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  • Is Harvard Teaching Remedial Math? Trump Says It Is.

    Is Harvard Teaching Remedial Math? Trump Says It Is.


    In his epic battle to punish the nation’s most prestigious university, Trump claimed that Harvard is teaching remedial math. That was his way of saying that its standards of admission are very low because Harvard wants to recruit unqualified nonwhite students.

    Trump has refused to release his own academic record but his public statements indicate that he is in no position to tell Harvard whom to admit or what to teach.

    Only 3.6% of the students who applied to Harvard last year were admitted.

    The Boston Globe took a close look at the course that Trump–the stable genius–calls “remedial.”

    A star student at her small Alabama high school, Kyra Richardson graduated confident in her academic prowess in all but one subject: math.

    By the time she arrived at Harvard in the fall of 2024, it had been more than 12 months since Richardson‘s last math class. Even though she passed a college-level AP calculus course as a high school junior, Richardson said it felt more like she was memorizing formulas than truly understanding the concepts behind calculus.

    So when it came time for her to begin fulfilling the math requirement associated with Harvard’s pre-medical track, the university recommended (and Richardson agreed) she should take an intro-level calculus course called Math MA.

    Even with her previous calculus experience, she said, the Harvard course was far from an easy A. “I’m glad that I took a class that pushed me,” Richardson said.

    In recent months, amid the White House’s ongoing battle with Harvard, the Trump administration has used that class to questionthe university’s academic rigor. In what has become a familiar refrain, Education Secretary Linda McMahon, Josh Gruenbaum, a top US General Services Administration official, and President Trump himself have all labeled a modified version of the calculus course Richardson completed — known as MA5 — “remedial math.” 

    “I want Harvard to be great again,” Trump said in the Oval Office last month. “Harvard announced two weeks ago that they’re going to teach remedial mathematics. Remedial, meaning they’re going to teach low grade mathematics like two plus two is four. How did these people get into Harvard if they can’t do basic mathematics?”

    Richardson said she laughed when she heard the remedial math comment because “MA5 is the exact same class [as MA]. It just meets five times a week” as opposed to four. 

    According to an online course description of MA5, the extra day of instruction time “will target foundational skills in algebra, geometry, and quantitative reasoning that will help you unlock success in Math MA.” The homework, exams, and grading structure of MA5 are the same as MA, a course Harvard has offered for decades. Even MA5’s format is not entirely new. Five days of instruction was previously required for all students taking Math MA in 2018.

    “If you look at academic support and a college trying to help their students, and you think that’s unnecessary or it’s embarrassing that they have to provide that kind of support, then it’s coming from a place of ignorance,” said Richardson. “You have no understanding of how, not just college, but how learning works. You can’t learn without help.”

    All Harvard freshmen take a placement exam in mathematics prior to their arrival on campus. Based on how they score, the university suggests which course they should be placed into. Math MA5, MA, and its companion course, MB, make up Harvard’s most basic introductory calculus courses known as the M series. MA5 was introduced last year by Harvard to combat pandemic learning losses, which saw students show up to campus with gaps in their math knowledge, especially in early high school courses like algebra, as a result of virtual learning. 

    “When this first came out about us teaching remedial math, I was like, ‘Well, this is news to me and I wouldn’t even know how to do it,’” said Harvard’s director of introductory math Brendan Kelly. “Thinking about how to explain addition to somebody is an expertise that your elementary school teachers and middle school teachers have. … We focus on much more advanced mathematics.”

    Only 20 students took MA5 this past academic year according to Kelly. The course was taught across two sections, each with 10 students, Kelly said, all of whom have declared majors like economics or biology that necessitate a strong foundation in calculus…

    Remedial math courses in higher education are typically defined as “non credit bearing courses that cover middle school and high school content below that of college algebra,” said Chris Rasmussen, a professor of mathematics at San Diego State University. “So we’re talking fractions or some basic algebraic manipulation.” Rasmussen — who was part of a team of outside professors that recently conducted a full review of Harvard’s math department — said “in no way is MA5 a remedial math course. It’s a rigorous calculus course.”

    The article includes a PDF with the course syllabus. How many members of Congress could pass it? Not many. Certainly not Trump or Secretary McMahon.



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  • How teachers can use AI to listen, reflect and build math classroom community

    How teachers can use AI to listen, reflect and build math classroom community


    I wasn’t expecting a math journal entry to shift my perspective. But as I scanned through my students’ reflections that morning, one response stopped me in my tracks:

    “It’s more important to me that my teacher sees me as a person than if I get all the answers right.”

    A student, who I’ll call Jason, had been in my class for months — quiet, polite, barely noticeable. Not failing, not thriving. Just…there.

    Jason’s words reflected what many students feel but rarely say. As I reviewed other journal entries, I discovered an echo of voices expressing uncertainty, quiet resilience and a desire to be heard. I highlighted themes and let their words settle in, but as responses piled up, I needed help seeing the bigger picture.

    That’s when I turned to artificial intelligence (AI), using it to help summarize journal entries — not replacing my judgment but sharpening it. ChatGPT surfaced patterns I might have missed: anxiety about speaking up, appreciation for kindness, the importance of being seen. AI didn’t give me a summary of responses — it gave me perspective, revealing what my students were telling me between the lines.

    Too many students walk into math class carrying untold stories — about race, failure, shame, invisibility. And math, with its perceived rigid right-or-wrong structure, often leaves little room for the messiness of being human. Reflective journals and AI made that space. They reminded us that learning is emotional before it’s cognitive.

    Some view AI in education as a threat to authenticity — something that might replace meaningful learning, weaken rigor, and erode the relationships. Much of the conversation focuses on fears of cheating and weakened critical thinking. But in my experience, the opposite is possible. When used thoughtfully, AI doesn’t dehumanize the classroom — it rehumanizes it, helping us tune in to students’ emotional landscapes and respond with greater clarity and compassion.

    For educators exploring how to move from algorithms to empathy, here’s what I’ve learned:

    Use AI as a reflection partner to surface trends in student voice. I introduced reflective journals with prompts like “How do you see yourself in math?” and “Where might math be important in your life?” When responses accumulated, AI helped me identify emotional throughlines—what students feared, valued, and needed to feel seen. It didn’t analyze feelings for me; it spotlighted patterns across dozens of responses, allowing me to respond not just as a content expert, but as a listener who could address the class’s collective needs.

