California is in the middle of a math war, and the conflict couldn’t come at a worse time.

With respect to student performance in math, signs of trouble have been evident for years, but the problem has gotten worse since the pandemic. On the 2022 statewide CAASPP/Smarter Balanced tests, the percentage of students meeting or exceeding standards declined by 7 points in math from 40% to 33%. The results are even more dire for older children, with 29% of eighth graders and 27% of 11th graders meeting or exceeding standards. Beyond test scores, just 45% of the 2022 high school cohort completed the minimum requirements for entry into the UCs or CSUs.

And although the state has been pushing community colleges to eliminate remedial math courses that often result in students getting stuck and dropping out, it has not addressed the core problems: Too many California students lack proficiency in math.

Of course, California is not alone in facing problems such as these. States all across the nation are struggling to improve student math performance and to close performance gaps between advantaged and disadvantaged student groups. But there is no question that California leaders could be doing more to help schools and districts improve math instruction and achievement.

Last year, the state considered implementing a new math framework that would have changed the kinds of courses students can take to meet graduation requirements. That attempt met with fierce opposition from opponents who claimed it would result in a watering down of math standards. The dispute between the two sides has resulted in a stalemate, prompting state officials to hold off on adopting new standards.

While the decision to postpone may have made sense politically, from an educational standpoint it is contributing to the problem. The delay is especially problematic in its trickle-down effects on curriculum materials. The state hasn’t adopted new mathematics materials since 2014, almost a decade ago. The last adoption took place just a few years after California adopted its current math standards, in the early days of Common Core, when the number of quality materials on the market was much more limited than today.

It’s also important to note that California’s adoption list is only advisory. The state has chosen not to require or even encourage districts to adopt high-quality materials. As a result of this hands-off approach, even a quick perusal of school report cards shows that California schools and districts have adopted a dizzying array of materials, many of them poorly rated by curriculum experts (if they’ve adopted any materials at all). This decentralized approach to curriculum also contributes to poor quality supports for implementation like misaligned assessments and weak professional learning, because it forces each district to figure these things out for themselves.

In the absence of clear standards and high-quality instructional materials, California’s 1,000-plus school districts and charter schools are left with the task of figuring out what to do. This is burdensome for individual district leaders and teachers, and it results in too many kids having poor-quality materials to learn math.

We agree with the critics that watering down standards is unlikely to help move kids successfully through our K-12 system. However, the critics of the proposed math framework have not been helpful in addressing the bigger question of what should be done to improve math performance.

The only path through this mess is with leadership from the state. Both the California Department of Education and State Board of Education have a responsibility to provide a clear vision of what districts should do to offer a high-quality mathematics education, and they must stand behind it. If the state believes that its version of the framework will lead to better math education for California students, it should point to the research and move forward with the framework.

But the state can’t just stop at offering a framework, yet again leaving the work of interpretation and implementation to local leaders and educators who are already overwhelmed in addressing the needs of students post-Covid.

Supporting educators to implement the framework starts with adopting quality curriculum materials, and California should follow other states in strengthening guidance for these materials. Ensuring every child has access to standards-aligned material is not a blue-state issue or a red-state issue; it’s the bare minimum that a state can do to ensure opportunity for children.

It also eases the burden of standards implementation for teachers. Teachers want quality materials, even if they may not want a script for teaching. But beyond quality curriculum materials, the state needs to develop a coherent strategy for supporting professional learning and assessments that reinforce the quality materials, rather than undermine them.

We understand that leading during periods of controversy is not easy, especially given the polarization across the country. However, we must try to make education a nonpartisan issue, and we can begin doing this in math by relying on good research to inform policy decisions.

•••

**Pedro Noguera** is the Emory and Joyce Stoops Dean of the Rossier School of Education at USC. **Morgan Polikoff** is an associate professor of education policy at Rossier.

