Educator explains what's different about nontraditional math

Saturday, October 4, 2008 | 7:59 p.m. CDT
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For simple math problems, traditional and nontraditional math take different approaches.

COLUMBIA — Columbia Public Schools Interim Superintendent Jim Ritter's decision to take nontraditional math curricula off the table in kindergarten through 8th grade has left many wondering what the differences are between nontraditional and traditional methods — and why the debate surrounding them seems so controversial. 

In a traditional curriculum, students are taught using standard algorithms. They learn how to do a skill first then apply and practice what they learn in order to memorize it.

In a nontraditional curriculum, teachers lead students to their own algorithms, said Bob Borst, a math coach at Smithton Middle School. These algorithms could be generated by the students with the help of a teacher, taught in other countries or learned from a parent.

For example, in a traditional curriculum, students asked to add 99 and 25 would stack the numbers, first adding the 9 and the 5 to get 14, carrying the 1, then adding the 1, the 9 and the 2 — all leading to an answer of 124.

In a nontraditional curriculum, students might change the problem to 100 plus 25 to make it easier to add in their heads. After they get 125, they would subtract the 1 they added earlier to get 124. Or they might find a different way of solving the problem, said Jenifer Smith, curriculum coach at Russell Boulevard Elementary School.

"Students can choose and use ways that work best for them," she said.

The textbooks for traditional and nontraditional math vary in their presentation.

The nontraditional textbook begins the exponential growth unit with a story to engage students. The traditional textbook begins with formulas on how to calculate growth followed by exercises for students to practice using the formulas. These exercises make up a majority of the problems in the unit.

Word problems showing students how to apply exponential growth are given about 40 questions into the traditional textbook's exercises. This means they have less of a chance of being assigned, Borst said.

In the nontraditional textbook, nearly every problem is a word problem. The exercises are meant to develop understanding of math concepts instead of rote procedure.

"The reform math looks different from how we learned math in school, so it takes more growth on the teachers' and parents' part," Smith said.

At a work session of the school board in September, parents voiced concerns that they would not be able to help their children with math at home because they are not familiar with the nontraditional approach.

Borst said that is a legitimate concern, but the nontraditional curriculum teaches students to solve problems multiple ways so that if they are not successful using one algorithm, they can try another.

Parent Chris Graham says that the current nontraditional math curriculum in place does not properly prepare students for high school algebra. Graham said for some students taught nontraditional math, "hitting algebra is like a bug hitting a windshield."

"They try to use visual aids and symbols to get them to understand," said Graham, who has a degree in engineering. "But when you get to algebra, you have to understand the actual mechanics of math."

Graham said his son got a "C" in the subject in his freshman year at Hickman High School. He retook algebra in summer school and received "A's" and "B's" in the traditional track through pre-calculus.

His daughter, who started eighth grade honors algebra at West Junior High this year, recently asked her parents for a tutor.

"She likes math, but she doesn't have the tools for it," Graham said.


Elementary mathematics coordinator Linda Coutts said that even though the district is going back to a traditional curriculum next year, it does not mean that teachers won't continue to use multiple strategies.

"I don't believe the community wants teachers not to teach for understanding," Coutts said.

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Greg Johnson October 5, 2008 | 5:12 p.m.

“What’s different about nontraditional math?” Multiple and thus nontraditional algorithms are one difference. Here are four additional distinctions I’ve noticed.

• The social classroom: Instead of a grid or U of isolated students focused on the front, students collaborate in pods of three or four.

• Discovery learning: Students get a scenario and hints that help them discover mathematical relationships--or discover patience to wait for the book, teacher, or another student to explain the situation.

• Wordy workbooks: These develop--and require--reading and writing skill.

• Less segregation and sequencing of math topics: A month on exponents, a month on triangles, segue to graphing, ... Many countries use such a mix successfully, thanks in part to a national curriculum. A kid who changes schools in the US is not so lucky.

A course with textbooks 30 years old can support some of these innovations and others: more technology, more tests, more projects. Parents and students ought to beware of labels "traditional" and "nontraditional" and ask: What helps? What hinders?

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