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according to the report, this approach "fails to adequately capture the level of content mastery, rigor, and depth of change necessary to meet the expectations of college and career readiness in the Common Core standards."

the report identified several other challenges affecting implementation:

Ongoing budget crises at the state and local level;

The misconception that the Common Core State Standards are federal standards;

Initiative fatigue on the part of teachers in the midst of simultaneous and sometimes conflicting educational policy shifts;

The need to modify teacher preparation programs;

The need for colleges and universities to adapt their admissions practices based on the changes happening at the K-12 level; and

Communications between state agencies and educators.

Educators themselves also identified several concerns, including the need for:

Information about how Common Core implementation will affect policies governing their careers and teaching practices;

Access to model lessons, resources, and professional development;

Time for planning; and

Information about Common Core assessments and the technologies that will be required to implement them.

Fordham’s review does not unequivocally say the standards are higher, either. They may be higher than some state standards but they are certainly lower than the best of them

Nor are the Common Core standards necessarily clearer.

Andrew Porter, dean of the University of Pennsylvania’s Graduate School of Education

conclusion was stark: Those who hope that the Common Core standards represent greater focus for U.S. education will be disappointed by our answers. Only one of our criteria for measuring focus found that the Common Core standards are more focused than current state standards…Some state standards are much more focused and some much less focused than is the Common Core, and this is true for both subjects. We also used international benchmarking to judge the quality of the Common Core standards, and the results are surprising both for mathematics and for [ELA].… High-performing countries’ emphasis on “perform procedures” runs counter to the widespread call in the United States for a greater emphasis on higher-order cognitive demand.

with only somewhat less redundancy in the middle grades

There is much to criticize about them, and there are several sets of standards, including those in California, the District of Columbia, Florida, Indiana, and Washington, that are clearly better.

Where this gap is most obvious, and most important, is in laying the foundation for college readiness in mathematics early, by grade 6 or 7. Judging by state standards, few people see a connection between elementary school mathematics and college math, let alone really understand how the foundation is built.

et Common Core is vastly superior—not just a little bit better, but vastly superior—to the standards in more than 30 states.

the standards don’t rank in terms of quality in the middle 20 percent of state standards, but, instead, fall in the top 20 percent.

Fewer than 15 states are explicit about the need for students to know the single-digit number facts (think multiplication tables) to the point of instant recall. States love to have kids figure out many ways to add, subtract, multiply, and divide, but often leave off the capstone standard of fluency with the standard algorithms (traditional step-by-step procedures for the addition, subtraction, multiplication, and division of whole numbers).

only 15 states mention common denominators. Common Core does a pretty good job with arithmetic, even a very good job with fractions.

do the math standards resemble those recommended by the National Council of Teachers of Mathematics (NCTM)

There will always be people who think that calculators work just fine and there is no need to teach much arithmetic, thus making career decisions for 4th graders that the students should make for themselves in college. Downplaying the development of pencil and paper number sense might work for future shoppers, but doesn’t work for students headed for Science, Technology, Engineering, and Mathematics (STEM) fields.

There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem.

There will always be the standard algorithm deniers

Some seem to believe it is easier to teach “high-level critical thinking” than it is to teach the standard algorithms with understanding. The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared. Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.

You learn Mathematical Practices just like the name implies; you practice mathematics with content.

At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics

NCTM followed shortly with its 2006 Curriculum Focal Points, a document that finally focused on what mathematics is all about: mathematics. Since then, NCTM seems to have regressed, as evidenced by its 2009 publication Focus in High School Mathematics, a document that is full of high-minded prose yet contains little rigor or specificity.

The Common Core mathematics standards are grade-by-grade‒specific and hence are more detailed than the NCTM 2000 standards, but they do resemble them in setting their sights lower than our international competitors, by, for example, locking algebra into the high school curriculum.

And they contain inexplicable holes even when compared to the much shorter NCTM Curriculum Focal Points, the major one being the absence of fraction conversion among their multiple representations (simple, decimal, percent). Other puzzling omissions include geometry basics such as derivation of area of general triangles or the concept of pi. One can argue those can be inferred, but the same can be said regarding all those state standards we acknowledge as “bad”—that all those missing pieces “can be inferred.”

How do the Common Core math standards compare to those in use in the world’s highest-performing nations?

the Common Core standards are not on par with those of the highest-performing nations.

