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>Wednesday, June 11, 2008BY ALFRED POSAMENTIERThe approach taken by the reformists is a nice form of enrichment, but it does not replace the need to teach children basic arithmetic skills.

FOR THE PAST FEW YEARS, parents and educators in this country seemed to be obsessed with the conflict about the best way to teach mathematics – particularly in the elementary grades.

This conflict, known nationally as “the math wars,” has recently flared up again in Wayne and Ridgewood, where the school system has been using a “reform program,” one that stresses arithmetic-concept understanding over algorithm skills.

The educational ideas that form the basis for this approach to teaching elementary mathematics are good and have their place on the instructional stage. Most math-savvy adults would agree that children should be exposed to these ideas, largely because they give students some useful quantitative insights.

However, when we adults look at this approach, we do so with a well-established arsenal of arithmetic skills; that is, we are thoroughly familiar with algorithms for the basic arithmetic operations, and we have many “number facts” solidly memorized.

Surely, from this vantage point, the approach taken by the reformists is a nice form of enrichment. But it does not replace the need to teach children basic arithmetic skills.

It is incumbent upon towns such as Wayne and Ridgewood to look at mathematics education from the vantage point of the learner who must get facility with arithmetic tools before, or while, being exposed to discovering quantitative patterns.

Familiarity with numbers

For example, if asked to multiply 25 x 28, some adults would say that this is equivalent to (25 x 4) x 7 = 100 x 7 = 700, or they might say 25 x 28 = (25 x 30) – (25 x 2) = 750 – 50 = 700, or other such combinations. However, we already know how to use an algorithm to multiply 28 x 25 directly. This sort of number facility might be less useful when multiplying 63 x 27, where the algorithm would be more desirable.

There is a school of thought among reformers that with today’s technology, arithmetic skills are less important. Yet, this position is taken by those who take their own arithmetic skills for granted.

As students gradually increase their quantitative talents – something we always enhance throughout our lives – they rely increasingly on the calculator, discounting their reliance on their now-well-ingrained arithmetic skill. They look at nifty number patterns and relationships and marvel at alternative ways of doing simple calculations based on these relationships.

Educators who discount their own arithmetic facility in making recommendations to others run the risk of providing inappropriate suggestions.

We constantly denigrate our own educational system – particularly when it comes to learning mathematics. We look overseas to other countries that seem to show better results on standardized testing. All too often, these tests are run on different types of populations and under different circumstances in different cultures, all of which clearly affect the outcome and render it inappropriate as a comparison.

Interestingly, many of these countries to whom we draw comparisons look to the United States as the educational paradigm to follow. This history of mathematics education of the past 50 years has been one of alternating fads, where we tend to go from one extreme to another, each time retaining some small particles from each extreme.

Aiming for the middle ground

We are once again at a point where the middle ground should be the goal.

Students must master arithmetic algorithms and as many number facts as they can, and then investigate number relationships and patterns, many of which they should be guided to discover on their own for a more genuine understanding.

The towns of Wayne and Ridgewood, which seem to have brought this issue to the surface through parental discontent, could serve to model these alternative forms of arithmetic calculation as mathematical enrichment, but only after students have attained a solid command of arithmetic, even if that is a somewhat traditional approach.

There is nothing wrong with a somewhat traditional approach. Quite the contrary, it is surely time-tested.

Alfred Posamentier of River Vale is dean of the School of Education at City College of New York and co-author of “Progress in Mathematics.”

>Sunday, June 8, 2008

BY ANDREA ALEXANDERSTAFF WRITER

What good is an innovative math program designed to raise national standards if it leaves some students unable to figure out a grocery bill?

That’s the question Wayne parents have raised as their school district struggles with an issue — the best way to teach students math — that has sparked nationwide controversy.

The debate, dubbed “math wars,’’ pits supporters of traditional math, which stresses the basics, against educators favoring reform programs that aim to make students better analytical thinkers and problem solvers.

Reform methods stress revisiting all aspects of math — for example, how to do fractions, subtraction and multiplication — over and over in a continuous “spiraling.” It includes such tools as lattice graphs, physical models and games as opposed to the old pen-and-paper approach.

