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Math Standards

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“Common Does Not Equal Excellent”: New Report Sheds Light on Deficiencies of Common Core’s Math Standards

The K-8 CCSS-M differ substantially from the standards of high-performing countries and are ultimately developmentally inappropriate. Leveraging topic coverage comparisons, Tuttle and Wilson demonstrate that the CCSS-M fail to embody the coherence and focus evident in the standards of high-performing countries. This failure stems in large measure from a focus on abstract-levels of cognitive demand and demonstration of understanding. In turn, such focus results in tasks that often stunt students’ learning. By contrast, higher-performing countries emphasize concrete levels of cognitive demand memorization, and procedural fluency.

Tuttle and Wilson assert that the “rigor” claimed by CCSS-M is not so much in the content as in the expectation that students display knowledge—a task for which they are frequently left without adequate tools. Though cognitively heavy, the CCSS-M remain procedures-poor. Focusing too early on the abstract drives an insistence on inefficient computation strategies. More effective, proven, and developmentally appropriate methods are delayed by up to two years. For instance, the CCSS-M does not introduce the standard algorithm for addition and subtraction until grade 4. Standard algorithms for multiplication and subtraction are thus withheld until grades 5 and 6 respectively. These delays result in inadequate preparation of students for algebra and beyond.

In addition to the CCSS-M per se, Tuttle and Wilson also explore the K-8 Publisher’s Criteria for the Common Core State Standards for Mathematics as well as Progressions for the Common Core State Standards in Mathematics, the latter written by the CCSS-M’s lead authors. Both documents go into greater detail concerning the strategies and instructional techniques embedded within the CCSS-M, laying out expectations for textbook, assessment, and instructional alignment. These additional materials clearly inform the use of CCSS-M in the classroom, essentially determining inefficient instructional delivery methods that undermine professional teacher judgment.

Tuttle and Wilson conclude there is no empirical support for either the claim or the expectation that CCSS-M will improve student achievement.

“Common Does Not Equal Excellent” has been made available in PDF format on the American Principles Project website. For additional information call 202-503-2010.

Highlights:

- A review of the CCSS-M shows that its standards do, in fact, repeatedly dictate instructional approaches. And if a curriculum is to be aligned with the CCSS, it must use these instructional approaches

- There are simply too many fundamental differences between the CCSS-M and the standards and practices of high-performing countries to argue similarity between them. The expectation that these cognitively heavy but procedures-poor standards will improve student achievement has no empirical evidence to support it.

- The Publishers’ Criteria provides guidance on what
the “focus” standards will be for textbooks and the assessments. It specifies that unless
approximately 75% of instructional time is devoted to these standards, the material is unlikely
to be aligned. The standards instructional elements will definitely be tested. The high stakes nature of testing will incentivize schools to not waste time teaching processes not included in the standards.

- The path CCSS-M put math instruction on is not based on evidence and has been well-worn by past reform-math initiatives that haven’t led to a rise in student achievement or an increase in global competitiveness for the United States.

From Ze'ev Wurman's testimony at Hearings on Missouri legislation to stop Common Core.

1. Quality of the Common Core Mathematics Standards

Missouri math standards have been rated quite low by the Fordham Foundation. Yet despite that low rating, Missouri achievement on the NAEP is close to the national average. This goes to show that standards in themselves are insufficient to assure success, and that Missouri has been doing many things right despite its low-rated standards. Hitching your wagon to the Common Core will replace Missouri ideas and Missouri innovation by ideas and innovation developed mostly elsewhere.

The Common Core proudly announces it will focus on only a few topics in each elementary grade because, it claims, that is what other successful countries are doing. Yet if one looks at Singapore or Korea, prominent members of that successful club, one sees that they are not nearly as narrow or as limiting as the Common Core. It seems that in its haste to be “lean and mean,” the Common Core ignored many skills that those countries – and Missouri’s own standards – expect of students. For example, the Common Core starts introducing the concept of counting money only in the second grade, while Singapore and Missouri wisely suggest starting in the first grade. Common Core forgets to teach prime factorization altogether, so it cannot ever teach least common denominators or greatest common factors. Worse yet, even when it comes to fractions, the topic of which it is most proud, Common Core completely forgets to teach conversion among fractional forms – fractions, percent, and decimals – which has been identified as a key skill by the National Research Council, the National Council of Teachers of Mathematics, and the National Advisory Math Panel.

