New Math Plan: a Plus for Pupils?

If you’re a parent of a student in a California public elementary or middle school, prepare to feel out of touch come next fall when your child sits down to do math homework.

The assignment will probably contain more words than numbers--or no numbers at all--with an essay replacing calculations. Students might be asked to measure potatoes or survey family members on their favorite flavor of ice cream.

When adding, subtracting, multiplying or dividing is required, it might not matter if a student uses a calculator. And if your child says there is no right answer, he or she is probably telling the truth.

Sound disorienting? Discouraging? Don’t feel too bad, because in all likelihood your son or daughter’s teacher will be confounded as well.

That statement is not meant to be snide. Rather, that is the assessment of some of the most progressive math education experts around the state. They estimate that between 50% and 90% of the state’s teachers are ill-prepared for what is described as the most dramatic change in the teaching of mathematics this century.

Beginning next fall, California’s decade-long effort to reform math instruction will kick into high gear, as public schools introduce new teaching materials that emphasize student discovery over calculation, deep understanding over repetitive practice.

Teacher training experts say the state would have to spend more than half a billion dollars annually--or $75,000 per school--for the next several years to get all its teachers ready. And those pushing the new teaching methods do not want to wait.

“If we wait for everybody to be ready, it’s just not going to happen and we are going to lose that whole new generation of kids . . . just at the time when, for the economic viability of the country, we need people who are mathematically, scientifically and technologically literate,” said Eunice Krinsky, who heads a state-funded math teacher training project at Cal State Dominguez Hills.

Up and down the state, schools are in the midst of selecting from a list of approved textbooks, calculators, videotapes and guidebooks that conform to the new way of teaching, which emphasizes concepts over calculations and formulas, relies as much on group problem-solving as individual effort, and begins introducing sophisticated subjects such as geometry and algebra in the earliest grades.

Those reforms began seeping into California classrooms 15 years ago, as part of an effort to increase enrollment in advanced math courses, better prepare students for college and improve the capacity of workers to think mathematically on the job.

Now, the advent of new textbooks and materials will pressure all teachers to subscribe to the reforms.

The result, many teachers believe, will be confusion and resistance. Not only are many unprepared to teach in a new way, but some experts believe that no amount of training will make it possible for teachers with little math background to make the switch. Others worry that the methods remain untested, particularly with low-achieving students and those still learning to speak English.

Even Walter Denham, the state Department of Education’s top math expert, agreed that next year will be an experiment. “We don’t have empirical evidence that it will work in tens of thousands of classrooms,” he said.

California school districts will spend about $250 million this year and next on the new texts. Those most in line with the new “thinking” curriculum will require teachers to perform what will be, for some, the challenging role of coach and guide.

Rather than just checking pupils’ answers, teachers in every grade will be expected to question them about how they arrived at their solutions and to deduce from the responses their level of understanding. Even in the primary grades, teachers will need to be familiar with such areas of math as probability and statistics, geometry and algebra.

“You will find teachers who . . . find that these materials are a shock, but they will be teachers who haven’t kept up with their profession,” said Paul Giganti, a math education expert at the Lawrence Hall of Science in Berkeley and president of the California Math Council. “I think many teachers are ready and anxious to implement the new materials.”

But he acknowledged that parents--many of whom equate math homework with the endless calculations that past generations performed--are in for a surprise.

“There are a lot of parents who do not understand the changes . . . and it is our fault,” Giganti said. “We have good reasons for all of the things we have done, but . . . we have kept them largely to ourselves.”

His organization is working to address that. So are textbook publishers and school principals, who are hosting meetings to reassure parents that their children will still learn to calculate, and that high-achieving students will not be held back by the emphasis on group problem-solving.

Reed Middle School in North Hollywood began trying out one of the new textbook series last fall and found that students who previously had been adept at working math problems were struggling.

“The kids . . . were more used to having a math book give them an example and then 20 problems like it,” said Larry Tash, Reed’s principal. Now, however, the students are doing better and most parents have become supporters of the new curriculum, he said.

But in some school districts, parents have prevailed upon administrators to go slow in choosing textbooks or reject the new methods altogether.

In Palo Alto, parents objected to a state-sponsored program to promote the “thinking” curriculum in middle schools. Parents’ fears that children were being steered away from math fundamentals led to angry confrontations with teachers, and some parents threatened to pull their children out of the highly-regarded school district.

“Parents would call the teacher and ask for help and some of the teachers . . . were not able to satisfy the concerns that were being raised,” said Jack Gibbany, the district’s director of curriculum and instruction. Partly as a result, the district has delayed buying new math textbooks until next year.

The Chino Unified School District in San Bernardino County has also put off selecting from among the new materials, in response to parents’ concerns. Supt. Stephen Goldstone said the district may decide to stick with the almost decade-old books it uses now. He appointed parents to a committee to help advise the district on which way to go.

“There are some very good and very interesting aspects of some of these new textbooks, but some of them are so far-fetched that, it’s like, what are kids really going to learn about math when they are done with this class?” asked Anne Gluch, the parent of a Chino fifth-grader, who is serving on that committee.

Sales representatives of the publishers said that between a quarter and a third of the state’s 1,000 school districts are delaying making a choice, although some are doing so for financial, not philosophical, reasons.

One of the most vocal critics of the new textbooks has been Maureen DiMarco, Gov. Pete Wilson’s top education adviser. She and others warn of a repeat of the 1960s debacle known as “new math,” a highly abstract teaching method that was introduced into schools nationwide without adequate preparation for teachers and parents.

