by Matthew Beyranavand, K-12 Mathematics and Science Coordinator, Chelmsford Public Schools:
Teachers are learning about the benefits of growth mindset based upon the great resources associated with the With Math I Can campaign. So, now, what are some ways to help make changes in the classroom? With Math I Can supporter Jo Boaler details her favorite messages in Setting up Positive Norms in Math Class. With what context could these norms be established? There are a quite a few examples from the history and development of mathematics to help students develop a growth mindset.
1. Mistakes Are Valuable
When mistakes are made in the classroom, there are two natural reactions: 1) Students become frustrated and their learning is inhibited; or 2) Students have the mindset that mistakes are common and can be valuable as opportunities for learning. If we look back to Ancient Greece, we learn that Pythagoras incorrectly believed that all numbers were rational and learned his mistake when fellow Pythagorean Hippasus discovered natural numbers, which includes irrational numbers. Unfortunately, Hippasus was not rewarded for finding Pythagoras’ mistake, but mistakes are part of being a good mathematician. Also, a French mathematician had made mistakes with probabilities in a game of dice and was not afraid to ask for help. So, he solicited fellow mathematician Pascal for the correct mathematics. Making mistakes, accepting that they will happen, and working on correcting them are all part of a growth mindset.
2. Math Is about Creativity and Making Sense
The mathematics done by the Egyptians, Babylonians, and Greeks were very creative and made perfect mathematical sense. They did not believe in creating any acronyms to do calculations. The Egyptian method for multiplying does not require any memorization and works with fractions. The Babylonians’ method for solving quadratic equations is the only true way to complete the square. The Greek mathematician began with only five postulates, and from that, he was eventually able to prove that there are exactly five regular polyhedral (after the 13th book of the Elements). To learn about ancient number systems and some of the challenges people had, the best activity that can be done with high school students is to replicate the work from this article. Using creative approaches also can increase students’ interest in learning mathematics.
3. Value Depth over Speed
There is a recent push in math education for speed in math, especially in elementary schools, and is causing anxiety in students. Also, if students cannot figure out a solution in 30 seconds, they often lack perseverance and feel defeated. Sometimes, it takes a long time to solve a problem. Sometimes, it can take 358 years. Mathematician Andrew Wiles spent seven years isolated in his successful attempt to solve Fermat’s last theorem. Students need to know that many of the famous mathematicians took extensive time to solve problems. This is not only acceptable, but it was also encouraged for them to take their time doing math.
The research developed is clear about helping our students have a growth mindset and not a fixed mindset. Now, teachers are finding ways to incorporate this philosophy into their classroom. Discussing the history and development of mathematical concepts, such as the literature review Integrating the History of Mathematics into the Classroom and the movie The Story of Math, with students is not only tied to growth mindset, but it also can help increase students’ interest in learning mathematics.
How are you helping your students to develop a growth mindset in math? For more growth mindset resources, visit WithMathICan.org.
Dr. Matthew Beyranevand is the K-12 Mathematics and Science Coordinator for the Chelmsford, Massachusetts Public Schools. Through his website, http://www.mathwithmatthew.com/ Matthew provides visitors with podcasts, music videos, educational resources, and a video blog. After years as a middle school classroom mathematics teacher, Matthew transitioned into the school administration. He is leading a department of over 80 middle and high school math and science teachers. As a graduate instructor at UMASS Lowell and Fitchburg State University of over thirty semesters of mathematics and education courses, Matthew has become an expert in the best-practice techniques for instructing both new and established teachers.