    Let AI handle the grunt work so you can do the heart work. After AI helped me identify themes like “I don’t feel smart, but I try harder than people know” and “I’m not the only one scared to ask for help,” I shared these anonymous insights with my class. Heads nodded. The room shifted. These reflections weren’t about fixing students — they were about making space where vulnerability felt safe and mathematical identity could evolve.

    Design with AI — not for it. I didn’t start by asking what AI could do, but rather “What do my students need to feel seen, challenged and supported?” Only then did I explore how technology could help me meet those needs more thoughtfully and efficiently. The tools followed the vision, not the other way around.

    Treat AI like a co-teacher, not a substitute. AI will never replace the personal connections at the heart of teaching, but it can help me see what I might miss in the everyday chaos of the classroom. This partnership allows me to combine technological insights with the relational knowledge that only comes from knowing my students.

    The day after reading Jason’s journal entry, I greeted him more intentionally and shared that I had once felt the same way about being seen as a person first. It was a tiny signal: I see you. This breakthrough emerged from recognizing that community building in math class doesn’t require elaborate group projects or icebreakers. Sometimes it starts with something quieter: giving students space to examine their relationship with mathematics itself, then using AI to help us listen more deeply to what they’re telling us.

    A week later, Jason lingered after class. “Thanks,” he said. “For, like, sharing with me.”

    That two-second moment cracked something open — for both of us. Because behind every silence is a student waiting to be seen. And sometimes, the most powerful data we can use isn’t a test score or a benchmark — it’s a journal entry, a nod of recognition, or a quiet “thank you” made visible with the help of AI, reminding us why we teach.

    •••

    Al Rabanera teaches math at La Vista High School in Fullerton, California. He is a 2025-2026 Teach Plus Leading Edge Educator Fellow.

    The opinions expressed in this commentary represent those of the author. EdSource welcomes commentaries representing diverse points of view. If you would like to submit a commentary, please review our guidelines and contact us.





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  • Dissent, no funding yet for statewide teacher training in math and reading

    Dissent, no funding yet for statewide teacher training in math and reading


    Credit: RDNE stock project

    Legislation that calls for providing all state teachers and aides with math and reading training passed its first legislative hurdle despite the uncertainty of funding and the skepticism of advocates for English learners who dislike the bill’s nod to instruction in the “science of reading,” including phonics.

    Senate Bill 1115 has no secure source of money heading into a tight fiscal year, with Gov. Gavin Newsom all but ruling out money for new programs. His January budget includes $20 million for a designated county office to train coaches who would then train their own teachers in what they learned.

    Neither the bill’s author, Sen. Monique Limon, D-Santa Barbara, nor its sponsor, State Superintendent of Public Instruction Tony Thurmond, offered a cost estimate at a hearing of the Senate Education Committee last Wednesday, though it would cost at least hundreds of millions of dollars to train 300,000 teachers. They said they were willing to phase in and focus funding, such as concentrating on early literacy and numeracy skills, and to look for federal and dedicated sources of money.

    Thurmond said training teachers to enable all students to read effectively “is an issue of moral clarity.” Neither he nor Limon offered a cost estimate that could run into hundreds of millions of dollars.

    “In an age when we have access to substantial brain science about how students learn, it should be unacceptable to train only some educators in the best strategies to teach essential skills,” he said.

    School districts have received billions of dollars between federal and state Covid relief funding, including money to address learning loss — money that could be used for teacher training — but none of that has been earmarked for that purpose.

    State budgets have set aside $50 million to hire and train reading teachers in the most impoverished 5% of schools. But Thurmond said training of trainers, however, does not substitute for providing sufficient funding to ensure training for all teachers and support staff in “high-quality” programs in math and literacy.

    The bill calls for the Department of Education to identify and recommend those high-quality programs by Jan. 1, 2026.  For transitional kindergarten through sixth grade, those should align with “the science of reading” by focusing on results-driven methods of teaching, which may include, but is not limited to, offerings such as Lexia LETRS and CORE Learning.”

    Singling out those specific trainings in the bill were red flags for two nonprofits that advocate for English learners: Californians Together and California Association of Bilingual Educators (CABE). The science of reading refers to research from multiple fields of science that confirm or discount theories on how children learn to read. LETRS and CORE Learning are intensive programs that explain a systematic approach to teaching phonics and other elements of reading consistent with the science of reading.

    Californians Together and CABE, however, complain that those programs overemphasize phonics and “structured literacy” at the expense of English learners’ need for more attention to oral language and vocabulary development.

    Calling Californians Together’s position on the bill a “tweener,”  legislative advocate Cristina Salazar testified at a hearing last week, “We agree that we need more professional learning for educators, but we do have concerns with the bill.  Specifically, it mentioned the science of reading, and it also names commercial programs.”

    CABE legislative advocate Jennifer Bakers said her organization shares the same concerns and “hopes to have a collaborative conversation about a path to move forward.”

    Last year, at the Legislature’s direction, the state Commission on Teacher Credentialing adopted new standards for teaching reading that emphasize explicit instruction of fundamental skills, including phonics. Starting next year, candidates in teacher preparation programs are required to be trained in those strategies.

    Sen. Rosilicie Ochoa Boch, R-Yucaipa, asked Thurmond whether the intent is to train existing teachers in the new standards that new teachers will be trained on.

    “Yes, that is correct,” Thurmond said.

    Opposition from Californians Together and CABE this month factored into the quashing of a bill that would have required school districts and charter schools to train all TK to fifth-grade teachers and literacy coaches in instruction based on the science of reading and to buy textbooks from a list endorsed by the State Board of Education. Assembly Speaker Robert Rivas, D-Salinas, ordered Assembly Bill 2222 shelved without a hearing to give time for negotiations with opponents, including the California Teachers Association.

    At the hearing, Thurmond acknowledged similarities between the two bills, although AB 2222 would have been a mandate, while AB 1115 would recommend the selection of trainings.    

