Wendy Ward Hoffer is the author of Minds on Mathematics and Science as Thinking. In today's post, Wendy asks us to think of curriculum as a buffet, offering various hot and cold dishes: a Smörgåsbord.
Curriculum As A Smörgåsbord
By Wendy Ward Hoffer
When I talk with math teachers about shifting their instruction toward math workshop, one common concern arises: How do I cover everything if I dive into only one or two juicy problems a day and spend all this time talking about our thinking?
My answer: You won’t. You won't cover everything if “covering” means students turn every page and solve every problem in the book. No way. But that is all right, because what we are after in math workshops is student understanding, and research tells us that learners benefit more from completing fewer problems with deeper discourse than from solving a lot of them by rote.
Think of your curriculum and materials as a smorgasbord, a tempting buffet: you as a careful consumer with only so much space in your stomach (or your lesson plans) get to weigh and decide what is worth eating. Go for the interesting contextualized, conceptual questions that will get students really thinking as mathematicians. One complex task can touch on numerous discrete mathematical skills and concepts, and invite thoughtful problem solving with high quality mathematical discussion.
We can address a learning target by inviting students to wrestle with three rich, interesting problems.
This recommendation may seem to fly in the face of district pacing guides and prescribed curricula, which indicate which chapter or section one ought to be completing on a particular date. Yet nearly all school and district leaders agree that a teacher’s role is to meet standards, as efficiently as possible, and in a manner that best serves the students in their care. To concerned teachers, I explain that often, we can effectively address a learning target by inviting students to wrestle with three rich, interesting problems, discussing them in depth, rather than cranking through thirty on that topic by rote. Colleagues who take this approach find that learners are more highly engaged, and achievement soars.
Set learners up for success with carefully designed mini-lessons. Model the sorts of thinking they will need to do to solve the problem; then, you can allow them ample work time - with support of partners, tools and teacher conferring – to grapple with the challenging task. Plan sufficient sharing time for students to talk about their solutions and to critique the reasoning of others, all wrapped up with intentional reflection on the big idea of the day.
Math workshops of this sort ignite student engagement, inspire collaboration and promote deep mathematical understanding. When we let go of coverage and focus instead on thinking, students come to understand that math is about ideas and possibilities, and they learn a great wealth of skills and concepts along the way. Delicious.
Here’s one juicy problem to get you started:
You are planning a vacation for a family of three. Of the choices below, which is the least expensive deal, and why?
Kayaking: The list price of a five day sea kayaking expedition off Vancouver Island is $2259 Canadian per person. As a friend of the owner, you are offered a 40% discount, then you need to pay 5% tax. A Canadian dollar is worth $0.75 U.S.
Sailing: A six-day sailing adventure in the Cayman Islands costs $225 Cayman Islands dollars per person per day, and the third person is 50% off. Tax is 6%. For $200, you can buy a 10% off coupon for this outing. One Cayman Islands Dollar is worth $1.20 U.S.
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Wendy Ward Hoffer is the author of Minds on Mathematics (2012), Science as Thinking (2009) and Developing Literate Mathematicians (forthcoming from National Council of Teachers of Mathematics). She serves as Senior Director of Education for the Denver-based Public Education and Business Coalition (PEBC), and travels nationally to provide professional learning to math and science teachers at all levels. Contact her at email@example.com and follow her on Twitter @wendywardhoffer.