Palo Alto and Stanford communities: please do some research on how US K-12 math has been tragically misguided. The perennial math-science death march catastrophe on our youths caused by Stanford's educational school people can overwhelm the stellar contributions by all scholars from all other disciplines.
Some background information:
1. Getting rid of Algebra 2: Web Link Web Link
2. Some opinions:
Web Link
Web Link
Web Link

In China, algebra & calculus are taught in the traditional manner and it is not uncommon for grade schoolers immigrating to the United States with their parents to be sufficiently grounded in the fundamentals of mathematics.

As a result, AP coursework on the high school level often provides those students the minimal of challenges in this area of coursework.

Some American universities (e.g. Stanford University) tend to be very innovative when it comes to teaching complex math but it can also as you say, "come back to bite you in the ass."

There is no such thing as 'new math'. Mathematics is mathematics and there are no shortcuts.

This is a primary reason why many American students remain inept in this area and why a sizable number will never fulfill their lofty aspirations of entering the medical and/or science fields where a fundamental grounding in math is required during the first two years of college.

My son goes to UC Davis and everyone there says they are 'pre-med' students. Big joke as the Chemistry 1, Physics 2 & Organic Chemistry 8 series eliminates 50-60% of these pipe dreamers and there is always Liberal Arts to eventually major in.

That is why you see so many Chinese and East Indian physicians nowadays at the various medical clinics and hospitals. They were better prepared in the preliminary stages of their education and professional aspirations.

PAUSD is hiring the most destructive math reformist to reimagine middle school math.
Folks, please use your imaginations about the outcome...

From PAUSD website:
REIMAGINING MIDDLE SCHOOL MATHEMATICS
Since the Superintendent’s weekly communication with the Board and larger community on October 11, 2019, a team of staff from all three middle schools and the District Office have been engaging in a reimagination of the middle school math program. The team has been meeting weekly and working through the multiple elements required to evaluate the current status of the program and create a plan for moving forward that improves the experiences and outcomes for all students.
This task is complex and involves analyzing performance data, researching best practices, determining metrics for evaluation, looking at models from other districts, etc. Several experts in the field of education are supporting the work of the team through consultations. Jo Boaler, the Nomellini-Olivier Professor of Mathematics Education at Stanford University and faculty director of youcubed, has provided insight about mathematics instruction in the 21st century and will continue to provide support to the team as it relates to the way in which mathematics instruction is delivered. Linda Darling Hammond, President of the California State Board of Education and founder of the Stanford Center for Opportunity Policy in Education, has been consulted on her work in the state to identify positive outliers in closing achievement gaps and for her expertise on designing equity-focused programs. Finally, David Foster, Executive Director of the Silicon Valley Mathematics Initiative (SVMI), will be providing guidance to the team related to performance-based assessment that helps students and teachers better understand the thought process used to solve complex problems and identify where students have misconceptions.

>> Stanford, shame on you for indulging your faculty in ruining our children and our nation!

Remind me where there is a statistically valid comparison of achievement levels across the entire age group of school age kids. I've seen complaints like this since the 1960's, but, the problem is that if only 2% of 18-year-olds in a particular country are going to a (vague term) "college prep" school, then, it isn't surprising if all 2% show high achievement levels on Calculus. IMHO, this kind of test result comparison is meaningless -at best- if it doesn't have matching populations to compare.

I'm not saying math education in the US is great. I just want to see statistically valid comparisons.

@Anon, please read this: Web Link
A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

On another question, more than three-quarters of South Korean kids answered correctly. Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

For large scale data, please go to Nation's Report Cards or TIMSS data (PISA is not a good measure for math competence).

The very top American students are fine as they basically are self-taught. Top and upper students get supports from parents or tutors. The bottom--mostly disadvantaged students--have been tragically cheated and deprived by the "feel-good" math. Middle-range students are also short-changed.

Though touted as offering deeper thinking and conceptual understanding, the math currently taught in most schools and advocated by math reformers is "pretend algebra" and "rote understanding."

Coming from an education or psychology background and not knowing much real math, those math reformers have nearly ruined US K-12 math. In fact, algebra 1 or even algebra 2 (by current American standards) is really not difficult if one follows steadily the traditional approach.

