'New Math': What Does and Doesn't Add Up

Regarding your editorial "By the Numbers" (Dec. 8): If you look closely, you will see that your example of the "new" subtraction method of long division is exactly the same as the "old." It's true that the method you describe would allow the selection of other multiples than you have chosen (100,30,4), but those numbers are the quickest way to subtract out the division. They're also numbers that would be selected by the "old" method. That is why the "old" method was chosen long ago.

This kind of playing around with methods of doing arithmetic (not math) is precisely why we continue to fail to improve our nations' numeric literacy.

Charles Gahr

Nanoose Bay, British Columbia

"Modern math" or "new math" had its birth in the early 1960s. In 1962, the School Math Study Group (SMSG), funded by the National Science Foundation, the Mathematical Association of America, and the National Council of Teachers of Mathematics, attempted to make the teaching of elementary mathematics logical and reasonable. In 1963, SMSG published an extensive document detailing the concepts behind elementary mathematics.

Even though the emphasis was on simplifying and explaining the underpinnings of mathematics, textbook publishers rushed to include the buzzwords created by this new approach: sets, subsets, elements, inverse operations, arrays, binary operations, regrouping, and bases. They also included many of the symbols used by SMSG, like braces, brackets, algebraic symbols, and the positioning of numerals when carrying out various operations (addition, subtraction, multiplication, division).

SMSG used the new-math language and accompanying symbols to simplify "old math." Its intent was to present a new way of looking at mathematics and a new way of teaching it to children.

Unfortunately, textbook publishers didn't seem to comprehend this or were afraid of offending the more conservative educators who purchased the texts. For whatever reason, the most prominent educational textbook publishers included both the new and old math in the same texts. This confused everyone. And instead of simplifying things, it added a whole new vocabulary of terms and put problems together in such a way as to defeat many of the newer, streamlined concepts.

Most veteran teachers didn't understand the new-math concepts or approaches, and they resented the additional work that was added to their already-packed math lessons. This unfortunate situation lasted for many years and made teaching math less palatable than it had been before it was "simplified." It has only been in the past 10 years that I haven't heard any negative jokes about modern math.

In education, there is little that has not come and gone at least once - usually in 10-year cycles and frequently called by a new name each time. I have seen the method of teaching long division as repeated subtraction come around at least three times since the 1960s. Apparently, it is circling again. By the way, I found it fascinating when I was first introduced to it, too.

Dale Hammond

Spokane, Wash.

We don't need a space arms race

I refer to the article "Drawing Battle Lines in Space" (Dec. 17): Why does the US have to take the lead in the establishment of another arms race, this time in outer-space?

Once again we are demonstrating that we will accept world peace only on our terms. And the rest of the world will have to accept those terms or potentially face the deadly consequences of an attack by our "space rods." Why do we once again have to go through a massive and extremely expensive arms race that will later require treaties to dismantle? Why not move straight into the phase of negotiating treaties? It all seems so much more logical to strive for peace by peaceful means.

Rudy Ramp

Arcata, Calif.

Your letters are welcome. All letters are subject to editing. Mail to "Readers Write," One Norway St., Boston, MA 02115, fax to 617-450-2317, or e-mail to

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