    Along with mandating the science of reading approach to instruction, AB 2222 would have required that all TK to fifth-grade teachers, literacy coaches and specialists take a 30-hour minimum course in reading instruction by 2028. School districts and charter schools would purchase textbooks from an approved list endorsed by the State Board of Education. 

    Thurmond said the language of AB 1115 is well balanced in that it refers to both the science of reading and the state’s English Language Arts/English Language Development framework, which includes multiple strategies necessary for all students, including English learners, to learn how to read. 

    New math framework

    July will mark a year since the State Board of Education adopted a revised California Mathematics Framework, which took four years and three revisions to pass. The drafters and supporters agree that the framework, with emphasis on tangible applications of math, as well as a deeper conceptual understanding of it, will require a shift in teaching and extensive training. But no significant money has been allocated yet, and the process of reviewing textbooks and materials has yet to begin.

    In an interview, Limon said it is important to raise the issue of teacher training now, even if legislation is tied to a future appropriation.

    Part of the public debate in committing public dollars should be, What would the program look like, and how will it serve diverse students? she said. “There is value to that discussion,” she said. Before her election to the Legislature, Limon served for six years on the Santa Barbara Unified school board.

    In 2022-23, only 46.7% of California students met grade standards on the state’s English language arts test; the percentages were 36.6% for Hispanic, 29.9% for Black, and 35.3% for economically disadvantaged students. The scores were worse in math:  34.5% of students overall, with 22.7% of Latino, 16.9% of Black, and 22.9% of economically disadvantaged students meeting standards.





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  • To teach math effectively, California must focus on deep, conceptual learning

    To teach math effectively, California must focus on deep, conceptual learning


    Third graders discuss possible ways to solve a new math problem.

    Credit: Allison Shelley for American Education

    Fierce wars continue to rage around math instruction, but there are many practical changes we should make for mathematics students upon which most of us can probably agree, that could transform their ability to achieve. 

    A promising new initiative for California that we have both been involved with tackles two of the most pressing flaws of traditional math instruction with elegant solutions that should be appealing to many, no matter which camp they occupy in the debates. Ask any teacher of math what they wish they did not have to deal with, and they will tell you the excessive amount of content they need to teach, which leads to the second problem — the shallow coverage of hundreds of methods that students do not learn in meaningful ways.

    U.S. math textbooks are massive and heavy tomes. By contrast, math textbooks in Japan and China are small and slim. The reason for this is that U.S. curriculum repeats content every year. In China and Japan, content is taught less frequently but more deeply and conceptually. As teachers in the U.S. are forced to “cover” an extensive amount of content in every year of school, students only gain a shallow experience of mathematical methods and rules.

    The second problem, linked to the first, is that students are taught hundreds of methods as though they are all equally important, without experiencing the more foundational concepts deeply and conceptually. Some concepts are much more central than others because they link to other areas of content, and they deserve to be learned deeply, over multiple lessons, through applied tasks that relate to students’ lives.  An example of a central concept in grade four is “factors and groups.” Instead of learning about these through short questions and answers, students can learn them through rich tasks in which they are more deeply engaged, as can be seen here.

    Students can learn all foundational concepts, such as fractions or functions, by drawing, building and learning about them through real-world examples. Every important idea in mathematics can be learned visually, physically and conceptually, including algebra and calculus. Instead, most students work through pages of numerical calculations, absent of any connection to the world, and spend hours of algebra class manipulating X’s on a page.

    A solution to both of these problems is to teach the “big ideas in mathematics” for every grade, as set out in the California Mathematics Framework,  such as “being flexible within 10” (kindergarten) or “unit rates in the world” (grade seven), making sure that for each of the eight or so big ideas in every grade, students have a deep and rich experience of their underlying concepts: by drawing them, building them and talking about them. Even if it is only these eight or so ideas that are experienced in this way each year, they will serve as a foundation for everything else students learn as they progress.

    Many California school districts are now waiting for funding to be devoted to the training of teachers to move to the approaches set out in the framework. But in Kern County, leaders have been sharing these ideas for the past three years. Semitropic Elementary school, which serves mainly Latinx, English learners and socioeconomically disadvantaged students, is one example of a school that has moved to the approach of the framework. In the 2018-19 school year, before Covid-19 and the implementation of the new framework, only 5.6% of Semitropic students met or exceeded standards on math Smarter Balanced tests in grades 3-8, with less than 5% in grades four and five, and no students in grades 6 or 8. After the leaders in Kern County supported teachers in learning and implementing the ideas of the framework, through a series of professional development sessions to build capacity, with classroom demonstration lessons to model the new strategies, in action with their students, and coaching to meet teachers where they were, proficiency levels shot up, increasing to 16.3% overall, with the fourth grade showing the most significant increase, to 36.8%. There is more work to be done in this and other districts, but the demonstrable positive changes already unfolding are impressive.

    What changed in the classrooms of the schools in Kern County? The teachers focused on big ideas, such as “being flexible within 10” which starts in kindergarten and extends through the elementary grades. Instead of students learning 10 as a fixed number that they use to calculate, they now spend time learning how 10 is made up, and all the ways they can make 10. A powerful strategy teachers started to use was “number talks,” in which teachers pose a number problem and collect the different ways students approach the problem, representing them visually. They also started using richer, deeper tasks, encouraging students to discuss ideas and learn with visuals and manipulatives. The superintendent and county math coaches were thrilled with the high levels of engagement they saw in the classrooms, as well as the significant changes in state test scores.

    There are several problems with the systems of mathematics education in many states, and proposed solutions often spark disagreement. But perhaps we should all agree on one thing: Students need to learn important mathematical concepts deeply and well. They should not be working through sets of procedural questions that mean nothing to them, but rather should experience rich applied mathematics that inspires them, helps them learn effectively, and shows them that mathematics is important to their lives.

    •••

    Jo Boaler is a Stanford professor and author of “Math-ish: Finding Creativity, Diversity & Meaning in Mathematics.” She was one of the writers of California’s new mathematics framework.

    Cole Sampson is the administrator of professional learning for the Kern County Superintendent of Schools Office.

    The opinions in this commentary are those of the authors. If you would like to submit a commentary, please review our guidelines and contact us.