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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LogicalParent4 months ago4 months agoGIVENS: https://worldpopulationreview.com/country-rankings/pisa-scores-by-country https://wallethub.com/edu/e/states-with-the-best-schools/5335 https://edsource.org/updates/stem-professionals-and-professors-slam-californias-proposed-math-framework When it comes to California public education, it really needs systematic reforms. It needs to do an analysis of what works vs. what does not work by working with external California school districts that are successful and high ranking. It also needs some non-biased reviews and testing of math books, teaching material, and exams to determine what really works if they really care of about their students. Some parents had issues with the books and homework … Read More

GIVENS:

https://worldpopulationreview.com/country-rankings/pisa-scores-by-country

https://wallethub.com/edu/e/states-with-the-best-schools/5335

https://edsource.org/updates/stem-professionals-and-professors-slam-californias-proposed-math-framework

When it comes to California public education, it really needs systematic reforms.

It needs to do an analysis of what works vs. what does not work by working with external California school districts that are successful and high ranking. It also needs some non-biased reviews and testing of math books, teaching material, and exams to determine what really works if they really care of about their students.

Some parents had issues with the books and homework being difficult for kids to understand, which is wrong. The sad thing was the fact some parents had problems helping their kids with their homework. Some of the maths books I had examined are too wordy and have poor examples and some wrong answers. The only reason why the books cost so much was the fact they had too many pages of non-important material. I got the impression some reviewers were not doing their jobs in screening the books used for the teaching math. Maybe they were too busy being wined and dined by the book publishers, instead of looking out for the students.

For my daughter, I ended supplementing her math studies by purchasing some math books here: https://www.singaporemath.com/

Marshall Gordon4 months ago4 months agoResponse to Professors Noguara and Polikoff “Ending California’s Math Wars” The concern of Professors Noguara and Polikoff extends to mathematics being taught nationally. For, in essence, the traditional presentation format of mathematics that reflects the dedication of mathematics to being concise can be seen to share responsibility for the difficultly many students have in learning mathematics. That is, paradoxically it is the efficiency of demonstrations that can be seen as a source of the confusion. With … Read More

Response to Professors Noguara and Polikoff “Ending California’s Math Wars”

The concern of Professors Noguara and Polikoff extends to mathematics being taught nationally. For, in essence, the traditional presentation format of mathematics that reflects the dedication of mathematics to being concise can be seen to share responsibility for the difficultly many students have in learning mathematics. That is, paradoxically it is the efficiency of demonstrations that can be seen as a source of the confusion.

With traditional mathematics textbooks presenting algorithms and procedures and proofs without much if any discussion regarding how they came to be formulated, students often think it is their shortcoming in understanding, and the best they can do is to memorize the material. A further consequence is that students do not gain much experience as how to engage problems that require other than standard procedures.

Toward promoting their greater facility and understanding when engaging mathematics, Polya demonstrated how essential heuristics is to the development of mathematical understanding, defining it as the “the study of means and methods of problem solving” (1962, p.vi). It has proven very valuable to helping students make sense of mathematics as it can often be uncovered behind the formal demonstration of problem-solving procedures and proofs they are presented with. To help support students’ development in becoming more mathematically capable it is important to first acknowledge their concerns regarding difficulties they have had trying to understand as being legitimate. By making clear the confusions they have had can be seen to be a consequence of the formal presentation and not a reflection of their inability, they become more inclined to share their confusion and gain confidence in the process. The goal is for them to come to understand that “confusion is the foothills to the mountain of understanding” – a phrase shared with them by this author on a regular basis.

For example, sharing with students why the solution procedure of “invert and multiply” when dividing by a fraction actually makes sense; why the slope of a line is represented by m although it begins with s; and why it is found by taking the change in y over change in x and not the reciprocal; and how did anyone know that 360o filled a circle, helps them realize that their concerns are legitimate, and their confusion a realistic response to mathematical presentations absent of considerations regarding how such decisions, practices, and proofs came to be.

