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A comprehensive list being updated regularly through UMF Math Leadership team, Robert Jenkins and Margaret Griswold

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A comprehensive list being updated regularly through UMF Math Leadership team, Robert Jenkins and Margaret Griswold

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EDU 529 Portaportal (User Name: edu 529; Password: portaportal)

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iReady has great digital math tools, but your school would need to purchase in order to use.

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Log in to i-Ready®, online assessment and instruction that helps teachers provide all students a path to proficiency and growth in reading and mathematics.

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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National Library of Digital Manipulatives

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National Library of Digital Manipulatives

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National Library of Virtual Manipulatives

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A digital library containing Java applets and activities for K-12 mathematics

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Illuminations Home - National Council of Teachers of Mathematics

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Grade Span Differentiation:Assessing Across the K-12 Quantitative Reasoning Progression 

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Grade Span Differentiation:Assessing Across the K-12 Quantitative Reasoning Progression 

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Comparing the Common Core State Standards in Mathematics and NCTM’s Curriculum Focal Points

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Comparing the Common Core State Standards in Mathematics and NCTM’s Curriculum Focal Points

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Common Core math implementation: The good, the bad, and the ugly

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Common Core math implementation: The good, the bad, and the ugly

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The Fordham Institute's recent study, Common Core Math in the K-8 Classroom: Results from a National Teacher Survey, took a close look at how educators are implementing the Common Core math standards in classrooms across the nation. Using focus groups and a survey of teachers, Ann Duffett, David Griffith, and I gleaned valuable insights that ranged from good to bad to ugly. As we approach the forthcoming school year and 150,000 teachers prepare to teach math to students from kindergarten through eighth grade, it's worth taking stock of what we've learned.

Let's start with the good. With few exceptions, educators are very knowledgeable about what content is considered "grade-level" for the grades they teach, and they are prioritizing content that the standards designate as "critical areas." Teachers are also paying closer attention to applications, student use of language in the math classroom, and increased use of the number line. Across CCSS states, rigor, consistency, and cohesion in K-8 mathematics has increased-a very good (and necessary) thing!

Teachers are also spending more time collaborating, especially with their grade-level colleagues. Working together leads to better curriculum design (e.g., how much time to spend on a particular topic), better instruction, and more consistency across teachers in the same school and/or district.

Educators are also focusing more extensively on strategies for teaching procedures. This helps increase procedural fluency by giving students a repertoire of strategies and demonstrating when to use them to efficiently and accurately solve problems.

But these new strategies have also had some regrettable collateral consequences. Yes, teachers are teaching more of them. There's more pressure to do so, however, and little guidance on which problem-solving strategies to prioritize, how many might be appropriate for a particular topic, and (most importantly) why students benefit from knowing more than one approach.

This has created a second problem: Parents are less able to help their children with homework. Without a strong justification from a teacher for why their children are using non-standard algorithms, and without resources to understand the approach themselves, parents are not going to support change. Educators are often key implementers of reforms; in the case of Common Core math, we've neglected to bring parents and our communities along with us-at great cost.

The stress in middle schools is also beginning to show. These grades may have had the most dramatic increase in rigor across K-12 mathematics standards, and their teachers are still inheriting students who had to transition sometime in elementary school (potentially generating learning gaps). So it's no surprise that many middle school teachers see their students with heightened anxiety levels and think too many students will fall short of the standards' high expectations.

Finally, the production of Common Core-aligned curricular materials has lagged. We found that teachers are using a wide variety of different resources-and in many schools, different materials are being used in different grades. So while teachers are trying to focus on grade-level content, the textbooks they are relying on vary greatly. Some are even patching together items from various sources themselves, creating amalgamated materials that may not meet the standards' intended rigor.

To be sure, change is often messy. And there are some significant bright spots in states' implementation of Common Core's math standards. Yet the optimal balance between conceptual understanding, fluency of procedures, and the application of mathematics still eludes too many teachers.

Our report points to some important next steps we can take. First, we ought to provide more guidance on which strategies teachers must prioritize for specific content areas. For example, which "place value" strategies might be the best ones to explicitly develop with students, and how can educators do that effectively? And how might these unfamiliar strategies (along with justifications for why they are needed) be shared with parents?

Second, as teachers continue to pull teaching strategies and materials from multiple sources, more guidance is needed to influence teachers' choices. For instance, evaluation tools can help teachers determine whether their activities and lessons actually incorporate appropriate mathematical practices, address the optimal balance of concepts and procedures, or focus on procedural fluency in its entirety. Another insufficiently tapped resource is middle school teachers, whose experiences can help us understand necessary and effective changes in elementary-grade practices.

Finally, six years in, let's celebrate the good that has been accomplished, such as our country's historic levels of coherence and rigor. Stories of this progress ought to be shared with all audiences-not just educators. Our efforts are leaving students better prepared for mathematics than ever before.

Celebrating implementation's good effects, as well as fixing the bad and ugly ones, are key steps in not only ending the math wars, but also in developing mathematically proficient, globally competitive, and college- and career-ready students. In other words, better implementation is vital to ensuring that the Common Core accomplishes its intended purpose.
Jennifer Bay-Williams is the department chair at the University of Louisville's Department of Middle and Secondary Education. She is also the author, with Ann Duffett and David Griffith, of the Fordham Institute's recent report Common Core Math in the K-8 Classroom: Results from a National Teacher Survey.

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Common Core math implementation: The good, the bad, and the ugly

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The Fordham Institute's recent study, Common Core Math in the K-8 Classroom: Results from a National Teacher Survey, took a close look at how educators are implementing the Common Core math standards in classrooms across the nation. Using focus groups and a survey of teachers, Ann Duffett, David Griffith, and I gleaned valuable insights that ranged from good to bad to ugly.

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By NCTM President Diane J. Briars
July 2014

A little more than four years ago, on June 2, 2010, I was sitting with a small group of mathematics educators in the Peachtree Ridge High School auditorium in Suwanee, Georgia, on the occasion of the release of the Common Core State Standards (CCSS). Governors, state and district education leaders, business leaders, teacher union leaders, and a number of classroom teachers all described their strong support for CCSS and how having common, rigorous, world-class college- and career-ready standards would benefit both their students and the nation. Widespread adoption of CCSS was an unprecedented opportunity for systemic improvement in mathematics education in the United States. It would foster collaboration among adopting states and enable them to focus attention and resources on improving teaching, learning, and assessment to increase student achievement, instead of spending significant time, energy, effort, and dollars on creating and arguing about their own state standards.

Fast-forward four years, and where are we? While some states are moving forward, focusing on Common Core State Standards implementation, others are again becoming embroiled in public debates about the standards, and these debates threaten to squander the opportunity for systemic improvement that CCSS provides. With respect to the Common Core State Standards for Mathematics (CCSSM), what I find most troubling is that much of the rhetoric is based on false or incomplete knowledge about the standards and their development, or it confuses the standards with implementation activities, issues, and policies, including testing policies. Such arguments have little potential to improve mathematics education. Distinguishing CCSSM facts from fallacy is essential both for implementing the standards effectively and for engaging in thoughtful, reasoned critique of them for future refinements.

Two important features of CCSSM that are being ignored or misrepresented are their research base and development process.
The Common Core State Standards for Mathematics are based on evidence about how students learn mathematics.
The foundation for CCSSM includes the series of National Research Council reports summarizing research about mathematics education-for example, Adding It Up (2001), How Students Learn: Mathematics in the Classroom (2005), and Mathematics Learning in Early Childhood (2009)-as well as the best of previous state standards and a large body of evidence taken from international comparisons. Research results incorporated into CCSSM include both general findings about how students learn mathematics and specific information about how they learn particular content. For example, in alignment with a well-established general research result, CCSSM builds procedural fluency on a foundation of conceptual understanding. Examples of research-based treatment of specific content include CCSSM's treatment of the meaning of operations, multi-digit computation (moving from informal strategies to generalizable methods based on place value and properties of operations to standard algorithms), and ratios and proportional relationships (building understanding and solving proportions as equivalent ratios). For topics lacking a strong research base, CCSSM progressions draw on standards of individual states or high-performing countries. The series of Progressions documents written by leading researchers in the field summarizes the standards progressions for specific CCSS domains.
Many mathematics educators contributed to the writing of the Common Core State Standards for Mathematics.
Although the Common Core State Standards were produced on an ambitious timeline, large numbers of mathematics educators had opportunities to participate in the process of developing CCSSM. In addition to the three lead authors, William McCallum, Phil Daro, and Jason Zimba, a 51-member Work Team and a 19-person Feedback Group, including teachers, mathematics education researchers, and mathematicians, participated in the development process. The lead writers also commissioned essays on mathematics education research that informed the writing of the standards.

The writing team received more than 10,000 comments through a review process that included four drafts-three sent to partner states, plus a public review draft. NCTM and other mathematics education organizations provided feedback throughout the writing process, including on the four drafts. As a member of two review teams, I can attest to the careful scrutiny that the drafts received and to the impact that the reviews had on subsequent drafts. Furthermore, project staff members were continually comparing the various drafts with high-quality state and international standards. In short, the CCSS development and review process was quite extensive, despite its relatively short timeline. FAQs that address other common CCSSM issues are available.

In addition to having accurate information about CCSSM, we need to distinguish criticism of the implementation of the CCSS from criticism of the standards themselves. Standards specify what students should learn. Decisions about how that learning is to occur-including those related to instructional materials, activities, lessons, units, scope and sequence, course design, homework, or assessments-are implementation issues. Almost all instructional resources now are advertised as "Common Core aligned," with the result that materials that are simply skill worksheets may carry this label, even though the Common Core mathematics standards emphasize conceptual understanding, problem solving, and reasoning processes as well as skill fluency. Furthermore, incomplete understanding of particular standards, such as those calling for students to use various strategies to solve computation problems, may result in inappropriate assignments-for example, homework requiring students to solve each problem by using four different methods instead of one method of their own choosing or devising. Use of inappropriate materials or assignments is not the fault of the Common Core Standards but indicate the need for increased understanding of CCSSM and of resources that can effectively support students' learning of them. It does not indicate that the standards themselves are flawed.

Particularly problematic is a tendency to equate CCSSM with testing and with test-related activities and practices. In response to accountability pressures to increase high-stakes test scores, schools, districts, and even states have instituted a wide range of test-prep activities, such as practice tests, frequent benchmark tests, and test practice worksheets. Much of the criticism of CCSSM, especially from parents, is about these test-prep practices and pressure on students to perform well. These practices were prevalent well before CCSS and are not part of it. To the contrary, the best preparation for the CCSS assessments, with their commitment to assessing all the standards, including the Standards for Mathematical Practice, is high-quality instruction-not test-question drill sheets.

Finally, despite the anti-Common Core rhetoric, overall support for CCSS is still strong. For example, according to a recent Gallup- Education Week poll, two-thirds of district superintendents believe that CCSS will improve the quality of education in their schools. Business Roundtable supports the full adoption and implementation of the Common Core State Standards as a way to build a more skilled, prepared workforce. And the United States Conference of Mayors recently reaffirmed its support for CCSS. Even if a handful of states replace CCSSM with their own standards, CCSS will still be the standards adopted and in place in a majority of states.

The Common Core State Standards represent too important an opportunity to squander because of rhetoric based on incorrect and incomplete information and public confusion of the Common Core State Standards themselves with shortcomings in their implementation. NCTM has developed a three-pronged approach to support the CCSSM:

1. Clearly describe and publicize the practices, policies, programs, and actions required for successful implementation of CCSSM through wide dissemination of Principles to Actions: Ensuring Mathematical Success for All. NCTM cannot do this alone. Our Affiliates and their members are important partners in this effort.

2. Enhance and expand our professional learning opportunities related to Principles to Actions and implementation of CCSSM at our conferences and institutes and in our journals, and continue to build our collection of relevant professional learning resources. This spring, each NCTM committee developed specific plans for this work.

