Risk, Failure and Uncertainty - An essay on the habits and attitudes beneficial to solving complex problems
On the Role of Memory - Practice and RepetitionThroughout high school and possibly even in their first year of college, rote learning served my students well. Their past success encourages them to stick with what worked. And so, it's not surprising that many will try to rely heavily on a memorization-only approach when they begin organic chemistry. But memory alone will not suffice! Complex problems are challenging, in part, because they are new to solver; the solver has never before charted a solution to the problem at hand. Since the problem is new, it follows that the solver’s memory provides no record of the complete solution. And while memory alone cannot possibly provide a complete solution to a complex problem, a strong and productive memory does help the solver by allowing him / her to quickly generate relevant options at each step of the iterative process. Here it may be helpful to distinguish memorization that is productive from rote learning.
Rote learning is the act of storing information without meaning. To realize fast recall and to make proper connections, it's essential not only to have a wealth of relevant facts in one’s mind, but also to have those facts organized in an orderly manner. Rote learning fails to achieve this. Structured information, on the other hand, provides insight and a deeper level of understanding.
So how does one acquire a rich memory that is organized for solving complex problems? The answer is practice and repetition. By practicing a variety of complex problems, students are exposed to a wide range of fact-filled experiences. With repetition, they'll learn to construct associations and recognize patterns. In other words, practice grows their information warehouse while repetition organizes it. Practice and repetition are thus effective means to a strong and productive memory. And unlike rote learning, this memorization technique does help solve complex problems.
The role of memory is easily seen by comparing students with strong memories to those whose memories are deficient. When students with poorly developed memories reach into the information warehouse to generate initial-step options, they cannot find what they need, either because it’s not there or because the facts are not well organized. These students tend to grab and use whatever they find. The result is a poor set of initial-step options and almost certain failure. These students are relying on intuition that's biased because their information warehouse is limited or in disarray. In contrast, students who perform best have practiced solving complex problems over-and-over again. Having an extensive collection of organized facts, these students are able to reach into their memories in the heat of the moment and quickly find what they need. You might say they are developing "accurate intuition".
In tomorrow's post I'll conclude with a brief remark about what I see as the long-term educational significance and how my thinking will influence the way I intend to approach this coming year.