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The decision of whether to offer algebra in eighth grade – and when, how and for whom to accelerate math instruction – is for individual school districts and charter schools to make, the latest draft of the California Mathematics Framework made clear this week. The 900-page document was never intended to be a mandate.

With that controversy clarified, the addition of a couple of chapters and the deletion of politically charged references to racism behind past math policies and practices, the framework has now begun its third, and presumably final, 60-day review process.

It took 10 months, with hundreds of line edits and more substantial rewriting based on public comments and recommendations by a commission advising the State Board of Education, to revise this one. The State Board is expected to adopt the final version in July.

Advocates of the new guidance hope the changes will shift the focus away from criticism that the drafters sought to sacrifice rigor in the name of social justice. The goal, they say, is to make math interesting and relevant to students who have found it inaccessible and impenetrable.

“We really see equity as the future for better math learning for all students in California,” said Brian Lindaman, co-faculty director of the Center for Science and Mathematics Instruction at Chico State, and the lead of five authors of the framework. The goals of making math more accessible and high achievement are an artificial dichotomy, he said.

“I hope the outcome (of the framework) will be to give schools and districts more latitude to develop math courses and sequences that excite students and help draw more of them into STEM fields or to sophisticated math, no matter what they choose to do in life,” said Pamela Burdman, executive director of Just Equations, a nonprofit that promotes policies that prepare students with quantitative skills to succeed in college.

The framework provides voluntary guidelines to teachers and textbook publishers on how to teach the state’s academic standards. The new math framework will replace one adopted in 2013, which served a specific purpose: to differentiate for teachers the newly adopted Common Core math standards from the previous state standards.

The new framework has a more student-centered goal – to build an understanding of math concepts and relationships across grades and subjects while developing students’ critical thinking and reasoning skills.

That’s a tall order, but doable, said Rebecca Pariso, a teacher on assignment from Hueneme Elementary School District, north of Los Angeles, who served on the committee of educators that advised the first draft of the framework. “The framework offers solutions to engage students more in math, to see context of math in their lives and where they belong in a world of numbers,” she said.

Others question some principles of the framework, including the elimination of grouping students based on ability, and point to the recommendation to refrain from offering algebra until ninth grade as a source of their skepticism.

That issue was a flashpoint in the initial draft. Critics interpreted that position as a signal that the state was leveling down math instruction, delaying those ready for advanced math for the sake of misguided uniformity.

They said it would needlessly force students who want to major in science, technology, engineering or math in college to double up with an extra math course to fit in calculus as a high school senior. This could discourage Black and Latino students from pursuing those majors, in which they are already underrepresented.

In recommending that all students take Algebra I in ninth grade, the authors of the first draft heralded the success of San Francisco Unified. The district, which made the switch in 2014, released data showing an immediate improvement in math performance in ninth grade compared with eighth grade the year prior and in the number of students who subsequently enrolled in more advanced math courses as seniors. The district continued to argue that it was a sound policy.

But the district declined to make the data behind its findings public, and two analyses by critics of the policy, one by Ze’ev Wurman, a research fellow at the Independent Institute in Oakland, and the other by a San Francisco parents group with access to some unreleased information, concluded the data was flawed. The latest draft of the framework deleted mention of the San Francisco success.

“It’s progress that the writing team now acknowledges the need for better pathways to calculus in California public schools. But this second revision of the framework simply rehashes the same arguments from the first revision while simply deleting all references to (San Francisco’s) discredited claims of success,” said Elizabeth Statmore, a math teacher at Lowell High School in San Francisco. “It may be time for the California State Board of Education to stop wasting taxpayer money on magical thinking.”

A newly constituted school board in San Francisco, with appointees by Mayor London Breed following the recall last month of three of seven board members, is expected to reconsider the district’s algebra placement policy.

How best to accelerate

The revised framework acknowledges that offering Algebra I, also called Integrated Math I under Common Core, in eighth grade is an option for math acceleration. But it adds the caveat that districts should assess the readiness of students to take it and consider requiring a summer course or additional preparation.

As another alternative to algebra in eighth grade, the framework proposes that math experts design a new high school course combining four years of courses into three by eliminating repeated material. That too would lead to an advanced math course in the senior year.

At the same time, in a new chapter, “Structuring School Experiences for Equity and Engagement,” the framework urges districts not to create an advanced track for some students and a “separate track that filters most students out of high-level mathematics from a young age.” This approach historically has denied opportunities to underrepresented minorities. “Any system that includes acceleration options for some students should do so without excluding most students from reaching higher level mathematics by the end of high school,” it said.

