Although the State Board of Education adopted new Common Core standards in math and English language arts nearly seven years ago, some school districts are still in the process of implementing them.

Forty-one other states around the country have also adopted the standards, which were created to help U.S. students compete with high school graduates from around the world for 21st Century jobs.

Tests of California students show progress has been** **made over the past two** **years, but an achievement gap between low-income students and their wealthier peers remains, along with gaps between **higher-scoring Asian and white students and lower-scoring **African-American and Latino classmates.

The new standards emphasize critical thinking and class discussions about concepts, instead of passive lectures by teachers and multiple-choice tests.

This FAQ explains the new standards, while also touching on the national controversy that continues to swirl around them based on fears that the federal government has pushed the standards on states and concerns over the use of test scores in teacher evaluations outside California, among other reasons.

**What are the Common Core State Standards in California?**

Common Core math and English language arts standards explain what students should know and be able to do by the end of each grade level, from kindergarten through 12th grade. They are not the same as a curriculum, which tells educators how to teach the standards.

Each district and school can choose its own curriculum to meet the goals of the standards. However, the state has adopted “frameworks” – which are like blueprints – that explain how to teach them in California.

The state has also adopted lists of recommended curriculum materials for grades K-8 in math and English language arts, including materials for English language learners.

**What is different about English language arts standards in California under the Common Core compared to the previous standards? **

California’s previous state standards in English language arts stressed more fiction than the Common Core standards, which require students to analyze and compare nonfiction texts to prepare them for college and 21st century careers that require critical thinking and math expertise, such as computer programmers and other technology-related fields. The new standards are considered more rigorous and require students to think critically and use evidence to support their positions. They also stress literacy across all subject-areas, emphasizing reading, writing and speaking.

And because 21.4 percent of California students come to school speaking languages other than English, the state has adopted English Language Development standards that require teachers of every subject **–** from science to physical education **–** to stress academic vocabulary and class discussions to help English learners become fluent more quickly.

**What is different about math standards in California under the Common Core?**

The math standards are divided into two sections – one for subject content to be taught at each grade level and one for skills and techniques used to solve problems, called “Standards for Mathematical Practice.” The new standards show that there can be many ways to solve a problem and encourage students to explain how they figure out their answers.

The content standards include concepts such as counting, addition, multiplication, fractions and algebra, with an emphasis on understanding how math works instead of merely memorizing math facts or formulas.

The eight practice standards stress skills such as working at a problem until you get it right and tools such as diagrams, tables, graphs, charts and formulas that students use to solve problems. These standards are the same at every grade level, but they build on each other from year to year.

**Can the federal government repeal the Common Core standards?**

No. They are state standards. The new federal Every Student Succeeds Act, which replaced No Child Left Behind, prohibits the federal government from dictating or controlling a state, district or school’s “instructional content, academic standards and assessments, curricula, or program of instruction….”

The federal law, known as ESSA, requires states to adopt rigorous standards, but allows states to decide what those standards should be.

**Are the Common Core standards being implemented in all California schools? Is it mandatory for schools to use the standards to guide instruction? **

Local school boards have the discretion to adopt the standards and curriculum they believe best meet their students’ needs. So, while it is not mandatory for schools to use the Common Core standards to guide instruction under California law, the state strongly recommends that schools use them and expects all public schools and districts to implement them, including charter schools. However, it does not track whether or not they do.

State law requires all schools to teach English – including literature and English speaking, reading, listening, spelling, handwriting and composition. California law also requires schools to teach mathematics – including concepts, operations, and problem-solving.

In addition, the state requires all public** **schools – including charters –** **to create Local Control and Accountability Plans that show how they are addressing priorities established by the State Board of Education, which include implementing the Common Core standards. Private schools are not required to use the Common Core standards or to create accountability plans. But a spokesperson for the California Department of Education says it encourages private schools to teach to Common Core standards.

**How do California schools test students on the standards?**

Schools are required to administer math and English language arts tests created by the Smarter Balanced Assessment Consortium, or SBAC, to students in grades 3-8 and 11 each year. These tests are aligned to the Common Core standards and are computer-based. However, parents may choose to opt their children out of the tests. Last year, less than 1 percent of the nearly 3.2 million California students eligible to take the tests opted out of them.

