Curiosity, Wonder, Creativity, and What if…?

If you’re here because of you attended a session about What if…? at a conference, and would like to go straight to the conversation, click here to jump to the comments and type away! If you got here by some other means, please read on and feel free to join in the conversation as well.

Engaging students in rich tasks engages students, allows for multiple strategies, and brings everyone to the problem-solving table. But, often, at the end of the lesson, students stop thinking about math. Math class is over, so why should they keep thinking about it? What if there was a way to keep students curious? to keep students wondering? to give them permission to be creative? and keep them thinking about mathematics?

There is… It’s What if…?

Below are some resources that can be used to help incorporate What if…? into your mathematics teaching routine. You can start with one of these rich tasks. I’ve listed some other great resources for these types of problems at the end of this post.

After students have solved a rich task, we ask students to think about the problem they just solved and about what they’re still curious about. This might fall into one of three categories:

  • A change in the context of the original problem
  • A challenge of an assumption in the original problem
  • A new idea/alternate possibility added to the original

Students should only focus on one of these categories, initially. Trying to think in multiple directions will make this a frustrating experience, rather than a creative one. Most students tend to focus on adding a new idea/alternate possibility to the original problem or change one part of the context. Below you will find some structures to use to support students as they begin to think in terms of What if…?

Helpful tips:

  • Provide students with time to think privately about one of the questions in the template.
  • Provide students with time to talk with a partner/group about their What if…? ideas.
  • When it’s time to share as a class, be patient. It may take a minute to get sharing started – especially if this is the first experience with What if…?

Other resources for rich tasks:

Share your experiences, questions, and comments about using What if…?. Keep the conversation going.

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