Professor R. James Milgram of Stanford, the only professional mathematician on the Common Core Validation Committee, wrote when he declined to sign off on the Common Core standards: This is where the problem with these standards is most marked. While the difference between these standards and those of the top states at the end of eighth grade is perhaps somewhat more than one year, the difference is more like two years when compared to the expectations of the high achieving countries—particularly most of the nations of East Asia.

Professor William McCallum, one of the three main writers of the Common Core mathematics standards, speaking at the annual conference of mathematics societies in 2010, said, While acknowledging the concerns about front-loading demands in early grades, [McCallum] said that the overall standards would not be too high, certainly not in comparison [with] other nations, including East Asia, where math education excels.

Jonathan Goodman, a professor of mathematics at the Courant Institute at New York University,

“The proposed Common Core standard is similar in earlier grades but has significantly lower expectations with respect to algebra and geometry than the published standards of other countries.”

The enrollment requirements of four-year state colleges overwhelmingly consist of at least three years of high school mathematics including algebra 1, algebra 2, and geometry, or beyond. Yet Common Core’s “college readiness” definition omits content typically considered part of algebra 2 (and geometry), such as complex numbers, vectors, trigonometry, polynomial identities, the Binomial Theorem, logarithms, logarithmic and exponential functions, composite and inverse functions, matrices, ellipses and hyperbolae, and a few more.

What should we make, then, of a recent study purporting to “validate” that Common Core standards indeed reflect college readiness?

Look at California’s standards for example. They are great standards and have been unchanged for over a decade, but many in math education hate them. They think they are all about rote mathematics, but I think such people have little understanding of mathematics.

We, in this country, are still not on the same page about what content is most important, even if everyone says they’ll take Common Core. Without a unified, concerted effort to teach real mathematics, there isn’t much chance of catching up.

In other countries, if you say “learn to multiply whole numbers,” no one questions how this should be done; students should learn and understand the standard algorithm. In the U.S., even if you say “learn to multiply whole numbers with the standard algorithm,” some people will declare wiggle room and try to avoid the standard algorithm.

What, then, are your main areas of disagreement?

Ze’ev refers to Andrew Porter’s work to support his argument that Common Core lacks focus.

he says that 39.55 percent of grades 3‒6 coarse-grained topics for the states are on Number Sense and Operations, but Common Core gets 55.47 percent. To me, that says that Common Core focuses on arithmetic in grades where arithmetic should be the focus, and that the states did not focus on arithmetic.

If Common Core is mediocre, then mediocre is being set at a high standard. There are many states that set a very different, and much lower, standard for mediocre.

I would take these interview comments with a grain of salt. Everyone is an expert.

I can tell you that Ze’ev had not taught and I don’t think has spent any amount of time in the classroom. I served on a committee with Ze’ev evaluating questions for the California Standards Test.

Ze’ev is correct. I thought this long ago. It’s too vague and there is too much wiggle room. The wiggling will be in the downward direction. In fact, they don’t have to wiggle very much. Everyday Math will add a few more units and Math Boxes about standard algorithms, and then they will continue to trust the spiral.

BY FAR the majority of the population did not “get” math when it was taught using the methods and approaches these pompous mathematicians propose. Like so many uninformed “experts” they think that if we just teach math the way they learned it every things will be smooth sailing. But we taught math their way for a very, very long time and we failed. And that’s when the world hd very little technology, far less problems to solve, and agriculture and manufacturing ruled the world. But the world has changed fellas. And we now have scientific research that debunks the didactic, direct, one-way approach to learning math. For one thing we’ve learned that the brain doesn’t learn for the long term the way they propose. Their methods work to pass tests in the short run, but do little to instill knowledge retention and application of the mathematics in solving real problems. If their approaches to learning math worked, we wouldn’t have a very large segment of the adult population, including a lot of elementary teachers, saying things like, I never got math, I hate math, math is too hard.

Thankfully, we’re finally moving toward an educational system that honors the mathematical practices on which the CCSS were developed.

Bottom line… We need to ensure that our students are getting a solid foundation at the early grades to ensure that they are able to engross themselves in deeper, more abstract problems in the future. This, I believe will be enhanced by the common core although I would agree that the standards themselves do not fix the issues.

four questions to guide districts in supporting teachers during this transition.

these questions will help ground and steer districts to ensure teachers and students alike are ready.

first guiding question

what kind of professional development will clarify which previous strategies associated with past assessments should be kept and/or adapted, and which should be discarded?

