In the relatively recent past, people could make a living by performing mathematical procedures in their heads quickly and accurately. Math was taught to prepare them for this profession, emphasizing these procedures. With today’s technology, mental arithmetic is no longer a relevant professional skill. Today’s employers are hiring for skills such as creativity, collaboration and critical thinking, all of which students can learn in math classes emphasizing deeper learning.
In neuroscientific terms, deeper learning is intentional schema-building. A schema is a cognitive framework that helps us organize and interpret information. Students’ brains build new schemas when they make rich connections between ideas in their heads. The schema they build then helps them solve problems they haven’t seen before, which, to me, is the whole point of math. This sort of deeper learning is not only a powerful way to teach math; it’s an effective method of inspiring lifelong learners capable of making meaningful contributions to society. It begins with a clear understanding of how the brain stores information.
Building a web, not a card catalog
Many people assume that our brains function like card catalogs: We learn a series of disconnected facts, and our brains file them away to access them when needed. Neuroscientists have come to understand that this is not how the brain stores information most efficiently. The brain works best when it makes connections between concepts, building a web of ideas.
Math educators can facilitate this process by engaging students with the big ideas and then the slightly smaller ones. For example, when teaching fractions, first give students a chance to grapple with manipulatives to answer a question like, “When can a half be bigger than a whole?” (Half an extra-large pizza is more than the whole of a small pizza, so the big idea is fractions only make sense when you know what the “one” is). Teachers can later give time to the smaller ideas, such as “One-third is equivalent to two-sixths.”
When students use these ideas to build a schema, apply it to an unfamiliar problem and find a solution, they experience an ah-ha moment when their brain gets a dopamine surge. In that moment, math is fun.
Making math fun
Emotions impact how strongly the brain makes connections. If students have math anxiety that creates a negative emotional response to being in math class, their amygdala will release hormones that make their brain less effective. Rather than focusing on the math problem, their brain will focus on the issue of “How soon can I get out of this class?”
One way to counteract math anxiety is to create a classroom environment that encourages productive failure. Students need immediate feedback on their thinking that is delivered without any sense of judgment. A game-based or puzzle-based learning environment can be extremely helpful in this regard. In this case, the feedback on the student’s ideas is not coming from the teacher or any person but from the game. This can reduce the level of emotional anxiety students feel when trying out solutions about which they may be very uncertain.
The reward is intrinsic because teaming up with classmates to solve problems is fun. It’s not doing math and then playing games as a reward. It’s having the math discourse be so exciting, and the game be so engaging that there’s no delay between the flash of understanding students get when they figure something out and the emotional reaction created by the release of chemicals in the brain. For this to happen, the brain requires immediate feedback.
Providing immediate formative feedback
One of the key mechanisms that all mammals have is the perception-action cycle. It’s a survival technique that helps us build schema. For example, an animal that gets food from a location at a certain time of day will return to that location at around the same time every day, expecting to eat. If food continues to be at that location, the animal will keep returning, having built an increasingly strong schema about time, location and the likelihood of being able to eat. Our brain uses these very natural learning mechanisms to build a picture of how to interact with the world around us.
Formative feedback is an immediate response that contains information that can help the brain refine its schema. In basketball, for example, there’s a difference between missing a shot by a lot and missing by a little. You can find your range by continuing to shoot, but a coach sitting there saying only, “No, that missed,” every time you miss is useless. If the coach immediately says, “More arc!” or “Bend your knees,” those inputs become part of the process right away. This sort of immediate feedback is what makes virtual manipulatives powerful learning tools. One of the puzzles in the neuroscience-based instructional program ST Math challenges students to stack blocks to help JiJi the penguin cross a gully. If they see that JiJi is too low, they know right away to add a block, and if JiJi is too high, they need to take one away.
The resolution of the perception-action cycle is that the schema is held in the hippocampus, which compares the prediction and the reality. If the prediction and reality match, the brain releases chemicals that physically strengthen the connection that made that prediction, so that schema becomes physically stronger. If the schema is incorrect, it becomes less connected and weaker.
This cycle explains why empowering students to discover leads to deeper learning than just telling them how to perform procedures. Suppose a student has a misconception about something and finds that it does not solve the problem they’re trying to solve. In that case, that schema — their misconception in this case — will become weaker and eventually be replaced by a stronger schema.
Learning is the growth of wiring in our brains. Educational programs designed to work this way are effective and fun because they complement how our brains learn. They’re enjoyable because they ignite students’ intrinsic love of learning: They’re mastering the content, but they’re also learning that solving problems is exciting, a mindset that will serve them well throughout their lives and careers.
Opinions expressed by SmartBrief contributors are their own.
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