Don Shrubshell photo

Paxton Keeley fourth-grade teacher Camilla Gilliland displays a piece of paper that is divided into sections to teach her class common fractions.

Paxton Keeley Elementary School teacher Camilla Gilliland challenged her fourth-graders Tuesday to use a fraction to show that eight of the class’s 24 students have their ears pierced.

Don Shrubshell photos

Paxton Keeley Elementary School first- grade teacher Jenine Loesing uses an overhead projector to teach her students coordinates, direction, communicating ideas and moving around in spaces in math class. Below, Paxton Keeley first-graders Alyssa Noel and Zack Wirsing use coordinates and direction to solve a math problem in Jenine Loesing’s class.

Within seconds, pupil Savannah Parker relied on memorization to solve the problem.

"It’s one-third, because eight times three is 24," Savannah responded.

She later explained that she "just knew" the problem because Gilliland drills students with timed multiplication tests, asking them to solve 50 problems in three minutes.

Savannah, 10, came up with the correct answer, but Gilliland wanted her to double check it by shading in eight squares on a 24-squared strip of paper.

Other children took longer to find the answer. They needed to shade the squares or count out red, blue and yellow blocks to solve the problem. One boy drew three groups of eight marks to come up with the fraction.

Regardless of the strategy they used, the children were learning why eight-24ths equals one-third, said Linda Coutts, elementary math coordinator.

That conceptual understanding is the cornerstone of Columbia Public Schools’ Investigations in Numbers, Data and Space elementary school curriculum.

But it’s also the gunpowder that has set off the recent math battle in Columbia.

For some parents, math has become a four-letter word. They don’t understand why their youngsters aren’t learning multiplication tables and memorizing traditional methods like column addition or long division.

They are frustrated that children are expected to explain why two plus two equal four instead of just "knowing" it. At the same time, parents aren’t crazy about the fact that kids can use calculators in class. And they hate the flimsy workbooks that have replaced oversized math textbooks.

Students seem caught in the middle of the mathematical controversy. Some children are learning math strategies in school that are denounced when they get home. Back at school, some teachers aren’t allowing children to use the traditional methods their parents show them at home.

With those mixed messages, children might be the casualties of the ongoing math war.

NUMBERS DEBATE

Columbia Public Schools has been phasing in the Investigations curriculum for more than five years and has been using it in all K-5 classes since 2003. Coutts points to improving math scores on the Missouri Assessment Program test to indicate that the curriculum is working. Critics contend the MAP test results aren’t reliable because benchmarks were lowered last year, making it easier for children to reach the proficiency level.

National research on the effects of Investigations is limited and not without bias.

The curriculum was created by an education research and development group known as TERC. That group claims children who take Investigations do as well as or better than traditional students when calculating a problem. The developers also say their internal research shows their students have a better understanding of number relationships than their peers.

But Mathematically Correct, a national organization that reviewed math curricula in the 1990s, dubbed Investigations the "worst" of the selections the group had reviewed because it lacks "focus."

Research also doesn’t take into consideration the parents who enlist the aid of private tutors to supplement reformed math.

President George W. Bush created the National Mathematics Advisory Panel to study math curricula, and it is in the process of looking at Investigations. Its findings should be available early next year.

Until the U.S. Department of Education releases those conclusions, parents are relying on anecdotal evidence to deem the curriculum "failing." About 50 Columbia parents met Tuesday evening to swap similar concerns that their children aren’t learning the mathematics they need to succeed.

Parent Michelle Pruitt, who organized that meeting, brought Columbia’s math controversy to a boil when she voiced concerns about the curriculum to the school board in January. Other parents quickly joined the bandwagon, expressing relief that their children weren’t the only ones suffering through math.

Columbia isn’t unique. Other states have been waging war on Investigations and similar curricula for years. California implemented reformed math in the early 1990s but dropped it seven years later, citing poor test scores. In Utah, Investigations was left off the state’s most recent list of recommended textbooks. And the battle still rages in Washington state, where a parent organization known as Where’s the Math is rallying for a legislative change this year to do away with reformed math.

THE NEW MATH

Curricula such as Investigations were developed in the early 1990s after the National Science Foundation offered grant money to implement new teaching standards based on recommendations from the National Council of Teachers of Mathematics.

