This then caused me to reflect, which I will ask you to do as well, on the question "How often do I sit down and work on mathematical problems outside my own classroom?"
When I first asked this question, I sadly had to respond with "rarely or never". At the time, I would ask my students to try multiple questions daily, learn new ideas, consolidate older information and ultimately be problem solvers around questions they have never seen before; sadly I modeled none of this outside the walls of my classroom.
Perseverance, resiliency, creativity, and critical thinking is what I expected of my students on a daily basis around mathematics, but until I embraced these practices in my own life I didn't actually know what if felt like to be stuck in a problem without knowing what to do.
"What do you do when you don't know what to do in a math problem?" I asked this question to 800 Grade 4 - 12 students and the number one answer (by over 80% of the respondents) was "ask the teacher". This was startling!! I couldn't arm my students with authentic problem solving strategies until I actually put myself in their shoes. Once I tried working on problems that caused me to stop and ask "what should I do now?", I was able to understand that global problem solving strategies was missing in my own math classes.
Originally, I would teach "When working on a problem from unit X, try these strategies. On unit Y, try these.." and so on. The issue is that I wasn't teaching true problem solving but instead strategies specific to certain domains. After trying math on my own time, and at my own level, I quickly learned that some of the best strategies include, but not limited to, are:
- Visualize the problem; draw it out.
- Guess and check; change guess slightly and see how it changes the result.
- Approach it logically; Use "if then" statements to simplify information.
- Identify a pattern; change a number, a sign, or something critical and see how it changes the problem.
- Work backwards; if we can hypothesize the result, what else would have to be true?
- Solve an easier problem; simplify the problem into one that is easier to work with and see if you can identify anything new.
My challenge for myself now, and I am extending it you as well, is to try a math problem once a week. Ensure the problem isn't one that you can solve in seconds, or even minutes. Try and find one that makes you reflect on "What do you do when you don't know what to do in a math problem?"