To the Editor:

This letter was prompted by an article on school mathematics that recently appeared in the Wall Street Journal. The article painted a very misleading view of the new document ?Curriculum Focal Points,? published by the National Council of Teachers of Mathematics (NCTM).

Clearly, the Focal Points are not meant to replace the previous NCTM standards, which have influenced many state expectations, standards, assessment and textbook selection criteria. The Focal Points are meant to extend and build on NCTM?s previous work. Important mathematical topics in each grade, from pre-kindergarten through eighth grade have been identified in the Focal Points as the essential mathematical content children need to understand thoroughly.

The Focal Points are not just about the basics, as some of the media have inaccurately portrayed (Teaching Math, Singapore Style, New York Times, Sept. 18; Math Teachers Urged to Focus on Basic Skills, Register-Guard, Sept. 13). The Focal Points are about understanding of concepts to support the recall of basic facts, to develop fluency with efficient procedures and also to understand why the procedures work, so that they can be used to solve problems in a variety of situations.

I urge your readers, especially those involved with educational decisions, to become better informed about the real purpose of Curriculum Focal Points. I recommend that readers take a moment to go to www.nctm.org and read for themselves the documents posted there that introduce and describe NCTM?s ?Curriculum Focal Points.?

Winnie Miller, President

Oregon Council of Teachers of Mathematics

Lake Oswego, OR, 27 September 2006

To the Editor:

I found your editorial demeaning to the curricular challenges

regularly faced by mathematics teachers in this country. I present

the following for you to consider:

Forty-nine of our 50 states have developed state curricular

frameworks. Most of these have been influenced by the National

Council of Teachers of Mathematics' "Curriculum and Evaluation

Standards" (1989), or the more recent "Principles and Standards for

School Mathematics" (2000). Close to 30 of the states have revised

their curricular frameworks since 2003.

What some refer to as basic skills (for example, multiplication

facts, and fluency with the addition, subtraction, multiplication and

division of whole numbers) have always been a fundamental core of

elementary school mathematics. Always.

But we want more. We want children to understand the mathematics they

are learning and we want them to be able to solve problems, which is,

in the long run, why we do mathematics.

Our recently released "Curriculum Focal Points" identifies important

mathematical topics in each grade, from prekindergarten through

eighth grade. It identifies the mathematical content students need to

understand deeply and thoroughly for future mathematics learning.

It offers a framework to guide states and school districts as they

design and organize revisions of their expectations, standards,

curriculums and assessment programs.

This is not a change, but reflects what has been the council's

commitment to teaching and learning for more than 80 years.

Francis Fennell

President, National Council of Teachers of Mathematics

Reston, Va., Sept. 18, 2006

To The Editor,

Your editorial, Teaching Math Singapore Style, reports that NCTM reversed its decades long positions. This is factually untrue. NCTM, representing tens of thousands of math teachers like myself, never advocated eliminating the learning of multiplication facts or the quadratic formula. Instead, NCTM recommended that memorization without understanding was meaningless. Rather than an ?infamous fad,? math education in the last 20 years raised student achievement.

Focal Points is a response to the criticism that our curriculum is a mile wide and inch deep. It is welcomed by all of us who teach math because we know how unfocused the current curriculum is. The report does not speak to how these topics should be taught but rather, what topics to teach.

I would add a third recommendation to the editorial?s two. Avoid polemical words such as ?fad? and ?fuzzy? when talking about the serious business of raising math achievement in the U.S.

Andy Clark

K-12 Math Coordinator (retired)

Portland Public Schools

From: Daniel Raguse <danr@mathlearningcenter.org>
Date: September 19, 2006 5:43:24 PM PDT
To: letters@nytimes.com
Subject: Teaching Math, Singapore Style

Your recent editorial "Teaching Math, Singapore Style" is misrepresenting NCTM's new Focal Points so badly, that one wonders if you have even read the NCTM release. In no way do these new conceptual focal points reverse anything NCTM has been doing since 1989. If you read NCTM President Skip Fennell's introductory letter <http://www.nctm.org/focalpoints/president_letter.asp> , you would know that, as he says, "The focal points are compatible with the original Standards and represent the next step in realizing the vision set forth in Principles and Standards for School Mathematics in 2000." The NEXT STEP. NCTM isn't abandoning anything, they are building on what they have.

NCTM's work these past couple decades represents real reform in mathematics education and is certainly not a fad that has met its demise. They have never supported "fuzzy math" or "children wandering through problems in a random way without ever learning basic multiplication or division." Where did you get this? My guess is from some angry parent you know who hasn't a clue about the math her son is learning because it isn't being taught the way she was taught. (Even thought she never understood math but worked hard to memorize facts and formulas.)

For a reputable publication like the NY Times and Wall Street Journal to get this so wrong really frightens me. Please correct your short-sighted reporting. The focal points do not promote how to teach math but rather emphasize what to teach. They follow standards that promote conceptual understanding and reasoning in order to tackle real problems. They certainly don't promote rote memorization of the "basics" without understanding--something we routinely did for years that produced the math phobia so many adults have today. The basics have always been part of NCTM's standards and always will be. But reasoning and processing are also part of those standards. Don't mislead your readers/ Please go back and read NCTM's purpose for the Focal Points. Get it right so you don't set this country back 30 years.

Dan Raguse
The Math Learning Center