Getting Kids to Organize and Record Their Math Thinking

Even though I teach gifted kids, I run into trouble getting kids to show their thinking as they work some of the demanding math tasks I set them. Notice I didn't say showing their work. I encourage mental math, so I don't need kids to write out their arithmetic, unless they're practicing a brand-new skill. Besides, that's not what these tasks are for.

It's not always easy to find problems that require these kids to stop and organize their thinking. I use problems from the Math Olympiad Contest Problems (Find it here.) to provide enough challenge to make my students stop and think about strategy. Monday through Thursday, one of the math centers is a challenge problem. The next day, we engage in a whole class Math Talk to look at answers and strategies. They drive my fourth graders (who are in the first year of the gifted program) nuts, particularly, because they're so focused on getting done and being first that accuracy can get kicked to the curb. It takes a while to learn that doing it twice is frustrating and relatively uncool and that taking time to organize their thinking before engaging in endless (and often inaccurate) guess-and-checking saves a bunch of time and trouble in the long run.  

Having gone through this process, my fifth graders have learned that stopping to look for patterns, math rules, and strategies is the way to go. They think the problems are fun and do a really good job with them. 

Students for both classes turn in a sheet on Friday with one of the week's problems documented. They are required to provide a visual representation along with the steps of their thinking and proof that they're correct. It looks like this:

Yep. It's pretty simple. My fifth graders are also pretty adept at choosing a visual representation that helps them organize their thinking. This is the anchor that's in the room:

So, in all, teaching kids to organize and record their math thinking takes:
1. Challenging problems. If the problems are too easy, the students have no real reason to bother with other representations and no authentic need to document their thinking.
2. Time. Time to work and wrestle with a challenging problem, time to discuss their ideas, and time to bump their butts and learn the hard way.
3. Opportunities to talk with the greater group about what they did and how they did it, which also gives them chances to see others' strategies.
4. Time. (See number 2.)
5. Knowing that at least one of the problems will be graded, but having some choice about which that is.
6. Consistency and, oh yeah, time.

I hope you'll find these tips useful! Don't forget to pin the anchor chart so you can make yourself one!