Engaging Math Students in Productive Struggle
Successful implementation of the Common Core State Standards for Mathematics depends more on how we teach than what we teach. That's why I focus on the Standards for Mathematical Practice more than the content standards when I facilitate workshops for math teachers and instructional leaders.
And the practice standard I give the most attention to is Standard #1: Make sense of problems and persevere in solving them. The reason for this is that it transcends mathematics and, for that matter, school in general. Understanding problems and solving them with tenacity are critical skills students need to reach their potential in academic and non-academic pursuits.
But how can we teach students to make sense of problems and to persevere when a problem is challenging? In my experience, we can't. We can, however, create classrooms that cultivate these skills, and the formula for doing this is simple: provide students challenging problems, and empower them with the skills and resources they need to solve those problems. Then get out of their way. We need to insist that students exhaust all other resources before seeking our help. And even then, we need to respond to students questions with questions rather than answers.
We can't do this, of course, without rich problems that engage students in "productive struggle," a term I first heard from CCSS co-author Phil Daro. And there are plenty of great resources to pull such problems from. One of my favorites is the Port Angeles School District's math website. That's where I found this problem, which I use at workshops to engage participants in productive struggle and as a springboard for discussing CCSS Mathematical Practice Standard #1:
If seven cats catch seven mice in seven minutes, how many cats would it take to catch 100 mice in 50 minutes?
Now it's your turn to make sense of this problem and to persevere in solving it. I'll post the answer and share my solution strategy at some point. Please share yours in the meantime.
Image by Phildaint, provided by Dreamstime license
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