The phrase “new math” summons up laughs and groans from any parent trying to teach their kids math these days.
It’s a reference to the new procedures kids are being taught to solve math problems.
The math hasn’t changed — the way kids are expected to solve the problems has changed. It’s an attempt to teach kids various problem-solving skills.
But without first understanding the mathematical concept of, say, addition, the math steps kids learn don’t hold any meaning. Without contextual understanding, kids are unlikely to remember any set of steps.
Math concepts are the critical foundation for any lasting math mastery. But most parents who are homeschooling their kids are teaching math the way they were taught math. They’re focusing on math procedures - the steps you follow to solve a problem.
It’s not your fault if this is the way you’re teaching math. Math pedagogy is not easily improvised in the same way language arts are.
Homeschool parents like Anne are trying their best to teach themselves appropriate math teaching techniques. She relies on pedagogical books more than websites to help her structure math lessons and goals.
But Anne admits, “We’re not succeeding at reaching the academic goals I’ve set. It’s a slower pace than I’d like to see.”
She acknowledges that her own lack of confidence in math is likely impacting her math teaching.
“I never enjoyed math and found it confusing.”
Her 13-year-old son Will wants to pursue a career in science one day, and in light of that “I’d love to see him feel strong and confident in math,” says Anne.
Whether or not you had your own math anxiety as a kid, you’re likely feeling out of your depths trying to teach math to your kids.
But once you understand the paradigm shift this new math is attempting to achieve, it will help you reframe your own approach to teaching.
The good news is that focusing on mathematical thinking, rather than rote memorization, frees you from teaching many of the things you struggled with in math.
And playing games on computers or apps has shown to be a highly effective means of teaching mathematical thinking.
A 2014 interview with Keith Devlin in Forbes magazine should help you feel better about the challenges — and solutions — you face as a math teacher.
Devlin is a game and app teaching developer who has seen firsthand how his math games have dramatically improved kids’ math learning abilities.
He’s also the co-founder and executive director of Stanford University's Human Sciences and Technologies Advanced Research Institute — an “interdisciplinary research center focusing on people and information technology,” according to its website.
Devlin acknowledges that when we were kids, we were taught “standard procedures to solve well-defined problems that have unique right answers.”
But with the advent of technology came the ability to perform all those mathematics procedures faster and more accurately than humans.
“Suddenly, in a single generation, mastery of the procedural math skills that had ruled supreme for three thousand years has become largely irrelevant,” says Devlin.
That doesn’t mean that math itself is obsolete. It’s just that the mathematical skills we need to teach our kids are different from our own.
“It’s still the case that math gets you jobs, but the skill that is in great demand today — and will continue to grow — is the ability to take a novel problem, possibly not well-defined, and likely not having a single ‘right’ answer, and make progress on it, in some cases (but not all!) ‘solving’ it (whatever that turns out to mean).”
If that sounds vague and complicated to you, that’s entirely the point.
“The problems we need mathematics for today come in a messy, real-world context, and part of making progress is to figure out just what you need from that context,” explains Devlin.
It won’t be enough for your child to memorize their multiplication table or the Pythagorean theorem.
They need to understand how to apply mathematical concepts in various contexts in order to tackle the world’s undefined, complicated problems. They need to learn how to think mathematically.
So how do you teach your kids to think mathematically? That sounds a lot harder than just teaching them how to perform long division.
Parents like Anne who are relying on books and other resources need to consider the power of play as a teaching tool.
“The only way to acquire mathematical thinking ability is by a process of exploration – lots of trial-and-error and reflection. This is exactly what video games can deliver.
“They can provide small scale simulations of the kinds of open-ended, context-influenced, project-based, problem solving that is at such a premium in today’s world,” says Devlin.
He illustrates this point by using music as an example.
“Everyone knows that the best way to learn an instrument is to start playing it. We don’t ask someone to learn to read music before they sit at a piano or pick up a guitar. But that’s exactly what we do in mathematics.
“The reason we do is that through most of its history, mathematics did not have any instruments. Video games can provide math instruments you can use to learn mathematics.
And games aren’t just good at teaching math concepts, they’re also an excellent way to assess mathematical understanding, according to Devlin.
We don’t test people’s music ability by “instructing them in musical notation and testing how well they [can] write music using that notation. We ask them to sit down and play an instrument.
“Same with driving. Would you prefer to be driven by someone who had just passed the written part of the driving test, or would you want to know they had passed the road test?”
Devlin’s driving analogy is a great way to understand what we’re trying to teach our kids.
Like driving on the road, our kids will need to be able to use their math knowledge to improvise in real-world scenarios.
Games can serve as an excellent entry point to math concepts for learners of all skill levels and ages.
One reason why games are so effective is that “they tap into the way humans are hard-wired to learn: by doing.”
Anne has relied on Elephant Learning to teach her kids how to think mathematically through play. All three of her kids have mastered over two years of concepts after just five weeks of playtime.
The games ask Will, Lily, or Becca to manipulate animated characters to solve puzzles, like sorting pandas, or estimating how many butterflies are present or creating equal groups of blueberries.
The animated characters and difficulty of gameplay adjust to be age-appropriate for each player.
That means 13-year-old Will doesn’t feel like he’s playing baby games even though he’s using the same app as his sisters, 9-year-old Lily and 8-year-old Becca.
The app is designed to adjust the games based on your child’s existing math knowledge. While your child plays the games, the app assesses which concepts are fully understood and which need more reinforcement.
Concepts that do need more reinforcement are outlined for Anne, along with suggested games she can play in person with her kids.
This personal engagement between kids and a parent or teacher is a critical component of learning that Elephant Learning supports.
As Devlin notes, “People are social creatures,” and teaching kids well “requires close integration of the technologies with the human interactions.
“I think that people who see technology as a way to eliminate the need for good classroom teachers fundamentally misunderstand what it takes to help someone learn how to think a different way.
“Technology can help in significant ways. But it cannot replace a good teacher.”
Will, Lily, and Becca are averaging an hour’s worth of playtime on Elephant Learning each week, even though they only need 30 minutes of weekly playtime to achieve lasting math mastery.
Anne can supervise their app playtime to observe where they’re struggling, or she can focus on other tasks and review their progress later in the app’s progress reporting section.
She doesn’t have to stress over creating a math lesson from scratch anymore.
And with her family’s various medical expenses, the $35 a month fee is a sustainable option that covers all three of her kids for unlimited playtime.
For parents like Anne who see a blossoming scientist in their child, you should know that not all of the traditional math skills of the past need to be retired per se.
Rather, we need to re-prioritize math skills — placing more emphasis on creative problem-solving as the starting point for learning new math concepts.
Devlin captures this final point well:
“No one, least of all me, is saying we should abandon the traditional symbolic representation for mathematics.” That means learning what the division symbol or fraction symbol means.
“You need to master that language if you want to go on to a career in science or engineering, and many other careers as well.
“What I do say, based on a lot of hard evidence, is that… we should not make the symbolic representation [of math] the entry pathway into mathematics. It disenfranchises too many otherwise able people.
“What video game technologies can do is provide a user interface to mathematics that is much better suited to beginner-level learning.
“Today, the study of the symbolic representation can be postponed until after the student has mastered the basic mathematical thinking in a more efficient way.”