3. Actively advocate for the Common Core State Standards for Mathematics, correcting misconceptions, clarifying confusion, and highlighting ways in which CCSSM supports students in learning more and better mathematics . Most important, we need to help parents and the broader public become aware that the conceptual understanding and habits of mind-for example, problem solving, reasoning, and perseverance-that CCSSM calls for are essential for students' preparation for their futures

This third prong requires all of us, especially teachers and parents, to personalize CCSSM by describing its benefits for their students and children. I strongly urge you to get involved in the dialogue. Correct misconceptions. Separate standards from implementation issues. And highlight the benefits and opportunities that the Common Core State Standards for Mathematics afford to increase the mathematics learning of all students.

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Core Truths - National Council of Teachers of Mathematics

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A little more than four years ago, on June 2, 2010, I was sitting with a small group of mathematics educators in the Peachtree Ridge High School auditorium in Suwanee, Georgia, on the occasion of the release of the Common Core State Standards (CCSS).

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ASCD Works with CCSSO and NGA on Common Core State Standards Initiative

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ASCD Works with CCSSO and NGA on Common Core State Standards Initiative

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Phil Daro, Bill McCallum, Jason Zimba

You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. You object; he says "don't worry, I'll make sure that you get every single piece, and the markings are clear, so you'll be able to glue them all back together. I've got it covered." Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time. They promise their customers (the taxpayers) that by the end of the year they will have "covered" the standards.

In the Common Core State Standards, individual statements of what students are expected to understand and be able to do are embedded within domain headings and cluster headings designed to convey the structure of the subject. "The Standards" refers to all elements of the design-the wording of domain headings, cluster headings, and individual statements; the text of the grade level introductions and high school category descriptions; the placement of the standards for mathematical practice at each grade level.

The pieces are designed to fit together, and the standards document fits them together, presenting a coherent whole where the connections within grades and the flows of ideas across grades are as visible as the story depicted on the urn.

The analogy with the urn only goes so far; the Standards are a policy document, after all, not a work of art. In common with the urn, however, the Standards were crafted to reward study on multiple levels: from close inspection of details, to a coherent grasp of the whole. Specific phrases in specific standards are worth study and can carry important meaning; yet this meaning is also importantly shaped by the cluster heading in which the standard is found. At higher levels, domain headings give structure to the subject matter of the discipline, and the practices' yearly refrain communicates the varieties of expertise which study of the discipline develops in an educated person.

Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole. Arranging the Standards into new categories also breaks their structure. It constitutes a remixing of the Standards. There is meaning in the cluster headings and domain names that is not contained in the numbered statements beneath them. Remove or reword those headings and you have changed the meaning of the Standards; you now have different Standards; you have not adopted the Common Core.

Sometimes a remix is as good as or better than the original. Maybe there are 50 remixes, adapted to the preferences of each individual state (although we doubt there are 50 good ones). Be that as it may, a remix of a work is not the same as the original work, and with 50 remixes we would not have common standards; we would have the same situation we had before the Common Core.

Why is paying attention to the structure important? Here is why: The single most important flaw in United States mathematics instruction is that the curriculum is "a mile wide and an inch deep." This finding comes from research comparing the U.S. curriculum to high performing countries, surveys of college faculty and teachers, the National Math Panel, the Early Childhood Learning Report, and all the testimony the CCSS writers heard. The standards are meant to be a blueprint for math instruction that is more focussed and coherent. The focus and coherence in this blueprint is largely in the way the standards progress from each other, coordinate with each other and most importantly cluster together into coherent bodies of knowledge. Crosswalks and alignments and pacing plans and such cannot be allowed to throw away the focus and coherence and regress to the mile-wide curriculum.

Another consequence of fragmenting the Standards is that it obscures the progressions in the standards. The standards were not so much assembled out of topics as woven out of progressions. Maintaining these progressions in the implementation of the standards will be important for helping all students learn mathematics at a higher level. Standards are a bit like the growth chart in a doctors office: they provide a reference point, but no child follows the chart exactly. By the same token, standards provide a chart against which to measure growth in childrens' knowledge. Just as the growth chart moves ever upward, so standards are written as though students learned 100% of prior standards. In fact, all classrooms exhibit a wide variety of prior learning each day. For example, the properties of operations, learned first for simple whole numbers, then in later grades extended to fractions, play a central role in understanding operations with negative numbers, expressions with letters and later still the study of polynomials. As the application of the properties is extended over the grades, an understanding of how the properties of operations work together should deepen and develop into one of the most fundamental insights into algebra. The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from prior learning. To do this, instruction should reflect the progressions on which the CCSSM are built. For example, the development of fluency with division using the standard algorithm in grade 6 is the occasion to surface and deal with unfinished learning with respect to place value. Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.

This is a basic condition of teaching and should not be ignored in the name of standards. Nearly every student has more to learn about the mathematics referenced by standards from earlier grades. Indeed, it is the nature of mathematics that much new learning is about extending knowledge from prior learning to new situations. For this reason, teachers need to understand the progressions in the standards so they can see where individual students and groups of students are coming from, and where they are heading. But progressions disappear when standards are torn out of context and taught as isolated events.

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Phil Daro, Bill McCallum, Jason Zimba You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year.

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Every Saturday morning at 10 a.m., Jason Zimba begins a math tutoring session for his two young daughters with the same ritual. Claire, 4, draws on a worksheet while Abigail, 7, pulls addition problems written on strips of paper out of an old Kleenex box decorated like a piggy bank.

If she gets the answer "lickety-split," as her dad says, she can check it off. If she doesn't, the problem goes back in the box, to try the following week.

"I would be sleeping in if I weren't frustrated," Zimba says of his Saturday-morning lessons, which he teaches in his pajamas. He feels the math instruction at Abigail's public elementary school in Manhattan is subpar - even after the school switched to the Common Core State Standards.

But Zimba, a mathematician by training, is not just any disgruntled parent. He's one of the guys who wrote the Common Core.

And four years after signing off on the final draft of the standards, he spends his weekends trying to make up for what he considers the lackluster curriculum at his daughter's school, and his weekdays battling the lackluster curriculum and teaching at schools around the country that are struggling to shift to the Common Core.

Zimba and the other writers of the Common Core knew the transition would be tough, but they never imagined conflicts over bad homework would fuel political battles and threaten the very existence of their dream to remodel American education.

When Zimba was first hired to help write a new set of K-12 math standards in 2009, the groups behind the Common Core - including representatives from 48 states - set very ambitious goals. The tough new guidelines would match the expectations set for students in higher-performing rivals like Singapore and South Korea. The standards would not only catapult American students ahead of other developed nations but would also help close the gaps between low-income students in the U.S. and their wealthier counterparts.

The Common Core would drive publishers and test-makers to create better curricula and better tests and push school districts and teachers to aim for excellence, not just basic proficiency, for their students. And the guidelines would arm every principal, teacher and parent with the knowledge of exactly what it takes to get into college and succeed.

The champions of the Common Core - including organizations like the National Governors Association and the Council for Chief State School Officers - expected the task to be difficult. Overhauling textbooks would take a lot of time, and training teachers would take even more. But the bipartisan groundswell of opposition to the standards took them by surprise.

"The creation of the standards is enshrouded in mystery for people," Zimba says. "I wish people understood what a massive process it was, and how many people were involved. It was a lot of work."

As much as supporters emphasize the democratic origin of the standards and count out the dozens of experts and teachers who were consulted, the Common Core math standards were ultimately crafted by three guys whose only goal was to improve the way mathematics is taught. That, some experts argue, is what makes the Common Core better than the standards they've replaced.

"It was a design project, not a political project," says Phil Daro, a former high school algebra teacher who was on the three-man writing team with Zimba and William McCallum, head of the math department at the University of Arizona. "It was not our job to do the politics while we were writing."

But the backlash was perhaps inevitable.
The Inner Circle
On the surface, Zimba, 45, seemed an odd choice for a major national project like Common Core. McCallum and Daro were well-known and admired in the world of math and education. McCallum is a prominent mathematician who has authored algebra and calculus textbooks and helped write Arizona's K-12 math standards. In 2009, Daro was a senior fellow at a for-profit curriculum and teacher-training company, America's Choice. In the 1990s, he was involved in developing California's math standards.

In contrast, Zimba was an obscure physics professor at Bennington, an elite liberal arts college in Vermont. He wrote a quirky math and parenting blog with posts about complex physics problems, his kids, and the occasional political issue, including a 2011 post titled, "Numbers Don't Lie (but Michele Bachmann Does)."

He grew up as an outsider. Raised in a working-class household in suburban Detroit, he was the first in his family to go to college. He chose Williams College in Massachusetts. Academically, the school was a good fit. Financially, it was more of a challenge. His friend Eric Mabery said the two got to know each other because they were the only poor people on campus. "He was the only person who had several jobs," said Mabery, now a biologist at a San Francisco startup. "He was the only other person who couldn't fly home. We had to take the bus."

But from Williams, Zimba's career took off. He was chosen for a Rhodes scholarship to England's Oxford University in 1991. At Oxford, he befriended a Yale student from Manhattan, David Coleman. Coleman went on to become a consultant for McKinsey, the global consulting firm. Zimba returned to Detroit to do stints of factory work to help support his family, but eventually he headed to the prestigious math department at the University of California, Berkeley for a Ph.D. in mathematical physics. In 1999 he reconnected with Coleman, who had an idea for starting an education business.

At first, they considered going into educational video games, but they scrapped the idea in favor of an even bigger educational trend: standardized testing. The No Child Left Behind Act was still around the corner, but a growing education reform movement, which insisted that holding schools more accountable for student test scores would increase performance, had already pushed many states to expand standardized testing.

Coleman and Zimba's business, the Grow Network, found a niche in the burgeoning field of testing by producing reports that helped schools, teachers, parents and even students themselves interpret results from the new exams. "To design a successful assessment report, you need to be thoughtful about what the teacher really needs, what the student really needs," Coleman says.

Thanks to Zimba, Coleman added, they were. Zimba had a genius for creating reports that were mathematically precise but also humanely phrased, Coleman says. Grow Network was hired by states like California and districts like New York City and was eventually bought out by the educational publishing giant McGraw-Hill for an undisclosed price.

Zimba and Coleman went their separate ways. Coleman stayed on a bit longer with the company under McGraw-Hill. After a brief stint at a liberal arts college in Iowa, Zimba landed at Bennington, where Coleman's mother was president. Zimba and Coleman stayed in touch, often discussing a problem that had bothered them during their years studying standardized tests.

"We looked at a lot of standards," Zimba says. "Previous standards ranged from terrible to not good enough. The best of them were little more than test blueprints. They were not a blueprint for learning math."

Every state had its own standards, which varied widely in their expectations for students. For instance, some states required students to memorize the times tables, but about a third of states didn't, according to Zimba.

But what most worried Coleman and Zimba - and many education experts - was the sheer number of standards in most states. The common critique was that most American grade-level guidelines were "a mile wide and an inch deep," in stark contrast to the fewer but more intense expectations in high-achieving countries like Japan and Singapore.

In 2007, Coleman and Zimba wrote a paper for the Carnegie Corp., a foundation with interests in education (and one of the many funders of both The Hechinger Report and NPR). "We were just trying to think about what could really matter in education," Coleman says. "What could actually help? One idea we thought is that standards could be really focused and better. At Grow we'd spent so much time with the endless vast and vague standards."

The paper got the attention of several groups that had latched on to a similar idea, including the Council of Chief State School Officers and the National Governors Association, one of the original leaders of the Reagan-era standards movement. A couple of years later, when the two organizations joined forces to draft a set of "fewer, clearer, higher" standards, Coleman and Zimba were picked to help lead the effort.

The CCSSO contracted with a new organization Zimba and Coleman founded, Student Achievement Partners. It declined to disclose the amount of the contract or the total spent on the development of the Common Core but said funding was provided by the Bill & Melinda Gates Foundation (another supporter of NPR), Carnegie and other foundations, as well as state membership dues from CCSSO and the NGA.

