The Most Valuable Mental Habit

Years ago, in college, as my mind was being stretched and shaped by a few key professors, I remember being in conversation with Dr. Wickersham one day. I do not remember specifically what we were talking about, but I finally thought I had put together a solid and intelligent point, and as soon as I "had my footing" in the conversation, Wickersham took the whole thing to another level, examining what we were discussing from a larger perspective. He had cultivated the habit of seeing particular things as specific examples of a larger generalizable order. This habit, I believe, is the most valuable intellectual habit one can acquire in school. I have believed this since that conversation, and my experience as a teacher has only confirmed my original belief.

The ability to generalize and see something as part of a larger structure, as part of a pattern, not just an isolated incident, is especially important in math (the subject I teach). I am constantly trying to get my students to see the larger "class" of problems that a specific problem belongs to, because once we learn to solve a few specific examples, we can work out a general solution for all problems of that type. The quadratic equation is a good example of this. There are many variations on the theme of quadratics (2nd degree equations), and many ways to solve certain kinds of quadratics, but the quadratic equation is the general solution to all quadratics.

Some students seem naturally good at this skill, whether because of their environment, up-bringing, or personality. Other students have tremendous difficulty with this, even after it has been repeatedly demonstrated and highlighted. What interests me is: what is the most effective way to teach this concept and to get students to apply it on their own? If anyone has any thoughts, feel free to share them in the comments.

Also, I apologize for my absence recently; school has been very busy! Thanks to the reader who posted the nice comment about looking forward to my next post! It's always nice to know I'm not shouting into the wind.

Merry Christmas and Happy New Year to all!