I've spent three years researching US K-12 math and read countless papers and articles. I have never seen as many lies and fallacies anywhere as I have in American K-12 math education.

@See Sth Say Sth - The sad thing is that the decline of traditional math ends up contributing to the achievement gap. Wealthy parents send their kids to Kumon, tutors, or Chinese school in the afternoons to learn real math, while Tinsley kids ride the bus home. You can pretend that multiplication tables and long division for a while, but around middle school, reality comes home to roost. The kids who got supplemented are ready for algebra, and the kids who spent years in their math classes playing with blocks and strings on the floor like pre schoolers are screwed. The poor math education deprives a generation low income students of a chance at upward mobility.

>> For large scale data, please go to Nation's Report Cards or TIMSS data (PISA is not a good measure for math competence).

Do have a link (or a link to a page of links -- this site doesn't like too many links in a post)? I have looked at PISA in the past and what I saw was embarrassing-- ranking entities, such as countries, with wildly different populations taking the test.

Singapore is an interesting data point. Anyone know if there is anything at stake wrt the test results? If high scores are used as placement tests for special schools, for example, then there might be both tutoring-to-the-test and cheating that could bias the results. I'm NOT saying that US math education is good-- it isn't generally. But, I'm wary of test results that can be biased so many ways. As I said, Singapore is interesting, because I'm guessing that the student population taking the tests is well-defined, which is almost impossible across the US where education is a state and local responsibility.

See Sth Say Sth is right on. When my average IQ kids went to school in Palo Alto (about 20 years ago for middle school) it was the same thing...they called it "new math" back then. I made them memorize the 'times table', and made sure they could solve simple 'solve for X' problems...they could easily solve that length of wood problem in 8th grade...but few, if any of their friends could. PAUSD is employing a politically correct approach to cover for the so-called achievement gap between Asians/Whites and some minorities. I no longer vote for any bond issues...that is the way to send a message.

People who are interested in PAUSD math curriculum should come to this Tuesday's Board meeting (12/10/2019). Below is the math proposal.

Web Link

It includes another series of arbitrary placement practices rather than competent evaluation of knowledge with the NWEA MAP testing (which they are now dropping).

Web Link

"For years, despite the tremendous efforts by our hard-working teachers and administrators, PAUSD has been plagued by its students' alarming achievement disparties."

And the parents? It takes more than teachers and administrators. If parents don't take their kids education seriously, then the results are predictable. Students whose parents value education have a head start, and are far less likely to be underachievers.

What are the alarming disparities to which you refer?

"The Stanford Graduate School of Education is a hub for producing, promoting and propelling those crazy math education doctrines and methods in PAUSD and across the nation, for years and decades!"

If they don't know what they are talking about, then why do people listen to them?

"When my average IQ kids went to school in Palo Alto (about 20 years ago for middle school) it was the same thing...they called it "new math" back then."

Oh God, that moronic nonsense. Whatever genius came up with that bright idea should have been drawn and quartered, and the pieces fed to the piranhas. I was one of the victims of New Math when it first reared its ugly head in the 1960s. I later managed to become proficient at math, but not without a lot of extra effort. That and a middle school teacher who turned her class into a remedial course. I still remember the shocked, thoroughly disgusted look on her face when she discovered we lacked basic math skills. Thank god she was old school.

@ Kenny: It won't end until the money to support it ends! Don't vote for any future school bonds … until the nonsense ends. THEN support school bonds!

The members of the Board of Education are elected. Presumably, a mechanism exists by which they can be recalled. Wouldn't recalls, or at least an attempt to so, be the best way to stop this misguided experiment? Or maybe I am wrong and voting against bond measures would be more effective.

Paused sees fluency in numbers as punishment. Also this is the only thing they test for. Kids who practice are moved ahead.

Teachers do not correct math or respond to mistakes in real time. They correct tests but feedback is so slow the patterns of any mistakes are not understood

Elementary teachers do not have solid math foundation or understanding if higher math and get stuck in low level rubrics that lthey cling to instead of being able to respond to mixed levels. Every kid on the same page with low expectations and the s strange attitude that being proficient with hard work Somehow deserves animosity toward families that Value and practice a strong work ethic and success permeates all the pause curriculum.
However , the hs staff lives to pose by kids winning math awards that worked hard with outside help they paid for and their family supported them with.