All California public school students in grades 3-8 and 11 are expected to take the Smarter Balanced tests or California Alternative Assessments unless their parents opt them out.

Smarter Balanced provides accessibility tools to enable students who are not fluent in English or who have some physical disabilities to take the tests. Also, the state is developing an optional Spanish Assessment that it expects to pilot in the fall of 2017 to assess students’ proficiency in reading, writing and listening in Spanish. That applies to students whose native language is Spanish and students who are learning Spanish. Some students with significant cognitive disabilities can take the California Alternative Assessment.

The state reports test results for schools, districts and counties on its public website. Parents receive individual student score reports in the mail.

The Smarter Balanced tests are part of the California Assessment of Student Performance and Progress (CAASSP) System, which also includes science tests.

**What other standards are guiding instruction in California schools?**

Besides the Common Core math and English language arts standards, the state Board of Education has adopted standards related to the following subject areas: English Language Development for English learners, Career Technical Education, Health Education, History-Social Science, Next Generation Science Standards, and Physical Education. It has also adopted Model School Library Standards.

In addition, the state is revising its Visual and Performing Arts standards and is developing standards for Computer Science and World Language.

**How much support for the Common Core has there been in California? And how much opposition? **

Although opposition to the Common Core has been strong in some other states where high stakes are tied to test results – such as teacher evaluations and whether to retain students in their grade levels **– ** Californians have largely supported the new standards. The state adopted the standards in 2010 and many districts began transitioning to them in 2013-14, when the state piloted new Common Core-aligned tests. Most districts were expected to have implemented them by 2014-15, when the Smarter Balanced tests were first administered.

In 2014, more than 300 California business, nonprofit and children’s groups signed a statement supporting the Common Core State Standards.

In 2015, while a nationwide poll showed a majority of respondents opposed the standards, two California polls showed residents in this state favored the new math and English language arts standards.

And again in 2016, Californians showed greater support for the standards than other U.S. residents polled nationwide.

By 2017, when an anti-Common Core administration led by newly elected President Donald Trump took office, many education leaders from throughout California said the standards are here to stay. They said Californians support the state’s efforts to better prepare students for college and 21st Century careers.

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## Comments (14)

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ZOE J DANIELSON2 months ago2 months agoI would not send my children to a Common Core school. I am credentialed (California) in elementary education and science. Common Core is a make-work program for tutors. Yes, I make money teaching students the math and cursive handwriting they no loner learn in school.

Roland Preston Bockhorst2 months ago2 months agoSome examples of math problems was the link I followed. Where are they?

Josh1 year ago1 year agoLet's just be honest and say beyond basic education school doesn't help anyone do anything. Unless you are going to be a teacher/professor or historian, half the things they teach are unnecessary. Yes math is important for computer/science and healthcare professions. This common core takes so damn long I hope future doctors don't use it because their patients will die waiting for them to figure out the dosage. The education system is just a way … Read More

Let’s just be honest and say beyond basic education school doesn’t help anyone do anything. Unless you are going to be a teacher/professor or historian, half the things they teach are unnecessary. Yes math is important for computer/science and healthcare professions. This common core takes so damn long I hope future doctors don’t use it because their patients will die waiting for them to figure out the dosage.

The education system is just a way for the government to indoctrinate kids to be the brainwashed worker bees they want.

Ylondra Briggs3 years ago3 years agoI strongly believe in preparing our students for global competition for careers. Historical state standards and federal control have been outgrown with the advancement of technology that continues to grow. A team approach has been a long standing collaborative effort to advance the economy by employers which schools will now exercise including critical thinking and discussion. Teachers are now able to greatly influence their students toward a common goal for their students.

M. Hagopian3 years ago3 years agoEdSource, you disappoint me. This article is simply a restatement of the party line. No time was spent comparing our previous standards with Common Core standard to standard, grade to grade. No mention that when the previous standards were in place all students, including subgroups were making great progress in student performance. Some schools showed dramatic gains moving from below the 20th percentile to above the 80th percentile. Sadly, with Common Core all of that has been lost.