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  • High schools demand clarity about UC’s new math policies 

    High schools demand clarity about UC’s new math policies 


    High school students work together to solve a series of math problems.

    Credit: Allison Shelley for American Education

    Twice this year, the University of California faculty broadly reaffirmed which high school math courses are required for admissions. However, many school counselors and students, along with the president of the State Board of Education, complain they’re confused by a lack of details.  

    High schools want to know if their specific course offerings comply with UC requirements. Depending on a student’s interests and intended majors, counselors want to know which courses to recommend. And students want to know if taking less Algebra-intensive math classes like statistics and data science could affect their chances of getting admitted the campus of their choice.

    Schools and districts must have “clear, timely and consistent information” so that students and families “understand the impact of their choices,” wrote State Board of Education President Linda Darling-Hammond in a July 15 letter to the UC board of regents.

    Prodded by a regents committee, administrators with the University of California Office of the President last week promised to provide more clarity by the end of the summer.

    “I feel like we’re not coming at this from a student perspective. I feel we’re coming at this from an academic perspective, and I would really encourage all of us to maybe flip that a little bit, put yourselves in the shoes of a rising sophomore, a rising junior,” regent Alfonso Salazar, who is president of the UC Alumni Associations, said at the meeting. “That would be incredibly helpful because people are very nervous and concerned.” 

    The confusion centers on the ongoing debate over whether AP Statistics or data science can be substituted for Algebra 2.  Over the past decade, the UC faculty committee that determines course requirements approved AP Statistics and, more recently, introductory data science courses as substitutes for Algebra 2, which UC requires for admission. Those decisions will also apply to California State University, whose A-G course requirements for admission are nearly identical for the 23 CSU campuses.

    But faced with strong objections from science, technology, engineering and mathematics (STEM) professors, the faculty committee did a hurried about-face in July 2023, days before the state board adopted a math framework that outlined sequences of high school math courses. The faculty committee voted that AP Stats and introductory data science would no longer “validate” or substitute for Algebra 2, starting in the fall of 2025.

    The STEM community argued that the courses lacked sufficient Algebra 2 content to prepare students for precalculus, which is a precursor to calculus. Majoring in data science, computer science, and STEM all require calculus. Students who take introductory data science would be under the illusion they are ready to major in data science. UC and many CSU campuses don’t offer catch-up courses in Algebra 2. 

    Since 1999, the number of students majoring in STEM more than tripled, from 14,081 to 48,851 in 2022. The proportion of STEM majors at UC increased from 32% to 44% of all majors, according to UC data.

    Where does data science fit in?

    The immediate impact of the decision is expected to be limited, since more than 99% of applicants to UC have taken Algebra 2 anyway, according to UC data. But interest in data science, in a world of burgeoning AI and uses for big datasets, has been mushrooming, and promoters pointed to introductory data as a way to skip Algebra 2.

    The faculty committee, the Board of Admissions and Relations with Schools or BOARS, reaffirmed that position in February when it accepted a faculty workgroup’s report. The report examined the content of AP Statistics and the three most popular introductory data science courses and found “that none of these courses labeled as ‘data science’ even come close to meeting the required standard to be a ‘more advanced’ course (Algebra 2). They should be called “data literacy” courses, it said.

    But where, Darling-Hammond asked in her letter, does that leave the status of potentially hundreds of other courses in data science, financial math and non-AP statistics that UC previously validated as satisfying Algebra 2? 

    “Most districts will be starting the new school year in less than a month without sufficient clarity regarding the mathematics courses they will offer moving forward,” she wrote. “But the committee’s criteria and process are not yet fully transparent, and it has only evaluated four courses out of the hundreds that have previously been approved.”

    One complication facing BOARS and staff within the UC Office of the President, which annually evaluates courses that school districts submit for approval, is that there are no state standards for data literacy. Each course must be examined independently.

    Darling-Hammond’s letter raised a critical, intertwined issue: How will UC categorize introductory data science and other courses as fourth-year high school math courses?

    Neither UC nor CSU requires that high school graduates take four years of math, but they highly recommend it. According to UC data, about 80% of UC applicants take at least one course in advanced math beyond Algebra 2, usually precalculus or both precalculus and AP Statistics. The report did not include comparable CSU data.

    BOARS created a second, 12-member faculty workgroup of STEM professors to examine what math courses will best prepare students to succeed at UC in whatever field they choose. A report in June agreed that the current three required foundational math courses make sense: Algebra I, Geometry, and Algebra 2, or Math 3 in districts that offer an integrated math sequence. It also emphasized that “to be recommended for a fourth year of mathematics study, (a course) must build substantially on the content of the lower-level sequence.”

    With that in mind, the report, which BOARS adopted, divided high school math courses into four categories:

    • Category 1 consists of the foundational math courses
    • Category 2 courses, which include Precalculus and Calculus, best prepare students interested in STEM fields.
    • Category 3, which also builds on foundational courses, are courses suited for students interested in quantitative social sciences, such as psychology and history. It singles out AP Stats, but not data science.
    • Category 4, a catch-all for other courses in quantitative reasoning, would include data literacy. These courses “will continue broadening students’ interest and confidence in math” and may be appropriate for arts and humanities majors.

    Tension over fourth year designations

    Advocates for introductory data science argue that many of their courses cover the same Common Core statistic standards as AP Statistics yet could be cast into the lowest category. Counselors may discourage students from taking data science, and districts may retreat from offering it. That would stunt the growth of data science at a time when other states are encouraging it, said Aly Martinez, who helped design a two-year high school introductory data science and statistics course for San Diego Unified, using  CourseKata, a college course.

    “Other states are thinking about a wider range of rigorous math courses. California is not doing that. Many districts have done these innovations and seen success. It’s frustrating; it feels like California is closing the door versus opening it,” said Martinez, who is now the chief program officer for the national nonprofit Student Achievement Partners.

    Cole Samson, incoming president of the California Mathematics Council, seconded the call for more clarity. The latest UC faculty report “absolutely causes some confusion; it did not outline enough for the next steps,” he said.  