When faced with challenging mathematics problems, it would help students to think of their having “productive struggles”, which Hiebert and Grouws (2007) describe as expending “effort to make sense of mathematics, to figure something out that is not immediately apparent” (p. 387).

NCTM (2014) supports students seeing “struggles” as “opportunities for delving deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions” (p. 48). Also, considering problem solving from a problem-clarifying strategy (heuristic) framework can promote a greater willingness to think beyond the memorization of formulas and problem-solving techniques so as to promote a resiliency and dedication for engaging challenging problems.

That is, including the language of heuristics, such as tinkering, taking things apart, describing, reasoning by analogy, generalizing, choosing simpler numbers, etc., enables students to gain productive means working with confusing problems. However, what Polya pointed out decades ago still seems to be the case: “heuristics has not been given the focus it deserves, and so teachers of mathematics have not been educated in a systematic approach to heuristics” (1962, p.viii). Namely, the language of demonstration in mathematics textbooks tends to exclude heuristics, the language of investigation, and is at a distance from the language mathematics educators use to describe the content.

That is, what is shared with students in textbooks and classrooms tends to be the products of inquiry, while the inquiry process which provides the essential development is absent from the presentation.

Marshall Gordon

Mathematics educator for over 50 years who has taught mathematics in high school and college, and prospective and practicing mathematics educators.

A Concerned Parent4 months ago4 months agoThis article makes some important points and misses others. There is a lot of great information in some of these comments that gets at some of what is missed by the authors. It is true that we shouldn't politicize education. It is also true that in our current climate of extreme polarization that it is nearly impossible for education not to become politicized. We must therefore proceed with the understanding that compromise and a … Read More

This article makes some important points and misses others. There is a lot of great information in some of these comments that gets at some of what is missed by the authors.

It is true that we shouldn’t politicize education. It is also true that in our current climate of extreme polarization that it is nearly impossible for education not to become politicized. We must therefore proceed with the understanding that compromise and a willingness to listen with an open mind and consider opposing thinking will be necessary to achieve the desired outcome of enabling all of California’s students to succeed at the highest levels of mathematics with the greatest degree of success in our TK-12 education system.

Re: “If the state believes that its version of the framework will lead to better math education for California students, it should point to the research and move forward with the framework.” Let me add that the state should also be forced to speak to the *quality* of the research it is citing. This has been a huge issue in the current version of the framework. Aside from outright citation misrepresentation (see the work of Brian Conrad Public Comment #2 Citation Misrepresentation for more on that), it should be openly recognized that not all published research studies are created equal. The state should set parameters and give guidance to future framework authors in all content areas about how to ensure we are citing reputable well-crafted studies that are published in rigorous journals (and not just pseudo-academic journals that are essentially only part of the public relations apparatus of special interest groups like the National Council of Teachers of Mathematics).

There should be a website that will tell any member of the public about the relative quality of a study or journal. Think of it, wouldn’t it be fantastic if there was an independent website like charity navigator that would evaluate the quality of academic journals and research studies that we are citing in any curriculum framerwork?

There is plenty of non-controversial solid/extensive research/evidence (some of which is mentioned in other comments) that we should be looking at in California. How a 900+ page document about teaching and learning math does not mention retrieval practice even one time is as astonishing as it is disappointing. But aIso, it is simultaneously unsurprising – just look at how long the brain science was ignored in reading in CA (and nationwide). The ignorance is often not because of malice or even political machinations, but it does often represent a further disappointing intellectual decadence that allows so many to ignore so much of what is so obvious if only we will take the time to look. And in the end is is the students and teachers that suffer. Just ask any cognitive scientist and they will agree -just like in reading there is clear evidence about how the brain learns math and we should be following it.

As the authors start to get at -in order to achieve truly equitable outcomes we need to make more explicit and transparent “what good looks like” for teaching and learning mathematics in CA. We should also recognize the tremendous load that educators carry in our state. Teachers have a lot on their plates! It is the toughest of professions -as every parent trying to be a teacher to their children during the pandemic learned at a visceral level.