Zeev Wurman3 years ago3 years ago“The new standards emphasize critical thinking and class discussions about concepts, instead of passive lectures by teachers and multiple-choice tests.” That is, indeed, what the Common Core standards claim and attempt to explicitly promote. That is not, however, what the Common Core standards actually do, or are likely to achieve. For example, in the 1980s and 1990s, California led the country in explicitly promoting student “self-esteem.” It took some time until researchers showed that directly promoting … Read More

“The new standards emphasize critical thinking and class discussions about concepts, instead of passive lectures by teachers and multiple-choice tests.”

That is, indeed, what the Common Core standards claim and attempt to explicitly promote. That is not, however, what the Common Core standards actually do, or are likely to achieve. For example, in the 1980s and 1990s, California led the country in explicitly promoting student “self-esteem.” It took some time until researchers showed that directly promoting self-esteem, rather than promoting achievement that LEADS to self-esteem, promotes narcissism and bullying behavior and decreases achievement (Leary & Baumeister, 2000). Similarly, *directly* exhorting focus on “understanding,” rather than on a balance of ability to perform AND understand, is likely to undermine both achievement and understanding.

Further, the statement above contrasts “critical thinking” with “multiple choice tests.” This is an incorrect contrast, falsely implying that multiple choice testing does not involve critical thinking. Consider the following multiple choice question:

“A student divides 1 by 23 on a calculator and sees that the result is 0.0434782609. Is the quotient rational or irrational? (A) Rational (B) Irrational (C) Both (D) Can’t tell.”

This is short, clear, and requires understanding.

“Common Core math and English language arts standards explain what students should know and be able to do by the end of each grade level, from kindergarten through 12th grade. They are not the same as a curriculum, which tells educators how to teach the standards.”

This is factually false. Here is a key first grade Common Core and the California old standards:

Common Core: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)

Old: Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory.

And here is a key geometry standard:

Common Core: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Old: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Anyone with a bit of sense can see how the Common Core specifies not only the WHAT but also the HOW. In contrast, our previous standards defined only the WHAT.

“The new standards are considered more rigorous and require students to think critically and use evidence to support their positions.”

I know that is what the Common Core propaganda says, yet can you find even a SINGLE reputable analysis that argues Common Core to be more rigorous than the previous California standards? Even the Fordham Institute – a Common Core supporter – analysis gives Common Core ELA and math B+ and A- respectively, while the previous California standards get a straight A in both.

>> “The content standards include concepts such as counting, addition, multiplication, fractions and algebra, with an emphasis on understanding how math works instead of merely memorizing math facts or formulas.”

Anyone with any understanding of math can easily see that previous California standards included both demand for understanding AND proficiency with procedures rather than “merely” memorizing. It is true that Common Core focuses LARGELY on understanding to the deprecation of procedures and memorization.

As researchers who studied Common Core reported, “… the results are surprising both for mathematics and for ELAR. Top-achieving countries for which we had content standards put a greater emphasis on ‘perform procedures’ than do the U.S. Common Core standards. High-performing countries’ emphasis on ‘perform procedures’ runs counter to the widespread call in the United States for a greater emphasis on higher order cognitive demand.“ (Porter et al., 2011)

>> “The federal law, known as ESSA, requires states to adopt rigorous standards, but allows states to decide what those standards should be.”

That is a superficial and misleading reading of the law.

ESSA *requires* that state standards be “aligned with entrance requirements for credit-bearing coursework in the system of public higher education in the State and relevant State career and technical education standards.” Yet ONLY Common Core is AUTOMATICALLY and without evidence considered “aligned.” This effectively pushes states to adopt and retain Common Core, even if their previous standards were superior. As was the case in California.

In summary, I find that this article glosses over Common Core deficiencies and reflects Common Core propaganda more than reality.

