Credit: Allison Shelley for American Education

The debate that continues to simmer over California’s new math guidelines is a reminder that divisions remain deep over approaches to instruction, the pacing of algebra in middle school and the offerings at high school, particularly for students interested in STEM in college.

The State Board of Education has pushed back the adoption of the California Math Framework to sometime in 2023, an indication that it is taking seriously hundreds of suggested changes and critiques and that potentially extensive changes may be coming. 

At the heart of the issue is a disagreement over how best to motivate and raise the math success of underperforming students, including Black students, Latino students and English learners.

Similar to frameworks in English language arts and science, the math framework is intended to offer guidance on translating state standards — the Common Core — to the classroom. A framework is not a mandate; districts can pick or reject whatever suggested lessons, tactics or strategies work for them.

But it is important, not only to publishers, who will base textbooks on it, but also for teachers, superintendents and education advocates. California students lag behind the nation in math, scoring in the bottom fourth of states in fourth grade and bottom third in eighth grade in the National Assessment of Educational Progress.  

Only 34% of students overall, 18% of African American students and 20% of Latino students met or exceeded standards on the state’s 2019 Smarter Balanced standardized test in math, the last time that all students took it until this past spring. Those results aren’t out yet.

Teachers haven’t had a framework since 2013, and that one was done after the adoption of Common Core; its purpose was to explain and prioritize the standards. Teachers have been eager for guidance on how to make math more engaging, fun and relevant to students and expressed that in focus groups, said Ma Bernadette Andres-Salgarino, assistant director for integrated STEM development at the Santa Clara County Office of Education and president-elect of the California Mathematics Council. 

“They wanted a focus on habits of mind, and a huge component of that is to ensure we have equitable participation from people of color,” she said. “Teaching mathematics through an equity lens was overwhelmingly shared by educators and students.”

In the introductory chapter, the framework explicitly says it is designed to respond to structural barriers that impede math success: “Equity influences all aspects of this document.” 

Despite criticism, the framework continues to resonate with classroom teachers who participated in the framework process and with advocacy groups for low-income children. “We believe that the guidance in this Framework, if effectively implemented, has the potential to transform mathematics instruction to ensure that all students have equitable access to rigorous and relevant coursework,” said a letter from two dozen organizations, including Children Now, the California Mathematics Project and Californians Together, that advocate for English learners.

Critics, unmollified by changes so far, continue to argue that the framework pushes social justice over rigor — a charge the drafters of the document deny — and that its policies, if implemented, will ultimately set back many of the students it’s intended to help.

“We fully agree that mathematics education should not be a gatekeeper but a launchpad,” said a letter signed by more than 1,700 science, technology, engineering and math educators or professionals from California and elsewhere. “However, we are deeply concerned about the unintended consequences of recent well-intentioned approaches to reform mathematics education, particularly the California Mathematics Framework.”

Failure of the status quo

The framework stated that a different approach is needed because traditional math instruction turned off many students by stressing rote memorization of “meaningless formulas” and procedures; along with being boring, it was disconnected from students’ lives and experiences.

Instead, math should build positive math mindsets among all students, but especially for students of color who have become convinced they’re not capable of doing well. Teachers should stress problem-solving and inquiry, the framework said. “Mathematics learning, understanding, and enjoyment 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,” according to the framework. 

Departing from a traditional approach, the framework discourages lessons based on individual Common Core standards, including the priority standards identified in the first framework. Instead, teachers should create more complex tasks around “big ideas” that involve clusters of standards and make connections across grades between concepts like number sense and probability to give students a bigger picture.

“The value of focusing on big ideas for teachers, and their students, cannot be overstated,” the framework said.

Writers of the framework and proponents like Andres-Salgarino acknowledge the framework will require teachers to teach differently. “Creating such classroom experiences is not easy,” the framework said.  Extensive training will be needed, she said.

 Kyndall Brown, executive director of the California Mathematics Project Statewide Office, which is affiliated with the University of California, and a proponent of the framework, agrees. Teaching a conceptual understanding of math will require discussion and take more class time at the beginning of the year, as teachers “are trying to retrain students to problem-solve on their own,” he said. “But once they get used to that way of thinking, then you actually get through more of the curriculum. It’s like going slow to go fast.”  