"We were looking for a skill set that was fairly unique," says Chris Minnich, executive director of CCSSO. "We needed individuals that would know the mathematics - Jason and the other writers obviously know the mathematics - but would also be able to work with the states, and a bunch of teachers who would be involved."
Writing The Common Core
In September 2009, Zimba started writing the Common Core math standards. Although his second daughter was due the same month, the standards were all-consuming. Zimba recalled getting a text in the delivery room from one of his co-writers telling him to stop responding to emails about the project: "It's time to be a dad now."

That fall, though, finishing the Common Core math standards came first. He was still on the faculty at Bennington, although on leave for part of the time, so the standards were mostly written at night, in "the barn," an old garage on his property that he had transformed into a study.

"It was hard on us as a family," he says. "I gave an awful lot." In October, his mother, who had worked most of her life as waitress, died. Zimba kept working.

They started with a blueprint that laid out what students should know by the end of high school. It was written by Achieve, a nonprofit f ounded for the purpose, and by the testing groups College Board and ACT. Then they began consulting the research on math education and enlisting the ideas of experts in various fields of mathematics. During the course of the next year, they consulted with state officials, mathematicians and teachers, including a union group. Draft after draft was passed back and forth over email.

"We'd be up to 3 in the morning," says McCallum. "Jason would be up till 5 in the morning."

The final drafts of the standards were released to the public in June 2010. By the following year, thanks in part to financial incentives dangled by the Obama administration, more than 40 states had adopted them. Zimba quit his job at Bennington to work full time at Student Achievement Partners to promote the standards.

The backlash didn't really begin until 2013 in states like New York, where new Common Core-aligned tests had sent scores plummeting, and Indiana, where conservatives were leery of the Obama administration's support of the standards. It hit the mainstream in early 2014, when a dad in North Carolina posted a convoluted "Common Core" question from his son's second-grade math quiz on Facebook, along with a letter he'd written to the teacher. "I have a Bachelor of Science Degree in Electronics Engineering which included extensive study in differential equations and other high-math applications," he wrote. "Even I cannot explain the Common Core mathematics approach, nor get the answer correct."

Glenn Beck and other conservative pundits picked up the post, and it went viral. A couple of months later, the comedian Louis C.K. complained about his daughter's Common Core math homework on Twitter, and late-night comedians like Stephen Colbert began mocking the standards, too. Critics called the standards too convoluted, too abstract and too conceptual because of the focus on getting students to explain and discuss their answers.

By the summer of 2014, Indiana and Oklahoma had pulled out of the Common Core, other states had passed legislation to replace the standards in the coming years, and still others are threatening to do the same this year. Supporters of the standards, including teachers unions and the Gates Foundation, are now trying to salvage Common Core by calling on states to hold off on the stakes associated with new Common Core tests, including new teacher evaluations in many states based on student scores.

The backlash has both annoyed and baffled the writers. "When I see some of those problems posted on Facebook, I think I would have been mad, too," McCallum says. Daro tells a story about his grandson, who brought home a math worksheet labeled "Common Core," with a copyright date of 1999.

They argue there's actually very little fuzziness to the math in the Common Core. Students have to memorize their times tables by third grade and be able to do the kind of meat-and-potatoes problems Zimba asks of his daughter during their Saturday tutoring sessions, requirements he believes the so-called Common Core curriculum at her school essentially ignored.

Hung-Hsi Wu, a mathematics professor at Berkeley and one of the expert advisers in the Common Core process, blames the Common Core's problems on bad - and ubiquitous - textbooks that the publishing industry is reluctant to change. "Publishers don't want to bother with writing anything because they've gone through too many sets of standards," he says.

And that is the irony of the debate over the standards, and what may be their undoing. As powerful and influential in reshaping American classrooms as the standards could be, they don't include lesson plans, or teaching methods, or alternative strategies for when students don't get it.

Even as Zimba and his colleagues defend the standards against cries of federal overreach, they are helpless when it comes to making sure textbook publishers, test-makers, superintendents, principals and teachers interpret the standards in ways that will actually improve American public education, not make it worse.

Like McCallum, Zimba agrees with the North Carolina dad that the question on his son's Common Core-labeled math quiz was terrible. But as long as Americans hold to the conviction that most of what happens in schools should be kept under the control of states and local communities, the quality of the curriculum is out of his hands. "Like it or not, the standards allow a lot of freedom," he said.
To Triumph Or Die
Zimba gave up an academic career in which he had the freedom to wonder about abstract physics problems in the peace and quiet of his Vermont barn. But, he says, "I'm now participating in a much more urgent problem."

That problem is how to elevate the academic achievement of American students, especially the most disadvantaged, so the country can maintain its competitive advantage in the global economy. These days, Zimba and his colleagues acknowledge better standards aren't enough.

"I used to think if you got the assessments right, it would virtually be enough," he says. "In the No Child Left Behind world, everything follows from the test."

Now, he says, "I think it's curriculum."

This year, Zimba persuaded his daughter's school to try out a new curriculum that's better aligned to the standards he wrote. He is also devoting his time at his nonprofit, Student Achievement Partners, to create checklists other schools can use to find good textbooks that match the Common Core. The group has published training materials, including videos in which teachers demonstrate Common Core lessons.

On a recent rainy afternoon in Manhattan, the organization gathered in a conference room to hash out ideas for an online tool, funded by the Leona M. and Harry B. Helmsley Charitable Trust (also among the many funders of The Hechinger Report), that could help teachers better understand the standards.

One idea for this tool was a "swipe-y" app that teachers could use to figure out whether students grasped a standard or not - something that would function much like Tinder, the matchmaking site. In the end, the group was most enthusiastic about a more low-tech option: a hotline that teachers and parents could call to find out if the Common Core-labeled math problems they found in their textbooks and homework were good or bad.

Daro and McCallum are leading their own efforts. McCallum founded a nonprofit called Illustrative Mathematics that produces sample tasks linked to the Common Core, trains teachers and produces curriculum blueprints. And Daro is actually writing an entire Common Core math curriculum for use on tablets, to be put out next year by educational publisher Pearson.

But it's unclear whether their efforts, and similar ones by like-minded nonprofits and funders like the Gates Foundation, will trickle down to the millions of classroom teachers attempting to adapt to the new standards. Or if the bad curricula still circulating, coupled with the nation's fractured politics, will do them in.

For his part, Zimba is optimistic. "The influence of the tests on the curriculum, it's negative," he says. "They've been a pale imitation of mathematics. I've talked to teachers who say teaching these standards, 'I feel like a teacher again.' That's not going to be easy to take away. Once you taste that, that's powerful."

This story was produced by The Hechinger Report, a nonprofit, independent news service focused on inequality and innovation in education. Read more about Common Core.

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Every Saturday morning at 10 a.m., Jason Zimba begins a math tutoring session for his two young daughters with the same ritual. Claire, 4, draws on a worksheet while Abigail, 7, pulls addition problems written on strips of paper out of an old Kleenex box decorated like a piggy bank.

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 Four ways state math standards have improved

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 Four ways state math standards have improved

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Overall, mathematics standards in the United States are far stronger today than they were in 2010, when Fordham conducted its last fifty-state review. And much of that improvement is due to the Common Core math standards, which earned a rating of A- in our 2010 report and a score of 9 out of 10 in our most recent review. In general, the states with the strongest math standards are the ones that have built on the Common Core, modified it in minor ways, or independently drafted separate standards that mirror its pacing and organization.

So why are today's standards better than the math standards of a decade ago? Here are four strengths that our expert mathematics reviewers found in state math standards in 2018.
1. Stronger focus on arithmetic in grades K-5 Many states include solid arithmetic standards, but these are buried among a multitude of distracting and less important content... By failing to clearly prioritize this essential content, states fail to ensure that it gets the attention it deserves. Only a few states either explicitly or implicitly set arithmetic as a top priority. More often, states devote fewer than 30 percent of their standards in crucial elementary grades to arithmetic.
Because it is the foundation for much of the mathematics that students will encounter in higher grades, experts agree that arithmetic should be the primary focus of math instruction in grades K-5. Yet in 2010, the biggest problem we identified in state math standards was that arithmetic wasn't a sufficient priority. As mathematicians Steven Wilson and Gabrielle Martino lamented at the time:

Thanks in large part to the Common Core, that is no longer true. To the contrary, a clear focus on arithmetic is now evident in most states' K-5 math standards. For example, most states' standards begin with a clear focus on counting, whole numbers, and place value. And most also expect students to know their single-digit addition, subtraction, multiplication, and division facts-and to be proficient with the standard algorithms for these operations, as well as strategies related to place value and the properties of operations (usually by the end of third or fourth grade, depending on the operation and the expectation). Finally, most states systematically develop a strong understanding of fractions and decimals.
2. More coherent treatment of proportionality and linearity in middle school
To be clear, topics such as geometry and measurement, the representation of data, and algebraic reasoning are also included in most states' elementary standards. However, in strong standards these topics are connected to number and operations-enhancing rather than diluting the focus on arithmetic.

The study of fractions is closely tied to proportional relationships and reasoning (i.e., rates and ratios). And such reasoning, in turn, provides students with a platform for understanding slopes and linear relationships (e.g., y=mx+b), which are a key foundation for algebra. Thus, the sequence and pacing of these topics is critical to helping students move from elementary to middle to high school mathematics.
3. Appropriate balance between conceptual understanding, procedural fluency, and application
In recent years, the treatment of all of these topics has improved in many states. For example, in most states that used the Common Core as a starting point, ratios and proportional relationships is a main topic in grades six and seven, slope is developed in grade seven, and linear equations are an important part of grade eight, where they are both analyzed and used to describe linear relationships for bivariate data.
To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided.
In the past, math experts quarreled over the relative importance of students' conceptual understanding, procedural fluency (or ability to compute quickly and accurately), and ability to apply what they have learned. Yet, as the 2008 National Math Advisory Panel noted in its final report:
4. Better organization and teacher supports
Thankfully, judging from their current math standards, most states have embraced the importance of each of these capacities and the implicit compromise represented by the quote. For example, the introduction to the Common Core states that "mathematical understanding and procedural skill are equally important" while also asking students to "make sense of problems and persevere in solving them." This tripartite mission is also evident in the standards themselves. For example, most states now ask students to explain their reasoning, in addition to performing computations and solving problems. And in addition to standards about formal mathematical proof and carrying out mathematical procedures accurately, most states' high school frameworks now include modeling, which links classroom math and statistics to everyday life, work, and decision-making.

Well-organized math standards do at least two things. First, they provide an account of key themes for each grade level or course, as well as a list of major benchmarks to ensure that instruction is appropriately focused. Second, they are organized in a mathematically coherent way that highlights how mathematical topics fit together within a grade or course and how they are connected to prior and future work.

The Common Core math standards are a clear example of well-organized standards. For example, prior to the content standards for each grade level (K-8), there is an introduction describing the focus for the grade and a bulleted list of critical topics. Similarly, each high school domain (or area of math) includes a narrative introduction, followed by the individual standards for each of the clusters in that domain. In general, the organization of the Common Core into domains and clusters provides teachers and other stakeholders with conceptual cues about the connections between individual standards and the intended learning progressions within and across grade levels. And helpfully, states such as California and Massachusetts have extended these positive features to high school courses, a step other states should also consider.

In addition to content standards, most states have also adopted practice or process standards, reflecting the broad consensus among math experts that there are certain "mathematical habits of mind" that educators at all levels should seek to develop in students. For example, the Common Core includes eight "Standards for Mathematical Practice," abbreviated versions of which are listed in the introduction to each grade (K-8) and high school domain. And again, states such as Massachusetts have helpfully expanded on this approach by articulating particular expectations for each of three grade spans: pre-K-5, 6-8, and 9-12.

Finally, most states now include a mathematical glossary in their standards, as well as other resources and links. The form and content of these are too diverse to summarize here, but many are likely to be useful for teachers. For example, a number of states have developed "vertical alignment charts" that describe the desired progressions for particular topics across grades, and there is a " coherence map " for the Common Core that shows connections across both topics and grades.

