Technique versus Truth: promoting gradual mastery of mathematical theory.

Pacific University
Talk Abstract
At all levels (elementary, high school, and university), doing mathematics is at once about discovering truth and getting the right answer. It is interesting that getting the right answer is often possible without understanding why the method works. Using examples from all levels of mathematics, I argue that it is actually not always bad to give our students algorithms without explaining why they are true. At times it takes two or three passes through a topic before a student is ready for the underlying theory. Sometimes the prudent course is to give just a hint for the intuition the first time around, and I will give examples from the Calculus sequence. Reflection on this pedagogy should also include seeing the importance of finally achieving mastery of the theory. (How many Calculus students remain mired in bad algebra habits because they can’t distinguish in complicated contexts which moves are legal, not grasping the underlying ontology that determines what is allowed?) Finally, a pedagogy of gradual introduction of theory leads to a solution of a thorny problem: inspiring in students a desire for mathematical theory without leading to too many complaints on evaluations.
Talk Subject
Mathematics Education