Replies

Brandon Michaels3 years ago3 years agoYour comparisons between old and new standards and the suggestion that the new standards enforce a curriculum are simply incorrect. You suggest that 'anyone with an understanding of math...' but your misrepresentation of the differences between the standards discredits the rest of your arguments. For Geometry, which parts of triangles would you propose should be used if not angles and sides? And how is that in any way dictating a curriculum? Your comparison of the subtraction standards … Read More

Your comparisons between old and new standards and the suggestion that the new standards enforce a curriculum are simply incorrect. You suggest that ‘anyone with an understanding of math…’ but your misrepresentation of the differences between the standards discredits the rest of your arguments.

For Geometry, which parts of triangles would you propose should be used if not angles and sides? And how is that in any way dictating a curriculum?

Your comparison of the subtraction standards in the primary grades is equally disingenuous. The objective you cite as the old first grade standard should more accurately be compared with the related second grade standard: “Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.” The learning objectives are different between the standards you cite. Furthermore, one of the previous first grade standards was “Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented as 4 + 4,5 + 3, 2 + 2 + 2 + 2, 10 − 2, 11 − 3). ” and “Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 − 6 = 8) to solve problems and check solutions. ” With the exception of ‘creating equivalent…easier,’ the old and new standards are effectively the same – just broken up and worded differently. And that last bit can be counted as a potential example of the former ‘Use mental arithmetic to find the sum or difference of two two-digit numbers.’ standard.

I’m not suggesting that the article is without fault, but I find that your comment misrepresents Common Core deficiencies and reflects anti-Common Core propaganda more than reality.

M. Hagopian3 years ago3 years agoSuggesting anyone should have to compare a first-grade standard to a second-grade standard is ludicrous. Further, it explicitly demonstrates how Common Core has dumbed down our previous rigorous, achievable California standards. The second-grade standard to which you refer used to be our first-grade standard under Number sense 2.0 (Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.) Our former first-grade standard expands on this concept by saying students: 2.1 … Read More

Suggesting anyone should have to compare a first-grade standard to a second-grade standard is ludicrous. Further, it explicitly demonstrates how Common Core has dumbed down our previous rigorous, achievable California standards. The second-grade standard to which you refer used to be our first-grade standard under Number sense 2.0 (Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.) Our former first-grade standard expands on this concept by saying students: 2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory, 2.2 Use the inverse relationship between addition and subtraction to solve problems. 2.3 Identify more than one, one less than, 10 more than, and 10 less than a given number, 2.4 Count by 2s, 5s, 10s to 100, 2.5 Show the meaning of addition (putting together) and subtraction (taking away, comparing, finding the difference), 2.6 Solve addition and subtraction problems with one- and two-digit numbers (e.g. 5+58 = ___), 2.7 Find the sum of three one-digit numbers.

Others can more eloquently explain the problems with the directive of “using mental strategies” and how such wording directly favors a constructivist philosophy/curriculum (better known as fuzzy math). Under CC our second-grade studendents are already a full year behind first graders who were taught with California’s previous standards. Extrapolate what this means over time. With each year the content students learn is less rigorous causing them to fall farther and farther behind. If you really believe CC is rigorous and prepares all students for college, then I believe you drank the Kool-Aid.

Brandon Michaels3 years ago3 years agoNowhere did I advocate for Common Core or suggest that it was better than the previous standards. I did, however, suggest that Ze'ev Wurman was being disingenuous in comparing old and new standards. I have no problem with a healthy debate about the Common Core standards. Ze'ev's cherry-picking tends to discredit the rest of the argument presented. That's unfortunate, because rather than foster debate, it is polarizing and seems to be in the service of … Read More

Nowhere did I advocate for Common Core or suggest that it was better than the previous standards. I did, however, suggest that Ze’ev Wurman was being disingenuous in comparing old and new standards. I have no problem with a healthy debate about the Common Core standards. Ze’ev’s cherry-picking tends to discredit the rest of the argument presented. That’s unfortunate, because rather than foster debate, it is polarizing and seems to be in the service of the same propaganda decried in the original comment.