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As others have noted, strong math standards are just the beginning. To implement them well, policymakers, curriculum developers, principals, and, above all else, teachers must understand why they are strong so that textbooks, professional development, pedagogy, and practice reflect the same shared vision of mathematical excellence.

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Four ways state math standards have improved

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Overall, mathematics standards in the United States are far stronger today than they were in 2010, when Fordham conducted its last fifty-state review. And much of that improvement is due to the Common Core math standards, which earned a rating of A- in our 2010 report and a score of 9 out of 10 in our most recent review.

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The “left behind” kids made incredible progress from the late 1990s until the Great Recession. Here are key lessons for ed reform

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The “left behind” kids made incredible progress from the late 1990s until the Great Recession. Here are key lessons for ed reform

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This summer, I've been trying to make sense of the sizable gains made by America's lowest-performing students and kids of color that coincided with the peak of the modern education reform movement. Today, I wrap up the series by offering some personal reflections on what we've learned. But first, let's recap the facts and acknowledge the vast amount of ground yet to cover.

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From the mid to late 1990s, and generally until 2010 or so, National Assessment of Educational Progress (NAEP) scores at the fourth and eighth grades for the lowest-achieving children, and for students of color, shot up in reading, math, and most other academic subjects. The gains were greatest at the low end of the spectrum-as seen in trends at the 10th percentile of achievement and a big drop in the percentage of students scoring at the "below basic" level.

By 2010 or so, our African American, Hispanic, and low-achieving students were reading and doing math two and sometimes three grade levels above their counterparts in the early 1990s. That's historic, life-changing progress. And it surely contributed to more recent gains in the high school graduation rate for these groups, as many more kids came into ninth grade closer to being on track.

That's the good news. The bad news is that there was less progress at the middle and top of the performance spectrum; essentially no achievement gains at the twelfth grade level; and most of the progress hit a wall around the time of the Great Recession. Results for middle-class kids over this period got a bit better in math, but not much in reading.

Those are the facts. The interpretive challenge is to understand why. Why did we see so much progress for the kids who had previously been "left behind"? I spent several posts digging into that question, and concluded that our schools could take only partial credit. Yes, it was a time of frenetic reform activity, and yes, it was also a period of significantly increased investment in our public schools. And those factors mattered. But what likely mattered more were the vastly improving social and economic conditions for our poorest children. Our cities in particular were transformed over the course of the 1990s, with child poverty rates plummeting and the incidence of violence falling dramatically. These trends-as much as anything schools or policymakers or "reformers" did-likely explain much of why our students started to learn so much more.

But back to the schools. Rigorous evidence indicates that accountability policies and increased spending both helped to boost achievement. That much is clear. What's less clear is how. How did schools respond to accountability pressure to increase student learning? Was it in ways that policymakers had hoped, such as by moving the best teachers to the neediest schools and classrooms, or embracing evidence-based practices and high quality curricula, or shifting resources to the kids who need them most? Or were these improvements in math and reading made at the expense of other important pursuits? Were other academic subjects squeezed out of the curriculum? Did schools stop doing so much on the whole-child front, such as sacrificing recess and P.E.? And if so, were these choices good ones? And how did the increased spending lead to better results? What did they spend the money on?

These aren't meant to be rhetorical questions-they are empirical. Unfortunately, we don't have much data by which to answer them effectively. The sad fact is that we analysts have very little insight into what's actually happening in our schools today, much less over the past quarter-century. But working toward answers to these questions would still be worthwhile (I'm talking to you, young academics looking for research projects!), as they would help us understand what worked and what we might learn for our efforts going forward.

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So to restate, one last time: The achievement of low-performing kids and children of color rose dramatically from the late 1990s until the Great Recession. That was mostly because of improving social and economic conditions for these children, but accountability reforms and increased spending played a role, as well. Over the last decade, that progress has mostly petered out. And the gains we made were, of course, not nearly enough, as they mostly meant getting more kids to a basic level of literacy and numeracy and walking across the high school graduation stage-nowhere near the goal of readiness for college, career, and citizenship that is the proper objective of our K-12 system.

Here are a few personal reflections about these conclusions.

First, we reformers and policy wonks need to be much more humble about putting ourselves at the center of the story. It's a great human temptation. We all want to be the hero in our personal narrative. But we need to bring some maturity and wisdom to the decades-long work of educational improvement, and be willing to acknowledge that the ups and downs of NAEP scores, college completion rates, and all the rest are more likely to be driven by what's happening outside of schools than within.

I'm chagrined to admit that I really believed, back in the heady No Child Left Behind days, that it was policy that was leading to those test score gains among the neediest kids. And to be sure, solid research indicates that NCLB and similar state policies do deserve some credit. But only some. Somehow I-we?-missed what was happening in society at large-the declining poverty rates, the increasing supports for needy families, the plummeting crime rate. Of course those things would affect student learning.

And we did it again when the progress stalled around 2010. Some of us claimed that happened because we took the foot off the gas of accountability reform. Others said it was Common Core's fault, or the flaws in new teacher evaluation systems. Those are all reasonable hypotheses, deserving of analysis. But what if it was mostly about the Great Recession, the spike in the unemployment rate, the increase in child poverty, and the decline in school spending? In other words, fellow reformers, it's not all about us!

That doesn't mean education policy or reforms like charter schools or Teach For America and the like don't matter. Some states have consistently beaten the socioeconomic curve. And I don't think it's a coincidence that the states that made more gains than one would predict over this past quarter-century-like Massachusetts, Florida, and Indiana-are the ones that embraced education reform. They weren't immune to the larger social and economic trends. But thanks to strong leaders and smart policies, they did better than expected.

So we should be humble about what policy can achieve, but we shouldn't be despairing. It still matters.

Finally, this look at a quarter-century of student outcomes has reminded me of the importance of patience. Yes, that one's tough for reformers, since the moral authority of our work comes from its urgency. Kids are in bad schools right now. Children don't have a second chance to get a great education. And despite the gains we've made in basic literacy and numeracy, many kids are going to get crushed by the real world if we don't help them achieve at much higher levels than that.

So a sense of urgency is critical in this work.

Yet we've seen time and again that we can make big mistakes by declaring something a failure too early. That was famously the case with the early Gates Foundation initiative on smaller high schools-which was thought to have flopped until rigorous studies finally emerged that showed significant gains, at least in some cities. Such was the case with No Child Left Behind, too. Jay Greene and Mike McShane are right that we need to learn from failure -but we also need to learn not to declare something a failure too soon.

I worry we might be doing that again today. Though the backlash to testing and accountability has subsided somewhat, there are still plenty of policymakers-and even some reformers-who would be happy to leave all of that behind. To which I would say: Hold your horses! We have spent the past decade overhauling standards, tests, and accountability systems, and finally committing real resources to capacity-building, especially in the form of curriculum implementation. These pieces have only come together in the last year or two, with the release of the first school ratings under the Every Student Succeeds Act. Now that Accountability 2.0 is finally in place-and we have a booming economy once more-let's see if we can drive real improvements in achievement once again, and not just at the low end of the distribution this time.

What we need, then, is balance. We need to combine patience and urgency, humility and optimism, the passion of youth and the wisdom of experience. Let's try to remember that in the school year ahead.

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The "left behind" kids made incredible progress from the late 1990s until the Great Recession. Here are key lessons for ed reform.

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This summer, I've been trying to make sense of the sizable gains made by America's lowest-performing students and kids of color that coincided with the peak of the modern education reform movement. Today, I wrap up the series by offering some personal reflections on what we've learned.

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From Common Core Standards to Curriculum: Five Big Ideas

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From Common Core Standards to Curriculum: Five Big Ideas

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You may have heard about the Common Core State Standards (CCSS) but do you know what they mean for your child's education? The CCSS were developed by a range of education stakeholders: educators, education experts, business leaders and parents like you.

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For the first decade of Fordham's existence, starting in 1997, reviewing state academic standards was our bread and butter, but the pattern always seemed to be the same: A few states had done a commendable job of identifying the knowledge and skills-grade by grade-that their students needed to master to be on track for success after high school. But most state standards were horrendous-poorly written, disorganized, incomplete, and replete with dubious ideas. All that began to change in 2010, when we reviewed the final drafts of the Common Core State Standards (CCSS). Our State of State Standards-and the Common Core-in 2010 found that the CCSS were clearer and more rigorous than the English language arts (ELA) standards in thirty-seven states and stronger than the math standards in thirty-nine. Naturally, we encouraged those states to adopt the CCSS instead of starting from scratch.

But as readers know, by 2013 the country was engulfed in a full-fledged culture war over the Common Core, with a loose coalition of populist conservatives teaming up with educational progressives in a push to dump the standards and vanquish testing. Some states responded by "un-adopting" the Common Core; others tweaked, renamed, or rebranded them. In the end, the Common Core, as reviewed (and lauded) by us, was not very common.

So we find ourselves, once again, commissioning reviews of state ELA and math standards. The result is our new report, The State of State Standards Post-Common Core.

This turned out to be worth doing because even the most steadfast states have room for improvement. No matter how good they are, every state's academic standards need to be updated periodically to reflect the latest advances in content and pedagogy, as well as lessons learned during their implementation. So the overarching goal of the present report is to provide helpful guidance to states as they look to update and improve their standards in the years ahead.

Because many states retained the Common Core (or a variant thereof), this report-unlike our previous state-standards reviews-does not formally review standards in all fifty states. Instead, it focuses on the states that have made the most substantive changes to the Common Core ELA and math standards, as well as those that never adopted them. In ELA, that led us to fourteen states; in math, to ten. By taking a close look at their current standards, plus a fresh look at the CCSS, we seek to identify those changes and ideas that are worthy of broader adoption, as well as mistakes to avoid.

With those ends in mind, we assembled two teams of highly respected subject-matter experts-one for ELA and one for math-with deep knowledge of the content standards in their respective fields. The teams worked independently, so their paths inevitably diverged, and we advise against comparisons between or across the two subjects. Ultimately, what matters most is where states go from here-and what they do with the information and recommendations in the report.

We assessed standards on a ten-point scale and assigned each set one of four labels: strong, good, weak, or inadequate. For the most part, we reviewed the officially adopted state standards and didn't include supplemental documents that may accompany them. Although the latter may be quite helpful to teachers, they typically run hundreds of pages and include innumerable links, making it impossible to review them in sufficient detail.

In the end, no set of ELA or math standards received a perfect score, but the Common Core earned 9 out of 10 in each subject, reflecting the consensus among our reviewers that they are still a generally "strong" set of standards that states can and should continue to implement.

Texas, a "never-adopter" of CCSS, also had math standards deemed "strong." Another three states-Indiana, Tennessee, and Virginia-earned "good" ratings in that subject. Seven did the same in ELA: Indiana, Kansas, New York, North Carolina, Oklahoma, Pennsylvania, and West Virginia. Of the standards in this latter group, our reviewers found Indiana's to be particularly praiseworthy.

Further down the spectrum, five states earned overall scores of 5 or 6 in math or ELA, and were thus deemed to have "weak" standards: Minnesota, North Carolina, Missouri, Nebraska, and Oklahoma for math; Arizona, South Carolina, Texas, Nebraska, and Tennessee for English language arts. Our reviewers recommend that these standards be significantly revised before educators and policymakers devote any more effort to their implementation. At the bottom, our reviewers judged Pennsylvania's math standards "inadequate," and reached the same conclusion for Missouri's and Virginia's ELA benchmarks. All three need a thorough overhaul.

After completing their reviews, our subject-matter experts identified positive and negative state trends in both subjects.

In reading, more states are prioritizing writing, including foundational writing skills such as printing, keyboarding, phonics, and spelling, and also emphasizing vocabulary development. Yet these positive developments are partially overshadowed by numerous persistent failings. For example, states have engaged in a marked retreat from rigorous quantitative and qualitative expectations for reading and for text complexity, a development that leaves educators in the dark about what types of texts students should be reading, and at what levels. And there's a worrisome lack of standards showing how literacy skills extend beyond the English classroom into other disciplines such as history, science, and mathematics.