We should honor and recognize the heroic work that so many teachers do day in and day out. However, we should also acknowledge that teacher quality varies and that even if every educator had access to the best professional learning and the highest quality curriculum – whether or not that curriculum is used at all or with any semblance of fidelity will vary widely.

SFUSD Math Teacher4 months ago4 months agoThank you for your article. You state: "We agree with the critics that watering down standards is unlikely to help move kids successfully through our K-12 system. However, the critics of the proposed math framework have not been helpful in addressing the bigger question of what should be done to improve math performance." I believe this to be a false dichotomy. I agree with the first sentence, but not the last. There is a real, science-backed … Read More

Thank you for your article. You state:

“We agree with the critics that watering down standards is unlikely to help move kids successfully through our K-12 system. However, the critics of the proposed math framework have not been helpful in addressing the bigger question of what should be done to improve math performance.”

I believe this to be a false dichotomy. I agree with the first sentence, but not the last. There is a real, science-backed mathematics pedagogy, based on decades of statistically valid and appropriately designed studies. Please consider reading: “The Value of Direct Instruction for At-Risk Students,” Journal of Education and Development; Vol. 4, No. 2; August 2020, and “Putting Students on the Path to Learning: The Case for Fully Guided Instruction” for its impeccable citations.

We need to start training our teachers that an adaptive mix of direct instruction and group-centered approaches, along with

a lotof practice, are necessary for optimal mathematics learning. Right now, in CA, at least, teachers are being trained only in group learning (“discovery learning,” “project-based learning,” etc., etc. ad nausea), dubious allegiance to the arts of practice and memorizing, and that explicit instruction is bad, despite a paucity of valid research supporting these teaching methods. There has been a drastic policy change from past practice (it started about 15 years ago) towards these methods, and by all appearances it seems to have negatively affected CA’s student math outcomes, as measured by the NAEP and the Smarter Balanced Test.So, the critics of the CA Framework already have and have had a way forward, and it’s driven by actual, valid research. The writers of the CA Framework, notably, Dr. Jo Boaler from Stanford, do not have this kind of research to support their ideologically-driven methodologies. And it’s about time, as academics, for us to start gathering the valid studies, ignoring the invalid studies, and letting reason guide our policy choices, no?

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SDUSD Parent4 months ago4 months agoThis comment is so incredibly salient. I hope the state board of education takes note. As a parent, I want my children to be taught mathematics via an evidence-based approach and not a philosophy-based approach. We need not be subjected to a false dichotomy that ignores the plethora of research around how children (children that are novices and not experts!) learn. We should also take note at the reckoning that is … Read More

This comment is so incredibly salient. I hope the state board of education takes note. As a parent, I want my children to be taught mathematics via an evidence-based approach and not a philosophy-based approach. We need not be subjected to a false dichotomy that ignores the plethora of research around how children (children that are novices and not experts!) learn.

We should also take note at the reckoning that is continuing to unfold nationwide (and here at home in California) around the Science of Reading. We should not allow the same thing to happen again in math. We know so much more than we did 20 years ago about how the brain works and what it takes to move information from our working memory into our neocortex and long-term memory. Another great resource with quality citations comes from a group of cognitive scientists that are trying to take up the angle of the Science of Math (as a direct nod to all the attention the Science of Reading reckoning has garnered). Their website is an excellent resource: https://www.thescienceofmath.com/

Rick Nelson4 months ago4 months agoThe authors of this article are advocating buying textbooks to support math standards that science says do not work. Doing so will hurt children. Before you write about math education, I would recommend you learn what science says about working memory limits and automaticity. The science explains why students need both phonics in reading and flashcards to master math facts. See the collection of peer-reviewed science on these topics at https://bit.ly/3V7xCMc … Read More

The authors of this article are advocating buying textbooks to support math standards that science says do not work. Doing so will hurt children. Before you write about math education, I would recommend you learn what science says about working memory limits and automaticity. The science explains why students need both phonics in reading and flashcards to master math facts. See the collection of peer-reviewed science on these topics at https://bit.ly/3V7xCMc . To avoid giving harmful education advice, learn the science of learning.