Furthermore, I’ll suggest that taking standards one-by-one by grade level is dangerous. Better to take the overall grade objectives. And even that isn’t entirely correct. What matters most is where students end up. I am certainly not an expert on age- or grade- appropriate mathematics education at the primary level and am bound only by my anecdotal experiences with my own children. (My area of expertise lies at the upper end of the spectrum.) Therefore, I can’t argue your assertion that the standards have been ‘dumbed-down.’ I am also not willing to concede the point, though.

You suggest that a student currently in high school in California will either not be prepared or be less prepared for college than under the previous standards. Where is your evidence of this? How are you measuring this? Can students still take Calculus in high school? Yes, they can. Can they take and pass the Calculus AB and BC advanced placement (AP) exams? Yes, they can. Can students take other college-level mathematics classes at some high schools? Yes, they can. With this in mind, I’m having difficulty seeing where the overall effect and rigor differs substantively. Again, I’m not advocating for Common Core. I am, however, suggesting that the voices of those adamantly opposed to Common Core would be better served by thoughtful discussion rather than accusations.

(And that brings up one last point; while I understand your ‘kool aid’ remark and it is part of our American lexicon, it’s both offensive and off-putting. Over 900 people died in Jonestown, including infants and elderly who were forced to drink the poison. Comparing the perceived advocacy to a set education standards to a mass murder-suicide hardly seems a winning strategy and trivializes a great tragedy.)

Zeev Wurman3 years ago3 years agoIn my longish comment I made multiple points, yet Brandon Michaels chose to dispute only one of them. This did not stop him from accusing me of misrepresentation of Common Core, and of cherry picking. The cherry picking argument is ridiculous on its face. I have made multiple comparisons of Common Core to our previous standards, and they illustrate many problematic issues with Common Core as compared to the old standards. I simply illustrated the case … Read More

In my longish comment I made multiple points, yet Brandon Michaels chose to dispute only one of them. This did not stop him from accusing me of misrepresentation of Common Core, and of cherry picking.

The cherry picking argument is ridiculous on its face. I have made multiple comparisons of Common Core to our previous standards, and they illustrate many problematic issues with Common Core as compared to the old standards. I simply illustrated the case here with two simple examples.

Yet Michaels’ critique is telling. M. Hagopian already pointed out that his own critique indicates that Common Core is delayed relative to the old standards. Hence, I would like to comment only on his critique of the comparison of the geometry triangle congruence standard. Mr. Michaels writes:

“For Geometry, which parts of triangles would you propose should be used if not angles and sides? And how is that in any way dictating a curriculum?”

In my original comment I observed that anyone “with a bit of sense” can see “how the Common Core specifies not only the WHAT but also the HOW.” Yet Mr. Micheals seems confused, as he speaks of the WHAT, the corresponding triangle parts that are in the definition of congruency, and that are present in BOTH the old and the new standards, while completely ignoring the HOW – that Common Core demands the use of rigid motions, and only rigid motion – to prove the congruency. Our old standards properly left the question of how to prove open ended.

Some refresher of geometry might be in order.

Reynolds Cameron3 years ago3 years agoThanks for this. Could you please confirm that Common Core standards do not require districts to force students to abandon Algebra in middle school like SFUSD has done? In other words, that SFUSD made a political decision to ban tracking and honors classes for advanced students, and blamed it on Common Core so they wouldn’t have to account for their irresponsible actions.

Replies

Doug McRae3 years ago3 years agoReynolds: The Common Core standards are not mandatory for California school districts, but the California statewide testing program (Smarter Balanced) heavily influences many districts to establish local curriculum and courses to be consistent with the Common Core standards that are tested. The Common Core 8th grade standards that are tested include topics typically taught early in a traditional Algebra course, but not the full range of topics in a traditional Algebra course. So, … Read More

Reynolds: The Common Core standards are not mandatory for California school districts, but the California statewide testing program (Smarter Balanced) heavily influences many districts to establish local curriculum and courses to be consistent with the Common Core standards that are tested. The Common Core 8th grade standards that are tested include topics typically taught early in a traditional Algebra course, but not the full range of topics in a traditional Algebra course. So, for students prepared to take Algebra in a middle school grade, the tests measure material less rigorous than what those students are able to do. Some districts [for example, Long Beach Unified] have maintained Algebra for middle school grades as recommended by previous California math standards. Other districts have discontinued Algebra courses in the middle school grades, in order to be aligned with what the statewide assessment system tests. The statewide testing system does not include end-of-course tests such as a traditional Algebra test, either for high school grades or middle school grades, despite discussion and advocacy several years ago to include such tests.

