Gli Americani e la matematica

  Nella scuola secondaria pubblica degli USA, è opinione corrente che gli insegnanti di  matematica non rendono piacevole agli studenti  questa disciplina.

Il New York Times ospita un  dibattito, con interventi qualificati,  sulle possibili diverse modalità di affrontarne  l'insegnamento.

Alcuni esprimono la  convinzione che la matematica, piuttosto che ancella e supporto ad altre discipline scientifiche ( fisica, chimica, scienze) o applicazioni , sia bella in sè. E questo dovrebbe essere sufficiente per renderla apprezzabile agli studenti.

Piacevole è anche osservare come alcuni numeri godano di particolari proprietà. Ad esempio, il 2002 è un numero che può leggersi in entrambi i versi. E' cioè palindromo. Il prossimo anno con numero palindromo sarà il 2112. Cioè fra 110 anni.

La medicina sarà in grado di mantenerci in vita a quella data?

January 2, 2002

Madam, I'm 2002 — a Numerically Beautiful Year

By ALFRED S. POSAMENTIER

Now, in the year 2002, we are the last generation for more than the next thousand years to experience two palindromic years in a lifetime. Palindromes in mathematics are numbers that read the same in both directions, like 2002 and 1991. In the English language there are very well-known palindromic words, like "rotator" and "reviver," and there are also sentences that are palindromic, like "Madam, I'm Adam."

Palindromic numbers are not only pleasing in appearance, but also harbor some nice, curious qualities. For example, take any number, write it in reverse order and add the two numbers. The sum will likely be a palindromic number, and if not, then simply continuing this process by adding the sum to its reverse should eventually lead to a palindromic number. This surprising result is the kind of discovery that can pique interest in numbers even in students indifferent to math.

Teachers should be able to capitalize on the beauty in mathematics, and specifically the charm of some numbers to hook students on studying mathematics. But qualified math teachers who might actually inspire children are in short supply, and math teaching in today's schools is often dry and boring. The problem is not new. Math instruction at the elementary school level, when students form their first impressions about the nature of math and their own abilities with numbers, has historically been mediocre. Without a strong beginning, a student's chances for sustaining interest in this field are very small indeed. The problem is compounded by relatively weak teaching at the secondary level as well.

A number of quick-fix programs to increase the supply of secondary school math teachers have been put in place around the country through the process of alternative certification. Participants in one such program in New York City function reasonably well, but many also lack the ability to bring to their classes a depth of understanding of math that allows a teacher to do more than merely conform to the prescribed instructional plan. A marginally competent teacher may not necessarily be skilled enough to promote interest in or appreciation for math among students.

At a time when there is a national shortage of math teachers, made worse by a low supply of math-prepared students, we must look beyond the quick-fix solutions. We must develop better and more creative training programs for elementary math teachers. We need to give them more classroom time on this subject. And when students begin to pursue the study of math, we must make the teaching profession more attractive, financially as well as by giving teachers more control of how they teach.

The point is to make math intrinsically interesting to children. We should not have to sell mathematics by pointing to its usefulness in other subject areas, which, of course, is real. Love for math will not come about by trying to convince a child that it happens to be a handy tool for life; it grows when a good teacher can draw out a child's curiosity about how numbers and mathematical principles work. The very high percentage of adults who are unashamed to say that they are bad with math is a good indication of how maligned the subject is and how very little we were taught in school about the enchantment of numbers.

Alfred S. Posamentier is professor of mathematics education and dean of the School of Education at City College of the City University of New York.


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Math's Inner Beauty Is Enough

Alfred S. Posamentier ("Madam, I'm 2002 — a Numerically Beautiful Year," Op-Ed, Jan. 2) is quite right about the failure of our public secondary schools to make math interesting.

When I studied pre-calculus in high school, I wondered what made the formulas and equations we were working through true. Did they reflect the structure of the world? If so, was this structure physical? When I asked my teacher about this, however, I was told to be quiet and wait until I learned about such things in college. That was the last math class I took, as I concluded that English literature was actually more concerned with reality than math was.

ANDREW NORRIS
Philadelphia, Jan. 2, 2002
The writer is an assistant professor of political science at the University of Pennsylvania.
• 
To the Editor:

In his Jan. 2 Op-Ed article about mathematics education, Alfred S. Posamentier concludes that "the point is to make math intrinsically interesting." This is exactly what music educators have advocated for years about their subject.

It is misguided to justify teaching music by pointing to the marching band that glorifies athletic activities, or the fact that it "builds stronger minds," even though that may be perfectly true. Good teachers should teach students the enchantment not just of numbers, but of music, literature and the other arts as well.

  MARTIN MOSER
New York, Jan. 2, 2002
The writer is an adjunct professor of music at St. John's University.
• 
To the Editor:

"Madam, I'm 2002 — a Numerically Beautiful Year" (Op-Ed, Jan. 2), by Alfred S. Posamentier, does not completely explain the beauty of mathematics. It lies not only in the interesting things that happen when we play with numbers, but in the fact that we can understand why such things happen.

It will not help our children to study palindromes to the exclusion of long division. One is a cute dead end, while the other goes to the heart of our number system. Making math attractive to students and teachers does not have to mean skipping the good parts.  

JONATHAN GOODMAN
New York, Jan. 2, 2002
The writer is a professor of mathematics, Courant Institute of Mathematical Sciences, New York University.
• 
To the Editor:

After reading "Madam, I'm 2002 — a Numerically Beautiful Year" (Op-Ed, Jan. 2), by Alfred S. Posamentier, a thought occurred to me: at 8:02 p.m. on Feb. 20 of this year, there will be a minute that will extend this palindrome by eight digits (2002 0220 2002), something I imagine happens far less often than the annual variety Mr. Posamentier spoke of so lovingly in his article. (While I have used military time and include no commas, colons or dashes, these minor considerations melt away when faced with such a numerical force.)

I hope that everybody takes pause to savor this brief but timely moment.  

TOM HOOK
Fairfield, Conn., Jan. 2, 2002
• 
To the Editor:

In his Jan. 2 Op-Ed article about our palindromic year, Alfred S. Posamentier said, "We are the last generation for more than the next thousand years to experience two palindromic years in a lifetime."

As a 10-year-old, I look to the future and think that by the palindromic year 2112, medicine might be so improved that people live more than 110 years. People born in 2002, then, might live to see 2112. Or, people born in 2112 could also experience the next palindromic year, 2222.
BEN BERSOFF
Haverford, Pa., Jan. 2, 2002
• 
To the Editor:

While palindromes (Op-Ed, Jan. 2) are certainly an amusement for mathematicians and a challenge for verbal gymnasts, they are for molecular biologists the very essence of genetic regulatory functions and of target sites for many enzymes.
RICHARD P. NOVICK, M.D.
New York, Jan. 2, 2002
The writer is a professor of microbiology and medicine at New York University.
• 
To the Editor:

Re "Madam, I'm 2002 — a Numerically Beautiful Year" (Op-Ed, Jan. 2): I do not want to see any more articles about palindromic years until 2112.  

JAMES MURPHY
Boston, Jan. 2, 2002