Parents should turn to Russian school of math in Cupertino. With Waac approved excellent teaching staff that will not let kids fail and are not afraid of supported high expectations. I hated to take the extra time , but if my kids just depended on pausd math , they would be 4 years behind the rest of the world. The interesting thing about the higher expectations and standards they practiced with feedback in detail was a feeling of confidence in the higher math and a keen sense of mastery in other subjects.

Re: "They could never conquer Algebra 2 with their destructive reformist approach; hence, they resolute to annihilate it." -- perhaps they have not conquered Algebra 2, but apparently they have succeeded in destroying your ability to write a grammatically correct sentence.

"perhaps they have not conquered Algebra 2, but apparently they have succeeded in destroying your ability to write a grammatically correct sentence."

Undoubtedly the the result of being taught New English.

@Random Resident
Thank you for your critique. I welcome any help with correcting my writing. I am learning English every day in order to be able to write about U.S. K-12 math.

@Random Resident @Kenny
Thank you! I just searched that "resolute" is not a verb; "resolve" is the one.

The Stanford math reformist's “Vive la révolution” viewpoints on K-12 math:

Research has recently shown something stunning—when students make a mistake in math, their brain grows, synapses fire, and connections are made; when they do the work correctly, there is no brain growth. This finding suggests that we want students to make mistakes in math class and that students should not view mistakes as learning failures but as learning achievements. Students do not, as many assume, need to revisit a mistake and correct it to experience brain growth, although that is always helpful.

Instead of classrooms filled with short questions students are intended to get right or wrong, mathematics classrooms need to be filled with open-ended tasks that include space for learning as well as space for struggle and growth.

Teachers always know how well kids are doing, so you really don't need to test them. You really easily have teachers write down what kids know and can do. The kids themselves can also self-assess and tell if things are strong or not. They do that with extreme reliability. You can ask kids make a project, if you want, that tells us about what they know and can do. And most tests used do not assess what's important anymore. They might assess whether you are computationally fast — but that's the one thing computers do and we don't need humans for.

It’s bad enough when students receive grades at the end of each unit or course that tell them how capable they are.

On a visit to England at the beginning of term, she said that in an ideal world she would ban times tables tests.

“When we assign homework to students, we provide barriers to the students who need our support,” Boaler wrote, “This fact, alone, makes homework indefensible to me.”
She suggests that teachers and school leaders who want to promote equity by eradicating homework arm themselves with resources like “The Case Against Homework” by Alfie Kohn and “The One World School House” by Sal Khan, which reinforce these conclusions.
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Please visit Web Link to learn more about the reformist's advocacy for detracking, removing algebra 1 from middle schools, replacing algebra 2 with data science, visal math, finger math, number talk and so on.

Counter opinions from Ze'ev Wurman and others are also listed.

"The only way I can, after all those many years, explain to myself what is going on is that all those educationists [...] don't really care about education, and they don't actually believe in the importance of education. The reliance on Rousseau and educational romanticism is, in my opinion, largely fake. What they really are after is equality -- equality of outcomes."

"Somehow they believe that the world progresses on its own by the armies of mediocrity..."

Terrifying. I'm so glad I can afford to send my kids to private schools, and I feel so sorry for talented kids trapped in public schools, who will be forever hobbled by these people.

Since this issue is now getting attention at the district level, I hope that someone is able to raise the issue of regarding the level of mathematical achievement of the teachers. PAUSD teachers appear to be lagging in math achievement, so, it isn't likely that any change of textbooks and lesson plans will be able to fix the lagging performance.