Robert L Crawford4 months ago4 months agoHigh School students should be required to take 4 years of mathematics and should have to pass a test to graduate in math, English, history, and science. Raise the standards and get kids off calculators and hire more mathematicians to help reach these standards like they do in other countries. Stop allowing whiny kids dictate how much math they should take.

Lois4 months ago4 months agoI feel when they changed the math to common core math is where they went wrong. All kids aren't geniuses. Sure there's nothing wrong with challenging the minds of children. But I think core math should be given to children with high IQs and basic math for children with lower or average IQs. I am a grandmother of 11 grandchildren; all but 1 who has a high IQ understands and mastered that core math. … Read More

I feel when they changed the math to common core math is where they went wrong.

All kids aren’t geniuses. Sure there’s nothing wrong with challenging the minds of children. But I think core math should be given to children with high IQs and basic math for children with lower or average IQs. I am a grandmother of 11 grandchildren; all but 1 who has a high IQ understands and mastered that core math. I can’t help any of my grandchildren with their math. Math was one of my favorite subjects in school. I excelled in Math when it was basic. It doesn’t make since when parents have to spend extra money and go get a college courses just to learn something that you guys made too difficult for even so parents to understand.

They need to go back to basic math when Lord knows they will never use core math in the real world. It take the knowledge of basic math to count money. When we teach our babies how to count or even teach them times tables, it’s basic math process. So to steer from that is just crazy. Whoever made or came up with core math was drunk and on drugs. That’s my opinion.

SD Parent4 months ago4 months agoI agree that leaving this as a stalemate is a problem: it allows school districts to leave students languishing instead of learning. But I worry about "education leaders" drawing erroneous "conclusions" from "data." There are definitely some "education leaders" who point to "data" and draw "conclusions" that cannot be supported. Take for example San Francisco Unified, where they slowed the math course pacing, de-tracked advanced students and those needing more support into the same … Read More

I agree that leaving this as a stalemate is a problem: it allows school districts to leave students languishing instead of learning. But I worry about “education leaders” drawing erroneous “conclusions” from “data.”

There are definitely some “education leaders” who point to “data” and draw “conclusions” that cannot be supported. Take for example San Francisco Unified, where they slowed the math course pacing, de-tracked advanced students and those needing more support into the same classes, and provided educators with professional development in math – and then claimed success and concluded that all these changes were the holy grail. Not only was the “success” disputed (it has been discussed in depth elsewhere), but even if you could believe that the results were positive, which of the three changes made resulted in that purported success?

It’s clear that these “education leaders” do not understand how to test a hypothesis. Any scientist will tell you that you need controls and can only introduce a single variable to determine that the results seen are due to that change. Controversial changes like slowing pacing and de-tracking students need to be fully tested (individually) and proven to improve student outcomes before the state should adopt either. And that has just not been done.

I also suspect that most K-12 educators also do not, themselves, have a good grasp of math facts and concepts and so are unable to teach the subject well. I suspect this is especially true for elementary school teachers, and if a student’s math foundation is built on shaky ground, it’s no wonder students struggle with higher math. If there is professional development in Math that has been proven to improve instruction and student outcomes, that would be the most beneficial approach.

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Maya K4 months ago4 months agoI'm a San Francisco parent (my children are district alumni now but straddled this curriculum change). The public relations around what SF did was a master's class in misrepresentation. SF did not track previously, most everyone (district students) took algebra 1 in 8th as was the state policy. Then post common core nobody took algebra 1 in 8th grade. They made nonsensical claims that should have been red flags if one understood basic math. When they … Read More

I’m a San Francisco parent (my children are district alumni now but straddled this curriculum change). The public relations around what SF did was a master’s class in misrepresentation.

