stimulant

In 1980¹ Mindstorms, Seymour Papert wrote:

I have seen [a resistance to “debugging”] in many children’s first sessions in a LOGO environment. The child plans to make the Turtle draw a certain figure, such as a house or stick man. A program is quickly written and tried. It doesn’t work. Instead of being debugged, it is erased. Sometimes the whole project is abandoned. Sometimes the child tries again and again and again with admirable persistence but always starting from scratch in an apparent attempt to do the thing “correctly” in one shot. The child might fail or might succeed in making the computer draw the picture. But this child has not yet succeeded in acquiring the strate-gy of debugging.

It is easy to empathize. The ethic of school has rubbed off too well. What we see as a good program with a small bug, the child sees as “wrong,” “bad,” “a mistake.” School teaches that errors are bad; the last thing one wants to do is to pore over them, dwell on them, or think about them. The child is glad to take advantage of the computer’s ability to erase it all without any trace for anyone to see. The debugging philosophy suggests an opposite attitude. Errors benefit us because they lead us to study what happened, to understand what went wrong, and, through understanding, to fix it. Experience with computer programming leads children more effectively than any other activity to “believe in” debugging.

The distinction between convergent² and divergent³ thinking and learning is an old one. Nonetheless, I think that the distinction has a lot of mileage left on it. In particular, I have seen little attention paid the epistemological significance of the convergent/divergent choice. While it would be misleading to suggest that an activity or environment cannot have both divergent and convergent characteristics, it is important to understand the nature of the learning that goes on in each type of activity.

While much has been written about the process of deconstructing misconceptions in pedagogy, the issue seems to have been passed over in designing and structuring environments for learning and doing. Papert uses the debugging analogy to computer programming to point out that for most people, education is the process of fearful, controlled guessing. Rarely is there an opportunity to revise a guess based on feedback before being graded/punished/rewarded. Unfortunately, this not only means that we condition children against their natural instincts of perseverance and patience in the face of uncertainty, we actively hinder the development of metacognitive language and thought, in turn making it harder to disabuse learners of their misconceptions.

why not? instead of why?

I am often frustrated by the absence of documentation of why things are not the way they are not. For instance, authors of physics texts create a carefully crafted argument about why things are the way they are, given that we accept some axioms or experimental evidence. No matter how elegant or natural this line of reasoning, there is a chance I will misunderstand. When I work through a physics problem inccorrectly, I have either misunderstood, misdeduced, or miscalculated. Creating a watertight argument that allows no misconceptions is difficult, and therefore rare. This is dearth is felt keenly in introductory texts: exactly where an allowance for misconceptions does the most damage as the basic misconceptions propagate forward, unchecked. I would find the answer to the question, “Why doesn’t it work the way I thought it did?” far more valuable than an explanation for why it does work the way I didn’t think it did. Which is to say, I’m looking for the raw materials to create a debugger for my own thought process.

what does this have to do with {conv-, div-}ergent activities?

My teaching experience has capitalized⁴ on the naturally tinkerable character of entry-level activities in the domains of physics, building things, and electronics. By tinkerable, I mean that materials and activities reward incremental exploration. While it is easy to take some electrical components, a toy, and explore circuit bending, it is much less reasonable to expect mixing together arbitrary chemicals from a chemistry set to yield much except [potentially dangerous, but probably boring] sludge. In this sense, electronics supports exploration more naturally than chemistry. The important parameter here is the relative cost of the most accessible iteration. In electronics, the most accessible iterations are the cheapest⁵ , whereas in chemistry, the most accessible exploration is comparatively expensive⁶ . This has made my attempts to teach chemistry, for instance, much less successful than the rest of my teaching experiences, and it’s a problem basic to a lot of fields which are not naturally approachable.

While this is a “natural” cost in the case of teaching chemistry, we repeatedly incur a similar cost for essentially every other domain in our schools. Convergent problem solving artificially increases the cost of iteration by making exploration psychologically expensive. Ridiculously, this inhibits the very instincts which would hone a learner’s skill, lengthening — often indefinitely — the time to mastery.

What would a resource that is aimed explicitly at helping you avoid pitfalls — not necessarily finding “the right path” — in a field look like? Are there any precedents or analogues?

1. !!! [↩]
2. Meaning that an activity converges on the same endpoint for everyone — workbook problems are a textbook example. [↩]
3. Meaning that an activity has many possible endpoints — the goal is engagement with the process, not the product. [↩]
4. That’s a euphemism for “copped out.” [↩]
5. e.g. What happens when I disconnect this component? [↩]
6. Limited (no pun intended) reagents, time, sensitivity to initial conditions, etc. [↩]