Burdman said research is clear that a “race to calculus” can undermine the mastery and conceptual knowledge of math. The framework makes clear that students who take a standard math sequence starting in ninth grade should have options other than calculus to take as seniors – data science, financial algebra and statistics, which involve “how math is used in the real world, what it means to be quantitatively literate,” Burdman said.

“It is unfortunate that many see these as inferior pathways when they are central to our future,” she said.

Ellen Barger, assistant superintendent of curriculum and instruction at Santa Barbara County Office of Education, agrees.

“It would be useful, instead of fighting over theoretical dichotomies, that we start with common aspirations for children. We need to expand access to high quality math, including data science and statistics, because more students will need these applications” in their careers.

California ranks in the bottom third of states in math in the National Assessment of Educational Progress or NAEP. It now ranks 32 in the world, far below average, on the Programme for International Student Assessment.

Math mindset matters

The framework’s authors emphasize that raising the level of performance in math statewide begins with raising students’ self-confidence in math and their interest in it.

“All students deserve powerful mathematics; high-level mathematics achievement is not dependent on rare natural gifts, but rather can be cultivated,” the framework’s opening chapter reads.

Much of the framework details what equity in math looks like in the classroom – and what it takes to build a math mindset, particularly among students of color who have internalized that they’re not capable of doing well. The writing of Jo Boaler, a professor of mathematics education at the Stanford Graduate School of Education and one of the five authors of the framework, is cited frequently.

Enjoyment, the framework says, “comes when students are actively engaged with mathematical concepts – when they are developing mathematical curiosity, asking their own questions, reasoning with others, and encountering mathematical ideas in multi-dimensional ways.”

Teachers should give students open tasks that “allow all students to work at levels that are appropriately challenging for them.” They should use examples that relate students’ own lives because, the framework says, “mathematics is a quantitative lens through which to view the patterns that exist throughout the world.”

Many teachers personally didn’t experience math this way and will find it challenging to change how they teach math, Pariso acknowledged. “What will be important is helping teachers see value of what is in the framework; then they will want to make changes in the classroom,” she said.

Lindaman said the teachers will determine whether the framework makes an impact.

“I hope the framework will bring about conversations about how to improve math instruction for more learners,” Lindaman said. “Math is an animated, beautiful subject. We highlight how it can be made empowering.”

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  1. Mark D Perry 5 months ago5 months ago

    As a math educator who does not live in California, I was first really puzzled what I read about the framework, and even more puzzled when I read the intro of the literature to www.equitablemath.org. Reading further into the documents, however, causes me to wonder. If you read past the "anti-racist" rhetoric in the documents, and look at the ideas put forward by the aforementioned website, the ideas are all exemplars of good teaching of … Read More

    As a math educator who does not live in California, I was first really puzzled what I read about the framework, and even more puzzled when I read the intro of the literature to http://www.equitablemath.org.

    Reading further into the documents, however, causes me to wonder. If you read past the “anti-racist” rhetoric in the documents, and look at the ideas put forward by the aforementioned website, the ideas are all exemplars of good teaching of mathematics. Further, including ethno mathematics or Social Justice Mathematics is a nice way to welcome students of color into your class, however, there have to be caveats such as whether you have time to cover those ideas in an already very crammed curriculum, and how much re-teaching of the previous skills need also to be covered.

    Honestly, the fact that anti-racist rhetoric is attached to the framework makes me uncomfortable for two reasons: 1) It suggests that to be a good teacher following good teaching practices means that you are following “anti-racist” dogma as well, which while it aligns with what some groups want also means that 2) The good practices in teaching will become irrevocably tied to what outside forces call CRT in schools, and so math teachers will either be castigated for teaching children best practices in learning, or will return to traditional methods, which don’t serve the needs of all children (not just ELLs or BIPoCs, but students with special needs, LGBTQ+, students going through family trauma, etc).

    Teaching is an extremely difficult profession, the workforce for teaching is shrinking amidst all the brouhaha, and teachers deserve our support, not political tomfoolery. Students need good curriculum to learn, yes, and meaningful activities, yes, but they also need teachers.

  2. Dawn Isaacs 6 months ago6 months ago

    Will tracking also be avoided in other subjects such as orchestra/band/art/drama/sports? Will students disadvantaged in those area be included with advanced students?

  3. Chalone Warman 6 months ago6 months ago

    Who do we contact in the next 60 days with our comments?

