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Think Tank

Reinventing Math for the Computational Knowledge Economy

If you love geology, chances are you had a great teacher who introduced you to the subject. Most likely that teacher didn't simply teach you to appreciate rocks, but also instilled in you a greater curiosity about the evolutionary history of life. In short, this teacher made learning geology a joyful experience, one that was relevant to your world. 

Right now we have a serious need for more students to fall in love with all of the STEM subjects, which fall into the categories of science, technology, engineering, and mathematics. We know these fields fuel economic growth, so training a STEM workforce has been recognized as a key goal in education policy. And yet, there is an enthusiasm gap in these subject areas, and nowhere is that more evident than math. U.S. students don't think they're good at math, so they learn to hate it. As the video below points out, 50 percent of students would rather eat broccoli than do math homework. Not surprisingly, these students greatly underperform. So how do we change this?

The animated video below, courtesy of Conceptua Math, a company that is seeking to create a comprehensive online digital K-8 math curriculum, is a clear and succinct presentation of this problem, along with several proposed solutions. Watch here: 

What's the Big Idea?

As the video above makes clear, the way we teach math needs to be reinvented. In a nutshell, "students need visual and interactive curriculum that ties into real life." According to Conceptua Math's David Robertshaw, we need technology to support good teaching and bring joy back into learning. Technology can empower teachers, Robertshaw says, "even the ones who are not confident about out how to best teach math."

Trading in dry textbooks for engaging computer programs is a good place to start. Matthew Peterson of the non-profit MIND Research Institute has demonstrated through basic neuroscientific, mathematics, and education research that "language-independent software" lessons make teaching math both easier and more productive. 

Teachers can also utilize the tools of real-time data to see where students are struggling. Computers can offer sophisticated feedback that allows students of all different ages to be learning at their own pace. 

According to Sal Khan, founder of Khan Academy, the problem with the way math is currently taught is that lessons are "siloed from one concept to the next." Khan tells Big Think that when we administer exams, "some people do well and some people don’t do well. The people who don’t do well are given labels called grades that essentially tell them how smart society thinks they are. And then everyone moves on to the next concept. People end up with gaps."

Robertshaw points out that many technologists in the education industry are attracted to software that can “intelligently” adapt when students are failing in a particular topic. While technology is a powerful tool to spot gaps, "we believe that a teacher is best able to diagnose exactly how a student is struggling," he says. 

Current teaching methods are not the only challenge in math education. What about the curriculum itself?

"Do we really believe that the math that most people are actually doing in school practically today is more than applying procedures to problems they really don't understand for reasons they don't get?"

So asks Conrad Wolfram in a searing indictment of math education. Wolfram has no issue with math being taught as a compulsory subject. Math is, after all, "more important to the world today than at any point in history," he says. The problem is what we are teaching. 

Wolfram breaks math down into four components:

1. Posing the right questions
2. Turning a real world problem into a math formulation
3. Computation
4. Turning a math formulation back to the real world, verifying it. 

"The crazy thing," Wolfram says, is that we spend perhaps 80 percent of the time in math education teaching people to do computation by hand -- "the one step computers can do better than any human after years of practice." 

So why not use computers to calculate? After all, that's the math chore we hate the most. It may have been necessary to teach this skill 50 years ago. There are certainly a few practical examples of how hand-calculation can be useful today. Wolfram cites "mental arithmetic" as one of them. And yet, thanks to the ubiquity of calculating machines, math has been transformed today, "perhaps more than any ancient subject." Math has been "liberated from calculating." 

What's the Significance?

Not only are currently failing to teach proficiency in basic math skills, we are also missing out on an opportunity to teach students a much richer understanding of math. Wolfram envisions a new math curriculum that is "built from the ground up" and based on the ubiquity of calculating machines. The countries that do this best in computer-based math, he argues, will leapfrog others and develop a more advanced economy. 

Wolfram describes this as a transition from what we now call the knowledge economy to "the computational knowledge economy where high-level math is integral to what everyone does."

Watch Wolfram's full talk here

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Follow Daniel Honan on Twitter @Daniel Honan

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