The importance of productive failure, instant feedback, and mastery education in mathematics education was discussed in 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 at Meriden Public Schools, and Daniel Tracy, Principal Solutions Strategist at ST Math, a math education tool created by the non-profit organization MIND Education.
Watch the full webinar video on demand here (opens in a new tab).
key takeaways
process over product
Crispino talked about how, a few years ago, the Meriden Public Schools in Connecticut began to rethink their approach to mathematics education to better understand how students thought and 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 change from when I learned when I was right or wrong,” Crispino said. “We really wanted to emphasize that process over the product, because we knew that if we improved our processes, our product would eventually improve, so that was really our focus.”
These strategies have helped Meriden Public Schools increase math scores amid declines nationwide.
Instant feedback and degree of error
Tracy said an important part of processes like the one at Meriden Public Schools is providing students with instant feedback showing their degree of error. She likened this to a game of basketball in which simply missing a shot isn’t the same as an air ball: Traditional math lessons don’t do a good job of showing students when they’ve narrowly missed the correct answer.
“The only difference between fighting and productive fighting is the story the student tells himself,” Tracy said. “Do you think you can do it? And the way that she can make a child believe that he can do it is if she sees ‘Oh, I just kind of missed it’. I almost made it.’”
Instant feedback in math education, like basketball, is important. “The faster we can get feedback, the more accurate the feedback will be, the more it will show the degree of error, the more likely the student is to continue and persevere, and the learning takes place at a much faster rate,” Tracy said. .
Dominance and differentiation
Mastery and differentiation are also key. Math instruction at Meriden is student-led and students have time to work on key concepts until they are mastered. “If they are struggling with something that was previously taught, they will always have additional opportunities throughout the year,” Crispino said. “Students never just move on to something else when they haven’t grasped something previously.”
ST Math (opens in a new tab) it is based on reshaping students’ understanding of success and failure in education. “The idea is if we can reduce the cost of failure to where the student perceives mastery as most important, and it doesn’t matter how long it took them to master it, as long as they master it,” Tracy said.
See into students’ minds as they learn math
Another key component of the ST Math and Meriden Public Schools math education process is understanding how students approach their work on each math problem. “Instead of asking how do you teach math, which is an adult-focused question, what we’re asking is, ‘How do you learn math and does that really give you a tremendously different outcome?’” Tracy said. “So our focus is how you learn and then apply that information to deep mathematical ideas.”
Crispino said educators have put these ideas into practice at Meriden in a variety of ways. For example, students will work in groups and then discuss how they arrived at the solution to a math problem. “You can start comparing how the students solved [a problem]which is great because there are so many different ways to come up with an answer,” Crispino said.
Crispino has several ways of knowing if a math class is going well. “I want to see students collaborating, I want to see evidence [scrap] paper. I want to see people solving hard math problems, and not just give up,” she said.
In Meriden, this process is underway, he said. “We started to see it in front of our eyes, which is pretty powerful.”
