Palo Alto High School Math Teachers: Some Of Our Students Objectively Can’t Learn Algebra

Last April, fourteen of Palo Alto High School’s twenty math teachers petitioned their school board [pdf] against raising graduation requirements to include Algebra II:

We live in an affluent community. Most of our students are fortunate to come from families where education matters and parents have the means and will to support and guide their children in tandem with us, their teachers. Not all of them. [..] We are concerned about the others who, for reasons that are often objective (poor math background, lack of support at home, low retention rate, lack of maturity, etc) can’t pass our Algebra II regular lane course. Many of these are [Voluntary Transfer Program] students or under-represented minorities.

Since those students objectively can’t pass Algebra II, the next appropriate step is to compile a list of those students and prevent their enrollment in Algebra II in the first place. Otherwise, you’re putting them in a position to care about passing a class we can be objectively certain they will fail. If I were a parent of one of those students, this determinism would probably drive me out of my mind.

The signatories are Radu Toma, Suzanne Antink, Kathy Bowers, Judy Choy, Arne Lim, Deanna Chute, Natalie Simison, Misha Stempel, Maria Rao, Charlotte Harris, Scott Friedland, Lisa Kim, Ambika Nangia, and David Baker.

Featured Comment

Jason Buell:

Their hearts I think were in the right places but they whiffed badly. The point isn’t can every kid take Alg 2, but should they.

2012 Jan 16: Coverage from the San Jose Mercury News.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Wow. I know algebra can be very hard for some people, but isn’t this what teachers are for? They’re there to help students learn, aren’t they? I feel like these teachers have just given up on (some of) the students. I don’t believe anyone is unable to learn a given subject.

  2. What do they mean by “diluting the standards?”

    Also, I don’t think that these teachers are thinking long-term: less math now, means more math at the collegiate level, where everything is twice as fast. I have friends who didn’t take Algebra II and were forced to take an Intermediate Algebra class (college’s Algebra II) before they could start any of the math requirement. A lot of them are struggling because they are learning a year’s worth of algebra in only a semester.

  3. I understand the shocked/appalled reaction to this letter (giving up on children! Gasp! For shame!) and lots of their word choices are unwise, but I can also sympathize with these teachers. NY requires 3 years of math, and if kids had to pass regents algebra 2 with trig to graduate, our graduation rate would go down. A tad dramatically, I’m afraid, to the tune of three sections of kids currently enrolled in non-regents trig. And it’s not that all these kids couldn’t learn this material under the right conditions, but it would never happen in the status quo of so very much content crammed into one year culminating in the most ridiculous state examination you have ever seen. In a nutshell, if our board of Ed declared all kids had to pass regents alg2/trig, I’m not sure our letter would read much different.

  4. @Kate, the resources Palo Alto could deploy on behalf of those underserved students is staggering. That’s the salt in the wound.

    @Riley, Algebra II is a requirement for admission to the University of California system. High schools are just taking their cues from the UC which, IMO, should drop the Algebra II requirements. It’s about as useful to liberal arts majors as 19th-century French literature is to me. If there’s any kind of causal relationship between Algebra II completion and success in higher education, I’m willing to change my mind. I haven’t seen any.

  5. I am in Michigan where we require 4 years of math, Alg2 being one of them — for ALL students including LD kids. Parents can do a “personalized curriculum” which deletes the Alg2 req ONLY after the kid tries it for a semester (and fails).

    Personally, I think Alg2 is a bit much for all kids, not just “those” kids. I think we should require personal finance (credit/debt, bank statements, budgets, etc.) MUCH before Alg2.

    Luckily, Michigan’s 4th year math class can be integrated, such as: Accounting, Programming, Construction, Personal Finance, etc. The problem though is that MANY schools are stretching the Alg2 requirement over two years (and counting it as 2 years — that part I really don’t get).

    I think we should have grade level entrance exams. — If you can’t pass, you can’t get in. Kids are merely socially promoted through so many grades. When they come to high school with 3rd grade reading and math levels, I think Alg2 will be a little hard no matter how great that Alg2 teacher is.

  6. Dan… In your opinion, what kind of math should students learn in school. Which branches for which students? That is, would every students study the same topics or ones specialized for their future career paths?