There is more. Even in its core focus, basic arithmetic, the Common Core opens the way for the pernicious “fuzzy math” to creep back into the curriculum. On the one hand, it expects – even if later than our international competitors – that eventually the standard algorithms for the four basic operations be mastered. On the other hand, many prior years are full with intermediate standards that repeatedly demand students to explain their actions in terms of crude strategies based on various concrete and visual models or invented algorithms applicable only to specific cases. The consequence of this skewed attention is that students will end up confused and frustrated by the variety of pseudo- algorithms they are forced to study

Stanford professor James Milgram, a member of the Common Core Validation Committee, captured it well in his testimony before the California Academic Standards Commission, saying, “Within the document itself, there seems to be a minor war going on and this is not something we should hand over to our teachers.”1 Small wonder that a classic fuzzy math text like TERC Investigations can claim that “there is strong alignment between Investigations and the [Common Core] Math Content Standards,”2 or that Common Core curriculum in New York is promoting the following fuzzy foolishness: “Working in small groups, the students rotated through the classrooms in the second-grade wing to work at the various stations. Using edible gingerbread men, the second-graders utilized their math skills by tasting the cookies and graphing which portions of the cookies that they took their first bites of.”

In
the middle school, the Common Core does not expect students to take
Algebra 1 in grade 8, despite the fact that a large fraction of students
in Missouri and across the nation already take it. All the high
achieving countries, like Singapore, Korea, and Japan, expect
essentially all their students to take Algebra I in grade 8, or complete
Algebra I and Geometry by grade 9. Common Core abandoned this goal that
promoted much of our nation’s mathematics improvement over last decade,
and offers it only as an afterthought, unsupported by instructional
materials or assessment. Yet taking Algebra I in grade 8 is of critical
importance for those who want to reach calculus by grade 12 and enroll
in competitive colleges. When the standards don’t prepare all children
to be algebra ready, only the children of the affluent and well-educated
will be pushed and supported by their families to strive and achieve.
Children from disadvantaged backgrounds will have no chance to reach so
high, as they won’t have out-of-school tutoring.

In summary, by the middle school the Common Core mathematics falls one to two years behind our high achieving international competitors.

2. Common Core high school mathematics and its inadequate definition of college-readiness

Common
Core’s high school mathematics are partially experimental and of
middling quality. Its promise of college readiness for all rings hollow
and will cause even larger rates of remediation in college.

But
you don’t have to believe me: Jason Zimba, one of the main authors of
the mathematics standards, testified in front of the Massachusetts Board
of Education4 that Common Core’s ”concept of college readiness is
minimal and focuses on non-selective colleges.” It is hard to see how
such a low level of college readiness will benefit Missouri students.

The
Common Core-recommended Algebra 1 course includes only a subset of
typical Algebra 1 content. More specifically, it introduces a focus on
functional aspects of algebra, while de-emphasizing its computational
and technical foundations. Yet algebra is not a goal in itself, but
rather a tool to support further mathematics on one hand, and support
the learning of sciences on the other. An algebra course such as
promoted by the Common Core will only weakly support the study of
chemistry or other quantitative sciences.

Common
Core replaces the traditional foundations of Euclidean geometry with an
experimental approach. This approach has never been successfully used
in any sizable system; in fact, it failed even in the school for gifted
and talented students in Moscow, where it was originally invented. Yet
Common Core effectively imposes this experimental approach on the entire
country, without any piloting.

Essentially all four-year state colleges across the country, including Missouri own public universities, require at least the Algebra I/Algebra II and Geometry courses as prerequisites for enrollment. This is a rather minimal expectation for college readiness, as the growing number of students in remedial courses attests. To get a better sense of how marginal this requirement is, one may look to California’s assessments for college readiness used by the California State University system conducted in grade 11. Results indicate that among students who just take Algebra 2, only 7% are ready and 22% are conditionally ready (i.e., they need to take another year of math in grade 12). In contrast, among students that take a math course beyond Algebra 2, 22% are ready and 67% are conditionally ready – a huge difference.

Yet
the Common Core chose to lower the standards even more and eliminate
Algebra 2 content like geometric and arithmetic sequences, or
combinations and permutations, from its own version of Algebra 2 that it
offers as a measure of college readiness.

Read his full testiomony here.

Read James Millgram, Professor Emeritus Stanford University, Member of Math Validation Committee's detailed critique of CC Math Standards here.

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Language Arts Standards

From Sandra Stotsky's testimony on Missouri legislation to stop Common Core

1. Common Core's English language arts standards won’t lead to college readiness: Common Core’s “college readiness” standards for ELA standards have many flaws:

Common Core expects English teachers to spend over 50 percent of their reading instructional time on informational texts at every grade level. It sets forth 10 reading standards for informational texts and 9 standards for literary texts at every grade level, K-12. (An informational text is a piece of writing written to convey information about something, e.g., gravity, bicycles, nutrition.) There is no body of information that English teachers have ever been responsible for teaching, unlike science teachers, for example, who are charged with teaching information about science. In addition, English teachers are not trained to give informational reading instruction—by college English departments or by teacher preparation programs. They study four major genres of literature—poetry, drama, fiction, and nonfiction—and are trained to teach those genres.

