In the beginning stages of Common Core implementation for Mathematics, it is only natural for teachers to examine the shifts in content. We are driven to answer the question, “Exactly what skills do I have to teach?”
But if we are truly going to meet the requirements of the Common Core in Mathematics, there is a section of the CCSS that absolutely cannot be overlooked: The Standards of Mathematical Practice. These expectations focus not on the skills students must know, but rather on the processes and methods they use to approach mathematical problems.
A close reading of these practice standards will reveal that true CCSS implementation in math depends not only on what students must do, but also on how they do it.
I want to draw attention to one word within them that may be the key to unlocking the rest: Persevere.
The first Standard of Mathematical Practice is as follows: “Make sense of problems and persevere in solving them.”
In math class, how often do we ask our students to persevere? We all tell our students not to give up, but this practice standard calls for us to go beyond telling to teaching students how to persevere. How often do we teach them to try different approaches, test ideas and revise their thinking?
This won’t happen in one lesson of course. So how do we do it?
One idea is to commit to presenting students with regular mathematical challenges that have multiple steps and that require close reading.
I’ve called them the POWs, the Problems of the Week. POWs incorporate recent content but present challenging tasks that can be solved using several different approaches. And, especially with our earliest problems, the POW has rarely led to a correct answer on the first try.
For students, these incorrect answers were upsetting at first, to say the least. This just in: kids like being right! (Who doesn’t?) But when teachers create time for student collaboration and offer opportunities to debrief, students became increasingly comfortable taking risks, making errors and trying again. They learn to persevere.
Where do my POWs come from? I take the concept we are currently working on in math class and brainstorm authentic applications of the topic. Then I create a problem that requires multiple steps, a problem without one clear pathway to the solution. For example, when working with a 5th grade class, I developed the problem I titled “You Can Counter On Me:”
“Rafael is covering two countertops with tiles. The tiles are three inches by six inches.
For each countertop:
- Decide whether Rafael will be able to cover the entire surface with whole tiles (no gaps, no overlaps).
- Prove your answer by drawing a picture that has all dimensions labeled (LENGTH, WIDTH of both counter and tiles).
Countertop A measures 18 inches by 15 inches. Countertop B measures 24 inches by 24 inches.
I try to create POWs that can be tackled in multiple ways. For example, students could solve the problem above by drawing on the formula of length times width, but they could approach it in other ways too.
I also try to create problems that I can differentiate. I’ll often give different students different versions of the problem, based upon their ability levels. For example, when tailoring this POW for high-achieving students, I could have added information and a question about the cost of the tiles.
One final suggestion is to work to include parents in their children’s POW work. I want the POW to be something families can work on together at home. But since many parents are a few years removed from the grades I teach, it can be tough for them to provide support. That’s why I started creating a “vodcast” to accompany each week’s problem. I simply recorded myself solving a similar problem and posted it to my classroom blog.
Looking to see this kind of teaching in action? In the Teaching Channel video “Don’t Give Up! Plan, Persevere and Revise,” you’ll see teacher Madeline Noonan implementing a problem solving activity into her regular routine. It’s a problem that’s perfect for building perseverance, and Madeline is great at talking with her students about why perseverance is so important.
How are you helping your students build the perseverance needed to solve rigorous problems?