The importance of productive failure, instant feedback, and mastery education in math education was discussed at a recent Tech & Learning webinar.
The talk was hosted by Dr. Kecia ray and featured a lively discussion with Daniel Crispino, director of school leadership in Meriden Public Schools, and Daniel Tracy, senior solutions strategist at ST Math, a math education tool created by the nonprofit MIND Education.
Watch the full video of the webinar on-demand here.
Process Over Product
Crispino talked about how a few years ago Meriden Public Schools in Connecticut began rethinking its approach to math education to better understand how students were thinking and to encourage their productive struggle.
The district focused on encouraging students to take risks, accept some setbacks, and still gain confidence and demonstrate perseverance. “This is a shift from when I learned when it was right, or it was wrong,” Crispino said. “We really wanted to emphasize that process over product, because we knew if we improved our processes, then our product eventually would improve, so that was really our focus.”
These strategies have helped Meriden Public Schools increase math scores amid nationwide declines.
Instantaneous Feedback and Degree of Error
Tracy said an important part of processes such as Meriden Public Schools went through is providing students with instant feedback that shows them their degree of error. He compared this to a game of basketball in which just missing a shot is not the same as an air ball -- traditional math lessons don’t do a good enough job of showing students when they just barely missed the correct answer.
“The only difference between struggle and productive struggle is the story that the student is telling themselves,” Tracy said. “Do they believe they can do it? And the way you can get a kid to believe they can do it is if they see ‘Oh, I only missed it by a little bit. I almost made it.’”
Instantaneous feedback in math education, like basketball, is important. “The faster we can have feedback, the more accurate the feedback, the more it displays the degree of error, the more likely the student is going to continue and persevere, and the learning takes place at a much more rapid pace,” Tracy said.
Mastery and Differentiation
Mastery and differentiation are also key. Math instruction in Meriden is student-driven and students have time to work on key concepts until these are mastered. “If they are struggling on something that was previously taught, they're always going to have additional opportunities throughout the year,” Crispino said. “Students are never just moving on to something else when they haven't grasped something previously.”
ST Math is built around reshaping students’ understanding of success and failure in education. “The idea is can we lower the cost of failure to where the student perceives mastery as the most important thing, and it doesn't matter how long it took you to master it, as long as you mastered it,” Tracy said.
Seeing Into Students' Minds as They Learn Math
Another key component of ST Math and Meriden Public Schools’ math education process is understanding how students are approaching their work on each math problem. “Instead of asking how you teach math, which is an adult-focused question, what we're asking is, 'How do you learn math and that actually gets you a wildly different outcome?'” Tracy said. “So our focus is how do you learn, and then apply that information to deep mathematical ideas.”
Crispino said educators have put these ideas into practice in Meriden in a variety of ways. For example, students will work in groups and then discuss how they arrived at a solution to a math problem. “You can start to compare how students solved [a problem], which is really cool because there's a lot of different ways to get to an answer,” Crispino said.
Crispino has multiple ways he can tell a math class is going well. “I want to see students collaborating, I want to see evidence [scrap] paper. I want to see people grinding through difficult math problems, and not just giving up," he said.
In Meriden, this process is well underway, he said. "We've started to see it actually in front of our eyes, which is pretty powerful.”