1. Engage intrinsic motivation
Intrinsic motivation is a powerful force for learning. People are most often intrinsically motivated when they have control over what they’re learning and have a sense of competence while engaging in the learning. The activity isn’t too hard or too easy; it’s just the right amount of challenging to keep the mind engaged.
“If you do a task when you have intrinsic motivation it significantly increases your performance and what you learn,” Salimpoor said. Because the activity itself is highly engaging to the learner, he pays more attention and the brain records the information better. “Any time there is more dopamine flowing in your reward systems, you are much more likely to consolidate the information better,” Salimpoor said.
She has found the easiest way to recreate that sense of “flow” with her children is to infuse math into activities they already love. For examples, her son loves Legos, so in addition to letting him build whatever he wants, she sometimes encourages him to make blueprints of what he’s planning to build. She asks him to predict how many blocks he’ll need and to think about scale, perimeter and area. She’s essentially infusing spatial awareness into an activity he’s already excited to do.
“This only works for people who are big fans of Lego. That’s sort of the whole point of this,” Salimpoor said.
Another example might work for kids who are passionate about Minecraft. With just a few small tweaks like planning what to build ahead of time, playing Minecraft can be mathematical. And Salimpoor said practicing a little math every day is all it takes to keep skills sharp.
2. Engage emotional arousal
Emotion is an incredibly powerful part of learning that can easily get overlooked. “We can do a boring task over and over and not remember it, but you can experience an emotional moment once and remember it forever,” Salimpoor said. Emotion centers are tightly tied to memory centers, so when possible try to build emotion into summer activities.
It can be relatively simple to do. Even a project like building a kite together involves some climactic moments of heightened suspense that will be memorable. Making a stellar kite will require research, planning, measuring, sketches and probably some trial and error. The first time the child throws the kite in the air to see if it flies will be an emotional moment filled with suspense. And it’s more than likely the design will require more tinkering, and hence more math.
“The whole idea here is you’re thinking about it and revising your strategy,” Salimpoor said.
It could take all summer to build the perfect kite, but along the way will be several climactic moments, along with more learning, revising and planning. The math is embedded in a fun activity that has an emotional payoff.
3. Use extrinsic rewards wisely
Using extrinsic rewards to get kids to do things is a controversial, though common, practice. Some research indicates that when kids are rewarded for doing things they already like, they lose interest in the activity. That’s one reason some experts don’t recommend rewards for reading -- it implies that reading is work, not fun, and must be rewarded.
However, Salimpoor points out that there are some parts of math that just aren’t as fun as others. Practice is an important part of math and is perhaps the best candidate for gamification and careful use of extrinsic rewards. This is where understanding how the brain responds to different reward schedules is important.
“Knowing that a desirable reward is coming, but not knowing when it will come or what it will be is the highest output,” Salimpoor said.
She compares this kind of reward to the dopamine rush adults experience when playing the slot machines. The player knows it’s possible to win, but has no idea whether the win will come on the first try or 100th try. And, the size of the reward is also unknown. That makes winning even sweeter.
“Releasing dopamine is really good because it makes you want to continue and has the double effect of helping you consolidate the information,” Salimpoor said. “Knowing what situations are likely to release dopamine might be all you need” to make a dull task more exciting.
She has found that if she can build excitement and unpredictability into an activity, it creates a fertile ground for learning. She might reward her kids with tokens that can be exchanged for something they want after they’ve completed some number of problems or tasks. But the key, she says, is to vary when she gives them out and how many. It may seem counterintuitive, but this variability actually makes kids want to continue because they don’t know how much they’ll get.
Salimpoor said often parents try to be consistent with extrinsic rewards because that’s what they’ve learned works for moderating a child’s behavior. But the opposite is true with learning; variability primes the brain.
Salimpoor emphasizes that extrinsic rewards should be used sparingly and only for the kinds of tasks kids don’t really want to do. Gamifying them makes it more fun, and thus more memorable.
4. Engage the brain's predictive power
Part of being human is making predictions based on the schema we hold in our brains. And when the prediction leads to an exciting result the brain releases dopamine, which helps cement learning. Parents can harness this tendency by encouraging kids to predict things that have some significance to them.
Salimpoor says these strategies work well with things that regularly update and that a child can check daily. A parent might give the child a hundred imaginary dollars to buy stocks, for example. It takes some calculating and watching patterns to pick investments, and then together parent and child can check the stock prices every day.
“The idea is you’re getting excited to check this every day,” Salimpoor said. “You want to do the math to see how much you won or lost. And because you’re thinking about it every day, you’re calculating percentages and decimals.”
