Much has been discussed on this blog about the pedagogy of the revised curriculum. Some people (mostly in Manitoba) want to debate about whether the pedagogy of discovery, exploration, and constructivism actually works. This week, I had a conversation with a colleague, who shared the story of her two daughters with me. I hope my colleague isn’t a reader of this blog. I didn’t actually ask her if I could share the story. But it is too relevant not to.
Daughter 1 – High School Student
Daughter 1 is a product of the old math curriculum. She receives very high grades (in the 90′s). My colleague, a math educator, fears that these grades are earned by memorization and imitation, and have very little understanding behind them.
Daughter 2 – Junior High School Student
Daughter 2 is in her fourth year of learning with the revised curriculum. Her grades are decent, and she loves math. She has been fortunate to have four years of teachers who embrace the philosophy of the revised program of studies.
The Story
While on holidays over Christmas, my colleague’s husband took to reading alcohol content labels on the beverages he was buying. In their hotel room, Daughter 1 noticed a bottle with 6% alcohol and another with 12% alcohol. She commented that if mixed, the alcohol content would be 18%. Daughter 2 jumped in, and tried to correct her older sister. The older sister wasn’t understanding the explanation, so Daughter 2 used all the strategies we want kids to use. She drew pictures. She experimented (hopefully not by sampling). She convinced her older sister that the alcohol content of the mixture would lie between 6% and 12%. She even extended it the next morning at breakfast when comparing 1% and 2% milk.
Which daughter is better equipped to handle the rigours of University math?
This is awesome!
I have made similar observations with my children. My two eldest “made it through” school math and struggled through high courses. Then they dropped math as soon as they could.
My third child, who is currently in grade 9, is fighting the process and would prefer to get things done fast and be given an algorithm rather than understand what he is doing. (He experienced 6 years of the ‘old’ curriculum) At home I am trying to show him that he has the ‘power’ and can approach problems in many different ways. He is learning that it is his responsibility to choose a method that makes sense to him.
My youngest, who is currently in grade 4, has only experienced the revised Alberta Program of Studies. It is like night and day! He can pull numbers apart and put them back again to multiply two-digit by one-digit numbers quite naturally and with understanding. When he gets stuck, sometimes with a little prodding required, he connects what he already knows to problem solve and create his own new learning. It really is awesome!
This is anecdotal…not really a way to support a valid conclusion.
More anecdotal evidence to contradict your conclusion:
I gave this problem (12 oz bottle of 6%mixed with 18 oz bottle of 12 %) to my 7th graders today (Saxon math kids…totally “traditional”, non-constructivist), and 21 out of 30 students solved it correctly. Another 5 came close (arithmetic mistakes). 4 just cherry-picked the 18 percent.
This is just a mixture problem. Chances are, the child just had a poor Algebra 1 teacher. Personally, I don’t think it takes a constructivist approach to teach kids to solve mixture problems. It’s just a concept recognition issue….
I think the question here is not: “Can students find correct answers with traditional math education?” Most people writing about constructivism lived through traditional math classes, and succeeded, so yes that is possible. For me the question is more importantly, “Does a traditional approach equip our students with the habits of mind necessary to authentically problem solve?” Or in shorter terms, “What will a student do with a problem they have never seen before?”
I could care less if students can answer solution questions; that usually works well in a traditional classroom, because they are answering the same question over and over again (a question that they just saw their teacher do on the board). In my classroom I want humans interacting with the world, not parrots. I am assuming the junior high student in this story was never confronted with a mixture problem, but was able to abstract a very educated guess, even before explicitly learning mixture problems. This is the kind of creativity that I want to form in students, so when they are confronted with a new problem, they can adapt.
I feel that constructivism done well (that is the key point, “done well”) gives students those opportunities.