I’m not gonna lie… I loved this week’s reading! It took me so long to navigate through, because of taking notes, reflecting on my own practice, looking up big words that I didn’t know and rereading many parts. I have to respond to the first Discussion question:
After reading the review of work in this area, would you encourage a ‘drill & practice’ approach to learning math, or more of a conceptual strategic-based approach? Why or why not?
I would have to argue that BOTH approaches are necessary to learning math effectively, and hence, with the least amount of personal anguish.
On the Drill side, we have the bonuses of accessing the information with very little effort via the left AG. Maximizing the LTM that has already been established, it is akin to using a calculator as opposed to finding a strategy and processing the information using pen and paper. Our brains can just spit the solutions out as opposed to having our brains “crank the answer out.” It also seems as though folks who are particularly good at math are accessing their left AG, in combinations with other areas of the brain that us normal folk don’t even go near. Practice also seems to make these skills more automated and more quickly accessed.
On the strategy side, even though we are not accessing the coveted left AG, we are able to apply those strategies to “untrained” problems with much better success than those who rely solely on drilling. Applying knowledge in unfamiliar territory is a very valuable skill indeed!
Where curricula and educational fads run into trouble, in my opinion, is that when the pendulum swings towards “the new and shiniest learning strategy” (ex. Assessment for Learning, Inquiry Based Learning…), the baby is also thrown out with the educational bath water. I refuse to believe that “old school” methodologies are complete crap and I see real danger in going “all in” on these new strategies. Admittedly, AFL is not that new anymore. Ontario had been using it for years before BC got its claws into it. We had Pro-D upon Pro-D, learning about AFL. If you didn’t adopt it, you weren’t a team player— at least in my school. So I tried it for two years, saw my GPAs plummet and saw stress sky rocket. I consequently decided to create a hybrid AFL approach to eliminate its negative effects. Did I throw it all away? No. I kept the bits I liked and turfed the bits I saw as harmful to my students’ well being.
Speaking of babies thrown out with bath water… Ontario is apparently in a bit of a math pickle these days since it has fully embraced the Strategy approach over the Drill. Math scores are at an all time low. People are freaking out—well maybe not freaking out, but you can’t ignore that Strategy based math learning, on its own, is not good for the majority of students. An Ontario math teacher presented a GAFE conference I went to last year and I spent the entire hour wondering how it is possible for this approach to work? Her students had to answer about 8 questions per unit— when they correctly answered them, they then moved on to the next unit. The questions were challenging, without question, but there was no repetition, no drill, no rehearsing of simple questions prior to increasingly more difficult ones.
Hybrid approaches. I think this is my approach to pretty much everything in my practice! Except coffee. The coffee has got to be done one way, and it has to be done right.
Dana
PS. If you haven’t seen the movie Pi, it is about a math genius who gets hunted down by people wanting him to predict the stock market. The closing scene is him drilling into his own brain, into the left AG perhaps, so that he would no longer be able to do the bad guys’ bidding. I may have just called the police, but to each their own.