    High schools that submit math courses for approval in fall 2025 will need clear guidance and feedback on how to revise courses, said Sampson, who is director of curriculum, instruction and accountability for the Kern County superintendent of schools. Whether courses are approved or how they are categorized will affect student choices and master schedules. “UC should be mindful of local impacts,” he said.

    UC Provost Katherine Newman acknowledged the need for more information at the regents meeting. “There’s work to be done to communicate what those recommendations mean, she said, adding “I don’t sense amongst my colleagues any hostility toward data science.” On the contrary, she said that UC will work with “our K through 12 partners” to bolster data science courses so that students are well-prepared when they enter UC.

    At the end of their June report, the UC math faculty members acknowledged that many high school students find math courses, especially Algebra 2, “overfull of content” and uninteresting. They suggested the UC form another committee to look deeper into how high school math courses can be improved to help students better understand the mathematical concepts. Members should include faculty with expertise in improving the quality of K-12 math.

    Another workgroup examining math content, consisting of faculty from UC, CSU and community colleges, may examine this issue of alternative math courses in a report due later this summer.

    Sampson said he would welcome that broader opportunity. Many students view Algebra 2 as irrelevant and dull, he said. “It needs a makeover,” he said. “I would champion designing new courses.”

    he article was clarified to note that introductory data science courses contain far less algebra content than Algebra II but are not necessarily less rigorous. It noted that UC’s and CSU’s course requirements for admission are nearly identical, but have minor differences. The misidentification of Provost Katherine Newman was corrected.





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  • How one county is overhauling its math culture

    How one county is overhauling its math culture


    Riverside County teachers collaboratively learn with the Riverside County Office of Education math team around increasing student thinking.

    Credit: Riverside County Office of Education

    At the Riverside County Office of Education, we serve about 430,000 students across 23 districts, providing instructional support and other direct services in all content areas. In recent years, our state math assessment data has indicated a need for improvement in how our students learn math. As a state and county, we have struggled to show the hoped-for growth in math in our statewide Smarter Balanced Assessments.

    We don’t believe that recommending all our districts adopt new textbooks or curricula would solve the problem because we’d still be teaching math the same way. Instead, we decided to align to evidence-based practices to change our math culture countywide.

    This is how we, in collaboration with our districts, are working toward a better math learning experience for our students.

    Our renewed focus on math culture aligns with national organizations like the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics. The work we are doing also aligns very well with the California’s newly revised math framework. A few of the goals of focusing on culture are to increase student access, build positive identity and develop agency within students. These align directly with the ideas in chapters 1 and 2 of the new framework. Our approach to the teaching and learning of mathematics, informed by national reports such as “Adding It Up” and instructional models like cognitively guided instruction (CGI) honors what students bring to the classroom and builds on it while focusing on a balance between procedural skills, conceptual understanding and application.

    Due to numerous factors, mathematics instruction tends to spend a great deal of time on skills and procedures such as adding, subtracting, multiplying and dividing for the purpose of getting answers. There is a continued focus on procedural skills in elementary mathematics. But, instead of drilling students on these processes over and over, we could be spending time helping them understand the mathematics behind the processes by encouraging them to share their thinking.

    We’ve also seen an interplay between math culture improvements and equity. Changing people’s hearts and minds opens doors to more equitable access for students because educators start to recognize that there aren’t low, medium and high students. Rather, there are students who have had diverse opportunities to learn math, and we should listen to them about what they know and how they learn.

    Ultimately, this culture shift is about student engagement. If students in a classroom are tuned out, we can choose to continue with the status quo, or we can help them see the beauty in math and how it connects to their lives and the things they care about.

    Much of our work is additionally grounded in the Teaching for Robust Understanding framework, the book “Street Data” by Shane Safir and Jamila Dugan, and the Universal Design for Learning framework. These ideas underpin the three major aspects of our service: direct contract work with districts, countywide professional development, and the District Math Collaborative.

    We introduce ideas about math culture reform in our professional development contract work with districts. Districts reach out to us when they’d like to do customized professional development work to improve math teaching and learning.

    The District Math Collaborative began with seven districts in spring 2022, and we have continued to grow. Collaboration has centered around reflecting on teaching and learning systems, how they affect students, and how to continuously improve them.

    In addition, we have our annual Week of Math. This event is designed to allow educators, students and families to experience math differently — to find joy in mathematics. We partner with MIND Education to provide many of the games, stories and experiences through their MathMINDs program. We chose this program because it encourages the exploration, problem-solving and pattern-seeking that is the foundation of mathematics instruction we’d like to see in our classrooms. Students and their families delight in solving problems together, which builds community and reinforces the notion that everyone can be a “math person.”

    The anecdotal feedback has been great. We’ve visited schools to measure implementation and conduct surveys on how students perceive the changes. In classrooms with high implementation, we hear that students are more engaged, and that students who were labeled as low or struggling with low participation are now talking and engaging in meaningful ways.

    One of the schools that took the early initiative to work with us about five years ago — Quail Valley Elementary in Menifee Union School District — has exceeded state, county and district averages on assessments for the last two years in the grade levels with high implementation. We make sure to let all our districts know about this sort of success, because an important characteristic of culture is that it’s shared by a whole community.

    Our advice to anyone seeking to improve math culture is to find people who are energized by your ideas and lift them up. In time, they’ll lift others up as well.

    •••

    Dennis Regus, Karon Akins, Diana Ceja and Susan Jagger are the mathematics administrators from Riverside County Office of Education in California.

    The opinions in this commentary are those of the authors. If you would like to submit a commentary, please review our guidelines and contact us.





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  • New math placement rules undermine preparation of community college STEM majors

    New math placement rules undermine preparation of community college STEM majors


    Credit: Allison Shelley / EDUimages

    For an update on this topic, please see: Community colleges loosen STEM math placement rules, calming some critics

    It should come as no surprise to anyone that to succeed in a science, technology, engineering or math (STEM) field, one needs a solid foundation in mathematics.

    When my sons entered college, even though they had strong math skills, I encouraged all three to retake a transfer-level course they had completed in high school. This both solidified their mathematics foundation and started them off in college with at least one high grade toward their college GPA.

    Unfortunately, a new law, Assembly Bill 1705,  going into full effect in fall 2025, will prevent prospective STEM majors from acquiring or strengthening their foundational math skills at our community colleges.

