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The Myth of Individual Thinking
I enjoyed discussions with colleagues this week on the divergent goals of instructors and students. Based on reports of how students approach the math learning center, it appears that their primary objective is getting all the questions answered, in time for the submission deadline. From the instructor's perspective, this objective is only a means to an end: that the student learns mathematics.
How do we reconcile the breadth of our established curricula with the constraints on our students' time that prevent them from ruminating on the rich mathematical content long enough to attempt an unfamiliar problem with confidence? If a problem is too offbeat, we've seen them throw up their hands in frustration, bringing their homework to the math learning center and making it "somebody else's problem". Even for a question worded exactly the same as one of the worked-out examples in the textbook, I got the impression from Professor Anderson that the approach of making it "somebody else's problem" is still common.
Perhaps our students are just more aware of the inheritance they've received from generations of thinkers before them, as Yuval Harari points out in a recent book review:
Sloman and Fernbach take this argument further, positing that not just rationality but the very idea of individual thinking is a myth. ... No individual knows everything it takes to build a cathedral, an atom bomb or an aircraft. What gave Homo sapiens an edge ... was not our individual rationality, but our unparalleled ability to think together in large groups.
Students who acknowledge this debt should not regard it as a license to abdicate their individual ownership of the knowledge our courses seek to impart, although many of them seem to arrive at that conclusion. The instant availability of so much knowledge online has made our individual ignorance so visible that the generation of digital natives has internalized drastically reduced expectations of what any one person should commit to long-term memory.
A solid long-term memory, with which we hope our students will be armed when they face unfamiliar applications, is difficult to establish in the time frame constrained by their patience and financial means. To compensate for this gap, some instructors give open-note exams, so as to test understanding rather than memory. This novel approach to mathematics exams is an idea I might be tempted to explore in upcoming semesters.