Wednesday, November 15, 2006

Fuzzy Math: Fuzzy Thinking

From the NY Times, an article "As Math Scores Lag, a New Push for the Basics" about rethinking the teaching of "fuzzy math" in American schools.

"The changes are being driven by students’ lagging performance on international tests and mathematicians’ warnings that more than a decade of so-called reform math — critics call it fuzzy math — has crippled students with its de-emphasizing of basic drills and memorization in favor of allowing children to find their own ways to solve problems."

Here is an example of how fuzzy math works:

Fuzzy Math Problem: You have a nest with 5 birds. Three birds fly away. Question: How do the other birds feel? Well maybe that is a little bit of an exaggeration.

But many parents are concerned. From the NY Times article:

“When my oldest child, an A-plus stellar student, was in sixth grade, I realized he had no idea, no idea at all, how to do long division,” Ms. Backman said, “so I went to school and talked to the teacher, who said, ‘We don’t teach long division; it stifles their creativity.’ ”

The biggest advantage of learning and mastering the basics of math or writing at an early age: You have an advantage over your entire lifetime, because once you learn math/writing basics, you NEVER forget them. If you don't learn the basics of math and writing in grade school, it becomes increasingly hard to learn them later in life - the bad habits of poor math and writing skills become ingrained and well-established, and it is difficult to have to re-learn math and writing basics.

Poor math and writing skills are also consistent with poor thinking and poor reasoning skills. As Milton Friedman said: "Sloppy writing reflects sloppy thinking." Perry's corollary would be "Clear and careful writing reflects clear and careful thinking." And I would also say: "Fuzzy math promotes fuzzy thinking."


At 11/15/2006 10:01 AM, Anonymous Anonymous said...

I wholeheartedly concur with Professor Perry's writing and thinking corollary.

Once you obtain exceptional inquisitive, persuasive, and informative writing skills, honing your writing with just a few precise and concise pieces of writing a day keeps those skills sharp and at your immediate disposal.

Writing well achieves resounding results.

At 11/27/2006 6:32 AM, Anonymous Anonymous said...

Many readers of "As Math Scores Lag, a New Push for the Basics" will be interested to know that Milgram, Howe (Yale), Richard Askey (Wisconsin), Retakh (Rutgers), Fuson (Northwestern), the leaders of the math education system in Hungary (including International Mathematical Union President Lovász) and in Russia (including Ilyashenko (Cornell), Gutenmacher, Rabbot, Toom, Yashchenko and many Moscow Center for Continuing Mathematical Education team members), Namikawa (Nagoya), and Gardiner (Birmingham) and other European school mathematics leaders are behind the new mathematics programs (inspired early on by LiPing Ma) of ( The math programs are designed to bring the math competence of North American and Western European teachers and students up to that of their peers in the countries that consistently score at the top of international education rankings.'s Board group includes the likes of former Senator Bill Bradley, former Labor Secretary and current Berkeley Professor Robert Reich, Sun co-founder John Gage, and a growing list of European former Ministers of Education.

The mathematics programs encompass separate Master's Degree-earning programs for elementary and middle school teachers (starting 2007/January) as well as after-school programs (starting 2006/December), both for elite students and for students who need remedial guidance.

As will be expected by those who know members of the content team the learning approach is fundamentally different from the one of Kumon, in that it is based on fewer, harder, richer problems that develop a deep understanding of mathematical concepts. is at the absolute technological forefront in that the company's classrooms are set up so that the Master Instructors and program participants all see each other, from schools or their home, through high-quality Internet video, and in that the community knowledge is quickly expanded by the consistent use of wikis.'s infrastructure will soon allow it to serve, with much live and rich media interaction, some 300,000 teacher program participants and a similar number of student program participants.

In New York City is preparing to run sessions for math coaches - this as a stepping stone towards serving many of the more than 10,000 NYCDOE teachers who need extensive professional development even if strict subject specialization is introduced at the elementary school level.

For information email, with the Subject line preferably set to precisely
Policy and marketing/United States/National and Multi-State/Mathematics/General

Erik Syring

At 3/02/2008 12:57 PM, Anonymous Anonymous said...

The best mathematics education in the world is now available to students everywhere:

- Erik Syring


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