Maybe parents even give kids the interest on their stocks in real money, once they’ve calculated it. Another, less financially focused option, is to do the same thing with sports statistics -- updating and calculating averages and percentages.
5. Provide a larger goal
Stories and books inherently come with the bigger picture of a narrative, making them attractive to many kinds of learners. Often math isn’t taught with that bigger goal is mind, but it could be.
“Take math and make it more like reading a storybook,” Salimpoor said. She does projects with her sons that have a beginning, middle and end. Kitchen projects are often good for this type of longer-term project. For example, she and her sons did an experiment where they left different kinds of fruit in the sun and weighed them each day to calculate the water loss.
“It’s also great for the brain because you’re starting out by planning a framework of what you want to do, and how you’re going to do it, and that establishes a storyboard in your head,” Salimpoor said. Then every day of the project, the child has to review the information learned and add more to it. “This is the best method of learning because you're taking synapses that you’ve already formed and strengthening them.”
She even had her sons graph the fruit’s water loss as another way of adding math to this project. Another time they set up an experiment to see which kitchen containers preserved food the best. Each day they checked for mold, graphing the percentage of mold each day.
“It’s kind of fun to see and you look forward to seeing it because you want to see how your experiment has changed on a daily basis.”
6. Use math as a secondary element of a project
There are tons of ways to involve math in a project where the main purpose isn't mathematical, like baking. The point is the cookies (obviously), but it doesn’t hurt to figure out the fractions and ratios together along the way. This method has the added advantage of taking math anxiety -- a real phenomenon for many kids -- out of the picture.
“The reason this is my favorite is it helps you realize how math applies in the real world,” Salimpoor said. She has watched her sons begin to notice math throughout their lives and become more interested in it.
Other ideas Salimpoor has tried in order to infuse math into other activities :
- Make a spectrum of color using different ratios of color dyes and water.
- Calculate density with different solutions of water, sugar and dye. Try to get different densities for different colors.
- Calculate a summer budget. Have kids think about how much money they’ll need for summer expenses daily, weekly and monthly.
- When driving somewhere, ask kids to calculate the best route based on gas consumption, distance and time.
7. Use visual-spatial tasks
One of the difficult things about math is that it requires the ability to manipulate abstract concepts in one’s mind. Adults have established pathways for this type of abstract thinking built up over time, so it’s easy to forget how complicated that is for someone learning a math concept for the first time.
“For someone just learning these, it’s very important to take abstract ideas and connect them to visual or spatial concepts,” Salimpoor said. “The more we can do this the stronger the foundations will become.”
That’s one reason early elementary classrooms are filled with math manipulatives. Salimpoor says this is crucial, especially when kids are young, because it helps develop a more complete neural network connected to different senses. The abstract becomes concrete when it’s connected to experiences kids can see and touch.
“If all the systems link together to form a concept, that’s a great situation to be in because activating any part of this system activates the rest of the system as well,” Salimpoor said.
Once again Legos are a great toy to make abstract math concepts concrete. Salimpoor has also tried geometric bubble makers, encouraging her kids to play around with different shapes to see what kind of bubbles they make.
She has also had a lot of fun playing with music and math -- filling cups with different ratios of water, banging on them and talking about patterns in the sounds.
“Give them the activity to play around with,” she said. It’s tempting to tell kids how the ratios relate to sounds, or how different wand shapes affect bubbles, but kids will learn more if they discover it on their own.
8. Consider the cognitive load
Cognitive load refers to the amount of information one can keep in one’s head, manipulate and process at any given time. It’s often related to working memory, and is easy to overtax and is often overlooked. Sometimes kids experience math anxiety because they don’t have good working memory, not because they don’t understand the concepts.
“There’s a large difference in children's working memory even if they’re the same age,” Salimpoor said. “If their working memory is overloaded they can’t process new information as well.”
Taking detailed notes or using manipulatives are ways to free up working memory as a child is learning something new. Parents can spot cognitive overload if a child was engaged, but suddenly starts staring blankly. It’s also helpful to make new concepts as concrete as possible so they doesn’t require so much working memory.
Neuroscientists are still trying to understand working memory better. There’s consensus that it’s very difficult to generalize working memory, but why and how to improve it is less well understood. If the goal is to improve working memory on math tasks, the practice has to be on math tasks. Doing “brain games” will improve working memory only on those specific tasks, not all tasks.
“All of these things are very established things about how the brain works in humans and animals,” Salimpoor said.