  7. I just read this and am appalled! I teach in NYC and I teach the 2-year algebra I track. These kids were quite weak when I first started with them last year but with enough hard work and determination between me and the kids, I feel that we’ve achieved so much. From not being able to solve a one-step equation, now they’re able to solve quadratics and trig problems! I truly do believe that given the chance, these kids can and will make it to Algebra II, and they will do well. I’ve worked too darn hard (and so have they) for someone to pre-determine their future that way. I know for a fact that my brother never made it to Algebra II in HS, he only completed Algebra I. In college he had to make the jump from Algebra I to Calculus (he was a business major), which by far, was the most difficult thing he has ever endured! I always feel a sense of responsibility to help my students keep as many ‘doors’ open as possible, just in case. Maybe I’m delusional …

  8. This is not a new argument. I’ve yet to be in a school system where I haven’t heard one version of this same rant or another. And I too can sympathize, having been that teacher in a room full of unmotivated, under-prepared, and apathetic high school seniors.

    But I don’t agree with the authors and I think, rather, that it is the Algebra 1 curriculum that needs the real overhaul and not the Algebra 2… and unfortunately (or fortunately), that falls to us. If students were more successfully motivated in a rich mathematical environment that explored real depths of algebra from the beginning, I don’t think it would seem so insurmountable later on.

    Keep up the good work Dan, and all the rest of you too. My classroom certainly is benefiting, and hopefully that means more students will be prepared to leap the hurdles as they approach them.

  9. We require Algebra II for our sophs to graduate in 2 years. I believe that a math literacy course would benefit a portion of students that are not calculus bound. There are ways to give students math knowledge that will help them more than Algebra II.

  10. @Kate – Amen. You said it better than I will be able to.

    @Dan – First, can we agree that Algebra 2 is a ridiculously difficult class to find proper motivations for (it is comparitively easier to find “3 Act” topics of conversation for Alg1, Geom, or Calculus) and that without motivation, it is a class many will struggle to understand? Second, would you have been happier if they had replaced the word “can’t” in the phrase “…can’t pass our Algebra II regular lane course” with “would have to put forth Herculean effort”? I agree with Kate that the authors made some poor word choices, but the balance of the letter seemed to indicate that they were trying to keep students from taking a course that would give the students nothing but frustration.

  11. If students aren’t understanding content in the traditional method of teaching then teach it to them differently. Perhaps the teachers could read one of the books by Ron Clark about motivating students and holding all students to high standards. “The End of Molasses Classes: Getting Our Kids Unstuck. 101 Extraordinary Solutions for Parents and Teachers.” He is one of the most inspiring motivational speakers a teacher can ever see. I think the teachers you mention above would then feel more confident about being able to educate ‘those’ kids.

  12. UC is not the bogeyman here. I had occasion to find out exactly what the real UC requirements are, because I’m home-schooling my son in high school. I posted about it at

    Students can satisfy the math requirement with a 480 on the SAT 2 math 2 test or a 570 on the SAT 2 math 1 test (a level which probably doesn’t really require mastery of algebra 2). (Note: since my son, as as sophomore, is taking the Art of Problem Solving online calculus class, and got an 800 on the SAT 2 math 2 his freshman year, we weren’t worried about the UC math requirement. The English requirement, on the other hand, is much stricter and harder to dodge.)

    I think that, in general, it is a mistake for a high school to match their graduation requirements to the entry requirements for UC, which is supposed to take the upper 1/8th of high school graduates. Encouraging students to aim high is all very well, but requiring everyone to jump over a bar intended for separating the top eighth from the rest is not really fair. Since UC can’t take everyone, even if by some miracle all high schoolers in the state did pass Algebra 2, all that would happen is that the bar would have to be raised.

    The wording of the teachers’ statement was very poor–I hope that none of them also teach English or politics.

  13. First, can we stop being appalled? For Christ’s sake.

    Secondly, @Kate: I’m afraid this is the future for us too. The new CUNY requirements for admission (and stamping our students as College Ready) are getting above an 80 on either Algebra, Geometry, or Algebra 2 AND passing the Algebra 2 class. ALSO, next year, “College Readiness” will be one of the metrics for determining how good a school is here in the city. So, you know, scoring well on a bullshit test and completing some extra bullshit curriculum will now be forced down everyone’s throat or else they will try to close your school down and send everyone to some bullshit charter school where everyone is positive and Ron Clark can just teach every kid AND EVERY KID WILL WIN BECAUSE THEY PASSED ALGEBRA 2.

    @Dan: “Of all of the classes offered in high school, Algebra II is the leading predictor of college and work success, according to research that has launched a growing national movement to require it of graduates.” BUT THE WASHINGTON POST SAYS IT!

    Lastly, I’m really grumpy, mostly because I already have 3 preps, plus run an independent study, plus am a team leader, plus have other leadership positions, and because of these goddamn requirements I have to spend a prep period tutoring kids so they can retake the bullshit test (that they already passed, just not with an 80). All of this shit about “college readiness” is just more shitty hoops to jump through for everyone.