Katherine Stevenson, a math professor at California State University, Northridge, who has worked with teachers in Los Angeles Unified, said, “It’s very hard for teachers not to get lost in skills and practices that are very concrete, so I applaud the big ideas.” But, she said, preparing lesson plans and classroom tasks will require an intense amount of preparation and continuous training. “If you look at the framework as an aspirational document, I am OK with it, but I have real concerns as an actionable document.”

Misstated or misunderstood research

Brian Lindaman, faculty co-director of the Center for Science and Mathematics Instruction at California State University, Chico, chaired the five-person committee that drafted the framework, but the writer most identified with the framework and whose prolific writing is most often referenced in it is Jo Boaler. Boaler is a professor of mathematics education at the Stanford Graduate School of Education.

The most prolific and one of the strongest critics of the framework is a colleague at Stanford, Brian Conrad, a professor of mathematics and director of undergraduate studies in math. Conrad said he agrees that math is often poorly taught and needs to be improved. But he faults the framework’s solutions as simplistic, oversold and not grounded in research.

Conrad said he spent spring break reading not only the framework but also many of the citations from which the authors justified their recommendations. “To my astonishment, in essentially all cases, the papers were seriously misrepresented” and in some cases “even had conclusions opposite to what was said” in the framework. The misrepresentations of the neuroscience of math comprehension, de-tracking in favor of heterogeneous student grouping, the use of assessments and acceleration call into question the recommendations. Writers, he said, “should not be citing papers they do not understand to justify their public policy recommendations” fitting their perspectives.  

The first version had called for districts to discourage students from accelerating to take Algebra I in middle school; a more equitable approach, it indicated, would be to require all students to take the course in ninth grade. That, however, would force students to take extra courses, summer school or compressed courses to get to calculus by senior year.  After a big pushback from the STEM community and parents of high-achieving students, Conrad said, the writers have left it to others to recommend how courses could be consolidated to accommodate students forced to squeeze in extra math.

Alternative high school pathways

The chapters on high school math provoked the most comments, anger and division; it is also an area with the potential, with more work and needed clarity, for a resolution, said Stevenson.

A high school diploma in California requires two years of math. Admission to California State University and the University of California requires three, usually Algebra I, Geometry and Algebra II, either in a traditional sequence or an integrated sequence that blends content from the three. And for students interested in science and math majors, UC and CSU recommend at least precalculus, if not calculus.

For too long, the pathway to calculus for a competitive college has been the only option, proponents argued. “It doesn’t matter if you’re going to be a theater, journalism or arts major, students feel pressure to put it on their transcript,” said Brown.

And yet, he said calculus isn’t offered in many high-poverty schools, and in schools that do offer it, “they put so many barriers in place that the many students of color who attend those schools never get access to it.”

Seeing no relevance to their lives from calculus and no other options besides AP statistics, many students take no math in their senior year, which is a lost opportunity, Brown said.

The framework encourages alternative senior year courses, such as modeling or quantitative reasoning, which CSU campuses designed with state funding. It suggests a third pathway in addition to traditional and integrated math, called Mathematics: Investigating and Connecting, although it is vague on details. And it includes a lengthy chapter on data science in K-12, including design principles for a high school course.

“I like the emphasis on data science. It’s important for students to have a really good understanding of data, and it is a viable career field,” Brown said.

STEM professors and professionals say that Black and Latino students are already under-represented in quantitative majors; the framework, by proposing alternative pathways and data courses that avoid Algebra II and courses preparing students for calculus, would make that worse.

“Students who take a data science course as an alternative to Algebra II in high school will be substantially underprepared for any STEM major in college, including data science, computer science, statistics, and engineering.  Such students will need remedial math classes in college before they can even begin such majors, putting them at a considerable disadvantage,” stated a letter signed by more than 400 academic staff at California universities.

Conrad said that the framework conflates data literacy, an essential skill that can be taught in many courses, and data science, which requires advanced math as a career pursuit. And he objects to a “bias” toward data science in the framework with language that implies that it offers a more interesting and equitable career. All fields of math can be taught well or badly,” Conrad wrote. “All educators should object to the notion that students of color or girls cannot excel in mathematical fields other than data science.”

Stevenson said she wished the framework had not used the term data science, an evolving academic discipline that uses linear algebra, calculus, statistics and computer science to analyze large data sets. “If you start saying to K-12 kids ‘You are in the data science track’ but when they get to UC they cannot make that jump, you are creating a second-class pathway and have actually created what you are trying to eliminate; you just gave it a different name.”

Conrad and others urge the state board to eliminate the proposed Mathematics: Investigating and Connecting high school pathway and to rewrite the data science chapter from scratch by a group of “disinterested content experts” from industry and colleges along with high school teachers.

