ARI SHAPIRO, HOST:
As kids head back to school, they are likely to be full of questions. One of them might be, why do we have to study this, especially when it comes to math? The NPR Ed team's Gabrielle Emanuel went in search of the answer.
UNIDENTIFIED CHILDREN: (Singing) Ones, tens, ones, tens, hundreds.
GABRIELLE EMANUEL, BYLINE: On the second floor of the Baldwin School in Cambridge, Mass., Amy Moylan's first graders are getting in the mood for math.
UNIDENTIFIED CHILDREN: (Singing) Four, five, six, seven, eight, then comes nine.
EMANUEL: Next, these kids gather around a small table, each student with a little dry erase board.
AMY MOYLAN: Skyler.
SKYLER: Ten plus five - that equals 15.
EMANUEL: Skyler gets it, but when I was in school, I was constantly answering math questions with that famous question, why? So I asked these kids.
OK, guys, I want to know why we study math.
SAM: So we can become experts at math.
ASHKAN: Because so I can be very quick, and then I can go play.
UNIDENTIFIED CHILD: You learn so you don't have a tiny, tiny, eensy-weensy brain.
EMANUEL: That's basically what I was told. It's good for you. It makes you smarter. But that answer wasn't satisfying to Houman Harouni at Harvard, where he lectures at the Graduate School of Education. For Harouni, it wasn't so much why we teach math but why we teach this math.
HOUMAN HAROUNI: Why these topics? Why in this order? Why in this way?
EMANUEL: He found the answer in history.
HAROUNI: You can go back all the way to Babylonia, ancient Sumer, ancient Egypt.
EMANUEL: Looking at how they teach math, Harouni found three main approaches. The first one is one we all know.
HAROUNI: Four plus five equals...
EMANUEL: Nine - addition followed by subtraction, then multiplication and so on - the primary goal...
HAROUNI: Calculating and predicting something.
EMANUEL: This, Harouni says, is the dominant form of math, and it has been for centuries. It goes all the way back to merchants in Florence in the 1300s.
HAROUNI: They have a curriculum that is so similar to the curriculum that we have right now that it might as well have been written by the good folks who wrote the Common Core.
EMANUEL: But there's one difference. It was associated with banking and seen as un-Christian.
HAROUNI: A vile, corrupt and corrupting science.
EMANUEL: Nevertheless, all those accountants, traders and merchants had to know this stuff, so they created schools to teach their kids. But Harouni says there are actually two other equally valid ways to teach math. It doesn't always have to be four plus five. In the second model, nine isn't the answer. Instead, it's the question.
HAROUNI: Nine equals question mark.
EMANUEL: This is the philosophical approach.
HAROUNI: To leave the student to come up with all kinds of answers. And the more math you know, the more answers you can come up with.
EMANUEL: Students might answer 3 squared or the square root of 81. The emphasis wouldn't be on the outcome of an equation but on the relationship between numbers. So for a long time in Europe, this is how math was taught to the elites - numbers as a concept, as an idea. So there's the economic approach and the philosophical approach. And that third one - it's the stuff taught in apprenticeships.
HAROUNI: People who are building things, artisans.
EMANUEL: Artisanal math - here it's more about measuring than counting. Tools and materials are key. Like, if you're told to divide a plank into thirds, you can figure that out with a piece of string. And if there are numbers, it's not always as simple as four plus five.
HAROUNI: Four of what, five of what - four cats plus five chickens.
EMANUEL: If you have 4 inches and 5 feet, the answer certainly is not nine. So there are lots of ways to teach math, and 7-year-old Ashkan in Amy Moylan's class can tell us which approach won.
ASHKAN: The nine plus four equals 13.
EMANUEL: The economic model. Houman Harouni says whether you like it or not, we have to study this stuff. Why? Well, we live in a world where money matters, and our math curriculum can prove it. Gabrielle Emanuel, NPR News.
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