    Oh, no, sorry, this is the last thing: I don’t think anything would give me more pleasure right now than kicking Ron Clark in the nuts.

  14. I’ve been struggling lately with my mission, which seems a lot like trying to squeeze square pegs into round holes. I think we sometimes miss the question. It’s not *can* we get all students to learn Alg 2, but *should* we? I agree with a previous poster that there’s a lot of math we could teach besides Alg 2 that would probably be more beneficial for students than Alg 2 (namely stats).

    I get frustrated with the single-mindedness of college preparation. Not every kid is going to college. Or should go to college. I think we over-push college on kids. There are a LOT of great career opportunities for hs grads that don’t require a college degree (or Alg 2), and we do students a disservice by implying that it is needed.

    Final thought: kids come to us with a wealth of talents and abilities. That group of unmotivated, disengaged students that drives us all nuts is probably that way because “what they’re good at is not valued, or is actually stigmatized in school.” (Sir Ken Robinson- see the full TED talk here:

    Can we teach high level math to every kid? Probably. Does every kid need high level mathematics? I remain unconvinced.

  15. Somehow, seeing someone else grumpy about having three preps plus etc plus life makes me feel a little more normal for going frickin’ crazy with four preps (one of which I actually had never actually, y’know, learned before teaching it – anyone care to learn about double-entry accounting, because I am now the frickin’ MASTER).

  16. Ha, Ha… no wonder of my former students at UCSB posted on facebook that our school did little to prepare them compared to others. We can’t even even convince everyone that Algebra 1 for everyone is a good thing. Welcome to the Meth capital of the world.

  17. I wanted to scream SHAME. But @jason buell got it right (comment 14). Instead, SHAME on Math Education writ large, and specifically in CA. Why can’t mathematics education remake itself from its public school origins meant to prepare mathematicians to develop the logico-mathematical mind of all children? [yes, I did just drop some Piaget] I often wish I could re-find some cognitive science research I read 15 years ago suggesting that the cognitive requirement necessary to learn language was more demanding than what was necessary to understand the mathematics of calculus.

  18. Seriously?

    Is a high school diploma (the piece of paper) important? There’s a vast difference in what someone with a high school diploma earns compared to someone without one. About a 50% bump in earning power. It’s important not to dumb it down, but it’s also important that kids can get there.

    The question is what math should a student need to make it through to be granted a high school diploma, and access to these higher paying jobs.

  19. It seems so obvious to me that Algebra II is useless to such a huge percentage of the population that it should certainly not be mandatory in high school. This is the epitome of rigor solely for rigor’s sake.

  20. Buried in the lit review of:

    You’ll find:
    Accepting the widespread idea that students are generally not prepared for college coursework, many studies have turned to identifying which influences result in college
    achievement and have found a link between high school math courses completed and postsecondary academic success (Ruban & Nora, 2002; Kirst, 2001; Bottoms & Feagin, 2003;
    Keller, 2001; U. S. Department of Education, 1997; Adelman, 1999; Perkins, 2004). A 1999 study from the U.S. Department of Education found that taking a math course beyond Algebra II in high school more than doubled a student’s likelihood of completing a bachelor’s degree. As
    the highest level of secondary math rose, the likelihood of degree attainment followed, culminating with more than 80% of students who took calculus receiving a degree (Adelman,
    1999). Other analyses concluded that students who took calculus were 28 times more likely to be a “high achiever” in post-secondary work, and that the level of math taken, regardless of factors such as race, socio-economic status, or type of high school, was the largest indicator of
    college achievement level (Ruban & Nora, 2002; U. S. Department of Education, 1997). A high school transcript study conducted by the National Center for Education Statistics found a link between scores on a mathematics assessment test and the length of time since a student’s last
    math course. Scores were highest for students who had their last earned math credit in the 12th grade, followed by students whose last coursework was in the 11th
    grade. The lowest scores were by those who had not taken math since their 10th grade year (Perkins, 2004).

    A white-paper by the ACT folks says:
    Taking higher-level mathematics courses in high school is associated with increases in students’ chances of success in first-year mathematics courses (by 3 to 28 percentage points).

    *The WP claim listed above relies on the Adelman (1999) paper.

    *But, I’m pretty sure a lot of this data says, “good students are good students.” It’s correlations that they’re looking at, not causation.

  21. @Dan: If there’s any kind of causal relationship between Algebra II completion and success in higher education, I’m willing to change my mind. I haven’t seen any.

