"I see more student engagement. I see more students feeling comfortable and becoming involved in the discussion and the thinking process," explains Tourini.
This is not the new math that became popular in the 1960s. This is new new math -- memorization is no longer emphasized. Neither are the mechanics of addition, subtraction, multiplication and division. Instead, children are encouraged to use language and problem solving skills to find answers to problems. And the answers don't have to be exact. That's all made new math pretty controversial.
"I think that they own it more," says Tourini. "They understand it more than just having to memorize x and y."
Proponents of the new system say it's not the math that's new, it's the teaching method.
"We know more about learning today than we did 20, 30 years ago," says Fran Curcio, who helped develop the new curriculum. "And we know more about teaching than we did 20, 30 years ago."
Curcio believes it keeps kids more engaged.
"It's the problem that presents a situation that allows children learners to think about 'What do I need, what do I know, what do I need to find out?'" she says. "And then they employ the tools of computation to solve the problem."
But other mathematicians just hate new math, and believe it will not prepare students for college.
"There is a feeling among...a substantial part of the college and math research communities that some of what went on was that the baby got thrown out with the bath water," said Dr. Sylvain Cappell, a mathematician at NYU's Courant School of Mathematics.
"Look, we can't change the fact that mathematics is hard. It's hard for mathematicians too," Cappell said. "One should approach math with a sense of play and a sense of fun as well as with the knowledge that it takes rigorous work. But it can't just be feely-touchy. There is hard work to be done."
Mathematicians are so concerned about new math that more than 200 of them took out a full-page ad in the Washington Post imploring Education Secretary Richard Riley to withdraw the department's endorsement of it.
Then there are parents like Elizabeth Carson. She's not concerned -- she's outraged.
"It's not a matter of not understanding and it's not a matter of being adverse to what the thrust of the program is. It's a matter of identifying that there is a clear deficiency in these programs in terms of the development of basic skills. It seems silly that...parents and others have to ask and demand and force the schools to teach children basic skills."
Carson's son Nicholas is a student in one of New York City's best school districts. Fearing her son wasn't being challenged, Carson led a crusade to get the new math curricuum thrown out. She began supplementing Nicholas' regular homework with a tutor to teach old-fashioned mathematics after school.
"Our children are caught in the middle of this. Our children, some of us feel, in a sense are guinea pigs. Our children are being sacrificed to a kind of experimentation."
No one from Carson's school district would to speak to CBS News to respond to her charges. Other school districts caught in the controversy maintain parents often don't understand the program. For Curcio, the objective now is to find some middle ground.
"We all want to accomplish the same thing," says Curcio. "That is to improve the mathematics curriculum, improve the success rate, and help children to feel good about themselves in the study of mathematics so they'll go on to study more."
In apparent acknowledgment of the criticism, the National Council of Teachers of Mathematics voted last month to revise its standards. As one official put it, the new bottom line is, "get the right answer."