    An earlier law restricted colleges’ ability to place students into remedial courses that carry no college credit. The noble intent of AB 1705 is to increase equity and student success, in part by extending those placement restrictions on remedial courses to credit-bearing prerequisites to calculus for STEM majors. Well-intentioned special interest groups convinced our politicians that calculus prerequisites such as trigonometry, college algebra or precalculus somehow represent inequitable roadblocks, rather than what they actually are: the building blocks to STEM success.

    This is despite emerging research showing that these kinds of policies only provide short-term benefits and are not actually helping the students in the long run.

    Community colleges have long used multiple measures, including student grades and other assessments, to evaluate mathematics proficiency. STEM majors who need stronger mathematics skills are then placed into college-level foundational courses such as trigonometry, college algebra or precalculus. These STEM building blocks carry college credit. And all students have the option to enroll in these courses to strengthen their math skills if they so choose. The credits and grades earned count toward graduation and toward their college GPA. But under the new law, a community college will only be allowed to enroll a STEM major into a prerequisite to calculus if the college meets strict validation requirements demonstrating that:

    1. The student is highly unlikely to succeed in the first STEM calculus course without the additional transfer-level preparation.
    2. The enrollment will improve the student’s probability of completing the first STEM calculus course.
    3. The enrollment will improve the student’s persistence to and completion of the second calculus course in the STEM program, if a second calculus course is required. (section 3 (f) AB 1705)

    The new law is completely tone-deaf to the critical role broad mathematics skill plays regarding college and career success in STEM fields. Furthermore, these validation requirements have predictably (and perhaps intentionally) proven to be extremely difficult to meet. A statewide study by the RP Group, a nonprofit community college research organization, failed to validate any group of students as needing the prerequisite classes, including even those who had never completed Algebra 2 in high school.

    The study concludes, “Based on high school GPA or high school math preparation, no group was highly unlikely to succeed in STEM Calculus 1 when directly enrolled and given two years.”  Without the validation, the law prohibits colleges from requiring or even placing STEM majors into any calculus prerequisite. Instead, colleges must enroll them directly into calculus.

    While the legislation forbids requiring prerequisites for calculus and STEM without the specified validation, it still allows students to drop the calculus class imposed on them and enroll instead in a calculus prerequisite. But based on the RP Group’s failure to confirm that any group of students meets the law’s absurdly strict validation requirements, the Community College Chancellor’s Office has inexplicably concluded no group would be helped by such prerequisites (see the February 2024 memo, page 5).

    As a consequence of this horrific misinterpretation, their implementation plan will forbid local community colleges from offering STEM majors any calculus prerequisites and instead require them to offer extra support to students while they are in Calculus. (See the Chancellor’s Office FAQs, “STEM Calculus Placement Rules” top of page 15). This means no STEM major would be able to enroll in any building block course like trigonometry even if they want to. The plan clearly goes beyond the law and will accelerate the dismantling of foundational math offerings at the community colleges.

    Having taught math in both the California Community College and State University systems for decades, I and all the math professors I know are convinced the end results of AB 1705 and this extreme implementation policy will be disastrous.

    The elimination of prerequisite courses represents a new artificial barrier that will prevent any underprepared STEM major from achieving the strong mathematics foundation they need to succeed and flourish. This will disproportionately affect underrepresented minorities and eliminate the “second chance” for students who didn’t develop sufficient math skills in high school. And that’s a lot of students. Data from the RP Group report show that between fall 2012 and spring 2020, over 68% of STEM majors were enrolled into foundational prerequisites (25,584 students). These students will now be denied any foundational coursework opportunities and instead be forced directly into calculus.

    We will flood our community college calculus classrooms with a large majority of students inadequately prepared. Grade inflation, increased student failure rates, discouraged faculty and the inadequate mathematics preparation of STEM majors transferring to the California State University and University of California campuses will be the sad but certain outcomes. You can say goodbye to the common sense of building strong mathematics foundations in our community college STEM majors. And cutting off this “second chance” will definitely discourage students from opting to major in a STEM field in the first place.

    The chancellor’s implementation, scheduled to take full effect by fall 2025, must make mid-course corrections to avoid a STEM preparation meltdown.

    The law itself needs major revisions to accomplish its noble equity ambitions. And all of us concerned with equity should be paying close attention to emerging research documenting the longer term outcomes of these experiments with restrictions on mathematics prerequisites.

    •••

    Richard Ford is professor emeritus and former mathematics and statistics department chair at California State University Chico. He served as chair of the Academic Preparation and Education Programs Committee (APEP) of the Academic Senate of the CSU in 2021-2022. A deeper analysis by the author of the AB 1705 implementation policy can be found here.

    The opinions in this commentary are those of the author. If you would like to submit a commentary, please review our guidelines and contact us.





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  • High school math placement is too important to leave to subjective recommendations

    High school math placement is too important to leave to subjective recommendations


    A student practices graphing in Algebra I at Rudsdale Newcomer High School in Oakland.

    Anne Wernikoff for EdSource

    Enrolling students in high school math courses is a high-stakes endeavor with an outsize effect on students’ college opportunities and even on their entire careers.

    The pressure to reach Calculus by a student’s senior year of high school often translates into pressure to take Algebra I, the first course in a five-course sequence, by eighth grade. Algebra I (or Integrated Math I) is considered a ninth grade course, but taking it on that schedule typically doesn’t allow students to meet the prerequisites for Calculus in their remaining three years of high school. This is important when we consider that advanced math classes on a student’s transcript can boost their chances of admission to certain colleges.

    But the benefits of eighth-grade math acceleration are neutralized when students who perform well in Algebra I are nevertheless required to repeat that course in ninth grade.

    Students of color and low-income students face that predicament disproportionately under their schools’ placement practices. This glaring inequity was highlighted more than a decade ago by civil rights advocates in California — and confirmed in multiple research studies since then, including this one by our organizations last year.

    Legislation targeting this unfair practice was passed in 2015. It requires the use of multiple objective measures to place students. “Successful pupils are achieving a grade of ‘B’ or better, or are testing at proficient or even advanced proficiency on state assessments. Nevertheless, they are held back to repeat 8th-grade mathematics coursework rather than advancing to the next course in the recommended mathematics course sequence,” the legislation noted.

