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The Common Core wasn't necessarily supposed to change how math is taught, but in many schools that's exactly what's happening.

Many – some might argue most – American math teachers once followed a simple format: Explain a formula to the class, show an example on the board, then let students practice on worksheets.

Now, many of those same teachers are attempting to lead seminar-style discussions on the division of fractions or the Pythagorean theorem. They're assigning longer-term projects in which students discover and experiment with math concepts, instead of training students in tricks like the "butterfly method" for adding and subtracting fractions.

Related: Common Core math experts say teachers need to stop using shortcuts and math 'tricks'

Teachers are trying out these new methods even though Common Core – guidelines, which have been adopted by over 40 states, for what students should know in math and English by the end of each school year – don't speak directly to how math should be taught.

"The Common Core is silent about how to teach," said Phil Daro, one of the lead writers of the math standards. "When we wrote the standards we were prohibited from addressing how to teach, that's not what standards are supposed to do."

Common Core teaching
Student work in the hallway of Eastside Elementary shows the "partial product" method of solving a multiplication problem, one of many methods students have learned with Common Core. Many teachers say the new standards go deeper than the old standards and should not be dropped. (Photo: Jackie Mader) Credit: Jackie Mader/The Hechinger Report

But there's a debate about whether the new content requirements alone are enough to improve students' understanding of math. Many in the world of math contend changing how teachers organize their lessons and lead their classrooms is essential to making a difference.

Steve Leinwand, principal researcher at the American Institutes for Research's Education Program, argues that the failings of the old format for teaching math has led countless Americans to the conclusion that learning math isn't something they can do.

"We don't have an achievement gap in this country," said Leinwand. "We have an instructional gap."

Like many Common Core supporters, Leinwand says the "I, we, you" model – where first teachers go through a problem for the class, then have the class work together on similar problems and finally have students work independently on problems – has dominated American math education for far too long.

"I, we, you sometimes makes sense," said Leinwand. "But sometimes teachers need to turn it on its head with some version of you, we, I. That requires students to struggle, explore, share, justify, compare and debrief."

Some experts question whether it's smart or even necessary for teachers to overhaul both the content and their pedagogy at the same time, though.

Related: Will weak teacher training ruin the Common Core?

"The problem was with what we were teaching, not how we were teaching," said Daro at a conference of the Association of Mathematics Teachers of New Jersey. "Countries have varying levels of teacher quality but are still high performing."

Daro thinks that the Common Core addresses the main problem of the math classes of yore – that curricula went a mile wide and an inch deep – asking teachers to cover so many topics that none were given appropriate attention.

"In higher ed, we were asking why were these students taking AP Calculus, when they needed to spend much more time on algebra," said Daro.

And indeed, many states and districts – and teachers — are struggling with juggling the huge project of overhauling both their curricula and their teaching simultaneously.

"Are math standards going to help?" asked David Wees, a former New York City public school teacher and a formative assessment specialist for New Visions for Public Schools, a non-profit that advises 75 New York City public schools. "Yes, but there are the standards as written, there are the standards as practiced by teachers and there are the standards as students will receive them."

He says districts shouldn't expect for every teacher to master the new curricula and new teaching methods at the same time. Instead, he says districts should work on the changes more gradually.

"Professional development sessions, where you go over things with teachers very briefly, aren't enough. They need to see it more than once," added Wees. " There aren't very many model teachers in this country and they tend to be concentrated in only some schools. We need to create more model classrooms, instead of trying to fix the teaching of 3 million, we should be trying to fix the teaching of 1,000 good teachers so that their classrooms can be resources that other teachers visit."

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Emmanuel Felton is a former staff writer. Prior to joining The Hechinger Report, he covered education, juvenile justice and child services for the New York World. He received a bachelor's degree from...