Learning By Doing: The Neurology of Math

“Schemas are context-sensitive connections that help us understand,” said Matthew Peterson, Chief Scientist and co-founder of MIND Research Institute at a recent Neuroscience Symposium.  “Experiences that build and apply these connections are called learning.”
“You have to do stuff, you can’t learn passively,” said Dr. Peterson who led an audience of superintendents through a series of hands on learning challenges including building a life-sized brain replica from a bag of goodies.
Mathematics is more than a set of rules; it is more than a language; it is a system for understanding the world around us.  “Schemas have to be built, you’re not born with them,” said Peterson.  Schemas, or mental models, take lots of practice and feedback to develop.  Children (and adults) learn by creating and testing hypotheses.
Feedback from these trials is added to how we understand parts of the world.
Peterson created a sequence of experiences where symposium participants encountered word puzzles and didn’t have a schema for interpreting them or, in other cases, attempted to apply a wrong schema.  Participants learned a new language for interpreting and communicating human movement.  Like learning Braille, the language of choreography was a schema few had considered.
The empathy moment—where panic and confusion cut a path to long-term memory—three hours into the session was when Peterson noted “those feelings of confusion are common for learners new to a subject.”  When students learn math they experience the same panic and confusion from struggling to develop a new schema or applying a wrong schema.
It’s not that confusion is bad.  In fact, confusion is a good sign that a learner has developed and applied a schema—they just didn’t get the expected result.  It’s this process of testing and revising understanding that promotes critical thinking, the ability to generalize, and sound mental models.
Peterson designed ST Math as a sequence of challenging games that require students to develop and test hypotheses.  The games are linked in a way that promotes the ability to learn by doing and generalize from a developing schema.
Last year MIND Research Institute, an Orange County nonprofit, introduced ST Math for iPad.  They redeveloped over 800 games for the touch screens.  The change took time but it wasn’t a stretch because the intuitive challenges are a natural on the touch screen.  “It’s like touch finally caught up with us,” said Andrew Coulson, president of the Education Division at MIND.
ST Math uses a simple premise—move JiJi the penguin across the screen. The challenges get increasingly difficult as students build their understanding of how math works.
With a couple of 45-minute sessions a week, it produces great results.  In over 1700 schools serving a half a million students, ST Math consistently boosts the percentage of students achieving math proficiency.
ST Math is a supplemental approach to K-8 math, but the MIND Research team is hard at work at a revolutionary core algebra product.
“We can get all students to generalize.” said Peterson.  He thinks there is a good chance to engineer pathways that dramatically increase the percentage of students proficient in math—and do it in this decade.
He also believes the concept of “schema is important to Common Core State Standards,” noting their insistence on fewer concepts and deeper learning.   Peterson is taking his deep appreciation for how children learn to the challenge of preparing more students to be college and career ready.
For more on Peterson and ST Math, see this Psychology Today profile.
If you want to do some schema skimming, here are a few references:

  • Anderson, Richard C. 1984. “Role of the Reader’s Schema in Comprehension, Learning, and Memory.” In Learning to Read in American Schools: Basal Readers and Content Texts, ed. Richard C. Anderson, Jean Osborn, and Robert J. Tierney. Hillsdale, NJ: Erlbaum.
  • Brewer, William F. 1987. ”Schemas Versus Mental Models in Human Memory.” In Modeling Cognition, ed. Peter Morris. Chichester, Eng.: Wiley.
  • Brewer, William F. 2000. ”Bartlett’s Concept of the Schema and Its Impact on Theories of Knowledge Representation in Contemporary Cognitive Psychology.” In Bartlett, Culture and Cognition, ed. Akiko Saito. Hove, Eng.: Psychology Press.

Tom Vander Ark

Tom Vander Ark is the CEO of Getting Smart. He has written or co-authored more than 50 books and papers including Getting Smart, Smart Cities, Smart Parents, Better Together, The Power of Place and Difference Making. He served as a public school superintendent and the first Executive Director of Education for the Bill & Melinda Gates Foundation.

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1 Comment

Jim Sporleder

My comment is more of a question, and very interested in hearing feedback from Mr. Vander Ark. The Adverse Chilhood Experiences....ACE Study, shows that trauma and toxic stress has a serious impact on Brian development. The ACE research will say that the brain developing under such intense stress of the home environment, that the brain is hard wired differently. Therefore some student's brain won't be able to process abstract concepts. I have seen evidence of students struggle in math such as Alg and Geometry. Wa state is going to deny HS diplomas to students not passing state math exam or Collection of Evidennce. These are students that have completed all state course requirements, will have all their credits, and will have passes 2/3 state standards. My question, is this a fair assessment to force student into dropout? Does educational science agree with ACE research on the impact stress has on the brain and the inability to understand abstract concepts?


Tom Vander Ark

Hi Jim, can't answer your specific question but checking with folks that can.

Tom Vander Ark

Dr. Pamela Cantor said, "Schemas take lots of practice and feedback to develop”, think learning to play the piano. This is not the education environment that the majority of our children, especially those growing up in concentrated poverty, experience. Such children, that need the opportunity to practice, experiment, take risks instead are relegated to states of passivity where rote memorization and quiet is more valued than the activities, conversations and problem solving they need to develop deep understanding of new concepts and use them." Turnaround (www.turnaroundusa.org) is dedicated to building such classrooms in high poverty schools by providing teachers with a specifically designed tool kit to create and manage classrooms that encourage cognitive growth.

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