In math, reviewers identified several positive trends in state standards, all of them at least partly attributable to the enduring influence of the CCSS-M. There is, for instance, a stronger focus on arithmetic in grades K-5, more coherent treatment of key topics in middle school (including rates, ratios, and slope), and more appropriate balance among conceptual understanding, procedural fluency, and application.

All good. Yet, as indicated by the low scores that some states' math standards received, there are exceptions to these trends. For example, some states do not explicitly require students to know their addition and multiplication facts from memory, while others make no mention of proficiency in the standard algorithms for the four major operations. Similarly, some states still have incoherent (or semi-coherent) middle school progressions that fail to make necessary connections between interrelated standards and topics.

The report offers specific recommendations for each state that was reviewed, as well as general advice, depending on whether a state kept the Common Core standards (or a close facsimile), or whether it markedly diverged or abstained from them. The former group tends to have stronger standards, and we recommend that they do three things going forward. First, focus on implementation, including subject-specific professional development. Second, undertake to address (carefully!) Common Core's particular limitations in math and English language arts. And third, consider adopting specific enhancements that other states have made. California, for example, reorganized its high school math standards to be more concise and user-friendly. And Massachusetts added numerous examples in both subjects, making the standards easier to interpret.

For those states that made the most significant changes to the CCSS (or never adopted them), in nearly every case the simplest "fix" would be to adopt (or re-adopt) the Common Core. But because there's little point in re-litigating that case, the individual reviews meet these states halfway by describing specific changes they could make to address the weaknesses in their current standards.

Our reviewers, as well as those of us at Fordham, believe that the Common Core standards have aged well. Still, we must remember that standards are only words on paper if they don't inspire stellar instruction in the classroom. On that front, there is clearly much more to be done, as we have learned from various implementation studies, including Fordham's own Reading and Writing in America's Schools, published last month.

Confusion still reigns in too many places: Do the standards expect young students to learn history, science, and other subjects in order to become better readers? (Yes.) Do they require high school English teachers to ditch classic works of literature? (No.) Do they want young children to master their math facts? (Yes.)

The standards, we believe, are clear and on target, on these and other important points. But something is getting lost in translation. Fixing that problem is as urgent as ever.

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For the first decade of Fordham's existence, starting in 1997, reviewing state academic standards was our bread and butter, but the pattern always seemed to be the same: A few states had done a commendable job of identifying the knowledge and skills-grade by grade-that their students needed to master to be on track for success after high school.

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Common Core education standards: why they're contested left and right

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Common Core education standards: why they're contested left and right

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When the final Common Core State Standards were released in 2010, they were notable, in part, for how little opposition they generated.

After prior attempts to create uniform national standards had failed, that goal seemed to have finally been accomplished, and in a way that was bipartisan. Kentucky was the first state to sign on, and two months after the standards were released, more than two-thirds of states had adopted the standards. With few exceptions, educators hailed them as a big improvement for most states, a chance to give some uniformity to education expectations across the United States and ensure that students graduate from high school with a deeper understanding of subjects, better critical thinking skills, and thorough preparation for college courses.

Fast-forward four years, and the headlines about Common Core are mostly consumed with who is dropping out - either from the standards themselves or from one of the two tests designed to assess them - or who is being pressured to do so.

The backlash is coming from both sides of the political spectrum. Among Republicans, supporting Common Core (aka "Obamacore") has become particularly toxic, with numerous politicians up for election this fall or maybe in 2016 vehemently reversing prior support. Criticism is almost as strong among some segments of the left, albeit for different reasons. And for both sides, Common Core seems largely to have become a proxy for whatever in education people are unhappy with.

For most states, this school year will be the first that the standards will be both fully implemented and tested, and it's an open question what will be the degree to which the backlash affects that process or the standards' effectiveness.

"The politics have reached the point where they're getting in the way of actually implementing" the standards, says Andrew Rotherham, cofounder of Bellwether Education Partners, an education research and policy group based in Sudbury, Mass.

"The perception is one of momentum [for the anti-Common Core people], and politics is a game of perception," he says. "If you end up with 25 states doing [Common Core] in a meaningful way, that's an enormous victory, but it won't be perceived that way."

Most people agree that for Republicans, the seeds of the backlash were planted when President Obama and Education Secretary Arne Duncan got behind the standards, encouraging states that wanted to apply for federal Race to the Top funds to either adopt the standards or adopt comparable ones deemed "college- and career-ready." [ Editor's note: The original version of this paragraph overstated the expectations placed upon states applying for Race to the Top funds.]

What had been sold as a state-led effort, supported by the National Governors Association, suddenly became associated with Mr. Obama, and rumors circulated quickly of a national curriculum (the standards don't actually prescribe curriculum) and a federal takeover of education.

"If it weren't for the Race to the Top funds and the No Child Left Behind waivers, you wouldn't have had 45 states sign on," says Shane Vander Hart, a conservative anti-Common Core activist. "There was executive overreach."

To date, the states that have actually dropped the standards - Indiana, Oklahoma, and South Carolina - are red states. Also, Missouri and North Carolina have made moves toward dropping the standards. Louisiana Republican Gov. Bobby Jindal, who used to be a strong Common Core supporter, has done an about-face and has tried (unsuccessfully so far) to withdraw his state from both the standards and the new tests. Governor Jindal is considered to be a presidential contender for 2016.

But there has also been vocal opposition from blue states - some around the standards themselves, particularly for younger grades, but much of it around implementation, as well as the tests and high-stakes consequences tied to the new standards. The varied quality of "Common Core-aligned" textbooks hasn't helped. This spring, the Chicago Teachers Union became one of the biggest local unions to officially oppose Common Core.

Bianca Tanis, an elementary special-ed teacher in Rockland County, N.Y., says many of the standards are "grossly inappropriate," especially for young students.

Common Core, for instance, places a strong emphasis on "text-based evidence," even in elementary school. Ms. Tanis says that while that may be fine for older students, asking third-graders to constantly go back to the text to explain answers is not only inappropriate, but also tedious.

"You have children who are reading, then furiously going back and looking for text-based evidence," Tanis says. "It has them stuck on two pages of 'Peter Pan' for weeks. It's taking the joy out of it, preparing them to be workers and preparing them for a test. Is that what education is?"

Still, a solid majority of teachers - about three-quarters, according to most polls - support Common Core. The two largest teachers unions - the National Education Association and the American Federation of Teachers - have been supporters, although they've been critical of the standards' implementation and the high-stakes consequences attached to the new tests.

In June, even the Bill & Melinda Gates Foundation - a major catalyst in the development and adoption of Common Core - called for a two-year moratorium on high-stakes decisions for teachers or students based on Common Core assessments.

"If you suspend accountability for two to three years, a lot of the political problems around Common Core, the mounting opposition, certainly from the left, goes away," says Patrick McGuinn, a political science and education professor at Drew University in Madison, N.J.

But some wonder if unions might turn a temporary delay into a more permanent one.

Some of the standards' biggest advocates are educators who say they've seen the difference the standards can make. A basic Common Core idea is that the standards are supposed to emphasize depth over breadth, ensure students really master concepts, and build on previous learning ("scaffolding" is the term some educators prefer).

Britton Kilpatrick, a high school math teacher in Ruston, La., says the difference he's seen is huge.

"Before, the Louisiana standards were entirely focused on 'Can you do the procedure? Do you know the algorithm?' " says Mr. Kilpatrick. Common Core, he says, "wants them to understand math deeply, so by the time they get to middle and high school, they'll be able to do this math and move at a different pace, because they will understand the foundational stuff."

The first few years with the new standards have been challenging, Kilpatrick acknowledges, mostly for students who came into advanced math courses without having the understanding they needed to meet the Common Core standards. But he says he's already seen huge growth for some students, and he expects it to get better with each year.

But he's concerned about the politics - that Louisiana could even withdraw from Common Core or the new assessment in the next few months. "I'm worried that all the political ideas about big data or a federal takeover are getting so intermingled with the actual Common Core standards that I'm afraid they'll poison the good that can come from the standards," he says.

In New York, one of the blue states where opposition has been most heated, Melissa McLean says she was initially apprehensive about Common Core when she knew her son Elijah, who just finished third grade, was going to take a new test aligned to the standards. But Ms. McLean went to meetings at her son's school, Achievement First Endeavor in Brooklyn, visited his classroom, and slowly got comfortable with the new material.

"The kids don't just need to have the regular 'I can memorize 1 + 1'; they need to have the critical thinking skills. That's what I want for my son," McLean says. "They're teaching him how to multiply and divide, and [students] can answer the question ... three different ways. I had a book with the multiplication table in the back, and I had to memorize it."

Stephanie Keenoy, the principal at Endeavor, says she's worked hard to help both teachers and parents at the school understand and support the shift. Common Core has meant a big change not just in what the students are learning and how they're learning it, she says, but also in what teachers' and parents' image of success is.

"It's no longer about students getting 100 percent [on tests]; that's not what makes an excellent teacher," she says. "It's about setting an unbelievably high bar, and when kids don't hit that bar, we help them get there."

Despite the backlash, Common Core is entrenched in a majority of states. Even Mr. Vander Hart, while he's pleased with some recent successes for the opposition, acknowledges that his movement is "an uphill climb." "You have [most] states still Common Core-aligned, and you have Gates's money behind it. It's definitely a David versus Goliath situation," he says.

Some states may keep the standards but drop out of the new assessments or implement Common Core in name only.

"Standards are just words on paper," says Frederick Hess, director of education policy studies at the American Enterprise Institute, a conservative think tank in Washington. In the end, he says, there may be just 15 states that are really serious about implementing and testing the standards, but Common Core will be judged based on the results in all the states that technically have adopted them.

Judging Common Core's success could take some time, notes Michael Brickman, national policy director at the Washington-based Thomas B. Fordham Institute, which has largely supported the standards. "Supporters or opponents who are looking for dramatic doomsday or utopian results from Common Core are going to have to wait. High standards is but one piece in the education reform movement," he says.

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Common Core education standards: why they're contested left and right

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When the final Common Core State Standards were released in 2010, they were notable, in part, for how little opposition they generated. After prior attempts to create uniform national standards had failed, that goal seemed to have finally been accomplished, and in a way that was bipartisan.

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Even When States Revise Standards, the Core of the Common Core Remains

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Even When States Revise Standards, the Core of the Common Core Remains

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For a while, the Common Core State Standards seemed to teeter on the brink of the abyss. State lawmakers were defecting left and right, convening committees to rewrite the standards.

But a review released on Monday of 24 states' revisions show that they have largely preserved the common core's most important features.

The report from Achieve, a Washington-based nonprofit that supports states' efforts to improve their academic standards, does not explicitly compare old and new standards. But most of the nonprofit's review criteria come directly out of the standards-such as a focus on "text complexity," or ensuring that students encounter progressively more difficult reading at each grade level.

In essence, the "core of the core" is maintained in most states' new English/language arts standards. In math, Achieve found that five states were missing elements that it deems necessary to set up students for later success. But states resisted the temptation to revert back to earlier standards, which were roundly criticized by math experts as overstuffed and incoherent.

"This is a good-news story; by and large, states do have strong college- and career-ready standards," said Michael Cohen, the president of Achieve, which helped lead the common-core push.

What's more, he said, most of the states' revisions were aimed at providing more guidance and clarity to teachers. "You could tell some thought went into these revisions," he said.

Core of the Core Preserved

The common-core standards, unveiled in 2010, were developed by groups representing the nation's governors and state education chiefs with the goal of readying high school graduates for college or the workforce. At their peak, 45 states and the District of Columbia had signed up. But the standards became a political liability after the U.S. Department of Education gave states financial incentives to adopt them-and as teachers scrambled to find matching curricula and fretted about new exams linked to the expectations.

