesses that I think are reasonable and if they are true provide a theoretical explanation as to why the lecture persists in spite of the increasing evidence that lectures are not an effective mode of instruction. Further, one can readily get the result for lectures without an appeal to the idea that faculty shirk in their teaching and lecturing is low effort mode that is tantamount to shirking.

In order to make 1 – 6 the basis of an appeal to faculty to alter their teaching, there would first have to be an embrace of MBTI. This would require showing first, that an individual’s type doesn’t change over time (here is such a study that focuses on such time invariance of type) and then the type must be shown to be a reliable predictor of behavior in many instances that are relevant to teaching and learning in the higher education setting.. Those pre-conditions don’t exist nor are they likely to exist any time soon. Thus, my piece may seem like idle theorizing.

But I think there is value to the approach especially if we consider all of us faculty as instructors in the role of students with regard to choice of the mode of instruction. If you as evangelist for a new mode of instruction want me to abandon my lecturing, how can you make your arguments on my terms. The current vogue seems to be to situate the arguments in the learning of the students, but to entirely abstract from the learning of the instructor. That, it seems to me, is a serious error.

An effective argument needs to engage the learning of the students and the learning of the instructor simultaneously, to make a case for where similarities prevail (and hence where the instructor is best able to be sympathetic to the learning issues that students face) as well to identify where there will be mostly differences (and hence where the instructor needs to be careful not to indulge his own egocentricity when determining the pedagogic approach). The MBTI is a construct to aid in coming to this type of argument. Once having reached this point, however, it has served its useful purpose and can be abandoned, just a Feynman abandoned some of his own early constructs. What remains is a more mature perspective of how we learn and why we teach the way we do.