Not your grandmother's math
There are 27 sheep grazing in field. Twenty of the sheep are white and seven are black. A farmer comes over the hill, bringing 18 more white sheep with him. How old is the farmer?
Young students hear a problem similar to this one and respond, “Huh? I can’t figure it out!” Of course they can’t. The question is nonsense. However, research on math instruction in America suggests an alarming number of older students, when faced with a “word problem” similar to the sheep farmer’s story, put their nose down, their pencil to paper, and start busily adding numbers. Why would older students try to tackle the impossible? The answer is simple — they no longer stop to make sense of the problem.
In fact, “In far too many classrooms, math is taught as algorithms, steps to be learned by heart and replicated under a specific set of circumstances. Learners rehearse and regurgitate procedures, yet rarely understand them,” says Ward Hoffer, author of Minds on Mathematics.
Although American schools are improving, international data reveals that when measuring high school students’ math abilities, our country ranks 24th out of 30 industrialized countries.
When you ask, “What are our Whitefish Schools doing about it?” I answer, “A great deal.”
Our teachers are diving into Common Core Standards and learning about teaching models that focus on thinking strategies. Redesigning math instruction demands profound shifts in lesson design. Teachers are learning how to create math lessons that build student ownership of math content, invite learners to “flex their mental muscles,” and ensure that the procedures students are memorizing actually make sense to them.
I am proud of the initial steps our teachers are taking to improve the rigor and understanding of their math instruction. Two weeks ago, for instance, Whitefish hosted a Minds on Math Institute in which 45 of our teachers and administrators, as well as 20 teachers from other school districts, spent two days learning from two national math specialists whose expertise specifically addresses thinking strategies in a “workshop” model. The two days together were challenging and fruitful, and Whitefish teachers have immediately begun to reshape math instruction. Our teachers will be supported in their ongoing efforts through our district’s commitment to professional development.
Is there evidence that our teachers’ learning is improving students’ math understanding? While instructional improvements take time, the short answer is “Yes.”
I offer one small example. Recently some of our young middle school students were reviewing their understanding of area calculation. Rather than merely memorizing the formula for area, they were busily working in teams, trying to figure out how much money they needed to paint a local barn.
Students were given the dimensions of the barn, the cost of paint, and some information about paint coverage. One team defended their calculation of 18.3 gallons, which they “rounded down” to get 18 gallons. It wasn’t long before another student said, “That doesn’t make sense. If you round down, won’t you be short on paint?” The ensuing conversation focused on whether one could skimp to save money, and risk running short on paint.
While they wrestled with the economics, I’m sure their teacher was delighted to hear math students working at “making sense” in math. What a step in the right direction!
— Kate Orozco is the Whitefish School District Superintendent