From a former district parent: “Keep It Simple” is my advice.
These wild kooky swings in Math curriculum do not serve anyone. Yes, I know, the kooky State of CA sets some rules, however vague or oddball.
I like direct instruction, with high quality textbooks, regular homework, quizzes, tests . Have occasional special topics. Offer support as needed but encourage students to pay attention, learn, work through challenges. I like teachers worthy of respect - and they should respect students, too.
Discourage cheating Tiger Moms paying for outside tutoring to lead their Tiger Cubs ahead.
Otherwise, complete a body of work by moving positively and actively through a solid curriculum. This leads to accomplishment. PAUSD should have strong mainstream curriculum.
I have a kid who did first grade in a basic religious school (only there for that school year) that had an excellent Math text. This kid ended up highly accomplished in Math (can’t say more, to protect privacy). We did not do sly paid tutoring or etc.
A strong basic foundation should not require “rocket science!’ It’s common sense! Fads, excuses, spirals....yuck.
Varying expectations for students and/or grades and vagueness do not equate to accomplishment. They sound like pandering to special interests. Be FAIR.

"A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?"

I want to know who contrives these silly "math problems." Who is ever going to cut up a piece of wood, or anything else, using a whacky prescription like this one? And why would anybody propose to waste our students' time on this nonsense, when that time could be productively used for education?

The truly smart students will see through the sham and be turned off by this nonsense that is being presented as math.

@Curmudgeon: I commonly used multi-variable algebra, trig and some optimization calculus in my daily business (and to solve carpentry problems). Don't know where you have been, and what problems you got wrong (and cost you too much money). Beyond all the practical stuff, a solid foundation in math sharpens the mind to make more acute decisions. We should stop cheating our kids in PA schools with watered down curriculum. It won't change until we stop paying for the lowest common denominator!

The foundation of math is to be able to solve problems quickly. Such "automatic" or "muscle memory" allows the brain to soar through problems and data. The same is true of tennis or a musical instrument: rote practice until one no longer hears notes, but rather muscular expessions of chords.

Understanding follows from fluency, not the reverse.

How I Rewired My Brain to Become Fluent in Math: Web Link

Oh, and please please understand that the being able to think in matrices (as geometric operators on space) is fundamental to all higher math. To get there, you have to go through Algebra 2 and beyond.

You can delane, but all must drill, test, repeat until fluent. And almost all students can get there. It will be life changing for them.

Posted by Gary Bradski, a resident of Greenmeadow

>> Understanding follows from fluency, not the reverse.

To my knowledge, procedural fluency and conceptual understanding go hand in hand and build on each other. Citations to various papers here:

e.g. Web Link

Either way, mastery of a subject starts with a student who wants to learn and a teacher who has sufficient subject matter expertise to teach.

BTW, Testing Conceptual Understanding - sometimes now referred to as TCU, is a difficult subject in itself.

Excerpt from: Web Link

A recent New York Times commentary by American engineering professor Barbara Oakley has, once again, stirred up much public debate focused on the critical need for “Math practice” and why current “Discovery Math” methodologies are hurting students, and especially girls. “You and your daughter can have fun throwing eggs off a building and making paper-mache volcanoes, “ she wrote, “but the only way to create a full set of options for her in STEM is to ensure that she has a solid foundation in math.” Mathematics is “the language of science, engineering and technology,” Oakley reminded us. And like any language, she claimed, it is “best acquired through lengthy, in-depth practice.”

That widely-circulated commentary was merely the latest in a series of academic articles, policy papers, and education blog posts to take issue with the prevailing ideology in North American Mathematics education, championed by Professor Jo Boaler of Stanford University’s School of Education and her disciples. Teaching the basics, explicit instruction, and deliberate practice are all, in Boaler’s view, examples of “bad math education” that contribute to “hating Math” among children and “Math phobia” among the populace. Her theories, promulgated in books and on the “YouCubed” education website, make the case that teaching the times tables and practicing “multiplication” are detrimental, discovering math through experimentation is vital, and making mistakes is part of learning the subject.

Boaler: "There are also political undercurrents to keeping the system as it is now - some people don’t want teaching to be more equitable. They do not want to open the doors to everyone. " “My main point is that it may not be enough, as a math teacher, to treat students equally in the pursuit of equity...Some students face additional barriers and disadvantages, and we must work to address those quite deliberately if we are to achieve a more equitable society.”

Barry Simon (CalTech): "If anyone is racist or sexist, it is those who claim that women and minorities are unable to deal with traditional mathematics."

Reform math churned out of Stanford GSE damages students' math ability like a mass-destructive weapon.