The first Common Core Standard for Mathematical Practice calls for students to “Make Sense of Problems and Persevere In Solving Them.” It should go without saying that the benefits of having students persevere in solving a problem are very obvious. Ideally you want to challenge your students with multi-step problems that require planning and problem solving. When you challenge them you want them to break through any walls they hit and make sure giving up is not an easy option.
Naturally we all want this of our students, but I know many teachers who are left scratching their heads saying, “How do I teach my students to persevere.” I completely understand where this thought comes from as most people would view perseverance as a personality trait that cannot be taught.
I would however argue that there are some practical things you can do to impart perseverance to your students. The first is a very simple idea that many of you may already be doing, but not realizing the power it has. Use personal dry-erase boards.
There are the standard boring white boards or there are the new clear boards that you can put in template sheets which are becoming all the rage. The only true common denominator that matters though is a surface that can handle dry-erase markers. I find that students are much more willing to try something again if they can easily and quickly erase and write with a marker.
The only drawback of using marker boards are the temporary nature of dry-erase. To combat this I sometimes have students write down a final working out of a problem so they can look back at it later. If you are in a very technologically hip class then you can take pictures of the boards with iPads or iPod Touches… or cameras.
A dry-erase board and marker does not guarantee perseverance, but it does give students less excuses.
Another very real, tangible way to show students how to persevere is to make sure they know various strategies to problem solve. I often find myself very confused that a student doesn’t think to draw a picture to help them think through a problem or make a table of values. There are basic problem solving strategies that if students are familiar with can give them another vantage point to see the problems from.
I would recommend at the beginning of the school year going through several problem solving strategies that can be used in a variety of problems (a list is farther down). After showing them how to use each strategy it might be a good idea to either create posters or have the students create posters of the strategy to display in your room.
In the future when a student gets stuck hitting a wall and is about to give up you can point to the posters on the wall and say, “which strategies have you tried?” “Where’s your picture or diagram?” This will hopefully give students a new lease to try something new and different. To possibly look at the problem from a different angle using a new strategy.
Some strategies I have seen are: draw a diagram, make a model, guess and check, work backward, find a pattern, make a table, solve a simpler problem, act it out, make an organized list. I’m sure this is not a conclusive list and you could argue that some of these are repeats (I would). So I am not advising you use all of them. Pick a solid 4-6 to create a problem solving foundation for your students and ensure that your students use them to help increase their stamina.
Have any other thoughts - I would love to hear them!