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Risk vs. Reward in the Math Classroom

Posted by Chris Brida

Feb 16, 2015 7:00:00 AM


Coming from a business background, I tend to view the teaching practice very similar to that of operating a business. In the business world, particularly in that of finance (shout out to all my college roommates!), there is a constant evaluation of risk versus reward. As it goes, the higher the risk, the greater the chance of reward. Investing in mutual funds is a low risk, low reward proposition. Betting on individual stocks is a bit more high risk, high reward—the payouts are potentially greater. So where am I going with all of this? A similar proposition is going on with my students on a daily basis, but they are nervous about taking the risk in order to receive the potential payout of becoming more mathematically literate.

Risk Develops Independent Thinking

A student of mine told me the other day, “it (insert any math skill) is so much easier when you are here to help me with finding the answer.” On face value, of course that makes sense.

The support that I provide my students is something that I view as being beneficial—it is my job after all. But thinking about the risk versus reward argument, my unyielding support for my students is a low risk proposition for them—that is, if they never take the risk of being wrong, and failing, they also might never take the risk of learning in a way that will allow them to continue learning when they leave the classroom, which would be an incredible return on their investment of time as compared to only learning when I’m there to help—and as a result, they may not be receiving the full reward in my class.

Going back to that student I mentioned above, what is she gaining by me helping her? Well first, my help does clear up potential misconceptions that she may be having about a particular skill, but again, I think that is a face-value view. Her risk in the situation is low because she doesn’t have to worry about being wrong if I am going to help walk her through the problem. The problem is that there is no reward for her, or for me here. I don’t know whether or not she actually understands the problem on her own, and I am limiting her potential for growth. The brain, and more importantly knowledge, is a malleable thing. Intelligence is not fixed and is something that can be developed over time. But this development of intelligence is only created through those high-risk situations, when a student tries to answer a problem on their own—tries to think on their own, which is one of the ultimate goals of education—risking failure but also taking important steps toward being an independent thinker. Teaching in a low-income, urban school district is inherently difficult. It is made exponentially more difficult when you factor in very differing middle school experiences for many of my students. I liken it to a starting line and finish line situation (that’s my track and field background). While everyone has the same finish line (a certain grade, the state exam, etc), many of my students have a head start and many of them start way behind the starting line, making reaching the finishing line that much more difficult. While my responsibility as a teacher is to provide as much support to my students as possible, I am also doing them a disservice if I don’t push them to learn on their own.

Create Persistent Learners

Going back to my original situation, let’s say I let my student struggle on her own to try and come up with a solution. Maybe she wouldn’t have answered the question correctly, but is the only value in mathematics in getting the answer right or wrong?—All math teachers say it with me: NO WAY! Math is truly about process An important concept in education today is the growth mindset. The idea behind this type of learning is that intelligence is something that can constantly evolve. Students should focus on improvement through applied effort rather than worrying about how smart they are. Students who focus on the growth mindset are students that are hardworking, reflective, and persistent learners. They are the type of students who see the value of taking high risks, which end up leading to high rewards, especially in the math classroom.  

Frame "Failure" as a Learning Opportunityand understanding the equifinality (i.e., there is more than one way to get to the finish line) of process. The value of this student answering incorrectly if she applies the right process of approaching the problem through careful thought and work is vastly greater than me assisting her in getting to the right answer. 

As I mentioned, students that see value in the growth mindset are also students who are willing to take risks. Many of my students are unwilling to take risks in class because they have been programmed to think that there is a right answer and a wrong answer, and only one of those is acceptable. As Stanford psychologist Carol Dweck summarizes in her book about this type of mindset, a growth mindset accepts challenges and sees risk as having the ability to create great reward. Failure is not considered to be a sign of unintelligence, but instead, should be seen as a starting point for growth and for building upon existing skills. If all students were to have this kind of mindset, the potential for growth in the math classroom—in any classroom!—would be unlimited. If my students were able to see wrong answers as a positive rather than a negative, imagine the growth in each of those students individually. Instead of moving my students to the starting line, I’d be able to change the length of the race, change the finish line for each one of my students. 

Cultivate a Growth Mindset

In my business mind, there is so much potential to be tapped in each of my students. It is my responsibility as the manager of their class to enable this growth mindset in each one of them. While this type of change takes time, the true value will be realized later down the educational road. But how do I encourage my students to take the “growth mindset” approach to learning? For starters, by creating an environment in my classroom where risk-taking is rewarded, and where wrong answers are nearly as important as right process—that is, as trying hard to think your way through a problem, even if you end up getting an incorrect answer at the end of all that hard work. If I can get my students to see the value of taking calculated risks in the classroom now, the potential for reward in mine, and future classes, is so great!

Chris Brida teaches mathematics in Baltimore. He'll be blogging for us throughout the spring semester, so stay tuned for more!


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