    Replies

    • John Fensterwald 6 months ago6 months ago

      This was in the box accompanying the story, Charlone: The public will have through May 16 to submit comments, preferably by email, to mathframework@cde.ca.gov. To provide a comment by physical mail, send to Instructional Quality Commission; 1430 N Street, Room 3207; Sacramento, CA 95814. To fax: 916-319-0172. All comments will be made available to the members of the State Board of Education. Personal contact information, such as emails, phone numbers, and addresses, will be redacted. Read More

      This was in the box accompanying the story, Charlone:

      The public will have through May 16 to submit comments, preferably by email, to mathframework@cde.ca.gov. To provide a comment by physical mail, send to Instructional Quality Commission; 1430 N Street, Room 3207; Sacramento, CA 95814. To fax: 916-319-0172. All comments will be made available to the members of the State Board of Education. Personal contact information, such as emails, phone numbers, and addresses, will be redacted.

  4. Marina Teramond 6 months ago6 months ago

    To tell the truth, it is cool that math can become interesting and relevant to students who have found it inaccessible and impenetrable because it is a really decent goal which needs to be implemented into reality. Math takes an important place in our life and it is necessary to develop new effective frameworks for its study in order to push education to a new level. It is essential when the subject arouses interest and … Read More

    To tell the truth, it is cool that math can become interesting and relevant to students who have found it inaccessible and impenetrable because it is a really decent goal which needs to be implemented into reality. Math takes an important place in our life and it is necessary to develop new effective frameworks for its study in order to push education to a new level. It is essential when the subject arouses interest and when the student is really engaged in it because, otherwise, it doesn’t make sense.

    I absolutely agree that students’ self-confidence in math has a paramount and decisive importance because it is a true key for raising the level of performance in math. It is a true key for developing a math mindset and fulfilling your true potential in this field. Of course, all students deserve powerful mathematics and it will encourage many students to achieve huge results in this subject.

  5. Abby C 6 months ago6 months ago

    I have been talking about 'social justice as a driving factor in math' and 'math is racist' to everyone around me. The people I talk to are shocked, outraged and incensed. I am a liberal democrat who is currently politically homeless for reasons like this. I am RELIEVED to see this article, as a start. Math is not racist. Social justice has no place in math. Let our kids interested in math excel. My 10 year … Read More

    I have been talking about ‘social justice as a driving factor in math’ and ‘math is racist’ to everyone around me. The people I talk to are shocked, outraged and incensed. I am a liberal democrat who is currently politically homeless for reasons like this.

    I am RELIEVED to see this article, as a start. Math is not racist. Social justice has no place in math. Let our kids interested in math excel. My 10 year old is one of these kids. I want him to advance, excel and continue to love math.

    I have been looking around for alternative schooling options to ensure he can get advanced math. He’s currently doing algebra at home with me and loving it. Now I can consider keeping him in public schools. This gives me huge relief to see some modicum of sanity.

  6. JudiAU 6 months ago6 months ago

    No one should be hindered from progress at their own pace. No one should be held back because of bias. But districts that follow these weak policies will find that deepens the divide between private and school opportunities and from those with means. The divide will deepen. Russian Math School opened seven branches in the Bay Area during this San Francisco policy. Russian Math School, Korean math schools (usually Beast Academy), AOPS, CTY, CTD all … Read More

    No one should be hindered from progress at their own pace. No one should be held back because of bias. But districts that follow these weak policies will find that deepens the divide between private and school opportunities and from those with means. The divide will deepen. Russian Math School opened seven branches in the Bay Area during this San Francisco policy. Russian Math School, Korean math schools (usually Beast Academy), AOPS, CTY, CTD all charge tuition. CTY is the only one that offers any financial aid and I am pretty sure John Hopkins is not paying to educate CA.

    Math acceleration early is very easy for an interested kid. All of my kids mastered arithmetic by playing board games. I distinctly remember my daughter learning to multiply as second grader to stop older brother from “cheating” by knowing more math and winning. She memorized them that summer to win. That is also how she learning division, fractions, and exponents.

    She took Pre-Algebra in fifth grade through CTY to demonstrate mastery but took no other outside classes or tutoring. A. And received an A in Algebra I as a sixth grader through the district. Her needs deserve to be met as well.

    There are kids all over LA with interest and curiosity and LAUSD is great at encouraging them into different math pathways.

    What we really need is the opportunity to move 1-3 faster in elementary school. Lots of kids would be more engaged if they acceleration earlier and before they turned into teens.