Common Core reduces literary study—what English teachers are trained to teach. Common Core does not specify the literary/historical knowledge students need in its standards. It offers no specific criteria for selecting literary or informational texts for study. It provides no list of recommended authors, never mind works. It requires no British literature aside from Shakespeare. It does not require study of the history of the English language.

Common Core’s middle school writing standards are an intellectual impossibility for average middle school students. Adults have a much better idea of what "claims," "relevant evidence," and academic "arguments" are. But most children have a limited understanding of these concepts, even if Common Core’s writing standards were linked to appropriate reading standards and prose models. Nor does the document clarify the difference between an academic argument (explanatory writing) and persuasive writing, confusing teachers and students alike.

Common Core’s college-readiness standards are chiefly empty skills. Skills training (such as how to use Google or a card catalogue or find a main idea) alone doesn’t prepare students for college. High school students need to be taught how to read and understand the content of complex literary texts in order to do “critical thinking.”

2. Common Core’s standards lack a research base, international benchmarking, and credible authors: Common Core’s Validation Committee, on which I served, was supposed to ensure that its standards were internationally benchmarked and supported by a body of research evidence. Even though several of us regularly asked for the names of the countries the standards were supposedly benchmarked to, we didn’t get them. Nor did we get citations to the supposed body of evidence supporting the idea that an increase in instruction in informational reading in English or other classes will make students college-ready.

We did not get evidence on international benchmarking because Common Core is not about “rigor for all,” despite all the parrot talk. In grades 6-12, it is about “rigor for none” or educational rigor mortis. Its goal is not to increase all students’ achievement—the goal of the Bay State student standards and tests, and teacher standards and tests. Common Core’s goal is to close the demographic gaps in student achievement the easiest way that Gates and the USDE could figure out—which is why Jason Zimba, the mathematics standards writer told the Massachusetts Board of Elementary and Education at a public meeting in March 2010 that college-readiness for Common Core means readiness for admission to a non-selective community college. The aim of its high school mathematics standards is not to strengthen the high school curriculum and to prepare a regularly increasing number of students for college freshman calculus courses.

All state standards need to be reviewed and revised if needed at least every five to seven years by identified Missouri teachers and discipline-based experts in the arts and sciences, and parents. In addition, all state assessments should be reviewed by Missouri teachers and discipline-based experts in the arts and sciences before the tests are given. This can’t happen with Common Core’s standards and assessments. Missouri has lost control of the content of its children’s education under Common Core. Its main task is simply to pay for its costs. The future costs for staying with Common Core will far outweigh the costs for leaving while leaving is still possible.

Read Dr. Stotsky's full testimony here.

Read her full critique of the ELA standards here.

From Language Arts, Volume 89 Number 1, September 2011 National Council of Teachers of English

"[t]he CCS argue that the purpose of education is readiness to participate in college and careers. Many of these standards focus rather narrowly on students’ ability to participate in a university classroom that would have seemed normal in the 1950s; there is, in fact, next to no substantial focus on “career.” Whatever Anchor Standard is supposedly getting students ready for this college experience is then stretched back through the grades all the way to kindergarten. Mainly, the standards’ authors expect students in college to be asked to write about texts—to give analytic reasoning about texts, arguing something with textual evidence to support their claims. This, as we will see, is a form of literacy that receives attention in early childhood as well...

Here, however, is Kindergarten Writing Standard #1: “Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is . . . ).” And here is First Grade Writing Standard #1: “Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and pro- vide some sense of closure.” In these standards for primary grades, the Common Core Standards in fact ask young children to engage in essentially the same literacy practice as the one that is “college ready,” albeit in a way that makes sense with the ways young children compose—with drawings and oral language, as well as writing. That is, they are asked to make a text about a text and provide evidence from the first text for what they claim in the second.

It’s reasonable to ask whether such an expectation provides the best curriculum for young children. For example, if this is difficult for some children, should they be asked to do it again and again until they catch on? How much of a writing curriculum, after all, should focus on this literacy practice, named here as Standard #1? How does this kind of writing interact with writing about concrete experiences? How does this kind of writing inter- act with writing in the same form as the texts they commonly read (since, after all, approximately zero children’s books are written in the genre described in this standard)? Secondary literacy educators, such as those in NCTE leadership, have worked for much of English discipline’s history to prevent so much of the writing curriculum being focused on writing about literature (Applebee, 1996). If a focus on this kind of narrowly academic or school- like writing isn’t a persuasive curriculum for high school, how convinced should primary teachers be that they should spend much attention on it?...

Certainly no research demonstrates that teaching evidence-based argument in very early schooling contributes to students being able to do it in college.