Let Me Try it First
I remember this frustration in my grade school math classes. I wanted to explore the problem, have time to think about it, and make sense of it before I was told how to solve it. In fact, I still find myself preferring to learn anything new by first having some time to reconnoiter it myself.
And yet, skip forward to my time as a teacher. One of my greatest struggles was letting go of that control, allowing my students to explore solutions on their own, before I showed them how to do it. Giving students time to make sense of a problem is a new concept for many teachers, but doing so can be absolutely rewarding.
Here’s how it looks. A teacher introduces a problem. Rather than telling students how to solve it (and then giving them numerous worksheets to practice), she first steps back and allows them to try finding solutions on their own. They draw on past knowledge to create new connections and relationships as they explore a variety of approaches. The teacher begins a discussion that allows students to collaborate and share different ideas, often leading to more connections. Last, the teacher offers an approach or algorithm for solving the particular problem. Students discover the rich connections that can occur within mathematics rather than a boring set of repetitive procedures to follow.
When students explore a variety of ways to solve a new problem, it often leads them to further develop the understanding linked to the algorithm because they had a chance to explore the relationships between the problem and the solution. In her latest book, Mathematical Mindsets, Jo Boaler explains this method and its rich benefits. Students “stop thinking narrowly about single methods and consider mathematics more broadly,” and “they realize they have to use their own minds—thinking, sense making, and reasoning.” Students don’t just repeat the same method, but rather they start to think about applying an appropriate method, thereby making those resonant connections. This in turn motivates them to keep trying new problems and looking for new solutions. They feel a sense of affirmation as they discover that their methods are directly linked to the solutions. Mathematics is no longer a set of arbitrary repetitive methods, but rather a “subject full of rich connections.”
Ana Butler is a professional services coordinator for MLC.