  7. Maya K 6 months ago6 months ago

    In my opinion this is the buried lede "The latest draft of the framework deleted mention of the San Francisco success" It is appalling to me that the framework authors and SFUSD promoted data which couldn't be reproduced with California Public Records Act data (CPRA). CPRA requests is how Families for San Francisco (https://www.familiesforsanfrancisco.com/updates/inequity-in-numbers ) discovered the problems with the claims that were made not just in the draft framework but in major publications across … Read More

    In my opinion this is the buried lede “The latest draft of the framework deleted mention of the San Francisco success”

    It is appalling to me that the framework authors and SFUSD promoted data which couldn’t be reproduced with California Public Records Act data (CPRA).

    CPRA requests is how Families for San Francisco (https://www.familiesforsanfrancisco.com/updates/inequity-in-numbers ) discovered the problems with the claims that were made not just in the draft framework but in major publications across the nation. The framework authors went on a PR tour convincing many nationwide that SFUSD’s math experiment was a grand success. It was not.

    Here is the CPRA data received from the district:

    https://drive.google.com/drive/folders/1Ia-NG2dogL1MS-JKkVQEtoG-gmEJKiDC

    The much touted grade improvement between the last group with 8th grade Algebra (class of 2018) and the first delayed (class of 2019) isn’t true. The grade distribution remained unchanged, with the 8th grade Algebra cohort doing slightly better.

    The repeat rate was based on a competency exam 8th graders had to pass to be placed in geometry. This was removed when the sequence was delayed. The 40% repeat number itself could not be reproduced with CPRA data, it was much less. The district has so far refused to respond to CPRA requests asking them to show how they came to the 40% number.

    The advanced math increase claim similarly collapses under scrutiny.

    They are counting the compression class which is much like the class proposed in the second draft framework to reach Calculus in 12th grade but still delaying Algebra 1 to 9th. SFUSD’s class leaves out important precalculus content but contains enough so a student can take AP Calculus AB (not BC). UC does not recognize this class as either advanced math or precalculus. The district however includes it in their advanced math count to claim enrollment increased. It is also incorrectly put on high school transcripts as precalculus.

    It is amazing to me that there is no accountability. The framework authors just delete references in version 2 with no comment. “Nothing to see here” seems to be the appropriate meme.

    The nonsense of saying many kids have to repeat calculus in college so why bother is breathtaking not just in not valuing math for knowledge sake, it also ignores the reality that the students who have had calculus in high school are taking the class in college as credit recovery. They are familiar with the material. The student entering with no prior exposure is at a disadvantage as the class will move at the pace of those who do have familiarity.

    This framework reads as a new age self help book rather than a serious document whose intent should be in closing these gaps and improving math education. We are falling behind. Would the states and countries ahead of us implement this framework? I don’t think they would.

  8. Rahul Akhaury 6 months ago6 months ago

    This should empower all the students to enjoy Math and succeed!

  9. Chris Stampolis 6 months ago6 months ago

    Note that it is illegal for UC or CSU admissions team members to consider any part of a 12th grade GPA for admissions consideration. I L L E G A L. Only 10th and 11th grade scores are allowed to be considered as all students must meet the November 30 application deadline. Kids who have completed Calculus by the end of 11th grade thus demonstrate high proficiencies in mathematics and of course that impacts … Read More

    Note that it is illegal for UC or CSU admissions team members to consider any part of a 12th grade GPA for admissions consideration. I L L E G A L. Only 10th and 11th grade scores are allowed to be considered as all students must meet the November 30 application deadline.

    Kids who have completed Calculus by the end of 11th grade thus demonstrate high proficiencies in mathematics and of course that impacts their admissions opportunities at competitive campuses, including UC and CSU.

    Jo Boaler has zero peer-reviewed math proficiency data to back up her assertions to force delays in Algebra 1 to 9th grade. So what if she is from Stanford? Superintendent Vincent Matthews at SFUSD has lied repeatedly to the public about the outcome of slowing Algebra to 9th grade.

    Replies

    • Bruce William Smith 6 months ago6 months ago

      “Kids who have completed Calculus by the end of 11th grade thus demonstrate high proficiencies in mathematics and of course that impacts their admissions opportunities at competitive campuses, including UC”: that’s precisely why all of our students take calculus during the 11th grade, which is an important year for proving the ability to do higher level work, something the equity warriors tend to overlook.