    But nine years since the bill’s passage, we still lack a clear picture of its impact — if any — on equitable ninth-grade math placement. In the meantime, numerous states have adopted policies that have demonstrated preliminary success in expanding access to acceleration opportunities in middle and/or high school.

    California cannot afford to leave this equity issue to chance — especially because what we know to date about the implementation of California’s policy is not encouraging.

    The law, the California Math Placement Act of 2015, requires a “fair, objective, and transparent” math placement policy using multiple objective measures of student performance to determine placement. It discourages the use of subjective measures such as teacher recommendations, because of the risk of bias. In particular, it says that teacher recommendations may be used only to advance students, not to hold them back.

    But, according to a recent report from Rand Corp., high schools in California are more likely than schools elsewhere to use teacher recommendations to inform how students are placed into math classes.

    In fact, data from the survey of high school principals analyzed in the report suggest that 95% of California high schools that track students into different math courses use teacher recommendations as part of their placement process. That’s more than the national average of 86% and far more than other large states such as Florida (56%), New York (78%) and Texas (70%).

    In what appears to be a violation of the law, almost a third (31%) of California schools — more than twice the national average of 14% — use recommendation data exclusively.

    Put another way, only 69% of California principals report using some form of assessment data — whether grade-level tests, diagnostic tests, in-class tests, or classroom assignments — to inform placement decisions. Nationally, the proportion was 85%, the researchers found.

    Without further research, we won’t know why these teacher recommendation practices prevail. More importantly, we won’t know whether the past decade has brought any improvement in access to accelerated course sequences for students of color and low-income students. The available research on 12th grade course-taking before the Covid-19 pandemic shows continued inequities in access to advanced math for students who are Black, Latino, socioeconomically disadvantaged or English learners.

    The issue of teacher recommendations is a nuanced one, as researchers from the Public Policy Institute of California (PPIC) pointed out in 2016. If bias is addressed, teacher input can have benefits — by accounting for factors such as students’ motivation and persistence, which metrics such as test scores may obscure. But no research suggests they should be used to the exclusion of objective measures.

    The provision that teacher recommendations can be used only to advance students creates opportunities for students who perform better in class than on standardized assessments. PPIC noted that schools need better guidelines to comply with that provision. Many schools using recommendations may be doing so appropriately. But without further research, it’s hard to imagine how the 31% of schools that are relying solely on teacher recommendations and no assessment data could be doing what the law envisioned.

    That is why we need clear measures of how students are being placed into math classes across the state.

    While California has been in the dark about students’ math enrollment patterns, numerous other states have adopted automatic enrollment policies. Under such policies, students who meet a certain benchmark in math are automatically enrolled in an advanced math course the following year. Such enrollment policies have shown promise to address the very problem California lawmakers set out to fix nearly a decade ago.

    • Beginning in 2014, districts in Washington state widened access to more rigorous math for Black and Latino students, whose enrollment in accelerated sequences increased by 3.1 percent more than their peers. As a result, Washington mandated automatic enrollment across the state in 2019.
    • North Carolina adopted similar legislation in 2018, guaranteeing accelerated math opportunities for students who score at the highest level on an end-of-grade test.
    • Schools in Dallas have also demonstrated success with this approach. From 2019-20 to 2022-23, the proportion of Black and Latino students who met fifth-grade standards and subsequently enrolled in sixth-grade honors math increased from 58% to 92% and 69% to 94%, respectively. These results led Texas to adopt its own statewide automatic enrollment policy last year.

    Given the major role math placement exerts on students’ future opportunities, California leaders similarly should insist on rigorously measuring access to advanced math courses to ensure that it is equitable regardless of race or socioeconomic background.

    •••

    Pamela Burdman is executive director at Just Equations, a policy institute that reconceptualizes the role of math in education equity.

    Rachel Ruffalo is senior director of strategic advocacy at EdTrust-West, an evidence-driven advocacy organization committed to advancing policies and practices to dismantle racial and economic barriers in California’s education system.

    The opinions expressed in this commentary represent those of the authors. EdSource welcomes commentaries representing diverse points of view. If you would like to submit a commentary, please review our guidelines and contact us.





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  • How California can transform math education for English learners

    How California can transform math education for English learners


    Credit: Allison Shelley for American Education

    In California and across the country, English learners are too frequently an afterthought.

    Though they are one of the largest student groups — California has more than 1 million students who are learning English as a second language, and that number is growing — their academic performance has barely budged over the last two decades. According to the National Assessment of Educational Progress (NAEP), only 4% of English learners are proficient in eighth grade math, compared with 29% of non-English learners. Furthermore, NAEP reading scores revealed that only 10% of fourth grade English learners are proficient in reading, compared to 37% of non-English learners in the same grade.

    There are many reasons for this. But one of the most important is also one of the most fundamental: The textbooks and other instructional materials used in classrooms every day are typically not written with English learners in mind. While these textbooks may be rigorous and aligned with state standards, they lack the cultural relevance and language support necessary for students who are learning English. Teachers know this to be true. A survey found that 82% of teachers believe their current materials either somewhat or not at all reflect the needed academic rigor for English learners.

    Fortunately, California has an opportunity to start making this right. Next year, our State Board of Education will release its first math adoption list of state-approved curricula since 2014 — recommending math instructional materials that state education leaders believe align with California’s revised math framework. While some California districts have already started or completed their selection process, many districts in the state will soon choose a new math curriculum from that list.

    There is a common misconception that mathematical concepts transcend linguistic differences, so the needs of English learners shouldn’t be a concern. However, the reality is that language is critical for math instruction — and so math instruction materials that incorporate language support can help all learners. If the state recommends materials that center on the needs of English learners — and districts ultimately purchase and adopt them — we can make significant progress toward making our math curriculum more accessible for all students.

    Curriculum adoption may feel technical and esoteric, but it is essential to promote equity — especially for English learners. High-quality instructional materials serve as a “floor” for instruction, providing teachers with the materials they need to connect with every student in their classroom. 

