Productive Struggle

​This quote from the NY Times article The Singular Mind of Terry Tao speaks to what Math is and what it means to do math:

               ...Tao told me that his view of mathematics has utterly changed since childhood. ‘‘When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed,’’ ...‘‘I sort of imagined a committee would hand me problems to solve or something.’’ But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory,’’ he said, looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much later.’’

Other Articles Link to this section

• Seeing Struggling Math Learners as ‘Sense Makers,’ Not ‘Mistake Makers’ This article from Mind/Shift describes how teachers can shift our perspective to what we can learn about how students are thinking, based on the work (right or wrong) they produce.
• Engaging Math Students in Productive Struggle from the Education Week Teacher Blog
• Common Core Math Playlist: Engaging Students with Productive Struggle from the Teaching Channel 
• The Struggle for Productive Struggle  from Emergent Math