Advocates say the new methods force pupils to tap into long-term memory, rather than learning a topic by rote memorization, only to quickly forget it. But critics say reform math doesn’t allow children enough time on any one aspect to master it.

Schools in Wayne and Ridgewood have joined the debate in the past year.

Wayne has been using a reform program, Everyday Math, for more than 15 years. It’s one of the top-selling elementary school math programs — used in 185,000 classrooms by about 3 million students, according to Andy Isaacs at the University of Chicago, a director for the latest edition of the program.

But Karen Stack of Wayne says, “I have a son who is an A-plus student, but in a store he can’t figure out how much money he needs if he buys three of something.’’

And during a family game of Monopoly her third-grader “has to use a sheet of paper to do calculations,’’ Stack said. “He doesn’t have the drilling to just know.’’

Illustrating the perplexing nature of the debate, however, not all Wayne parents fault the program.

“I think it gives them a variety of ways to look at a problem rather than being locked into one method of doing things,’’ said Joyce Duncan, a parent of three Wayne students.

When she asked her fourth-grade son to solve a multiplication problem, “he showed me three different ways to do it,’’ Duncan said. “If my children can show me three different ways to do multiplication, I think that is a plus.’’

Nevertheless, so many Wayne parents are alarmed that this spring they put more than 800 signatures on a petition — representing about 20 percent of elementary school families. They expressed concern that the program did not teach basics, and they asked for a more balanced approach toward math education.

The issue flared in Wayne a year after doing so in Ridgewood. There, nearly 200 parents last year signed a petition demanding that the district adopt a traditional curriculum. A newly hired superintendent backed out of the job amid the controversy two weeks before he was to begin work. The Ridgewood schools use two different reform programs and a traditional program in elementary schools.

Both districts have formed committees and hired consultants to seek solutions. Ridgewood hired a conflict-resolution specialist to lead community meetings and wants to seek advice from a university on the next steps, said interim schools Superintendent Timothy Brennan.

Wayne has hired a consultant to oversee a review of its program. It also has surveyed elementary parents and teachers and has hired facilitators to run math committee meetings. The committee is working up a report.

Wayne’s interim schools Superintendent Cindy Randina expects the findings will include the need to emphasize basic skills.

“Our goal is to improve instruction,’’ Randina said.

Everyday Math, one of four or five reform programs available, started 25 years ago at the University of Chicago in a project funded by industries.

“There were concerns that the American worker was not being educated to compete in the international marketplace,’’ Isaacs said.

Jessica Garofalo, a second-grade teacher at Wayne’s Packanack Elementary School, said the program is geared toward a new generation of learners who are used to constant stimulation.

Instead of presenting an equation such as 10÷2=5 and expecting children to remember, Garofalo said, she hands pupils 10 blocks and ask them to divide them into two groups.

“The way we are teaching gives them a solid understanding of what they are doing,’’ she said.

The program also is geared to accommodate the way kids learn, she said — “That is how the brain works: You do it and you form your own meaning; as opposed to: We tell them and they forget.’’

It’s the difference between telling someone how to change a tire, and making them change the tire, Garofalo said.

But parents critical of the program say its not teaching students the basics, including automatic recall of the multiplication tables.

And some are skeptical that reform math is succeeding in making American workers more competitive in the global marketplace.

“I see my children not mastering skills, and I am reading reports that children are not as successful as they should be,’’ said Robyn Kingston, a parent who wrote the petition that circulated in Wayne.

She doesn’t want to see the program’s critical-thinking aspect eliminated, but says, “We need to make sure we get back to basics, and we need to make sure they are mastering skills.’’

Educators predict that future math programs will meld elements of both styles.

Brennan, Ridgewood’s interim superintendent, said it’s an “illusion” that districts can go “back to basics.’’

“ÿ‘Back’ means when you used to sort out kids and give some of them advanced math knowing that some of them would be able to go down the street to the factory or the mill and get a good job and work 40 years without ever having to master advanced math,’’ Brennan said.

“Those places are gone. They are replaced by the global distribution of the workforce,’’ he said. “Now we have to figure out a way for every student to learn advanced math.’’

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