In Josh Yother's classroom, students can spend more than 40 minutes on a single math problem.
Today's topic is algebraic expressions, but students are never told outright how to solve the problem.
Yother tells his fourth-graders: Johnny feeds his dog for 15 minutes every day. He also walks his dog every day. How much time each day does he spend caring for his dog?
Students must write formulas with variables representing the unknowns: how much time Johnny spends walking his dog and how much time in all he spends caring for the dog each day. Some choose subtraction, others addition. One even chooses multiplication.
They get 60 seconds to think privately about the problem and start scratching formulas on their mini dry-erase boards. They'll divide into pairs, discuss their methods and even hold a mock trial in front of the class to argue out which is the right way of arriving at the answer.
"We've got an interesting array of work here," Yother said. "I look forward to some debate."
The teacher doesn't immediately tell them which is right (He's looking for an algebraic expression like n + 15). Instead, he peppers the kids with questions, mainly: Why? They convince themselves that addition was the way to go. Yother confirms their conclusion.
This probably isn't the way you learned math.
Yother's classroom is a look at how Common Core State Standards are changing not only what is taught in math classrooms, but how it's taught. Officials here note that math has been slowly progressing for more than a decade, moving away from straight process and memorization (2+2=4) to a more conceptual understanding of why math works the way it does, using number lines and 10 blocks to help make the ideas concrete. Tennessee's implementation of the Common Core standards is ushering in that transition more quickly.
But this kind of instruction is causing growing pains with teachers, politicians and parents.
Common Core has become a lightning rod political issue in Tennessee and across the country. Just this month, Tennessee state senators approved a bill to delay the state's implementation of the standards. Other states have made similar moves.
Aside from the politics, many parents and grandparents complain that this way of learning math is confusing and too difficult for young children. Hamilton County school board member Rhonda Thurman this month compared the approach to "trying to teach them to build a skyscraper before they show them how to dig a foundation."
And she's not alone. A local retired algebra teacher says he can't believe the convoluted homework his fourth-grade granddaughter brings home.
School officials are well aware of the parental pushback. They say it will take some time for parents to acclimate to this type of instruction. It's just not the way most of us are used to doing math.
"We learned the procedure. But we never really were taught why -- why we do it that way," said Ganns Principal Allyson DeYoung. "Now Common Core is teaching children the why behind the procedure. It's giving them a deeper understanding."
Frank Davey knows his math.
He's a retired algebra teacher and retired Marine pilot. Now he helps his fourth-grade granddaughter with her math homework and can't believe the type of work she's doing. He says it's not age appropriate.
There are formulas like this: 80 = 8 (y - 79)
y = ?
He said schools needn't reinvent the wheel. Most adults learned math the traditional way, which relied heavily on rote memorization.
"Why are we doing this to our kids?" he said. "Why is it we have this attitude that it is nasty to memorize?"
Davey, who said he has tried to speak to the county school board about its math approach, said he fears students are going to get too confused at an early age. He worries that frustration won't allow them to build the foundation they need to do higher-level math.
"Everything we do in algebra has a basis in basic math," he said. "And if we don't learn basic math, algebra might as well be rocket science."
Pundits have maligned Common Core for a multitude of reasons. Some say the standards are too weak, others say they're much too difficult. In the weekly political magazine The National Journal, New York teacher David G. Bonagura Jr. called Common Core math a "doomed educational experiment." He likened it to the also-conceptual "New Math" that spread across the country more than 50 years ago. Bonagura said he doesn't disagree with presenting students with the basic concepts of mathematics.
"But there is a difference between learning basic concepts and expressing the intricacies of true mathematical proofs that Common Core desires. Mathematical concepts require a high aptitude for abstract thinking -- a skill not possessed by young children and never attained by man," he said.
"What will happen to students who already struggle with math when they not only are forced to explain what they do not understand, but are presented new material in abstract conceptual formats?"
But Common Core supporters say the new standards are already giving students a deeper understanding of what they're learning. They think this approach will give students a better foundation, because they'll understand earlier what the math problems are computing. Even with the more conceptual approach, officials say that math today still requires basic memorization of, for example, multiplication tables.
And this transition is not all about Common Core, said Stacey Roddy, Hamilton County's director of elementary math and science.
The Common Core standards are still being implemented locally. Teachers have been given extra training and some have reached out to parents to help them understand how math is changing. But Roddy said the strategies -- like using physical representations like blocks and finding multiple ways of solving a problem -- have been around for years. She says many of those are traced to the National Council of Teachers of Mathematics' recommendations for best practices.
"A lot of these strategies have been around for decades," she said. "It's just that we haven't always used them in the classroom. So this is not new math in that sense."
Tennessee's old standards required teachers to whiz through teaching in order to cover a multitude of topics. But the Common Core shaved down the number of standards required. That gives teachers more time to explore each topic and ensures kids have more than just a surface-level understanding, said Jamie Parris, the district's director of secondary math and science.
"Common Core does not promote the check-list approach," he said.
Yother, the Ganns teacher, says he was skeptical at first.
A few years ago, his kindergarten-age daughter started bringing home math problems that at first seemed like nonsense. It wasn't the way he was taught. He resisted.
But she was able to explain the problems, not just the answer, and why that was the answer. She's now in his fourth-grade class. And he says she can run circles in math around his sixth-grade daughter who attends a private school.
Some of his students' parents had the same initial reaction. He sent a letter home this fall explaining what was changing and sympathizing with parents' confusion. Many have come around now, he said.
"I have parents who come up to me and say, 'I don't know who's learning more, my daughter or me,'" he said. "It all depends on your attitude."
In Yother's class, students are encouraged to try problems multiple ways. They get to come up with their own ideas, write about them and defend them in front of the group. Not only are they understanding math on a deeper level, but Yother says when taught this way students develop communication and leadership skills.
"We're still looking for an answer," he said. "But at the end of the day, don't you want your children to think?"
Contact staff writer Kevin Hardy at email@example.com or 423-757-6249.