    Unfortunately, our classrooms — especially those serving English learners — too often fail to reach that floor. A recent report from the Center for Education Market Dynamics revealed that California districts with greater percentages of English learners are the least likely to have adopted a new math curriculum. Many of those districts are waiting for the state adoption list before moving forward. This means that the adoption — and the curricula ultimately selected by districts — will have a dramatic effect on the academic experience of English learners, in particular.

    How can we get this process right? While California provides a list of state-approved curricula, it does not review instructional materials for specific populations, including English learners. This means districts and counties must figure out which math curriculum is most supportive of English learners. State leaders should provide guidance and resources to county offices of education so that districts are well positioned to run their own adoption processes. To support these efforts, California created math criteria that feature guides for how curriculum should support language and English learners. Districts should then base their curriculum selection on clear, research-based criteria focused on meeting the needs of all learners.

    Many districts in California and across the country are facing fiscal challenges due to the expiration of federal Covid-relief (ESSER) funding, declining student enrollment and other factors. This is likely to reduce the resources districts can target to the needs of English learners and other marginalized groups. 

    But selection and adoption of instructional materials is likely already in district budgets — and so, by picking an inclusive curriculum, district leaders can make significant headway on equity without significant additional investment. After all, it will always be more resource-intensive and less effective to supplement or modify curriculum after the fact.

    Additionally, teachers currently spend their own money on supplemental materials to fill gaps in existing curricula, a trend that is both unsustainable and inequitable. By adopting inclusive materials and ensuring teachers are supported in implementing those materials, districts will reduce these additional costs and provide a more cohesive and effective learning experience for all students.

    We are proud to say that California’s math vision is strong and there are many possibilities in terms of changing the way instruction happens in the classroom. It’s time to ensure that districts act wisely in their curriculum adoption. 

    School districts with high English learner populations need to come together and demand better options for our students. We have a chance to set the tone for the rest of the nation in developing and adopting instructional materials that truly support all students.

    It is time to invest in adopting educational resources that reflect our state’s — and our country’s — wonderfully diverse student population. 

    •••

    Crystal Gonzales is the founder and executive director of the English Learners Success Forum. Martha Hernandez is the executive director of Californians Together.

    The opinions expressed in this commentary represent those of the authors. EdSource welcomes commentaries representing diverse points of view. If you would like to submit a commentary, please review our guidelines and contact us.





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  • California needs high-quality instructional materials to support teachers, boost math learning

    California needs high-quality instructional materials to support teachers, boost math learning


    Credit: Andrew Reed / EdSource

    As a former math teacher, every Teacher Appreciation Week reminds me of the math-themed gifts I received from students — from a personalized calculator to a coffee mug adorned with equations.

    As I reflect on my time teaching, I realize that alongside these gifts, what would have empowered me most as a math teacher was consistent access to a high-quality curriculum: one that is content-rich, enables each and every student to deeply understand and apply math in meaningful ways, and supports — not replaces — teachers’ professional judgment.

    Research shows that high-quality instructional materials, together with teacher professional learning aligned to them, are a potent combination to help teachers improve math outcomes for students. Plus, high-quality materials save teachers precious time, as teachers spend an average of seven hours per week searching for or creating their own materials.

    Ensuring access to high-quality instructional materials aligns with the California Mathematics Council (CMC) mission to support and empower a thriving mathematics community dedicated to fostering effective teaching and learning for every student in California. We believe that mathematical thinking, reasoning, and problem-solving are critical to students’ future success and to our state economy.

    We also know that California students and educators have incredible strengths and potential. I have seen firsthand how students and educators thrive when given opportunities to engage with authentic, relevant math content. Unfortunately, though, the most recent Nation’s Report Card shows that California students’ math achievement lags behind national averages and remains below pre-pandemic levels.

    Moreover, California trails the nation in how our education leaders understand, identify and use high-quality instructional materials to boost math learning. A recent poll from Gallup found that only 11% of California’s district leaders and school principals are very familiar with high-quality instructional materials, compared to 20% of their peers nationally. Similarly, only 13% of California leaders said their district had an official definition of high-quality instructional materials — significantly lower than the 25% of leaders nationally who said the same. And only 11% of the leaders in our state say all the math professional learning in their school or district is aligned with their math curriculum, compared to 22% nationally.

    For high-quality instructional materials to empower teachers to unleash their care, creativity, and knowledge in supporting students’ math learning, California must have a stronger and clearer vision of what constitutes quality in curriculum. This should start at the state level, as Gallup found that more than three in four California district leaders and principals say they look to state guidelines when deciding whether a curriculum is high-quality.

    Fortunately, state leaders have an imminent and critical opportunity to lead with a clear definition of quality. This summer, the state will engage teacher-reviewers to evaluate and select instructional materials to include on the state list of recommended math curricula. In advance of the review process, the state’s Instructional Quality Commission should define ‘high quality’ in math curricula and ensure that all of the recommended materials meet this definition. The recommended materials should also align with state standards and include the instructional strategies reflected in the 2023 California Math Framework to promote every student’s access to grade-level content.

    Also at the state level, leaders should provide professional learning to support the implementation of these materials and allow teachers to lead this work with integrity and impact. Gov. Gavin Newsom allocated $250 million for math coaches in the budget he proposed in January. It is critical that the Legislature acts on the governor’s proposal and continues to invest in math teachers’ development, including through professional learning and coaching aligned with high-quality materials.

    District leaders must also clearly define what high-quality materials mean in their context and use this definition to guide their district’s math materials selection process. This definition from a coalition of organizations committed to high-quality math materials offers more guidance for district leaders as they define their vision.

    For both our students and our state to thrive, we must ensure our teachers have high-quality materials to foster achievement and joyful experiences in math. Let’s appreciate California’s teachers — during this Teacher Appreciation Week and every week — by equipping them with the high-quality resources they deserve as they do the indispensable work of nurturing the mathematical understanding of each and every student.

    •••

    Ma Bernadette Andres-Salgarino is the president of the California Mathematics Council. She is also the assistant director of iSTEAM at the Santa Clara County Office of Education.

    The opinions expressed in this commentary represent those of the author. EdSource welcomes commentaries representing diverse points of view. If you would like to submit a commentary, please review our guidelines and contact us.





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