Many states subsequently tweaked the standards, renamed them, or replaced them. The Achieve report is probably the most comprehensive look at the post-common core landscape, and provides insights into the challenges other states will face as they revise their student expectations. (Most states do so every seven to 10 years.)

The study examines changes in 24 states: Alabama, Arizona, Arkansas, California, Florida, Georgia, Idaho, Indiana, Iowa, Louisiana, Massachusetts, Mississippi, Missouri, New Jersey, New York, North Carolina, North Dakota, Ohio, Oklahoma, Pennsylvania, South Carolina, Tennessee, Utah, and West Virginia.

Six reviewers conducted the review against the criteria set out in the report.

In ELA, 20 of the 24 states included all of the markers Achieve looked for, including foundational reading skills; working with literature and nonfiction texts; and having students cite evidence from text when analyzing and making arguments.

Many states made additional clarifications or explanations to broaden features of the standards, the report notes. South Carolina, for example, includes standards on fluency all the way through 12th grade, while Alabama has students write poetry as early as grade 2.

Weaker in Math?

The report found more variation among the states' math standards.

Every state still outlines expectations through Algebra II, and most preserved references to the mathematical practices-eight core ways students should grapple with math, such as being able to reason quantitatively. But it also found some gaps. Twelve of the states, for example, did not emphasize mathematical modeling in high school math; six also lacked statistics topics for high school.

Achieve deemed Oklahoma's and Pennsylvania's standards to be missing the most benchmarks, judging that they did not, for instance, sufficiently emphasize arithmetic in grades K-5 or require students to know single-digit sums and products by heart.

"It is no surprise that Oklahoma standards for English/language arts and mathematics would score differently than other states on indicators aligned to common core," Tiffany Neill, the executive director of curriculum and instruction at the Oklahoma education department, said in a statement. "After repealing common core in 2014, Oklahoma was tasked with developing comprehensive standards and chose to engage thousands of Oklahoma educators and education stakeholders in every stage of their development. Our inclusive design process, and the final standards themselves received constructive and favorable reviews by Oklahomans, experts, and other evaluators."

The state has also developed curriculum frameworks to help flesh out the standards, she added.

While the report aims at objectivity, it contains a strong viewpoint about what standards for students should contain. For example, it critiques states that added language expecting students to relate what they've read to their own lives, a common teaching practice in the pre-common core era.

And states were downgraded for not giving enough guidance on how to help teachers understand and use gauges of text complexity.

Both of those features wade into continuing debates over the best way to teach reading. Some critics of the common core have questioned whether it's appropriate to have students of varying reading levels grapple with the same piece of text, for instance.

States received the report late last week, and due to the Veterans Day holiday, were still digesting the findings on Monday.

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Even When States Revise Standards, the Core of the Common Core Remains

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For a while, the Common Core State Standards seemed to teeter on the brink of the abyss. State lawmakers were defecting left and right, convening committees to rewrite the standards. But a review released on Monday of 24 states' revisions show that they have largely preserved the common core's most important features.

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NCTM 100 Timeline - National Council of Teachers of Mathematics

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NCTM 100 Timeline: Looking Back, Moving Forward

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A required part of this site couldn’t load. This may be due to a browser extension, network issues, or browser settings. Please check your connection, disable any ad blockers, or try using a different browser.

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The exact skills you need

Planning a lesson or prepping for an exam?
We've custom-built IXL skills to reinforce each topic within your:

State standards

Virginia Standards of Learning (2016)

Textbooks

See skills that match every chapter of 80+ popular textbooks

Assessments

Use IXL for the NWEA MAP, ACT, SAT, and more

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IXL | Math, Language Arts, Science, Social Studies, and Spanish

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IXL is the world's most popular subscription-based learning site for K-12. Used by over 15 million students, IXL provides personalized learning in more than 10,000 topics, covering math, language arts, science, social studies, and Spanish. Interactive questions, awards, and certificates keep kids motivated as they master skills.

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XtraMath - 10 minutes a day for math fact fluency

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XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts.

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Illustrative Mathematics provides resources and support for giving their students an enduring understanding of mathematics.

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Online Math & Reading Programs for Students | DreamBox Learning

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Discover Engaging Online Math & Reading Programs For Students With DreamBox Learning. Foster Academic Growth & Success With Our Interactive Platform Today!

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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achievethecore.org's digital tools and resources for teachers have been made possible by contributions from teachers across the country as well as through generous support from the Leona M. and Harry B. Helmsley Charitable Trust and the GE Foundation.

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These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifying the tasks.

The tasks for 3rd Grade through High School were developed by the Mathematics Assessment Resource Service (MARS) of the Shell Centre for Mathematical Education, University of Nottingham, England. The tasks for 2nd Grade were developed by the Silicon Valley Mathematics Initiative's Mathematics Assessment Collaborative (MAC).

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Performance Assessment Tasks | Inside Mathematics

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These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifying the tasks.

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4th Grade Multiplication Resource Platform

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4th Grade Multiplication Resource Platform

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Print this page

Standards define what students should understand and be able to do.

Clusters summarize groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.

Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

These Standards do not dictate curriculum or teaching methods. For example, just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B.

What students can learn at any particular grade level depends upon what they have learned before. Ideally then, each standard in this document might have been phrased in the form, “Students who already know A should next come to learn B.” But at present this approach is unrealistic—not least because existing education research cannot specify all such learning pathways. Of necessity therefore, grade placements for specific topics have been made on the basis of state and international comparisons and the collective experience and collective professional judgment of educators, researchers and mathematicians. One promise of common state standards is that over time they will allow research on learning progressions to inform and improve the design of standards to a much greater extent than is possible today. Learning opportunities will continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.

These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that these standards are not just promises to our children, but promises we intend to keep.

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Introduction » How to read the grade level standards | Common Core State Standards Initiative

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Standards define what students should understand and be able to do.

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Maine Learning Results - Mathematics

The Maine Learning Results, which incorporates the Common Core State Standards, is a single set of clear educational standards for mathematics. These standards are designed to ensure that students graduating from high school are prepared to go to college or enter the workforce, and parents, teachers and students have a clear understanding of what is expected of them.

K-12 by Strand

By Grade Span

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The Maine Learning Results, which incorporates the Common Core State Standards, is a single set of clear educational standards for mathematics. These standards are designed to ensure that students graduating from high school are prepared to go to college or enter the workforce, and parents, teachers and students have a clear understanding of what is expected of them.

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Mathematics Standards – Common Core State Standards Initiative

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For more than a decade, research studies of mathematics education in high-performing countries have concluded that mathematics education in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on this promise, t…

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Updated Maine Learning Results Explanation

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Updated Maine Learning Results Explanation

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Do you know an outstanding educator who through dedicated service has demonstrated a commitment to Maine's mathematical community? If so, consider nominating them for the 2023 Jacqueline Mitchell Mathematics Educator Award by filling out the form linked here. Nominations for the 2023 award close on Saturday, January 15, 2023.

You deserve a ! The ATOMIM Executive Board is pleased to announce the ATOMIM Grant Incentives For Teachers Program benefiting Maine students in mathematics, which are meant to enhance either the classroom or the teacher's practice.

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Do you know an outstanding educator who through dedicated service has demonstrated a commitment to Maine's mathematical community? If so, consider nominating them for the 2023 Jacqueline Mitchell Mathematics Educator Award by filling out the form linked here. Nominations for the 2023 award close on Saturday, January 15, 2023.

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Overview - National Council of Teachers of Mathematics

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The National Council of Teachers of Mathematics (NCTM) is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.

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The American public education system does not realize the potential of all students, an issue that is most acutely experienced by Black students and students who are English learners. Focusing on the needs of these historically underserved students helps us in supporting all students. We believe challenging K-12 academic standards, in the context of culturally relevant teaching and equitable classroom practice, are non-negotiable when it comes to improving student outcomes. We believe that effective educational leadership and instruction persistently takes action to eradicate racist systems and policies so that all students can thrive academically. In partnership with other passionate change-makers, we design tools and resources, professional learning, and other supports, grounded in research and the realities of the classroom.

Where We Started. Where We're Going.

Our Team

Student Achievement Partners is a non-profit that holds firm to the idea that education can be reimagined and redesigned, working as committed collaborators who share leadership and power.
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Meet our team members

Work with Us

Co-design with Us

Have an idea, hurdle, or solution you want to explore with us? We want to hear about it. We believe that improving education is possible, but that we can't do it alone. We're always listening for new ways we can serve teachers and students--we'd love to collaborate with you in this work.

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Write for Us

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Inspired by Students. Designed for Change.

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The American public education system does not realize the potential of all students, an issue that is most acutely experienced by Black students and students who are English learners. Focusing on the needs of these historically underserved students helps us in supporting all students.

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We create practical, timely, affordable professional learning to help educators and instructional leaders provide students with a modern, equitable, and quality education.

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Mathematics instruction supports Maine's mathematics learning standards in grades Kindergarten through 12. The Maine Department of Education mathematics specialists offer free and open resources, tools, technical assistance and professional learning opportunities on instructional practices, learning progressions, assessment, and curriculum development.

**New Maine DOE Math Listserv**

The DOE Mathematics Specialists will use this NEW listserv to share upcoming events, opportunities, and information with Maine educators. The first announcements will be coming late summer/early fall. We hope that you will subscribe to receive quarterly newsletters and to hear about current events and opportunities in Maine mathematics. To subscribe go to the DOEMATH Listserv registration page.

Professional Learning Opportunities

The table below provides a list of the current available professional learning opportunities for the school year 2021-2022. Each event has multiple training dates available to better accommodate your schedules. Please take note of the dates you are registering for. Some offerings are series of dates; please plan to attend all the dates in the series. The table will be updated as more opportunities become available. For any questions about the professional learning opportunities listed below or for additional professional learning needs please email Michele Mailhot or Jen Robitaille.

Event/Cost

Description

Contact Hours

Dates/Time

Registration Link

Early Mathematical Diagnostic Interview (EMDI)

(no cost)

The goal of this Series is to provide you with experiences, information, and resources to guide you in the areas of diagnostic assessment, identifying students' mathematical needs, and developing knowledge of instructional strategies that have an impact on students' mathematical learning.  We will focus on the Early Mathematics Diagnostic Interview for grades PK-5. Time will be spent on the EMDI tool, assessment, and scoring, as well as many routines, strategies, and learning trajectories for elementary mathematics. Please plan to attend all 4 virtual dates.

For more information, email Jen Robitaille at  jennifer.r.robitaille@maine.gov.

15

Winter Series

Tuesdays 3:30-6:30 PM, Nov. 2, Nov. 9, Nov. 16, and 3:30-7:00 PM Jan. 11

EMDI
Winter Series Registration

Spring Series

Wednesdays 3:30-6:30 PM, Mar. 2, Mar. 9, Mar. 16, and 3:30-7:00 PM May 4

EMDI
Spring Series Registration

the Math Pact: Achieving Instructional Coherence Within and Across the Grades

(no cost)

This 5-part virtual professional learning opportunity is specifically designed for a team/sub-team of a school leadership team consisting of 4-6 members (which includes at least one administrator) to support the development and implementation of a mathematics whole school agreement.  This opportunity will utilize the book series the Math Pact: Achieving Instructional Coherence Within and Across Grades by Karen Karp, Barbara Dougherty, and Sarah Bush, which will be provided to your team at no cost.  Please plan for your team to attend all 5 virtual dates.

For more information, email Michele Mailhot at  michele.r.mailhot@maine.gov.

10

Series A

Wednesdays 3:30-5:30 PM, Sept. 22, Oct. 6, Oct. 20, Nov. 3, and Nov. 17

the Math Pact

Registration closed

Series B

Thursdays 3:30-5:30 PM, Sept. 23, Oct. 7, Oct. 21, Nov. 4, and Nov. 18

the Math Pact

Registration closed

Series C

Wednesdays 3:30-5:30 PM, Mar. 30, Apr. 12, April 27, May 11, May 25

the Math Pact
Series C Registration

Series D

Thursdays 3:30-5:30 PM, Mar. 31, Apr. 14, Apr. 28, May 12, May 26

the Math Pact
Series D Registration

The Mathematics Standards: A Vertical Articulation

(no cost)

This one 3-hour virtual session will provide an overview of the standards review process and the K-12 vertical progression of concepts within the 4 strands (Quantitative Reasoning, Algebraic Reasoning, Geometric Reasoning, and Statistical Reasoning) of Maine's Learning Results.