    Is there “any kind of causal relationship” between ANYTHING and success in higher education?

  22. @Mark: When have you ever used the Pythagorean Theorem to solve a real world problem? When has it ever mattered to you where the circumcenter of a triangle lies? When has it been of upmost importance where a parabolas vertex lies on a Cartesian plane?

    We don’t teach Algebra and Geometry because they’re extremely applicable in the real world. We teach post-secondary math because it helps students learn to think and problem solve.

    @Anyone Stupid Enough To Think Kids Need A Break:
    Imagine for a second a world without AP Literature, without Algebra II and Trig and Calculus, without US History and Foreign Language classes. Why learn any of this nonsense when all I want to do with my life is go cut hair or teach gym or work at McDonalds.

    Next, I want you to look at our youth. Do you see the next Bill Gates? Do you see the next Albert Einstein? Do you see the next Steve Jobs? Pause and reflect. Do you see people capable of going to work for Google, for Facebook, for Apple? People capable of betting the world we live in. Pause and reflect. Do you see people who think critically and solve problems? Do you see people who are curious about the world around them? Do you see people who you want to run our country?

    Granted, not EVERY single student can be molded into a productive member of society. Our society couldn’t function without a lower class to work crap jobs at McDonalds or clean up garbage. But do you want your son or daughter to end up in one of those jobs? Or do you want them to have EVERY SINGLE opportunity to succeed and make something of themselves? Do you want them to have teachers who push and strive for greatness? Who are capable of making students think and enjoy Algebra II or History of Chemistry?

    Just think about the future before you make rash decisions. I have plenty of students in my Algebra II classrooms who wouldn’t be there if they weren’t required to be. I know in my heart of hearts that some of them could care less about Algebra II, but when you look at the data for the state of Tennessee, and my public school ranks 10th out of the entire state in Math ACT scores, behind 8 private schools and Oak Ridge, then I know we’re doing something right.

  23. I agree with the other posters that Alg2 isn’t appropriate for everyone. However, if a student is college bound, then I do agree they need a minimum of Alg2. In my state, students must take at least 3 years of math in grades 9-12 that are Alg1 or higher. However, we do have a few alternatives (Math of Finance instead of Alg2, etc) and we provide elective support classes for students for Alg1 and Alg2. I think most students can learn Alg2 if provided the correct support. I don’t think I would want to be the determining factor on a student’s future based on my beliefs of whether or not a kid will be successful. Instead, I would rather put my time and energy into finding methods and ideas to reach and motivate those students.

    @Dan – if I recall correctly, your Alg1 and Geo students were lower-level and I wonder if 15 years ago, these same teachers that wrote the letter about Alg2 would have written a similar letter about students not being able to pass Alg1. However, you and many other teachers have shown that *those* students can learn and pass Alg1.

  24. @timfc. “*But, I’m pretty sure a lot of this data says, “good students are good students.” It’s correlations that they’re looking at, not causation.”
    I so agree! I teach both ends of the spectrum, and often wonder how can I help change the not so good students into good students. Last year, in a College prep geometry class I had a student who stepped outside of what was normal for him and took that class rather than regular geometry. He struggled the whole year and despite my encouragement felt discouraged he could not reach the grades the others in class seemed to be able to do with ease. The biggest factor? His parents. They never encouraged him to try these classes earlier in his education, they were satisfied with just passing, and that was the level he worked to. The disadvantage this created for him was huge! How do we change that, when there are families whose values and cultures do not value education? He is sticking with the college prep ( honors) program, and still struggling, but doing better. He is very motivated and will be the first one to go to college in his family. I am very proud of him, but he is swimming upstream against a strong current with his family. He is rare. How can the education system make that difference for all of the others in those situations? Very frustrating!

  25. I have to say, I sorta agree with this sentiment. I mean, not everyone has the patience to take the six-year-high-school graduation plan. When a student comes in at a fourth grade math level, you can help them improve, but they’re not going to get Algebra 2 the first go-round….or the second….or maybe even the third. If they want students to graduate with a higher math competency, put some more stringent requirements on social promotion in lower grades, instead of counting on high school teachers to pick up all the slack or water down their grading.

  26. @ Timfc: I like your summation, but I’d even go a step further: “good high school math students are good college math students.” Not really any surprise there.

    I still sense an emphasis on college preparation, and I don’t believe that our sole purpose of existence is to prepare students for college.

