In Defense of Algebra: What the PhotoMath App Can’t Teach

January 13, 2015

Maybe you’ve heard of it: PhotoMath, the app that does your Algebra homework. Take a picture of any linear equation and the app produces a step-by-step solution. Voices around the Internet hail PhotoMath as the app that “could revolutionize math.”  A Slate article declares that PhotoMath “will make Algebra class seem even more pointless.” One blogger calls it “the app that allows you to cut out math altogether.”

Is PhotoMath the beginning of a revolution? Is this the end of Algebra?

In a word: no.

Computer algebra systems have solved equations step-by-step since the 1960s. In fact, many of today’s calculators come equipped with equation-solving technology. But math educators didn’t abandon algebra when the first computer algebra system was developed 50 years ago. And if they’re smart, they won’t abandon it now.

The data tell a powerful story: According to a 2006 study, students who failed Algebra I were 4.1 times more likely to quit school. A separate study showed that students who complete Algebra II are more likely to graduate from college.

Solving for a variable may seem arcane. But at its heart, learning to solve equations means learning to think logically. Students take what they know, in the form of an equation, and use it to reason out what they don’t know—the value of x. It’s a window into something really quite beautiful: by understanding the way numbers behave, we can transform a messy equation into a clear solution.

And in a sense, we do this every day. Every challenge we face, every problem we solve, asks us to synthesize knowns and unknowns to draw logical conclusions.

Yes, algebra can be challenging. But grappling with difficult material strengthens students’ abilities and prepares them for the hard problems they will inevitably face: in school, in work, in life. Studying algebra equips students to think through challenges logically and fearlessly. After all, when you’ve been working with variables, there’s nothing overwhelming about a question you can’t answer right away. Take what you know, and use it to reason out what you don’t.

For mathematicians and engineers who solve equations regularly, technology is a valuable time-saver. But without a conceptual understanding of how to solve equations, students miss out on a set of problem-solving skills that will serve them well, no matter their career.

More impressive than a computer algebra system, in fact, is the app’s “computer vision”: its ability to process complicated input to “read” an equation. Differentiating objects is easy for humans, but turns out to be very difficult for a computer. Researchers around the world continue to investigate ways to improve computer vision. But it’s a hard problem, and making progress will take persistence and problem-solving.

Good thing they learned algebra.

 

Post by Paulette Willis, Knowledge Engineering Team Lead and Maisie Wiltshire Gordon, Educational Media Writer

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