Stevenson suggested that creatively redesigning some math courses could offer a middle ground that leads to post-graduation options, not dead-ends.  Examples could be a three-year integrated pathway that blends statistics or a two-year course in statistics after the first two years of high school math that combines Algebra II.

“There could be consensus around that,” she said.

Freed from a looming deadline, the state board and the California Department of Education have the time to look at these and other alternatives that could temper the debate and do right for students.

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  1. Daniel 2 weeks ago2 weeks ago

    To become proficient in high school level math, it takes a Herculean amount of effort for most students. The way math is typically taught (with rules and algorithms), the subject ends up making intuitive sense only to: 1) those students who are lucky enough to have been endowed with superior intellectual gifts and 2) those students who, fearing that their entire future is at stake if they don't do well, sacrifice hours upon hours … Read More

    To become proficient in high school level math, it takes a Herculean amount of effort for most students. The way math is typically taught (with rules and algorithms), the subject ends up making intuitive sense only to: 1) those students who are lucky enough to have been endowed with superior intellectual gifts and 2) those students who, fearing that their entire future is at stake if they don’t do well, sacrifice hours upon hours trying to “get it.” This is a lousy situation, but it’s what we have at the moment. Personally, FWIW, I think educational technology ultimately will get us out of this hole.

    But until it does, as the graphs show, African-American kids have it the worst. White and Asian kids have it best, and Hispanic kids are in the middle. It’s good that people are worried about “equity.” It means we care about the kids who are doing worse and are not content with the situation.

    But an important, missing ingredient in this discussion is the racism in our country. I’m not wagging my finger at anyone, but it is a fact of life, particularly for African-American people. African-American kids (and, to a lesser, but real, extent, Hispanic kids) know about our country’s racism. They feel it every time they are treated differently by people of the White or Asian race. That takes a toll on a person, especially an adolescent who is hyper-attuned to issues of acceptance and rejection.

    Long story short, Black kids, after struggling with some math topic (the same as everyone else), throw in the towel sooner. They don’t separate the math that is giving them trouble with the society it comes from. “I’m done.” A rare few persevere, but most (other than the lucky, gifted ones) cut their losses and look for another way. You can’t blame them, or their parents. They are dealing with the world as it has been given to them.

    But racism, not math, is what we are really fighting against here. That is the enemy. Our way of teaching math is bad, no question, but the disparity that results from it differs for different groups. Can we fix our math instruction to “get around” the problem? I don’t know. Good luck. But I wish we were looking at the real issue and not an outcome of the real issue.

  2. LogicalParent 2 weeks ago2 weeks ago

    Givens: US PISA Math Rank of 37 from 2018: https://factsmaps.com/pisa-2018-worldwide-ranking-average-score-of-mathematics-science-reading/ State education rankings: https://worldpopulationreview.com/state-rankings/best-states-for-education You need to ask yourselves the following questions: 1. What is the United States doing wrong when it comes to teaching STEM? 2. What is the ranking of our educational materials, quality of teaching, and training compared to top countries and states? 3. Why can't we copy what other top countries and states are doing when it comes to teaching STEM? 4. What is our state doing wrong that other … Read More

    Givens:
    US PISA Math Rank of 37 from 2018:
    https://factsmaps.com/pisa-2018-worldwide-ranking-average-score-of-mathematics-science-reading/
    State education rankings:
    https://worldpopulationreview.com/state-rankings/best-states-for-education

    You need to ask yourselves the following questions:
    1. What is the United States doing wrong when it comes to teaching STEM?
    2. What is the ranking of our educational materials, quality of teaching, and training compared to top countries and states?
    3. Why can’t we copy what other top countries and states are doing when it comes to teaching STEM?
    4. What is our state doing wrong that other top states are doing right when it comes to STEM education?

    California use to be at the top when it comes to education but not anymore. Why not?

    Something is wrong when you have STEM industry and higher ed. professionals complaining about the California Department of Education.

  3. Andrew Dempsey 3 weeks ago3 weeks ago

    Why would you encourage students not to take a math class that they are ready for? Why..? The idea that some students aren't ready for algebra 1 in middle school so no one should take it until later is disturbing. We should want to challenge our students as much as possible and develop their skills as soon as possible. And yes, what the other comments said - we should take a look at the other countries that are … Read More

    Why would you encourage students not to take a math class that they are ready for?

