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Math framework for Common Core ready for your critique



A draft of the California math curriculum framework went online Wednesday for public comments and suggestions. While weighing in at 1,200 pages, the document is actually a readable grade-by-grade manual that puts meat on the bare-bones Common Core standards that the state adopted in 2010. It  explains the rationale for key standards and puts them in context of what students will learn, while providing guidance on how they should be taught. Interspersed are numerous sample problems and illustrations that teachers can use in the classroom.

Although the Common Core Standards cover only transitional kindergarten through grade eight, the framework does provide suggestions for high school, where districts will have a choice between traditional subject courses (geometry, Algebra II and pre-Calculus) and integrated math courses, which blend traditional disciplines. Common Core is well suited for the latter. (Update: To quell rumors that it would not support integrated math courses, the University of California has issued a statement affirming its support for both the traditional and the integrated pathways.) And the document includes a chapter on options for accelerating math for those students ready to take Algebra I in eighth grade or, as an alternative for those taking Algebra I in ninth grade, combining three years of high school math into two years in order to enable students to take Calculus.

Assembled in only six months by a 19-member committee of math teachers, district administrators and college professors under the guidance of Tom Adams, director of the state Curriculum Frameworks & Instructional Resources Division, the framework borrows liberally from recommendations and ideas of other states, including New York, (through its EngageNY project), Massachusetts, Arizona and other state recipients of Race to the Top grants that had more than a year’s jump on California. That’s a key advantage of shared standards – learning from others, said Sue Stickel, the deputy superintendent of the Sacramento County Office of Education and chair of the math framework committee. “We do have a dialogue between states where before, with California’s own standards, we had a conversation with ourselves. This provides huge resources for everyone.”

For districts that have been putting off getting serious about Common Core, the framework could provide a jumping off point for discussion – and not a moment too soon. Unless the Legislature chooses to push back the start date – one option it will consider this year – the new Common Core assessments in math and English language arts will be given in the spring of 2015, two years from now and less than 18 months after the formal adoption of the math framework by the State Board of Education this November. The English language arts framework won’t be adopted until May 2014.

Teachers, math experts and the public will have the next 60 days to comment on the document before it advances to the Instructional Quality Commission, chaired by former State Superintendent of Public Instruction Bill Honig, which will make the final changes to the framework, based on public suggestions, before forwarding the document to the State Board this summer. Stickel said that regional county offices of education plan forums on the framework, and there may be other public sessions.  The state Department of Education has provided an online survey for comments as well.

Cautions on moving too fast to Algebra

The most anticipated chapter of the framework pertains to the contentious issue over whether Algebra I should be taught in 8th grade, as has been encouraged by the state for the past decade, or in 9th grade, the standard sequence under Common Core. The new State Board of Education position, adopted this year, is that Common Core 8th grade math will be the default curriculum; students should take Algebra in 8th grade only if they’ve demonstrated they’re ready for it. And there are other options for accelerating math in high school, such as taking double courses in one year or a course in summer school, leading to AP Calculus or AP Statistics. But the State Board left it to the Framework Committee to provide more specific guidance on how to offer “compact” accelerated courses and who should take them.

Common Core’s 8th grade math is more rigorous than the current non-Algebra 8th grade alternative to Algebra I. Common Core 8th grade math includes linear equations and about a quarter of the Algebra I course, along with elements of geometry. But half of it is pre-Algebra, leading advocates of 8th grade Algebra to warn about a backsliding in the percentage of students ­– about two-thirds – who currently enroll in Algebra in 7th or 8th grade.

“This was a hard chapter for the Committee to write, for members felt it (8th grade Common Core) was already challenging,” Stickel said. As the committee observed, “Common Core Standards for grades 6-8 are comprehensive, rigorous and non-redundant. … Therefore, careful consideration needs to be made before placing a student into higher mathematics coursework in middle grades. Acceleration may get students to advanced coursework, but this might create gaps in students’ mathematical background.” It refers to the “great challenge” for students and teachers for handling more standards that are more rigorous in a compressed time frame.

In Appendix A of the standards, the writers of Common Core laid out a potential course combining 7th and 8th grade standards in 7th grade, creating the opportunity for Algebra I in 8th grade. The committee referred to this and warned that accelerated courses should cover all of Common Core standards, not skip or skim over any of them. And students should show a fluency in math and a conceptual understanding, as measured by a portfolio of their work, before assigning them to an accelerated path.

The language and the caveats in the chapter struck Doug McRae, a retired testing publisher and an advocate of Algebra in grade 8, as “negative” in tone. “The draft seems to convey a message to the reader that algebra by grade 8 should be reserved for an isolated few advanced students. That message is not consistent with the experience California has from the past 15 years of our ‘algebra by grade 8’ initiative,” he wrote in an email.

