“The depressing thing about arithmetic badly taught is that it destroys a child’s intellect and, to some extent, his integrity. Before they are taught arithmetic, children will not give their assent to utter nonsense; afterwards they will.” — W.W. Sawyer, Mathematician’s Delight
This quote makes me think of those milestones in a child’s mathematical education when she gets several unintended truths about math. One is that math is about following procedures and memorization. Another is that speed and efficiency are valued above all. Another is that math needn’t make sense. Maybe the greatest is that not everyone is good at math. This quote also reminds me of Christopher Danielson’s post on standard algorithms.
One of the most concerning problems is a collective agreement that, at least at the lower grades, mathematics is arithmetic. I would venture to claim that, based on my limited experiences, the general public conflates mathematics and arithmetic. My wife does or at least she enjoys pointing out how bad I regularly am at arithmetic, despite my mathematical education. I think many or most elementary teachers do, too. How do we change this for teachers for whom the bulk of their experiences as math students is/was in classrooms where arithmetic was the goal of mathematics when our opportunities to change the beliefs of these very important and influential teachers are limited to one or two semesters?
None of these ideas are revolutionary. We thought this might be a good place to start. Ease you in to all the revolutionary ideas to come.