    Why..?

    The idea that some students aren’t ready for algebra 1 in middle school so no one should take it until later is disturbing. We should want to challenge our students as much as possible and develop their skills as soon as possible.

    And yes, what the other comments said – we should take a look at the other countries that are quickly passing us up in math and stem in general.

    Or we should get serious and start to consider that the system isn’t being managed in such a way as to support our students. As in, the assumed goal of our education may not exist anymore.

  4. el 3 weeks ago3 weeks ago

    Data science is a highly mathematical pathway and I think the basic idea is worthy - bring statistics and probability in earlier or as an option. When I was a student, statistics was a gory field that involved horrific hand calculations with relatively few problems that could be solved in a classroom setting. Today, with computers, statistics can be taught quite differently, with large and interesting data sets. Spreadsheet fluency, and later, computer programming are … Read More

    Data science is a highly mathematical pathway and I think the basic idea is worthy – bring statistics and probability in earlier or as an option. When I was a student, statistics was a gory field that involved horrific hand calculations with relatively few problems that could be solved in a classroom setting. Today, with computers, statistics can be taught quite differently, with large and interesting data sets. Spreadsheet fluency, and later, computer programming are key components of this work now.

    Calculus is important but it is also arcane – really the first Real Math that isn’t simply algorithms that most students encounter. They get it in senior year, often from teachers who aren’t strong it it themselves, and with little context about why it matters. Admissions decisions are being made based on the junior year transcript anyway. Even students who have access often are not really served well by these classes.

    Don’t get me wrong – I like calculus. I can explain in detail its value and solve problems with it. But also, I think that senior year of high school may be the worst possible time to introduce it. It’s a whole new way of thinking at a time when students are the least receptive to totally changing how they think about math. I’ve seen students do better with it with more maturity. At college they also may get better instructors. Conversely, really ambitious and engaged students may do well with it earlier, with the right teachers.

    Some people will argue that calculus is important to really get statistics, and so it should be taught first. But my experience suggests that teaching people statistics and getting them excited about solving problems in large data sets first works out better – students who may have noped out of calculus are starting to understand why they might want it, why they might need it. In general I find that getting students hooked on problems before teaching them the solutions is very useful for engagement. They want to know how the story ends, and it’s much more obvious then why they need calculus (same for algebra or trig really).

    Give us a good, rigorous, quality data science pathway that sets students up to take calculus as college freshmen. (Heck, also allow students excited about math to take both pathways if they so desire.) Partner with the universities to make this a reasonable path. We know the current pathway has big problems for retention; let’s try something different.

  5. Zeev Wurman 3 weeks ago3 weeks ago

    A minor beef. "Teachers haven’t had a framework since 2013, and that one was done after the adoption of Common Core; its purpose was to explain and prioritize the standards. Teachers have been eager for guidance on how to make math more engaging, fun and relevant to students and expressed that in focus groups, said Ma Bernadette Andres-Salgarino, assistant director for integrated STEM development at the Santa Clara County Office of Education and president-elect of the … Read More

    A minor beef.

    “Teachers haven’t had a framework since 2013, and that one was done after the adoption of Common Core; its purpose was to explain and prioritize the standards. Teachers have been eager for guidance on how to make math more engaging, fun and relevant to students and expressed that in focus groups, said Ma Bernadette Andres-Salgarino, assistant director for integrated STEM development at the Santa Clara County Office of Education and president-elect of the California Mathematics Council.”

    This quote is tendentious and obfuscates reality. The Framework was indeed updated after Common Core adoption, and the standards have not change, so the implications that “we must update the Framework” is misleading. California does have a regular update cycle for Frameworks yet in the past, when standards have not changed, such cycles have been skipped. The pretense that there is some real urgency for update now and that teachers are clamoring for guidance is a convenient excuse to try and infuse teaching of math with racist undertones and woke concepts.

    It’s not about improving mathematics but about undermining mathematics on the altar of political correctness and race-based politics.

  6. SFUSD Teacher 3 weeks ago3 weeks ago

    Conrad's statement, imho, is the crux of this dilemma. To wit: "“To my astonishment, in essentially all cases, the papers were seriously misrepresented” and in some cases “even had conclusions opposite to what was said” in the framework." The framework, and to a larger extent, the entirety of mainstream mathematics education research (especially Boaler, et. al.) is rarely - if ever - more than ideologically-driven opinion. Where are the replicated studies? Why is CA listening to … Read More

    Conrad’s statement, imho, is the crux of this dilemma. To wit: ““To my astonishment, in essentially all cases, the papers were seriously misrepresented” and in some cases “even had conclusions opposite to what was said” in the framework.”

