Have You Worked a Good Math Problem Lately?

My mathematics mentor, Dr. Dave Youngs, used to ask that very question. I think the question implied, was I a recreational mathematician?  Was I on a journey of playing with mathematics for life?  Yes, I am a lifelong mathematics learner.

When I am facilitating workshops, I ask classroom teachers if they do recreational mathematics or have mathematical conversations with their students. I am curious if they are asking students to provide mathematical evidence that shows an understanding of arithmetic facts. Given a chance, students can do this – through practice, conversations, and most importantly play.  Not unlike having students practice “sustained silent reading” (SSR), a classroom teacher should have his/her students practice recreational mathematics. The rewards for the students and the teacher will be worth it.

Math play will help students make sense of mathematics.  Through play students will rely on themselves more often to determine if something is mathematically correct, they will become better at reasoning mathematically, they will invent, make conjectures, and solve problems more readily.  Through play, students will naturally connect mathematical ideas and applications.

How does a teacher make sure that he/she is giving students quality recreational math problems? My favorite problems are those with multiple solutions, but whatever problem you choose to have your students work on, carefully consider your questioning. In my opinion, it all starts with the questioning that teachers use while debriefing recreational math problems. One of the goals of the Common Core Standards is that students become active learners and questioners. Modeling quality, open-ended questions allow students time to reflect and respond. Scaffolding your questions lead students to make new mathematical discoveries, real world connections, and to have constructive dialogue with their peers. There are countless resources on the subject of questioning. I encourage you to read some professional articles on the topic.  I like to use these questions when having students share their discoveries after working on recreational (good) math problems:

1. Can you explain how you found your answer?
2. Did you find more than one answer?
3. How can you represent the math in this problem?
4. Does your theory always work?
5. Did you find any patterns?

Here is a good math problem that you can have your students work on. Let me know how it goes. Tell me about the good math problems you are doing.