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Skills vs. Schema: Teaching Math How the Brain Learns

The terms skills and schema can be interpreted as synonyms. However, when we look at the bigger picture of how our brains learn, we can better see the difference between these terms. Even more so when we look at them specifically in the context of learning mathematics.

For example, conventional teaching methods present math as a set of procedural components that, through continuous practice, will eventually lead to mastery. But what happens when a student comes across a problem that is unfamiliar to them? They might try to apply the same set of skills in this new situation, but if they don’t grasp the underlying concept of what the problem is asking them to do, the skills they’ve been taught quickly become irrelevant. 

Schemas, on the other hand, go much deeper. Instead of relying on a standard set of memorized steps, schemas give us the foresight to determine what skills to use and when. Think of schemas as a scaffold, blueprint, and representation that describes an object, a string of events, an idea, or really...anything. 

This blog post is designed to be interactive, so we encourage you to watch each video before moving on to the next section. In the first video below, MIND’s VP of Content Creation, Nigel Nisbet, will explain why building schema enables students to be more flexible in their thinking so they can solve increasingly complex problems. Then, you’ll have the opportunity to participate in the schema-building process by playing one of our latest games. And finally, Nigel will sum up the learning process that just took place in your brain. 


The Neuroscience of Deeper Learning

From a neuroscience perspective, conceptual learning requires building schemas. When developing a deep understanding of mathematical concepts, there are four neural subsystems that work together to enable this:

Perception-Action Schema Building: a continual cycle of perceiving or detecting something, taking an action and then observing the immediate effects of that action and adjusting the next action.

Experiential, Episodic Knowledge: knowledge that results from an experience that’s vividly memorable, both emotionally and physically.

Problem Solving and Creative Ideation: applying facts and concepts in new and novel situations, and across academic subject areas.

Academic Discourse and Language Processing: putting ideas into words, and being able to explain and justify the reasoning for those ideas.

Learning By Doing

Now, time for a bit of fun. Let’s see how quickly you can build your schema by solving a few ST Math puzzles. Click the link to try your hand at our Pattern Machine Puzzle. 

Pattern Machine Quadratic (New Games)

When you first arrived at the Pattern Machine puzzle, what did you think the puzzle was asking you to do? Perhaps you observed the number line and the quantities between each line segment, or maybe you noticed that there weren’t any instructions to give you a head start. In the next video, Nigel explains why the puzzle is designed this way and the resulting neurological activity taking place as you try to figure out the solution. 


Learning by doing is a key differentiator of the ST Math program. Instead of spoon-feeding students with a prescribed set of strategies, students develop their spatial-temporal reasoning through testing various hypotheses to get JiJi to cross the screen. ST Math aims to equip students to become problem solvers in non-routine situations through a process called productive struggle. So, the lack of instructions is intentional, as it encourages students to figure things out independently and learn from their mistakes.

The ST Math Difference

ST Math begins by teaching math visually and then gradually introduces traditional symbols and language as students master mathematical concepts. With visual learning, students are better equipped to tackle unfamiliar math problems, recognize patterns, and build conceptual understanding. When math is presented as a rich web of connected ideas instead of isolated skills, students will be able to access higher levels of thinking and tackle new challenges that come their way. 

Further Reading

Interested in learning more about our remarkable, schema-building tool? Try some of our latest games!

Play ST Math Games


Parker Erickson

About the Author

Parker is MIND's Content and Community Specialist.


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