    The framework, and to a larger extent, the entirety of mainstream mathematics education research (especially Boaler, et. al.) is rarely – if ever – more than ideologically-driven opinion. Where are the replicated studies? Why is CA listening to folks who can’t provide strong evidence for their hypotheses? How did Stanford (et. al.) become a bastion of pseudo-science? It’s tragic, especially since an entire cohort of younger teachers have been trained with these ideas, to the exclusion of any other. I’m starting to think that it’s going to take a generation to undo the damage done by this group of mathematics education “researchers.” Really tragic.

    Replies

    • Maya K 3 weeks ago3 weeks ago

      "Why is CA listening to folks who can’t provide strong evidence for their hypotheses?" Why is CA listening to people who used discredited data for a nationwide push to remove algebra 1 from 8th grade? They were just allowed to remove all references to San Francisco and the claimed 40% fail/repeat rate that final year students took algebra 1 in 8th grade from version 2 with no questions asked. This claim was repeated everywhere. … Read More

      “Why is CA listening to folks who can’t provide strong evidence for their hypotheses?”

      Why is CA listening to people who used discredited data for a nationwide push to remove algebra 1 from 8th grade? They were just allowed to remove all references to San Francisco and the claimed 40% fail/repeat rate that final year students took algebra 1 in 8th grade from version 2 with no questions asked.

      This claim was repeated everywhere. Press releases from SFUSD, Op Eds from Boaler and others, published research papers, and on twitter. Thank goodness for public data requests which showed the actual fail rate was 4% and the repeat rate because of an exit exam the district removed after they delayed the sequence (yet conveniently forgot to disclose) was 27.5%.

      Advanced Math enrollment didn’t increase by leaps and bounds either. The district made up their own definition of advanced math calling their compression class precalculus when UC a-g categorizes it as algebra 2 because it is missing key content found in a one year precalculus class.

      Yet nobody is being held accountable for this 8 year boondoggle come fall.

      Meanwhile Boaler et al talk tracking when CA used to be an algebra 1 in 8th for all state. In San Francisco anecdotally, my son, who was the last with 8th algebra, wasn’t tracked (he’s now an electrical engineer) into algebra 1 earlier, none of the students in his middle school were. He had 6th grade math, 7th grade math and then algebra 1 with everyone in 8th. That was enough to get him to Calculus BC in 12th and prepare him for his electrical engineering degrees (BS & MS).

  7. Paul Muench 3 weeks ago3 weeks ago

    I’m thinking about sidewalks on college campuses. Maybe we should take a look at where students are actually going to learn math and see what’s happening there. There must be some data on what’s happening with online learning.

  8. Jim 3 weeks ago3 weeks ago

    What is missing is any reference to how better performing countries teach math. For some reason the debate does not reference the other 7.5 billion people in the world.

  9. Jan Johnston-Tyler 3 weeks ago3 weeks ago

    This is truly concerning...what is missing is any discussion on how students learn math. My personal and professional experience tells me that there are 'concrete' thinkers who do well with rote memorization and formulas and algorithms, and those who are 'visual' thinkers' who do better with big picture, story type learning. I am poor at memorization (poor working memory), but I have a Masters and run a business. Further confounding this problem in high schools … Read More

    This is truly concerning…what is missing is any discussion on how students learn math. My personal and professional experience tells me that there are ‘concrete’ thinkers who do well with rote memorization and formulas and algorithms, and those who are ‘visual’ thinkers’ who do better with big picture, story type learning. I am poor at memorization (poor working memory), but I have a Masters and run a business.

    Further confounding this problem in high schools is the mandate community colleges now have which has disallowed them to provide those remedial students who need more help with mathematics prior to pre-calc or stats — the gap for these students is now much wider.

    To say that ‘all students must’ or that ‘all teachers must’ also leaves out a considerable portion of students with special needs, who are often graduated — with a diploma, into the world — with math and ELA as low as 4th grade. They get a pat on the head, and told ‘Good luck’.

    Now, with no available remediation at community colleges, what are they supposed to do? The State is inadvertantly sending more and more kids into poverty with no real way to get ahead — or even stay afloat. According to OSERS/BLS, even entry-level jobs require a minimum of 8th grade skills, which many graduating kids do not have.