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Math is a discipline that is commonly associated with memorization, timed quizzes and silent classrooms full of students just trying to get the right answer. What if math class felt more like humanities or science? What if it felt more experiential like music or art?
Imagine a room full of children discovering, connecting, discussing, reasoning and collaborating as they use models and materials to draw out ideas that they construct themselves. This is the type of environment in which children see themselves as mathematicians. And when they do, they can believe in themselves and use math as a way to understand the world around them.
New research conducted at Stanford University, led by Jo Boaler, challenges our cultural assumptions about learning math with brain science. Her website, youcubed.org, offers a multitude of resources for students, schools and families.
The research reveals how we as adults can transform children's ideas and experiences of math through a positive growth mindset. These findings show that anyone's brain can grow, develop and change when provided with deep and meaningful experiences in a culture of growth mindset along with effective effort. Boaler cites Anders Ericcson’s groundbreaking study on the limits of people’s ability to memorize a random string of digits in her new book, Limitless (2019). Ericsson found that “deliberate practice” was key for those people who were able to continuously push past barriers. Boaler says, “When he hit what seemed like a limit, he developed new strategies to become successful… This approach illustrates a key takeaway-
when you hit a barrier, it is advantageous to develop a new approach and come at the problem from a new perspective.
Despite how logical this sounds, far too many of us fail to make adjustments in our thinking when we run into those barriers. We often decide, instead, that we cannot overcome them,” (Boaler, 2019) Integrating this research into mathematics education has profound effects on not only children’s beliefs and understanding of mathematical concepts, but it offers children a practical tool when they feel stuck by continuously asking themselves, “How else can I figure this out?”
Boaler calls to shift the cultural stigma of "math people" vs "non-math people" by celebrating the value of mistake making. Her research that in order for anyone to experience growth, one needs to be working on questions that are challenging- at the edge of understanding AND in an environment that encourages mistakes. In Limitless, Boaler cites author Daniel Coyle’s work on “talent hotbeds”, places that produce a larger proportion than normal of high achievers. Coyle found that high achievement had nothing to do with any type of natural born ability, but rather from a particular type of work and practice. This type of practice taps into a neurological mechanism in which myelin (a form of insulation that wraps around nerve fibers in the brain and increases their signal, strength, speed and accuracy) coats the neural pathways involved, and overtime that coating reinforces signals and slowly strengths pathways. Boaler says, “So how do we develop ‘super-duper-pathways’? This occurs when people are working at the edge of their understanding, making mistake after mistake in difficult circumstances, correcting mistakes, moving on and making more mistakes- constantly pushing themselves with difficult material,” (Boaler, 2019).
In early childhood math education, the emphasis on process is essential to children constructing a foundation for conceptual understanding. It is in this time that it is crucial for teachers and parents to welcome struggle. Quite sadly, in the most recently analyzed PISA (Program for International Student Ability) the United States ranked 38th out of the seventy-one countries participating. Curriculum was analyzed in various countries, and those in the top rank found that students spend much of their time inventing, thinking and struggling with underlying concepts, whereas students in the US engaged in this type of behavior less than 1 percent of the time. (p.53, Limitless)
As children are presented with mathematical problems, they must draw and build with mathematical materials and learn from their peers as they discuss what makes sense and why. Through this process, children learn to understand why strategies work and which strategies make sense to them. This work is crucial for young mathematicians to becoming a more autonomous learner, not just in math but in any area. Understanding oneself as a learner results in more effective problem solving and collaborative skills.
One of the most important things families can do to help their children, is to dispel the myth of a math person. Promoting the idea that anyone can learn anything, given the right opportunities and strategic practice, will help to alter how our society views mathematics. In addition, families should consider the following to support their children in making math fun and to increase achievement (Boaler):
Never share stories of math failure or dislike.
Research shows that when women in particular relay anxiety in math, their children are more likely to take on that anxiety. If you are helping with homework, be excited (even if you have to act!) to help and eager to hear how they are solving problems.
When you do help your children, do not lead them through problems step by step.
We give away how to break down the problem when we do that. Comprehending what is happening and learning how to prioritize what to do, in what order is a crucial component of learning.
Encourage drawing at all times.
When we do math, visual areas of the brain light up; creating a representation supports and makes sense of what we are trying to understand.
Encourage “making sense” rather than a rote set of procedures.
Ask, “What is the question asking?” or “How did you get your answer?” or “How could you draw this question?”
Encourage flexibility about numbers.
It is vital that students develop number sense which is developed by understanding the relationship of numbers.
written by Jessica Soodek
Jessica Soodek is a math educator, curriculum coordinator and math coach. She has taught children, trained teachers, and developed curriculum at many independent schools in New York City since 2007. She is a graduate of Columbia University, Klingenstein Center where she received a master’s degree in Independent School Leadership and earlier in her career completed a master’s degree at Hunter College in Literacy Education. She received Elementary and Special Education certification from New York State upon graduating from Hobart and William Smith as an undergraduate. Her mission is to flip the script on math education by empowering educators through research-based methodology to make math come alive for their students.
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