Those opposed to the latest changes in math have begun referring to them as the “new new math.”

“I’m truly alarmed that some radicals have taken ahold of the curriculum, and are convinced that basic skills are not important, when everybody knows that solid basic skills are the foundation on which you work to get to those higher order skills,” DiMarco said.

Furthermore, she said, there is no research that shows that children will understand math better if taught the new way. Even some mathematicians believe that the approach is misguided, no matter how well it is taught.

Cal State L.A. math professor Wayne Bishop has been campaigning for years against the state’s math framework, and the national guidelines on which it is based.

He argues that the approach is a retreat from standards and from true math--a rejection of substance in favor of form. “Learning your math by solving interesting problems is going to die--it’s just a matter of how long it will take,” he said.

But the publishers of the new-style books, and backers of the state math guidelines on which they are modeled, are convinced that the changes are essential.

In the past, they say, students were taught a standardized way of doing long division, but not necessarily whether the answer they produced made any sense. Now, they will be asked to think mathematically about real-world problems.

Although math textbooks always have included “story problems,” those in the new books are more open-ended and more ambiguous and are known as “investigations.”

One such problem, drawn from a fifth-grade textbook, is the following: A student crouching by a field of tall corn sees 72 legs of cows and chickens. How many different combinations of cows and chickens might there be?

The answer is 17. Some students might work out the solution using algebraic equations. More likely, they would write down a series of numbers showing the possible combinations and count them. They also might represent the combinations using toothpicks.

Usually, students would be expected to work cooperatively. Afterward, they would explain how they arrived at their answers, either orally or in essays.

In another typical problem, for younger students, the teacher would ask how many pencils would have to be purchased to furnish two for each of 30 students per week for a year. The answer is 3,120.

The Los Angeles Unified School District last month received a five-year, $15-million National Science Foundation grant that will help pay for teacher training. But Los Angeles, like other districts statewide, also will have to divert funds to training from other purposes because it is highly unlikely that the state will foot the rest of the bill.

Recognizing that many teachers might not be ready, or willing, to drastically change their approach to teaching, some of the publishers of the new math textbooks preserved more of the traditional lessons.

Teachers “can’t possibly be updated as much as we would like them to be” to take on the challenge of the new textbooks, said Carole Greenes, associate dean of the Boston University school of education and one of the authors of a series published by Silver Burdett Ginn. “We developed a series . . . that is within the powers of all teachers to get a handle on.”

But other publishers downplay that issue and offer step by step guidance to help teachers cope with the new style. Charlotte Gemmel, president of Creative Publications of Mountain View, Calif., said teachers will have no trouble using her firm’s materials even though they are far different from traditional texts.

“The book takes the teacher by the hand, with questions (and) typical responses of kids, and the book itself becomes a tool to learn and feel comfortable with this new approach,” she said.

But teachers are clearly ambivalent and that is showing up in sales meetings as the publishers visit schools to pitch their materials.

Donna Batson, a consultant for Addison-Wesley, recently presented that company’s materials to about a dozen teachers at Menlo Avenue School, just south of the Los Angeles Memorial Coliseum. Much of her talk was spent trying to reassure teachers that the series had not dispensed with traditional drills.

“I know it’s coming hard and fast . . . but if you take it slowly and try it out, I think you will have good results and enjoy what you are doing,” Batson told the group.

Afterward, teachers were divided in their assessment. Michael Rosner, who had tried the materials out with his third-, fourth- and fifth-grade students, was a believer. “I think it’s the best thing I’ve ever seen,” he said.

But third-grade teacher Nicholas Kelly was skeptical. “I’ve had parents come to me and ask me for more computations,” he said. “I will still do that. I don’t believe in throwing out the basics.”

And Charles Ferreira, the teacher who headed the school’s selection committee, said he is trying to moderate between the two views. “Personally, I don’t have a lot of faith in it,” he said. “But if we adopt it, we will go with it.”

(BEGIN TEXT OF INFOBOX / INFOGRAPHIC)

A Teacher’s Guide

This fall, many California schools will begin using radically different textbooks and other teaching materials that incorporate a new approach to mathematics. Here is a sample from the “Mathland” teacher guide, demonstrating a classroom exercise for fourth-graders:

THE PROBLEM

The teacher writes the problem 12 x 5 on the chalkboard. She asks the class for their answers and discussion ensues.

A SAMPLE DISCUSSION

* Teacher: “One answer we have down for 12 times 5 so far is 60. Does anyone get a different answer?”

* Student: “It might be 50.”

* Teacher: “Let’s add 50 to our list. I wonder which of these answers is right. What do you think?”

* Student: “I got 50 . . . because I learned last year you’re supposed to start with the ‘ones’ and do 5 times 2, then you write 0 for the ‘ones,’ and then I multiplied 5 times 1 and that’s 5 for the ‘tens.’ So it’s 5 and 0. That’s 50.”

* Teacher: “Convince me. Use what you know about the numbers to prove your answer is right.”

* Student: “Well, I know that five tens is 50. Oh, but it must be more because there are 5 twos, too, and that’s 10. So 50 and 10 makes 60.”

THE INTENT

According to Micaelia Randolph Brummett, an author of the series:

“The point is that the student who makes the error thinks it through and corrects him or herself. Instead of doing computation . . . kids do discussions of a few problems in class, but they do them very, very thoroughly. (The teacher) takes off the mantle of the authority . . . and gives that power to the student. They get excited about trying to defend their particular choice . . . and when they come to that final answer they believe in it.”