Not the traditional cycle

The primary purpose of the framework has been to provide guidance for publishers to create textbooks and materials. But the traditional cycle ­– standards first, followed by the framework, then textbook adoption, then teacher training and professional development using approved materials culminating with assessments – doesn’t apply to Common Core. A compressed time frame, with tests in 2014-15, won’t allow the districts to wait that long, and, under budget flexibility, districts have latitude to buy materials of their choice anyway. Low-cost and free digital materials and curriculum plans developed in other states have freed up teachers and districts to check out a wealth of options. The state Department of Education has already instituted the process of textbook approval, even without formal approval of the math framework.

Stickel said that one advantage of posting the framework online is that it can be updated with links to other useful sources as they become available.

Filed under: Common Core, State Education Policy, STEM, Testing and Accountability

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6 Responses to “Math framework for Common Core ready for your critique”

  1. navigio said

    on November 4, 2013 at 1:29 pm

    I have noticed some districts making the transition from the ‘traditional’ alg/geo/alg to an integrated math sequence already. Is there some kind of survey that outlines what approach different districts are taking and discussion/documentation on whether the latter is more beneficial for students? It is noteworthy that the compacted nature of the prep for the integrated sequence will likely make it next to impossible to implement what was traditionally an accelerated strategy (even though I expect some districts will claim they will).

  2. Doug McRae said

    on April 18, 2013 at 10:53 am

    To amplify a bit on the last full paragraph of your post, John, the purpose for any framework goes beyond simply providing guidance to publishers for creating textbooks and materials. The framework has major use for the teacher training / professional development portion of implementing any new set of content standards, and to provide guidance to local districts and schools for the actual instruction to be delivered. It also is used for the design of instructional assessments (formative, interim, diagnostic) and secondary use for the design of statewide summative assessments.

    The danger in deviating from the traditional logical sequence that is outlined — standards first, then frameworks, then instructional materials, then teacher training, then assessments — is that instructional materials will not be fully coordinated with the final frameworks that are approved, and then there will be conflicting guidance from the state level to schools/districts for teacher training / professional development and local instruction as well as conflict in the design of assessments.

    This result would be major flaws with CA’s implementation of the common core. There is nothing inherent in the common core standards themselves that suggests deviation from the traditional logical sequence, rather it is the spring 2015 date for potential implementation of statewide summative assessments that is driving the rush rush deviation from the traditional logical sequence.

    As the post notes, the legislature may well not go along with the SPI’s recommendation to implement new tests to measure the common core by spring 2015. Indeed, there are many concerns about that schedule, including the problem that E/LA frameworks and instructional materials and professional development for the E/LA common core will not be ready by the spring 2015 date, that there are no fiscal resources targeted for implementing the common core at the local district level, that CA will not have the technology resources to implement the proposed Smarter Balanced computer-adaptive tests by 2015, and that most kids will not have had sufficient experience with the computer protocols used for the SB tests to generate valid and reliable scores from computer-adaptive testing as early as 2015.

    If in fact the legislature does choose to push back the proposed spring 2015 summative assessment date, then it would be wise for CA to take a breath and reconsider the rush rush implementation timeline for common core math now in place — the review of math instructional materials now scheduled for summer 2013 can be delayed until after math curriculum frameworks are approved (now scheduled for Nov 2013)and the traditional logical sequence for implementing any new set of content standards can be re-instated. As is frequently the case, haste makes waste. Deviating from the traditional logical sequence in this case has all the markings for generating waste.

  3. Paul Muench said

    on April 18, 2013 at 7:40 am

    The framework suggests offering summer school as a pathway for acceleration. Is the anticipation that families pay a fee or will this be supported by districts and/or the state?

  4. Paul Muench said

    on April 18, 2013 at 7:37 am

    Yes, the framework language is ambiguous on acceleration. Not rushing and avoiding premature acceleration at all costs reflect two different attitudes.

    From the framework on acceleration:

    1. Decisions to accelerate students into the Common Core State Standards for higher mathematics before ninth grade should not be rushed.

    Placing students into an accelerated pathway too early should be avoided at all costs. It is not recommended to compact the standards before grade seven to ensure that students are developmentally ready for accelerated content. In this document, compaction begins in seventh grade for both the traditional and integrated sequences.

  5. Paul Muench said

    on April 18, 2013 at 6:27 am

    The common core state standards document found on the CDE’s website lists standards for calculus. Why is there no framework for calculus?

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