      • Sonny Yang 6 months ago6 months ago

        Who takes Calculus as a Junior? I went to a very high-performing high school (C/O 2001), and maybe a handful of kids took AP Calculus AB as a Junior. Most kids (myself included) took AP Calc AB as a Senior. These are the kids who went to the all the top college/universities.

        • Hannah 6 months ago6 months ago

          Lots of us take calculus as juniors. We’re the same people who took algebra in 7th.

        • Tammie 3 months ago3 months ago

          I was C/O ’96, calculus wasn’t even OFFERED until senior year. It was not a course available for juniors. My school had the highest overall AP pass rate in the state(IL)-for all classes(english, physics, as calc), but still, no Calc until senior year.

          That’s a new one on me!!

    • Maya K 6 months ago6 months ago

      Jo Boaler has spent years misrepresenting success in San Francisco but hasn't been asked how she got it so wrong. This was a nationwide campaign to delay algebra to 9th grade based on misleading presentations she made with the SFUSD math department. Superintended Matthews inherited this mess from the Carranza years so I do believe he's just saying what SFUSD Math people tell him to say because why wouldn't you trust your own people? … Read More

      Jo Boaler has spent years misrepresenting success in San Francisco but hasn’t been asked how she got it so wrong. This was a nationwide campaign to delay algebra to 9th grade based on misleading presentations she made with the SFUSD math department.

      Superintended Matthews inherited this mess from the Carranza years so I do believe he’s just saying what SFUSD Math people tell him to say because why wouldn’t you trust your own people?

      This disaster was a Boaler/Carranza production with enabling from the Board of Education at the time.

      My children straddled the implementation. My son had 8th algebra and is now an electrical engineer. My daughter was in the early years of this and I paid for her to take an on-line Algebra 1 class concurrently with Math 8 so she could start 9th with geometry. She is now a college sophomore biotechnology major. This was not equitable at all. It created a have/have not pathway in *public* schools.

      This fall the first cohort will be college seniors, that is how long this has been going on here. I hope one of the lessons learned here is when people make fantastical claims “40% to 8% repeat reduction” which sounds too good to be true? People don’t just believe but ask to see raw data.

      I never realized until this mess how many education decisions are based on fad chasing.

  10. Tom Kel 6 months ago6 months ago

    I have 7th and 8th grade kids who can't multiply or divide, and have trouble with simple addition and subtraction (like 13+16). They can barely read, any word problem stops them dead in their tracks. How am I supposed to teach them pre-algebra? Common Core was a scam, and so is this new initiative. While they invent new scams to cover up their failure, they force the schools to become even more … Read More

    I have 7th and 8th grade kids who can’t multiply or divide, and have trouble with simple addition and subtraction (like 13+16). They can barely read, any word problem stops them dead in their tracks. How am I supposed to teach them pre-algebra?

    Common Core was a scam, and so is this new initiative. While they invent new scams to cover up their failure, they force the schools to become even more permissive that student behavior is so bad that education of any kind is simply not possible. I was a progressive for most of my 30 years as an educator, advocating for many of the things that lead us here…but, we were wrong! We messed up bad.

    Replies

    • Sonny Yang 6 months ago6 months ago

      As a high school math teacher, the sad reality is that most of these students would not have performed differently using our old 1992 math standards. I am an advocate of the CCSS, but the reality is that the gap widening has so many layers to it. Layers that beyond the standards.

  11. DeWalter_White 6 months ago6 months ago

    9th grade Algebra I was mandatory in my Catholic High School…. in 1970. So there’s no getting out of it. Get kids off of TicToc and Instagram and have them memorize their times table and maybe you got a chance.

    Replies

    • Tammie 3 months ago3 months ago

      Why let them have such things at those young ages to begin with?? Kids should be outside playing & learning, not stuck inside with social media as a babysitter in elementary school!! My kiddos are 21, 19, 10, 9, & 8. The younger set has no social media, no way!! I do not see the value of teaching them to live for likes-AT ALL!!! Parents need to be parents and stop using technology as a babysitter all … Read More

      Why let them have such things at those young ages to begin with?? Kids should be outside playing & learning, not stuck inside with social media as a babysitter in elementary school!!

      My kiddos are 21, 19, 10, 9, & 8. The younger set has no social media, no way!! I do not see the value of teaching them to live for likes-AT ALL!!!

      Parents need to be parents and stop using technology as a babysitter all the time(ok, every so often on a sick day, whip out the tablet…but all day everyday??? NO WAY!!)