This question should be raised with teams of reading teachers, both schoolwide and grade by grade. Assessments related to advanced student learning not described by the common core should also be addressed. We believe previous lessons learned about alternate assessments and special populations, such as English-language learners, deserve special attention.

second question

There are no common-core content domains for reading, like those that are available for math. Therefore, what kinds of professional development should be designed to support the identification of curriculum-mapping and instructional strategies for reading? This question demands a long-term view toward comparative student growth across grades.

we have documented a proliferation of free online trainings at the state level that support transitioning to reading within the common core. Superlative examples of state-level offerings include those developed by the Oregon and Maine education departments.

third question, is which professional-development activities and resources should be generated at the district level?

it appears that extensive support programs for teachers are not as common at the district level. A few standouts at the district level include Orange County, Calif., and the city of Baltimore.

a variety of partial-, full-, and multi-day professional-development seminars for teachers and administrators related to the common-core English/language arts standards

The work in both Orange County and Baltimore illustrates a larger lesson: In deciding what kind of professional-development opportunities to create at the district level, a focused approach should be used, one that is resplendent with examples of both content and practice.

fourth and last question

Appropriate technology-based skills related to instruction and to formative, interim, and summative assessments of reading must be considered, leading to our final question: What professional-development activities would ensure the kind of teacher proficiency needed to administer, understand, and interact with computer-adaptive and computer-based testing specific to reading?

A baseline of teacher knowledge, skills, and attitudes related to technology must first be carefully documented before any professional development can be designed. Likewise, corresponding documentation of teacher growth should be maintained throughout the process.

basic professional-development needs among teachers implementing the common core include training on literacy assessment, technology skills, practical learning experiences oriented toward the new standards and assessments, time for professional collaboration, a teacher-leader in each school, and continuous networking between teachers.

we believe that states can minimize the cost by taking advantage of emerging best practices and consciously repurposing existing state funding streams focused on these areas.

We first estimated the expenses associated with a business-as-usual scenario, in which states simply spend more on traditional delivery methods—hard-copy textbooks, face-to-face professional development, and paper-based standardized tests. Such an approach would, according to our calculations, require an additional $12 billion in spending across the 46 states and the District of Columbia, or an average increase of $289 in per-student spending.

The increase here would represent less than 3 percent of that figure.

With some changes in approach—what we call "balanced implementation"—the total cost could drop to less than half the estimate: roughly $5.1 billion, or $121 per student. And if we consider the fact that some existing resources could be repurposed, the additional net cost for states could be even lower, likely less than $100 per student.

What does our balanced-implementation scenario look like? Our ideas include:

• Moving away from hard-copy textbooks and doing more sharing of online materials.

platforms are available for self-publishing textbooks,

We can already see examples of cross-state sharing of curriculum and materials, such as the tri-state materials-sharing platform utilized by Massachusetts, New York, and Rhode Island.

• Using computer-administered technology to offer formative assessments.

• Delivering professional development through a mix of in-person and online instruction

Customized professional development should address the needs of individual teachers, including specific gaps in knowledge and areas needing growth.

states are not treating common-core implementation as something above and beyond their usual use of materials, assessments, and professional-development practices. Instead, they are viewing the transition to the common core as an opportunity to adapt their practices in an effort to deliver 21st-century education.

• States, districts, and charter providers must be willing to stop purchasing goods and services from their existing vendors if they don't meet their current needs, and seek out new vendors willing to take advantage of the opportunities the new standards present.

the commonness of the common core has the potential to restructure these markets dramatically, thus opening up a host of new opportunities, including cross-state resource sharing.

The conditions are ripe for locally developed curricular modules, lesson plans, formative assessments, and professional-development resources to have a national impact.

The commonality of the standards should be a blessing for individual classroom teachers, allowing them access to resources that meet their unique needs. The common standards, coupled with 21st-century technology, have the potential to create a new kind of community of districts, school leaders, and teachers—a community liberated to improve instruction in ways that were once thought to be impossible.

ightened purse strings should force states to seek cost-effective solutions that make the best use of funds while leading to the use of high-quality instructional materials, assessments, and professional development. Implementing the common core won't be cheap, but the expense will be worth it if it leads to improved teaching and learning.