Here we will discuss three critical issues that have to be addressed for the CCSSM to succeed: math textbooks, assessment, and teachers' preparation.

Before the CCSSM were adopted, we already had a de facto national curriculum in math because the same collection of textbooks was (and still is) widely used across the country. The deficiencies of this de facto national curriculum of "Textbook School Mathematics" are staggering. The CCSSM were developed precisely to eliminate those deficiencies, but for CCSSM to come to life we must have new textbooks written in accordance with CCSSM. So far, this has not happened and, unfortunately, the system is set up in such a way that the private companies writing textbooks have more incentive to preserve the existing status quo maximizing their market share than to get their math right. The big elephant in the room is that as of today, less than a year before the CCSSM are to be fully implemented, we still have no viable textbooks to use for teaching mathematics according to CCSSM!

The situation is further aggravated by the rush to implement CCSSM in student assessment. A case in point is the recent fiasco in New York State, which does not yet have a solid program for teaching CCSSM, but decided to test students according to CCSSM anyway. The result: students failed miserably. One of the teachers wrote to us about her regrets that "the kids were not taught Common Core" and that it was "tragic" how low their scores were. How could it be otherwise? Why are we testing students on material they haven't been taught? Of course, it is much easier and more fun, in lieu of writing good CCSSM textbooks, to make up CCSSM tests and then pat each other on the back and wave a big banner: "We have implemented Common Core -- Mission accomplished." But no one benefits from this. Are we competing to create a Potemkin village, or do we actually care about the welfare of the next generation? What happened in New York State will happen next year across the country if we don't get our act together.

[As a side remark, we note that even in the best of circumstances, it's a big question how to effectively test students in math on a large scale. Developing such tests is an art form still waiting to be perfected, and in any case, it's not clear how accurately students' scores on these tests can reflect students' learning. Unfortunately, our national obsession with the test scores has forced teachers to teach to the test rather than teach the material for learning. While we consider some form of standardized assessment to be necessary (just as driver's license tests are necessary), we deplore this obsession. It is time to put the emphasis back on student learning inside the classroom.]

These misguided practices give a bad name to CCSSM, which is being exploited by the standards' opponents. They misinform the public by equating CCSSM with ill-fated assessments, such as the one in New York State, when in fact the problem is caused mostly by the disconnect between the current Textbook School Mathematics and CCSSM. It is for this reason that having the CCSSM is crucial, because this is what will ensure that students are taught correct mathematics rather than the deficient and obsolete Textbook School Mathematics.

It is possible and necessary to create mathematics textbooks that do better than Textbook School Mathematics. One such effort by commoncore.org holds promise: its Eureka Math series will make online courses in K-12 math available at a modest cost. The series will be completed sometime in 2014. [Full disclosure: one of us is an author of the 8^{th} grade textbook in that series.]

The current situation with the CCSSM puts math teachers in a precarious and unenviable position. They are being asked to implement a CCSSM-based curriculum that requires content knowledge that they, through no fault of their own, do not possess. The education establishment -- including institutions of higher learning -- is seemingly uninterested in teaching teachers this much-needed content knowledge. This is a critical moment when educators and mathematicians must rise to the occasion and work together to give teachers the means to acquire this knowledge.

For the past 14 years, one of us has been doing exactly that, giving three-week summer institutes for elementary and middle school teachers to help them systematically replace their knowledge of Textbook School Mathematics with correct mathematics. If more mathematicians get involved in this process, more teachers will be able to acquire the knowledge they need. And mathematicians should also help by visiting schools to show students the beauty of mathematics and how it is used in our daily lives.

Math education is a multi-dimensional problem. Its solution will require time, money, effort, and deep commitment from everyone involved. But this is a problem we must confront because the future of a generation of students is at stake. By introducing rigorous national standards, the CCSSM have made a major breakthrough, laying the groundwork for progress. Now the real work must begin.

Edward Frenkel is Professor of Mathematics at University of California, Berkeley and the author of the new book "Love and Math."

Hung-Hsi Wu is Emeritus Professor of Mathematics at University of California, Berkeley and the author of "Understanding Numbers in Elementary School Mathematics".

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Their concern -- detailed in Gregory Kristof's June 1, 2012 piece for the Huffington Post "Common Core Math in North Carolina Would Keep Elementary Students From Taking Middle School Courses" -- is that these students will be impacted negatively by having to study material that is no longer challenging or considered beyond grade level. As a result, a misguided hypothesis has emerged: the best way to educate our brightest students in mathematics is to let them accelerate through the grades. But, many of us in institutions of higher learning across the country do not agree.

We believe that the quality of the mathematics education is far more important. We feel strongly that students learning the basic topics in K-12 mathematics thoroughly and well is more important than how fast they can learn.

There are good reasons to believe that we are shortchanging all students, including those deemed the most advanced in mathematics. At present, the school math curriculum generally divides into two kinds of learning: it either emphasizes purely procedural knowledge with little reasoning for why it works, or emphasizes vague, conceptual knowledge at the expense of skills and precision. Neither leads to the kind of mathematics learning that will get our nation out of its present educational doldrums.

To improve, we must begin with a better set of math standards -- one that is mathematically correct and coherent. Overall, CCSSM meet these criteria in surpassing fashion. The CCSSM will undoubtedly be more challenging to all students because, for perhaps the first time, students will be asked to master both procedural and conceptual knowledge and learn each topic in a logical progression.

Learning the mathematics prescribed by CCSSM requires that all students, including those most accomplished in mathematics, rise to the challenge by spending the time to learn each topic with diligence and dedication. Skimming over existing materials in order to rush ahead to more advanced topics will no longer be considered good practice.

Mathematics is by nature hierarchical. Every step is a preparation for the next one. Learning it properly requires thorough grounding at each step, and skimming over any topics will only weaken one's ability to tackle more complex material down the road. The weakness usually shows up in students' scientific work in college. This is one reason why many of my colleagues bemoan the practice of acceleration in schools.

Parents of students in accelerated elementary school math need not worry. There will still be an abundance of new concepts to learn and apply. For example, the fifth-grade CCSSM are vastly different from North Carolina's previous fifth-grade math standards. If next year's math curriculum is consistent with the CCSSM, then students in North Carolina will learn the following topics that are not in the previous fifth-grade standards: the correct way to add, subtract, and multiply fractions; the correct way to divide whole numbers by a unit fraction and a fraction by a nonzero whole number; the reason why the area of a rectangle is the product of (the lengths of) the sides when the side lengths are fractions; a correct way to think of volume; and a correct conception of a coordinate system.

These constitute a very substantial portion of the elementary math curriculum.

I said earlier that, to improve student achievement in mathematics, we have to begin with a better set of math standards. Adopting the CCSSM is merely a beginning. Because the expectations of the CCSSM are substantial and rigorous, our effort should be focused on effective implementation of the CCSSM in a way that does them justice. We should not allow a sideshow about acceleration to overshadow our nation's drive to achieve excellence in mathematics education.]]>