What do your students have in common with Michael Jordan and Thomas Edison? How can these two heroes provide inspiration for your math class? The answer involves an important talking point in mathematics education today: productive struggle.
Productive struggle may sound like an oxymoron, but in fact, it’s an important facet in learning mathematics. It involves allowing students to interact with a problem that is slightly beyond their current level of knowledge. Often, the problem can be presented as an introduction activity to a new lesson that connects prior knowledge to a new concept or approach.
Example: Using Productive Struggle to Discover Volume of a Cone
To illustrate, imagine you are a middle school math teacher about to introduce seventh grade students to the formula for the volume of a cone. Follow these steps:
- Place the students into small groups.
- Give each group a hollow cylinder and cone (with equal heights and base areas), a few rulers, and a bag of small, dried beans.
- Tell them to discover the formula themselves. (They just might surprise you!)
Of course, you will be there to provide guidance.
Students might need to be reminded that they have already learned how to find the volume of a cylinder, and maybe there is a relationship between a cylinder and a cone. You may have a group simply count beans to find the volume of each and that is fine, too! All the different methods and ideas can be discussed after students have had some time to “productively struggle” with this new concept. Then together, you and your students can develop the formula for the volume of a cone and discuss how it relates to the volume of a cylinder.
Teach the Power of Mistakes
Productive struggle is, in a sense, learning by making mistakes. Remind students that mistakes are OK; they are part of the learning process (and an important part at that!). Encourage students to view a mistake as an opportunity to grow rather than just something they got wrong. Tell them that the attitude they adopt can make or break their success.
Let them read what Michael Jordan and Thomas Edison had to say about their failures:
“I’ve missed more than 9000 shots in my career. I’ve lost almost 300 games. 26 times, I’ve been trusted to take the game winning shot and missed. I’ve failed over and over and over again in my life. And that is why I succeed.” –Michael Jordan (via GoodReads)
“Results? Why, man, I have gotten lots of results! If I find 10,000 ways something won’t work, I haven’t failed. I am not discouraged, because every wrong attempt discarded is often a step forward.” –Thomas Edison (via ThomasEdison.com)
Too often we look at those who have achieved success—like Michael Jordan, Thomas Edison, and many others—and neglect to remember the struggles that came before the victories. When your students have a victory, whether it be large or small (and yes, they WILL have one), celebrate! Reward them for perseverance in pursuing excellence, and your students will learn the value of productive struggle.