How to best teach math has been debated since the beginning of the twentieth century.

One side, mostly mathematicians and a growing number of parents, believe that children need to master basic math facts and algorithms in order to fully understand and develop higher math reasoning skills. They also believe that mathematics is a fundamental academic discipline that is not only a prerequisite to higher learning but also a necessary skill for all people if they want to succeed in the technological future.

The other side, mostly educators and some psychologists believe that children need to come to an understanding of mathematics organically. They feel that children must be given the freedom to arrive at answers creatively and that teaching proven equations robs children of their creativity. They also believe that the ability to add, subtract, multiply and divide is unimportant now that children have calculators. The mathematics that this side promotes, stresses the ability to verbalize the answers with words. Over the last ninety years the educator’s philosophy has dominated math instruction in the United States.
Read The History of Mathematics Instruction in America

Twelve Myths About Math Education And Why You Shouldn’t Believe Them

Two education advocacy organizations of parents, mathematicians, and K-12 educators debunk arguments put forth by the supporters of Reform Math.
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NCTM Standards receives letter of opposition from mathematicians

Over 200 mathematicians and scientists, including four Nobel Prize recipients, endorsed a letter asking for the Department of Education to withdraw its endorsement of curricula based on the NCTM standards.
Text of Letter of Department of Education Director Riley

Mathematicians in California Create “Gold” Math Standards:

Stanford University mathematicians successfully wrote rigorous, focused, and coherent standards that were adopted by California in 1998. Results show improvements of 30 – 40% for low-income and ELL learners on the SAT 9.
California Math Standards Document(pdf 73 pages)

11 Questions & Answers on Progressive Math and Students … the Disadvantaged ~ Boys ~ the Gifted ~ Special Needs and ELL:

Disadvantaged students of all races live in environments that require survival on a day-to-day basis. Survival in poverty is concrete, whereas survival in school and work is usually abstract. Mental models must be built with basic strategies to teach organizational skills as well as concepts of abstraction—such as issues of time, space, appropriate language according to its setting, and part-to-whole relationships (cause and effect), according to Dr. Ruby Payne. Niki Hayes Article

U.S. declines in engineering graduates:

U.S. engineering graduates have declined 20 percent in the past twenty years. Of the nearly 1.1 million U.S. high school seniors who took the college entrance exam in 2002, less than 6 percent had plans to study engineering. That is a 33 percent decrease from 10 years earlier.
Purdue University Article

U.S. ranks at the bottom in international testing:

By 8th grade US students are 2-3 years behind global peers. This gap widens as grade levels rise. In 2003, the U.S. performance on the Program for International Student Assessment (PISA) tests in math literacy and problem solving was lower than the average performance for most participating countries. We ranked 24th out of 29 countries. The normally top 5 performing Asian countries did not participate in the 2003 test, thus inflating our abysmal standing.
National Center for Education Statistics Website – About PISA
Third International Math & Science Survey (TIMSS) (pdf 24 pages)

Singapore Method outperforms reform curricula:

In 2004, after a 4-year study using the Singapore Math Method, students at four schools in Montgomery County, MD increased math scores on their state annual test from the high 50’s/low 60’s to the upper 80’s/low 90’s, translating to a 50% increase in scores. NPR Radio Program about Singapore Math
http://www.cde.ca.gov/re/pn/fd/documents/math-stnd.pdf

No reliable studies verify the effectiveness of reform curricula:

In 2004, the National Research Council evaluated all studies of reformed math programs and concluded, “On the basis of the committees analysis of these 147 studies, we concluded that the corpus of evaluation studies as a whole across the 19 programs studied does not permit one to determine the effectiveness of individual programs with a high degree of certainty, due to the restricted number of studies for any particular curriculum, limitations in the array of methods used, and the uneven quality of the studies.”
National Academies Press – Book Review

Singapore curriculum prepares students better than CMP:

“The level of the mathematics in both CMP (Connected Math) and MIC (Mathematics in Context) is not as advanced as that in the Singapore curriculum…It is also our prediction that students wishing to take calculus before the end of their 12th grade year are likely not to be on track to do so after completing 8th grade CMP or MIC, but would be ready to do so after completing Singapore’s SL2. … Moreover, we are skeptical about the possibility of maintaining the interest of high-end students while progressing at the pace necessitated by the “discovery process”.” University of WA Report: Pp 163-164, Nov 2000.
UW Applied Mathematics Department Report (pdf 172 pages)

Tutoring is on the rise in the United States:

“Tutoring is a $4 billion business, and that figure is rising. It has become a staple of the middle class, with millions of students in both public and private schools using one-on-one tutors as well as supplementary education centers like Kaplan, Princeton Review, and Kumon.”
“Growth Spurt: Rise of Tutoring in America, NPR 6/6/05

Poor curriculum worsens the educational gap:

“Poor math curriculum is one of the reasons for the racial education gap in math. There is too muchflexibility in math standards, requirements and instruction.” Dr. William Schmidt, February 27, 2006, Seattle School District Meeting

Reform curricula is not recommended by top mathematics professors:

“The NSF funded curricula generally encourage overuse of calculators, do not give students sufficient support to achieve automatic recall of basic number facts, do not teach algorithms properly, and pay insufficient attention to the arithmetic of fractions. We regard the K-5 program "Investigations in Number, Data, and Space" (TERC) as especially deficient.” R. James Milgram, Professor of Mathematics, Stanford University; Wilfried Schmid, Professor of Mathematics, Harvard University March 2006