The council in 1989 advocated conceptual learning, challenging schools to teach math on a deeper level to ensure that children understand numbers and place value rather than just memorizing math facts. The charge seemed to de-emphasize the teaching of basic algorithms such as column addition or long division.

In September 2006, the NCTM printed Focal Points, which outlined important math topics that should be covered by eighth grade. The curriculum document also highlighted the importance of learning computation.

"The spirit of the Focal Points is almost diametrically opposed to the spirit of Investigations," said Harvard mathematician Wilfried Schmid, a member of the National Mathematics Advisory Panel and vocal opponent of reformed math.

"Virtually any other curriculum would be an improvement over Investigations," Schmid said in an e-mail to the Tribune.

Coutts isn’t dead-set on using the Investigations curriculum in the future. The school district is already in the early stages of an elementary math curriculum review, she said. But Coutts is sold on the idea that children need to make sense of numbers instead of just memorizing them. And to do that, children must be allowed to ask "why" numbers work the way they do.

That’s why it can be disadvantageous to introduce traditional algorithms to children who don’t understand why they work, she said. Simply borrowing a one from the next column of numbers when subtracting teaches nothing about place value and can confuse children about what the numbers represent, she said. Without conceptual understanding, memorizing traditional algorithms is "no different than memorizing your telephone number" because the numbers don’t mean anything to children, said John Lannin, a professor of math education at the University of Missouri-Columbia.

Some parents claim Columbia teachers won’t let their children use traditional algorithms in class, but Coutts said students who understand them can use them. It’s up to a teacher to deem whether a child is ready to apply those traditional methods.

Regardless of how they learn math facts, students are expected to solve math problems quickly by the end of a school year. The district gives internal assessment tests to determine how many problems a student can solve within a certain time frame. Some teachers, like Gilliland, give students those assessments on a routine basis as well.

Coutts said she understands parental concerns, but going back to the math of yesteryear isn’t an option. She compared the changes to upgrades in a dental office. Few people would continue to visit a dentist who still used the same equipment and techniques from 20 years ago, Coutts said.

MU math Professor Elias Saab said he isn’t against change, but the current curriculum goes too far. He said the district’s integrated math offerings on all grade levels aren’t preparing children for advanced coursework in college.

"I don’t want them not knowing the traditional methods," Saab said. "They spend an hour doing so many different things when they used to have that hour to learn traditional math. They’re not getting to the point where students can manipulate numbers. … Math really is a language. The more you postpone it, the harder it’s going to be for them to learn."

COMMON GROUND

If there’s any common ground to be found in the math debate, it’s that educators, parents and mathematicians want children to learn math so they can compete in an increasingly global and technological society. And, although the groups seem polarized on how to reach that goal, they might have more in common than they think, said David Geary, a curators professor in MU’s Psychological Sciences Department who specializes in the way children learn math.

Pitting conceptual learning against memorization is "off base" because the two learning approaches influence one another, he said. To solve complex math problems, children must understand what numbers represent, but they also need to know procedures such as borrowing from one column to the next, said Geary, who serves on the National Mathematics Advisory Panel.

Schmid recommends parents supplement Columbia’s elementary math curriculum with Singapore Math, a home-based course that he used when his own daughter was in an Investigations classroom. Although the curriculum incorporates conceptual learning, it also stresses memorization of math facts and does away with calculators in elementary schools, he said.

Coutts is familiar with Singapore Math, which wasn’t available when Columbia implemented Investigations four years ago. At this point, she and an elementary math committee are looking into it along with a number of other curriculum materials.

Geary offered little hope that any existing curriculum option would satisfy everyone. "I’m not really sure if anyone knows the best way to teach concepts to kids," he said.

Until such curriculum is designed, Columbia’s elementary school teachers will remain focused on teaching children math they can apply to real-world situations.

In Jenine Loesing’s math class Tuesday at Paxton Keeley, for instance, first-grade students learned to map out various routes on a blocked street grid in an attempt to grasp geometric concepts. Children were asked to choose a destination and write directions to that spot.

Working together, Chandler Westfall and Matt Ballard picked the most complex destination point and, after completing the task relatively quickly, challenged themselves by finding alternative routes.

"Let’s get a harder one," Chandler, 6, said. "Everything’s just, like, so easy."

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