For more information, email Michele Mailhot at  michele.r.mailhot@maine.gov or Jen Robitaille at  jennifer.r.robitaille@maine.gov.

3

October 27, 2021

(Wednesday)

Time: 3:30 pm - 6:30 pm
The Math Standards Registration

January 12, 2022

(Wednesday)

Time: 3:30 pm - 6:30 pm

May 5, 2022

(Thursday)

Time: 3:30 pm - 6:30 pm

Continuity of Learning Resources
https://www.maine.gov/doe/continuityoflearning/mathematics

Contact

Michele Mailhot
Secondary Mathematics Specialist
Phone: 207-624-6829 (Office)
Phone: 207-557-5134 (Cell)
michele.r.mailhot@maine.gov

Jen Robitaille
Elementary Mathematics Specialist
Phone: 207-215-4756 (Cell)
jennifer.r.robitaille@maine.gov

Quick Links

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Mathematics instruction supports Maine's mathematics learning standards in grades Kindergarten through 12. The Maine Department of Education mathematics specialists offer free and open resources, tools, technical assistance and professional learning opportunities on instructional practices, learning progressions, assessment, and curriculum development. The DOE Mathematics Specialists will use this NEW listserv to share upcoming events, opportunities, and information with Maine educators.

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Thomas B. Fordham Institute is America's leading education reform think tank. Learn more about Ohio policy and sponsorships here.

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100 Questions that Promote Mathematical Discourse

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100 Questions that Promote Mathematical Discourse

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Teachers’ Specialized Content Knowledge: Preparing Future Elementary School Teachers to Teach Mathematics

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Teachers’ Specialized Content Knowledge: Preparing Future Elementary School Teachers to Teach Mathematics

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EDU 530 S.Chapin Specialized Content knowledge

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Those Who Understand: Knowledge Growth in Teaching

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Those Who Understand: Knowledge Growth in Teaching

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Shulman, Knowledge Growth in Teaching (1986)

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Shulman, Knowledge Growth in Teaching (1986)

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CONTENT KNOWLEDGE FOR TEACHING:WHAT MAKES IT SPECIAL? 

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CONTENT KNOWLEDGE FOR TEACHING:WHAT MAKES IT SPECIAL? 

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You may be seeing this page because: You used the back button while browsing a secure web site or application. You may have mistakenly bookmarked the web login form instead of the actual web site you wanted to bookmark. You may have ended up here by loading a broken link.

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Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students

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Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students

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What Math Content Does Teaching Require?

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What Math Content Does Teaching Require?

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Review of Knowing and Teaching Elementary Mathematics

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Review of Knowing and Teaching Elementary Mathematics

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Review of L. Ma - Knowing and Teaching Elem. Mathematics

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Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing

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Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing

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Effects of Teachers' Mathematical Knowledge for Teaching on Student Achievement

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Effects of Teachers' Mathematical Knowledge for Teaching on Student Achievement

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Process - National Council of Teachers of Mathematics

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Standards for the goals of mathematics instructional programs from prekindergarten through grade 12 in the area of process.

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Mathematical Content Knowledge for Effective Teaching

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Mathematical Content Knowledge for Effective Teaching

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Terri had an excellent example of categorizing pedagogical knowledge into 5 categories:
Constructivist, Collaboration, Integrative, Reflective, and Inquiry-Based Learning.

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Multiplication: by one digit and two-digit numbers  UNIT PLAN

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Multiplication: by one digit and two-digit numbers  UNIT PLAN

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This unit plan provides quality pedagogical strategies to deliver excellent instruction to 4th grade students on multiplication strategies for one digit by up to four digit and two by two digit numbers.

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This is a useful document to rate educational texts or programs for K-8.

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This is a useful document to rate educational texts or programs for high school.

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Exploring the Common Core Practices in Secondary Classrooms

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Exploring the Common Core Practices in Secondary Classrooms

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Conrad Wolfram: Teaching kids real math with computers

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Conrad Wolfram: Teaching kids real math with computers

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Conrad Wolfram: Teaching kids real math with computers

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From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world.

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Developing Measures of Teachers’ Mathematics Knowledge for Teaching

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Developing Measures of Teachers’ Mathematics Knowledge for Teaching

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Developing Measures of Teachers' Mathematical Knowledge for Teaching

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If I ever imagine that I can see the edges of teaching, if I ever tell myself that I'm apprehending all of its angles and dimensions, I just call up my friends Sarah Kingston, Ben Spencer, and Megan Snyder at Beach Elementary School and ask them if they'll let me learn with some elementary school-aged children, an experience which corrects my vision for months.

Most recently, they let me think about time with some second graders - the youngest kids I've ever taught and probably ever met, I can't be sure - and especially how to tell time on an analog clock.

My goal in these experiences is always to find areas of agreement between the teaching of different age groups and different areas of math. Whether I'm learning about time with second graders or about polynomial operations with high schoolers or about teaching with math teachers, I'm asking myself, what's going on here that crosses all of those boundaries, not one of which is ever drawn as sharply as I first think.

One way teaching second grade is different from teaching high school.

The odds of me stepping on a child go way up, for one.

For another, these students were inexhaustible. Their default orientation towards me and my ideas was rapt engagement and an earnest, selfless desire to improve my ideas with stories about their friends, their pets, and their families.

My tools for curriculum and instruction were forged by students who communicated to me that "none of this matters" and "I can't do it even if it did." Those tools seemed less necessary here. Instead, I needed tools for harnessing their energy and I learned lots of them from my friends at Beach Elementary - popsicle sticks for group formation, procedures for dismissing students gradually instead of simultaneously, silent signals for agreement instead of loud ones, etc.

Even still, with these second graders, I tried to problematize conventions for telling time, just as I would with high school students. I asked students to tell me what bad thing might happen if we didn't know how to tell time, and they told me about being late, about missing important events, about not knowing when they should fall asleep and accidentally staying awake through the night!

I tried to elicit and build on their early language around time by playing a game of Polygraph: Clocks together. I told them I had picked a secret clock from that array and told them I would answer "yes" or "no" to any question they asked me. Then they played the game with each other on their computers.

One student asked if she could play the game at home, a question which my years of teaching high school students had not prepared me to hear.

One way teaching second grade is the same as teaching high school.

I saw in second grade the students I would eventually teach in high school. Students who were anxious, who shrunk from my questions, either wishing to be invisible or having been invisibilized. Other students stretched their hands up on instinct at the end of every question, having decided already that the world is their friend.

Those students weren't handed those identities in their ninth grade orientation packets. They and their teachers have been cultivating them for years!

Rochelle Gutierrez calls teachers " identity workers," a role I understood better after just an hour teaching young students.

All mathematics teachers are identity workers, regardless of whether they consider themselves as such or not. They contribute to the identities students construct as well as constantly reproduce what mathematics is and how people might relate to it (or not).

I have wanted not to be an identity worker, to just be a math worker, because the stakes of identity work are so high. (Far better to step on a child's foot than to step on their sense of their own value.) We wield that power so poorly, communicating to students with certain identities at astonishingly early ages - especially our students who identify as Latinx, Black, and Indigenous - that we didn't construct school and math class for their success.

I have wanted to give up that power over student identities and just teach math, but as Gutierrez points out, students are always learning more than math in math class.

My team and I at Desmos are forging new tools for curriculum and instruction and we're starting to evaluate our work not just by what those tools teach students about mathematics but also by what they teach students about themselves.

It isn't enough for students to use our tools to discover the value of mathematics. We want them to discover and feel affirmed in their own value, the value of their peers, and the value of their culture.

We've enlisted consultants to support us in that work. We're developing strategic collaborations with groups who are thoughtful about the intersection of race, identity, and mathematics. A subset of the company currently participates in a book club around Zaretta Hammond's Culturally Responsive Teaching and the Brain.

Before undertaking that work, I'd tell you that my favorite part of teaching Polygraph with second graders is how deftly it reveals the power of mathematical language. Now I'll tell you my favorite part is how it helps students understand the power of their own language.

"Is your clock a new hour?" a second-grade student asked me about my secret clock and before answering "yes" I made sure the class heard me tell that student that they had created something very special there, a very interesting question using language that was uniquely theirs, that was uniquely valuable.

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If I ever imagine that I can see the edges of teaching, if I ever tell myself that I'm apprehending all of its angles and dimensions, I just call up my friends Sarah Kingston, Ben Spencer, and Megan Snyder at Beach Elementary School and ask them if they'll let me...

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Adding It Up - Chapter 10 DEVELOPING PROFICIENCY IN TEACHING MATHEMATICS

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Adding It Up - Chapter 10 DEVELOPING PROFICIENCY IN TEACHING MATHEMATICS

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Read “Adding It Up: Helping Children Learn Mathematics” at NAP.edu

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Read chapter 10 DEVELOPING PROFICIENCY IN TEACHING MATHEMATICS: Adding It Up explores how students in pre-K through 8th grade learn mathematics and recomm...

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Mathematics Menu of Best Practices and Strategies

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Mathematics Menu of Best Practices and Strategies

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Constructivism: A Psychological Theory of Learning

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Constructivism: A Psychological Theory of Learning

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Constructivism- A Psychological Theory of Learning

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The Understanding by Design Guide to Creating High-Quality Units

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The Understanding by Design Guide to Creating High-Quality Units

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The Understanding by Design Guide to Creating High-Quality Units - ASCD

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The Understanding by Design Guide to Creating High-Quality Units offers instructional modules on the basic concepts and elements of Understanding by Design®® (UbD™), the “backward design” approach used by thousands of educators to create curriculum units and assessments that focus on developing stud

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Making Standards Useful in the Classroom

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Making Standards Useful in the Classroom

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Making Standards Useful in the Classroom - ASCD

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Has the standards movement in the United States led to improved classroom instruction and effective assessment? In too many cases, the answer is no. As authors Robert J. Marzano and Mark W. Haystead explain, two major reasons account for this situation: state and national standards documents typical

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Welcome to the Companion Website
"Wow! Mine the Gap for grades 3-5 teachers really unpacks! Not only does the book provide dozens of great mathematical tasks, but-perhaps more importantly-it gives teachers the chance to consider each task; anticipate student responses-a critical first step in formative assessment; analyze actual student responses; and then consider what they would do in the classroom. Thoughts about modifying each task provide another option for each task. At a time when teachers are encouraged to regularly provide students with tasks that promote reasoning and problem solving, this book will help teachers dig deeper as they mine for understandings."
-Francis (Skip) Fennell, Project Director Elementary Mathematics Specialists and Teacher Leaders Project; Past-President, National Council of Teachers of Mathematics

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Mine the Gap for Mathematical Understanding: Common Holes and Misconceptions and What To Do About Them (3-5)

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Welcome to the Companion Website"Wow! Mine the Gap for grades 3-5 teachers really unpacks! Not only does the book provide dozens of great mathematical tasks, but-perhaps more importantly-it gives teachers the chance to consider each task; anticipate student responses-a critical first step in formative assessment; analyze actual student responses; and then consider what they would do in the classroom.

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Visible Learning for Mathematics, Grades K-12

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Selected as the Michigan Council of Teachers of Mathematics winter book club book!

Rich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know…

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Understanding the Math We Teach and How to Teach It

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Understanding the Math We Teach and How to Teach It

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Understanding the Math We Teach and How to Teach It | Stenhouse Publishers

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Marian Small has written the kind of book teachers will keep on their closest shelf as they explore and return to the big ideas of mathematics. In her new resource, Understanding the Math We Teach and How to Teach It, Marian brings the support and insight teachers need to teach math with clarity and…

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Building Thinking Classrooms in Mathematics

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Building Thinking Classrooms in Mathematics

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Reviews

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"Building Thinking Classrooms in Mathematics exudes enthusiasm for students, how they think, and how those thoughts coalesce into powerful thinking classrooms. It's also deeply practical, describing how everything from the teacher's questions to the arrangement of the furniture can add to your students' learning."

