As the current school year draws to a close, planning for the upcoming 2012-2013 school year has already begun. New texts have been received, new curriculum maps have been designed, and the full implementation of the Common Core standards is on the horizon. One thing I am noticing is the focus on content (isn’t this always the case?) rather than on practice. The Standards for Mathematical Practice are so important to understand. They supply the answer to “how”, rather than “what”. So, over the next several weeks, I’d like to explore what each of these practice standards really mean.
Make sense of problems and persevere in solving them.
The first of the practice standards is the reason why we learn mathematics in the first place. It is a tool used to solve problems. And not all problems are so easy to solve, which is why perseverance is so important. How many times have your students said things like “I looked at the problem (for 5 seconds, maybe) and don’t know how to do it”? These students lack the ability to persevere in solving problems. It’s usually not their fault. They are probably accustomed to being “taught” how to solve a few standard types of problems in a rote manner. Anything that is slightly different, they can’t do because they haven’t been taught.
Bill McCallum, one of the lead authors of the Math Standards, has created a wonderful diagram (which can be seen at Common Core Tools and is reproduced below) relating the 8 standards and putting them into context.
As you can see, making sense of problems is an over-arching theme (along with precision), providing a reason to develop the other practices and habits of mind.
Children are born with the inherent ability to solve problems through perseverance. All babies have the problem of hunger. They will persevere in their quest to solve the problem through prolonged crying, not stopping until their problem is solved. Older children will be trying to solve the walking problem. Over and over, they will struggle until they get it right. A desirable object placed out of reach will have a child devising all sorts of methods to get what they want.
As educators, it is our responsibility to nurture this innate ability, helping children to learn to use it in more sophisticated ways. Very often, instructions in a traditional classroom of “sit still”, “be quiet”, and “don’t touch” end of destroying the very abilities we are trying to engage. Directing and enhancing those abilities, so that children can use them in more mature and effective ways, is part of our role as teachers.
Many teachers take to opportunity during the summer to invest some time in professional development. A particularly wonderful resource is the Annenberg Learner website, found at www.learner.org. If you are not familiar with this site, I highly recommend that you spend some time exploring all that it has to offer. Of specific interest here is an exploration of what good problem solving looks and sounds like in the K-2 classroom.
An excellent video by Phil Daro about problem solving in the classroom you can watch below!
Finally, anything by NCTM is bound to be amazing. Below are links to some of my favorite student activities related to problem solving, but feel free to investigate all of them:
Until next time-