SF did not track previously, most everyone (district students) took algebra 1 in 8th as was the state policy. Then post common core nobody took algebra 1 in 8th grade.

They made nonsensical claims that should have been red flags if one understood basic math. When they said 40% of the class of 2018 had to repeat Algebra 1 in 9th grade but the next year? After delaying Algebra 1 to 9th grade, the repeat rate dropped dramatically to 7%? What?? This sounds fantastical when one stops to really think what these percentages represent. And surprise! It wasn’t true. Yet? This was all breathlessly reported everywhere without anybody asking to see evidence.

The house of cards collapsed when CPRA showed that 100 students of the class of 2018, last group taking algebra 1 in 8th, failed in 8th grade. That is 4%. But there used to be an exit exam students had to pass even if they got an A, in order to take Geometry. Even then the 40% is not reproducible from the CPRA data received, it was more like 27.5%. No matter how many times one asks to see how this 40% was calculated? Nope. Just keep insisting without showing one’s work.

How does a claim like this not raise red flags? They got away with it because local papers were stenographers instead of doing any investigation.

Then came the bizarre claim that delaying math increased advanced math. This isn’t the tortoise and the hare fable. How is this possible? In their slide decks nationwide they did say they were counting post Algebra 2 as Advanced Math. Fair enough, UC does that.

However?? They called their compression class Algebra 2 + Precalculus, it was created for 11th graders to take so they could reach calculus. The only problem? It doesn’t meet precalculus standards and UC categorizes it as Algebra 2. There goes the advanced math gains.

So, no, no advanced math gains. No magic success in Algebra 1. Meanwhile students taking the homemade compression course are graduating thinking they took precalculus when they didn’t. Why the district is allowed to put misinformation like this on official transcripts is another problem with the state not having some basic regulations.

San Francisco Unified caused a lot of damage with their misleading claims, but the math education community as a whole which just took this all at face value played a role here too.

This was a classic shell game and the state almost followed SF. 8.5 years later? This is still going on and I don’t know if there is any end in sight. I hope so.

To read more about this with CPRA data included here is the report that exposed the con: https://static1.squarespace.com/static/60412a3a51d4863950d1bdf2/t/616e2f823696906267609f3f/1634611077888/Report-+Inequity+in+Numbers.pdf

Jim4 months ago4 months ago"Ensuring every child has access to a standards-aligned material is not a blue state issue or a red state issue" Of course it is. "Standards" are created by people who have certain agendas. "Whole language" was a standard at one time. Many of us knew it just an attempt by a few professors to create a reputation by sabotaging children's learning. "While the decision to postpone may have made sense politically, from an educational standpoint … Read More

“Ensuring every child has access to a standards-aligned material is not a blue state issue or a red state issue” Of course it is. “Standards” are created by people who have certain agendas. “Whole language” was a standard at one time. Many of us knew it just an attempt by a few professors to create a reputation by sabotaging children’s learning.

“While the decision to postpone may have made sense politically, from an educational standpoint it is contributing to the problem.” Does this mean the authors endorse the “war on algebra”? None of this touches on the current conflict over math tracking.

Who can argue against “quality” or “high-quality” instructional materials? “Point to the research” – point to what research? There is a woman at Stanford who points to her own research. Do the authors really think everyone is agreed on what the “research” says?

Suan Lee5 months ago5 months agoOne of the things that is missing in todays debate regarding math education is teachers competence in the subject itself. Many high school math teachers lack the necessary depth of knowledge of mathematics. This results in a teaching environment whereby students are taught on the "how" of mathematical algorithm without the needed "why" such algorithm works. Unless the state solve the problem on the "teacher quality", mathematics education will continue its decline. Read More

One of the things that is missing in todays debate regarding math education is teachers competence in the subject itself. Many high school math teachers lack the necessary depth of knowledge of mathematics. This results in a teaching environment whereby students are taught on the “how” of mathematical algorithm without the needed “why” such algorithm works. Unless the state solve the problem on the “teacher quality”, mathematics education will continue its decline.