Extra Credit Should Not be Where the Good Stuff Lives
This puzzle was posted on Twitter this week; I LOVE IT!
A new, and wonderfully charming new friend on Twitter posted this reply to it:
This reply got me thinking about the practice of “Extra Credit” in math classrooms. Up front, I have to state emphatically and truthfully that I have engaged in the tradition that I am about to excoriate. So insidious are the effects of prior experiences on our teaching practices.
So here is my puzzlement on the teaching of mathematics today…Why are the good, fun, interesting problems left for “Extra Credit”? Why can’t Simon’s picture above be the starting place for some lessons? What effect on student learning would this have?
As I am working on this little piece my friend, co-author, and kindred mathematical spirit Sunil Singh has just published this short piece with a similar theme, check it out here. While I was reading this piece, I am struck with the idea that perhaps it would be better to grow our students into flexible, creative thinkers who can tackle novel situations rather than regurgitate a formula and use it correctly in a narrow application?
Anyway back to the good stuff and it not being left for extra-credit…Look at that picture again. When I look, I see lessons involving Geometry: area, shape, transformation, shape naming and describing, proportionality, composition, and decomposition, perhaps you see others… I also see opportunities to develop: Number Sense, factors, composition and decomposition of magnitudes, links to primality, algebraic thinking. All that just on the face of the original question, so much richness here. If a teacher spends the time and massages out and teases the students with a few probing questions, you could learn a lot about how they are thinking, and what they really do understand. Further, you could ask focusing questions (not funneling questions) to help bring their perceptions into greater clarity.
Also, this picture with that simply stated, easily understood question does not need to be the end of this experience. Put students in groups and give each group a different pattern block but lots of copies of it, tell them “This is your 1” construct a puzzle for the other groups in the same fashion as the one in the picture, be prepared to ask your fellow students focusing questions to guide them. Then let them go, let them play, design, create and generally LEARN mathematical thinking.
Good problems are where good lessons should begin, not be tagged on and left to the few who choose to do extra-credit. Perhaps, if all our lessons began well, connected to many topics, created deep understanding, and provided opportunities for play and creativity; the need for extra-credit problems would disappear altogether.
I hope you see my problem isn’t with the practice of extra-credit, but really in general lesson design. Rich contexts, provide plentiful opportunities for learning. Let us strive to always place our students in places of abundance, not paucity.