As an aside, in the article section on how Common Core ELA standards are different from previous California standards, most national reviewers found Common Core ELA standards to have comparable rigor compared to previous California ELA standards, not more rigorous as the article states.

Brandon Michaels3 years ago3 years agoI agree that the tests are part of San Francisco Unified's rationale for removing Algebra from middle school. But there are other factors. From their own position paper on the subject: "Over the last decade, there has been a dramatic increase in the number and proportion of eighth grade students enrolled in Algebra 1 in California. Williams et al. (2011) report that, between 2003 and 2009, the percentage of eighth grade students taking Algebra 1 increased … Read More

I agree that the tests are part of San Francisco Unified’s rationale for removing Algebra from middle school. But there are other factors. From their own position paper on the subject:

“Over the last decade, there has been a dramatic increase in the number and proportion of eighth grade students enrolled in Algebra 1 in California. Williams et al. (2011) report that, between 2003 and 2009, the percentage of eighth grade students taking Algebra 1 increased from 32 percent to 54 percent. While the increase in eighth grade enrollment in Algebra 1 resulted in greater percentages of eighth grade students achieving either Proficient or Advanced on the Algebra 1 California Standards Test, it also led to larger numbers of eighth grade students achieving Far Below Basic or Below Basic on the test (Williams et al. 2011). Williams et al. (2011) conclude that the practice of placing all eighth graders into Algebra 1, regardless of their preparation, sets up many students to fail.

A recent longitudinal analysis based on California statewide assessment data revealed that California’s students that fail the state exam for algebra in grade 8 have a greater chance of repeating the course and failing the exam again in ninth grade compared to their peers who pass the state exam for general math in grade 8 (Liang, Heckman, and Abedi, 2012).”

This, coupled with the tests and the increased rigor in the 8th-grade CC standards (including statistics and some geometry concepts), suggest that SFUSD – while certainly attributing the change to CC – would likely bristle at Reynold’s characterization of the change as ‘irresponsible.’ I’m not suggesting it’s the right move – but I’m certain that it was made thoughtfully and deliberately. (See http://www.sfusdmath.org/secondary-course-sequence.html for more details.)

Doug McRae3 years ago3 years agoBrandon: I'd agree the Williams (2011) conclusion that the practice of placing all 8th grade students in Algebra, regardless of their preparation, sets up many students to fail. But that conclusion does not speak to a practice of not offering Algebra to any 8th grade student, regardless of preparation. The Liang et al (2012) study unfortunately compares apples to oranges, again by not taking into account whether or not students in either cohort … Read More

Brandon: I’d agree the Williams (2011) conclusion that the practice of placing

all8th grade students in Algebra, regardless of their preparation, sets up many students to fail. But that conclusion does not speak to a practice ofnotoffering Algebra toany8th grade student, regardless of preparation. The Liang et al (2012) study unfortunately compares apples to oranges, again by not taking into account whether or not students in either cohort studied were truly prepared to take Algebra.I’d suggest both the middle school “Algebra for All” and “Algebra for None” policies are poor policies. Rather, a policy of Algebra for middle school students who have documented preparedness for Algebra is the best policy, and a statewide testing program that tests students taking Algebra with a full Algebra end-of-course test and other students with the Common Core Smarter Balanced middle school grade level “less than full Algebra” test would be the best support for that policy. Unfortunately, California’s current statewide testing program does not support that optimum policy; many other current state testing programs (e.g., the PARCC program) do accommodate this design, and other Smarter Balanced states also accommodate this middle school Algebra policy by using this design with a non-Smarter Balanced end-of-course test for middle school students taking Algebra.