"I f your students are not the ones doing the thinking in your classroom, then this book is for you!Peter Liljedahl provides concrete advice on each of 14 research-based practices, along with answers to frequently asked questions and suggestions for getting started, which will help you build a classroom where student thinking is the norm."

Peg Smith
University of Pittsburgh

"Research in education that turns right around and informs our practice is invaluable in today's schools and classrooms.Peter uses evidence gathered in mathematics classrooms to directly inform how we make changes to our teaching and learning that enhances learning.This is the essence of evidence-based practice, practice based on evidence from the very classrooms we seek to influence."

"After years of leading lessons in an 'I do, we do, you do' format, I found that my students lacked a productive disposition towards mathematics and would give up on problems easily. I knew something had to change, but what was I going to change in my teaching practice and how was I going to get there? After 10 years of experimenting with different pedagogical approaches, classroom environment setups, and developing my own content knowledge, I realize that this book is the resource that could have helped me expedite the transformation I was after - moving from a classroom of "mimickers" to building a classroom of "thinkers". Save yourself years of experimentation by investing a few hours reading this excellent book. Your students will thank you."

"Building Thinking Classrooms prompts us to reflect on the potential of mathematics classrooms, teachers, and learners. Supported by numerous stories from classrooms, Peter methodically exposes the familiar structures of school mathematics that suppress the potential of learners, then carefully outlines a set of opportunities around which teachers of mathematics can organize a dynamic and responsive classroom."

"This book is timely and provides an accurate portrayal of what is occurring in mathematics classroom across the country. The book is a valuable reflexive tool that teachers can use as they analyze their own teaching practices."

" Peter's work in Building Thinking Classrooms has been the single most impactful (driver for) change in secondary mathematics education that I have witnessed. I have never seen another idea/approach/model capture so many teachers immediately, and make it past the point from learning to actual implementation in almost every classroom or instance that I have witnessed."

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Building Thinking Classrooms in Mathematics, Grades K-12

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Building Thinking Classrooms in Mathematics, Grades K-12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur.

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Knowing and Teaching Elementary Mathematics

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Knowing and Teaching Elementary Mathematics

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Table of Contents

A Note about the 20 th Anniversary Edition

Author's Preface to the 20 th Anniversary Edition

Series Editor's Introduction to the 20th Anniversary Edition: What Makes a Classic?

Author's Preface to the 2010 Edition

Series Editor's Introduction to the 2010 Edition

Foreword

Acknowledgments

Introduction

1.

Subtraction With Regrouping: Approaches To Teaching A Topic

The U.S. Teachers' Approach: Borrowing Versus Regrouping

The Chinese Teachers' Approach: "Decomposing a Higher Value Unit"

Discussion

Summary

2.

Multidigit Number Multiplication: Dealing With Students' Mistakes

The U.S. Teachers' Approach: Lining Up Versus Separating Into Three Problems

The Chinese Teachers' Approach: Elaborating the Concept of Place Value

Discussion

Summary

3.

Generating Representations: Division By Fractions

The U.S. Teachers' Performance on Calculation

The Chinese Teachers' Performance on Calculation

The U.S. Teachers' Representations of Division by Fractions

The Chinese Teachers' Approach to the Meaning of Division by Fractions

Discussion

Summary

4.

Exploring New Knowledge: The Relationship Between Perimeter And Area

How the U.S. Teachers Explored the New Idea

How the Chinese Teachers Explored the New Idea

Discussion

Summary

5.

Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics

A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance?

Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning

Elementary Mathematics as Fundamental Mathematics

Profound Understanding of Fundamental Mathematics

Summary

6.

Profound Understanding Of Fundamental Mathematics: When And How Is It Attained?

When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics

Profound Understanding of Fundamental Mathematics: How It Is Attained

Summary

7.

Conclusion

Address Teacher Knowledge and Student Learning at the Same Time 146

Enhance the Interaction Between Teachers' Study of School Mathematics and How to Teach It

Refocus Teacher Preparation

Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform

Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics

Appendix

References

Fang and Paine's "Bridging Polarities: How Liping Ma's Knowing and Teaching Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses"

Liping Ma's Response to "Bridging Polarities"

New to the 20 th Anniversary edition: A Critique of the Structure of U.S. Elementary School Mathematics

Index

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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States

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The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children. Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics.

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This lesson plan highlights mathematical pedagogy and strategies, technology, and formative assessment opportunities with strategies.

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Cosgrove:  Writing a Decimal in Standard Form

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OER Commons is a public digital library of open educational resources. Explore, create, and collaborate with educators around the world to improve curriculum.

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Open Author helps you build and publish Open Educational Resources for you and for the benefit of educators and learners everywhere.

Learn more about creating OER

Groups provides a flexible environment to organize, create, share, and discuss resources with others in your network. Collaborate with group members, tag and add resources to shared folders, create your own collections, all within a public or private group.

Groups

Search through collections curated by our digital librarians

Collections

Common Core resources organized for your needs

Common Core

Hubs

A Custom Resource Center

Projects, districts, states, and initiatives make use of Hubs to bring groups of educators together to create, organize, and share OER collections that meet their common goals. Explore Hubs

Microsites

Custom Digital Libraries

Microsites are custom, flexible sites that include all the features available on OER Commons. Microsites allow your users to search resource collections using a custom taxonomy at a unique URL. Contact Us

Our award-winning OER Professional Learning programs support instructors and curriculum specialists to gain the necessary skills required to find, adapt, and evaluate high quality open materials.

In-person and virtual OER workshops help focus instructors to develop a "commons" mindset, to experience the benefits of open processes using the platform's tools, collaborative features, and workflows. This can include using Open Author for creating, remixing, and publishing shared curriculum.

Learn More

How to Search OER Commons

View all How-to videos

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OER Commons is a dynamic digital library and network. Explore open education resources and join our network of educators dedicated to curriculum improvement.

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Written by Corinne Lestch
Feb 29, 2016 | STATESCOOP

Days after acting Education Secretary John King touted open educational resources during a House Education and the Workforce Committee hearing, his agency announced that 13 states that are going to dump textbooks for online school materials.

The initiative, called #GoOpen, was originally launched in October, but only 10 school districts said they would participate and transition from the printed word to the electronic version within the next year.

The states that have agreed to participate are Arizona, Georgia, Indiana, Maryland, Michigan, North Carolina, Oklahoma, Oregon, Rhode Island, Utah, Vermont, Virginia, and Wisconsin. They will adopt and execute a blanket technology strategy to offer teachers the ability to customize educational content for their students, and develop and maintain a repository solution for openly licensed resources, according to agency officials.

"States are powerful collaborators in supporting and scaling innovation," said Joseph South, director of the Office of Educational Technology. "With the launch of statewide #GoOpen initiatives, states are helping districts transition to a new model of learning by facilitating the creation of an open ecosystem of digital resources that can increase equity and empower teachers."

Just this week, King told lawmakers that "We think there's a huge opportunity for savings and sharing" in K-12 and higher education using open educational resources, known as OER, according to a report in Education Week.

Educational technology companies are offering platforms - a new business model - for schools and districts to search for and modify the materials.

Amazon Education will provide infrastructure and developer support for the Department of Education's Learning Registry, which runs on AWS Cloud, for two years, which will help about 15,000 school districts view and share content.

Microsoft, for its part, will deliver an LTI app that offers teachers and students access to OER from within other learning management systems and publisher platforms. There will also be updates to the company's Docs.com to allow people to create, rate and share OER that will be fully integrated with Microsoft Office 365.

"Switching to openly-licensed educational materials has enabled school districts to repurpose funding typically spent on static textbooks for other pressing needs, such as investing in the transition to digital learning," said Andrew Marcinek, Open Education Advisor at the department.
Reach the reporter at corinne.lestch@edscoop.com and follow her on Twitter @clestch and @edscoop_news.
-In this Story-

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States to 'Go Open' with online educational materials - StateScoop

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Days after acting Education Secretary John King touted open educational resources during a House Education and the Workforce Committee hearing, his agency announced that 13 states that are going to dump textbooks for online school materials.

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Illustrative Mathematics provides resources and support for giving their students an enduring understanding of mathematics.

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How Responsive Is a Teacher’s Classroom Practice to Intervention? A Meta-Analysis of Randomized Field Studies

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How Responsive Is a Teacher’s Classroom Practice to Intervention? A Meta-Analysis of Randomized Field Studies

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Beyond PD Teacher Professional Learning in High-Performing Systems

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Beyond PD Teacher Professional Learning in High-Performing Systems

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Professional Development To Support Instructional Improvement:Lessons from Research

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Professional Development To Support Instructional Improvement:Lessons from Research

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Underpinnings and Mapping of Framework for Leadership in Mathematics Education  through It’s Time and Information to Support PD Development

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Underpinnings and Mapping of Framework for Leadership in Mathematics Education  through It’s Time and Information to Support PD Development

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Resources - Mathematics | Department of Education

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In Maine, how schools implement standards is entirely a local decision. The Maine Department of Education has compiled the following resources that educators may find helpful as part of our commitment to supporting Maine’s learning community.

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Collaborative teaching, or co-teaching, is a powerful way to support the learning of students with diverse learning needs. But how do you know when you're doing it right? And if you're not, what can you do about that? Authors Wendy W. Murawski and Wendy W. Lochner introduce the Collaborative Teaching Improvement Model of Excellence (CTIME), a continuous improvement model that embraces personalized professional learning to ensure that teachers meet the core competencies for co-teaching without burning out along the way. Incorporating a systematic application of collaborative groups, data analysis, microteaching, feedback, and collegial support, CTIME is the culmination of the best research in the field.

As Murawski and Lochner walk you through their data-driven, no-fail model of co-teaching, you'll learn about

The CTIME process and how it works.

Co-teaching core competencies measured schoolwide and at the classroom level.

Assessment of progress toward mastery.

Co-teaching action plans.

Professional learning communities and schoolwide improvement.

Co-teaching communities of practice and microteaching.

Co-teaching facilitation, feedback, and reflection.

Offering a practical approach to achieving mastery of the co-teaching core competencies, this book provides dozens of strategies, resources, and templates that can be used by district-level administrators, principals, and co-teaching teams. If you're ready to examine your co-teaching practices to make sure you're achieving the best possible outcomes for your students, then Beyond Co-Teaching Basics is for you.

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Beyond Co-Teaching Basics: A Data-Driven, No-Fail Model for Continuous Improvement

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Beyond Co-Teaching Basics: A Data-Driven, No-Fail Model for Continuous Improvement [Murawski, Wendy W., Lochner, Wendy W.] on Amazon.com. *FREE* shipping on qualifying offers. Beyond Co-Teaching Basics: A Data-Driven, No-Fail Model for Continuous Improvement

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Teaching in Tandem: Effective Co-Teaching in the Inclusive Classroom

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Teaching in Tandem: Effective Co-Teaching in the Inclusive Classroom

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Teaching in Tandem: Effective Co-Teaching in the Inclusive Classroom

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Teaching in Tandem: Effective Co-Teaching in the Inclusive Classroom [Wilson, Gloria Lodato, Blednick, Joan] on Amazon.com. *FREE* shipping on qualifying offers. Teaching in Tandem: Effective Co-Teaching in the Inclusive Classroom

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Strategic Co-Teaching in Your School: Using the Co-Design Model

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Strategic Co-Teaching in Your School: Using the Co-Design Model

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Strategic Co-Teaching in Your School: Using the Co-Design Model

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Amazon.com: Strategic Co-Teaching in Your School: Using the Co-Design Model: 0884658657881: Barger-Anderson Ed.D., Richael, Isherwood Ed.D., Robert, Merhaut Ed.D., Joseph: Books