## A Nice Little Story

January 14, 2012 by John Scammell

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?

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on January 15, 2012 at 11:11 am |Timon Piccini (@MrPicc112)This is awesome!

on January 15, 2012 at 11:14 pm |ccampbel14I 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!

on February 23, 2012 at 12:20 pm |MansoorThis 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….

on February 23, 2012 at 2:05 pm |Timon Piccini (@MrPicc112)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.

on February 23, 2012 at 3:35 pmMansoorI agree that the ultimate goal is to get students to be able to solve problems they have never seen before. But I think that there is an enormous campaign of misinformation stating that “traditional” approaches do not prepare children to be creative problem solvers.

Experts claim that kids trained with a traditional approach in math are unable to solve complex, unique problems because they were simply trained to parrot canned algorithms to solve canned problems.

In my experience, when my students have truly mastered concepts (like adding fractions, solving two step equations, graphing linear equations), their minds are freed to explore and deal with higher order problems. I have a chemistry and physics background, so I like to give my 7th and 8th graders mixture and rate problems that would make a high school student cry, and my kids are fully equipped to deal with them.

I don’t really care what other teachers choose to do, but it’s frustrating to hear people malign traditional methods when there is no research supporting the idea that traditional approaches don’t work.

This isn’t a critique of the constructivist approach, it’s just a commentary on people who seem hell bent on attacking traditional approaches using misinformation.

What’s the motivation? It’s like they’re spreading christianity or amway or something.

on February 23, 2012 at 3:43 pm |John ScammellOf course it’s anecdotal. That’s why I titled it “A Nice Little Story”.

on February 24, 2012 at 8:40 am |Timon Piccini (@MrPicc112)@Mansoor, I see what you are saying, and I can agree that yes students can learn to problem solve in traditional classrooms, but I think we have now discovered another difference between the two camps.

Traditional classrooms want students to learn to problem solve. Constructivist classrooms want students to problem solve to learn. There is a big difference here.

As to your claims about the constructivist teacher not worrying about reasearch, I hope you can take some time to read Frank Noschese’s post on Khan Academy (http://fnoschese.wordpress.com/2011/12/02/you-khant-ignore-how-students-learn/). It is chalk full of links to research that point to the fact that when students engage, and are active participants in their learning, they learn better.

I am not a master teacher, I only have my own anecdotes right now, but just this year I see students have a better understanding of many topics, when i have let them explore the ideas first, and give them the rigour only after they have first jumped in for themselves, but to say that no research points to an interactive, constructivist, problem-based approach over a traditional is, I am sorry to say, a lie.