August 22, 2006|By ALFRED POSAMENTIER

NEW YORK -- The No Child Left Behind law, more than anything else, has alerted us to the age-old problem of poor mathematics skills among our elementary school students. Any objective observer could easily conclude from looking at the past 50 years of education history that we are in a vicious cycle that can only be broken by new thinking.

Students tend not to like mathematics instruction because they claim it is uninspiring and sometimes difficult. It is often taught by teachers who are uninspired, using a curriculum that gets attacked and modified every few years with the latest fad.

We keep trying to adjust the curriculum and teaching methods, without any drastic changes in the results. When we provide support for teachers, it is usually in the form of a "Band-aid solution" - that is, sharpening some methods of teaching or adjusting the teaching philosophy in one form or another. However, rarely, if ever, do we attack the root cause of this often-uninspired teaching: getting the instructor excited about teaching mathematics.

One way to break the negative perception of mathematics among elementary school teachers is to show some of the lovely relationships that exist in mathematics. This can be done by using a variety of unusual number relationships, arithmetic shortcuts, clever problem-solving strategies and some unexpected geometric phenomena.

The purpose here is to elicit the "wow" reaction. We want them to say: "I never knew math to be so interesting!"

For example, many two-digit numbers can be multiplied by 11 mentally simply by adding the two digits and placing a single-digit sum between them. Case in point: 24 times 11 is obtained by taking the sum of 2 + 4 = 6, then putting the 6 between the 2 and the 4 to get 264. If the sum is a two-digit number we must carry the one to the tens place. The goal here is not to re-teach arithmetic, just to ignite an interest in the surprised elementary school teacher.

Another useful tidbit is that a number can be divided into thirds only if the sum of the digits is divisible by 3.

Numbers also have some rather astonishing properties. There are numbers, such as 4,913, that are equal to sum of their digits raised to a power (here, (4 + 9 + 1 + 3) cubed = 17 cubed = 4,913). The only two-digit number for which this is true is 81, since (8 + 1) squared = 9 squared = 81. Problem-solving techniques that make a seemingly difficult problem very simple to solve can also motivate the uninitiated teacher.

The often-mentioned "real world" applications that are shown to students frequently miss their mark. Many of these applications are unrealistic or artificial, in which case students cannot relate to them - or the applications are appealing only to the adults who present them. This is compounded by the unfortunate fact that most adults do not like mathematics; many even take a perverse pride in having been poor math students.

Take for example, the well-known "rule of 72," which allows you to determine the number of years it takes money to double when it is earning compound interest. This rule simply says to divide 72 by the interest rate - say 6 percent - and that gives you the number of years (here 72 / 6 = 12) that it takes the money to double.

This may not be as exciting for youngsters, but it can be used to further motivate teachers that there is more to math than what they learned in school. As teachers become more enamored of these mathematics tidbits, they will begin to wonder why mathematics in their school days did not have this spunk.

If we ever want to change the results of mathematics achievement at the elementary school level, we must focus on arousing the teachers' enthusiasm for mathematics, which will then motivate them to enhance their knowledge. Nothing is as important as the teacher's contagious enthusiasm for the subject he or she is teaching. What you have, then, is a well-prepared and enthusiastic elementary school teacher. Only this will break the vicious cycle of this pervasive dislike for mathematics.

Alfred Posamentier is dean of the School of Education, City College of New York. His e-mail is asp2@juno.com.