  27. There’s a difference between “students objectively can’t learn Algebra II” and “students objectively can’t pass Algebra II class.” They used the latter wording, unless I missed something. I took that to mean that many students, due to objective reasons, are not able to pass Algebra II at the pace and rigor of their school. Keep in mind the school is next to Stanford and Silicon Valley and probably serves children of parents who have strong math backgrounds or with access to resources.

    Even if they spent the additional resources as you suggested they could, there will still be some students who will fail their Algebra II classes at their current pace and rigor. So it’s a choice between having kids go through a whole year of Algebra II and failing in the end requiring a waiver to graduate or watering down the course so students can pass just to graduate or, as they stated, kids with resources can “buy their units” thus unfairly punishing those with limited means who were the likeliest to fail in the first place.

    They feel their school has a reputation where the math grades mean something to colleges in the admissions process (anyone has insight?). They would prefer not changing that perception by watering down. They do offer an alternative where 3 years of math is the criteria for graduation instead of Algebra II. It would allow them to create classes that better targets the student in terms of ability, access, and motivation.

  28. @ Adam Hall: I would never argue for a world absent of Algebra or Calculus or any higher math. Don’t mix up “teaching high level mathematics” with “teaching every kid high level mathematics.”

    You’re right when you say we are going to need people to do the “crap” jobs. But we also need people to do a whole host of other jobs like plumbers, electricians, truck drivers, chefs, bank employees and [a thousand other great jobs] that pay well, make good careers for kids, and require NO HIGHER ALGEBRA OR CALCULUS to be successful.

    We need *some* kids to be taught and be successful at higher mathematics. We need to focus some extra effort at this group of kids. I know at our school that we are under-serving this population while we try desperately to get the bottom end up high enough to pass the state test at the end of their sophomore year. We expend very few resources taking mathematically gifted kids to the zenith of *their* abilities. And it makes me feel bad.

  29. @timfc. Yes, those students who take math beyond what their high school expects generally do better in college. Making everyone else take that course does not make them do better in college, it just waters down the usefulness of the course as a marker for academic ability and drive.

    I saw the same mistake being made in the push for algebra in 7th and 8th grade. Certainly, the kids who took algebra early did much better later on, but the causality went the other way: those students who were bright and interested in math took algebra early, rather than taking algebra early made them bright and interested in math. One can still see a clear correlation between math exam scores and grade level of the students–the youngest kids on the algebra and geometry tests generally do the best.

    @Coquejj The California Math Framework is probably one of the better documents for explaining what is expected to be taught. Algebra II starts on page 209 of
    For what is *actually* taught, I’m afraid you’ll have to ask individual teachers, as it seems to vary widely. A lot of math teachers have stopped using textbooks, so you can’t even look at the contents of the most popular books to see what is being taught. (Note: as a parent and a college professor, the difficulty in finding out what is actually taught in high schools is rather frustrating.)

  30. Dan, (or anyone else here), do you know what level of math is required for high school students in other countries?

  31. In England, the minimum level of maths required for university entrance in non-numerate subjects (recall that in the UK students specialise much earlier than in the US – a student might do no maths after the age of 16, though that’s been under discussion yet again lately) is a GCSE grade C. There are multiple different national exams that give you this. Here’s one web page:
    There are two tiers – you choose whether to enter at foundation tier, on which the questions are easier but the highest available grade is a C, or higher tier, with harder questions but grades A* to C available.

    You’re likely to be shocked at how little maths is required; we regularly have press stories about 5yos getting GCSE grade C, etc. Certainly it’s nothing like a pass at Algebra 2!

    For a numerate degree subject it’s very different; you then need maths at A level or equivalent, which is well above what’s indicated by a pass at Algebra 2.

  32. I think many people are missing the point. What is appalling is that it is PALO ALTO teachers who have given up on these kids.

    For those who don’t know, Palo Alto is one of the most elite suburbs in Silicon Valley. The population is mostly white, with very well educated families who live there because they either inherited the money or made big bucks (we are talking multi-millions) when their company took off during the Internet boom of the late 90s. It’s a city where you can’t buy a 1500 sq foot house for less than $1M. The 1500 sq foot condos *start* at around $850K. I know, because I have been looking for a long time to find something affordable in that neighborhood, and have failed so far.

    This school district has actually passed a parcel tax on top of the already sky high property taxes to fund the schools.

    We are talking about the cream of the elite, who have all the resources and then some to spare, giving up on their kids.

    That’s what makes this appalling.

  33. A lot of us have taken our eye way off the ball. There are worthy arguments to be made that Algebra II shouldn’t be required for high school graduation or college admission. None of that interests me as much as teachers who claim objective, advance knowledge of which students can’t pass a class. These teachers also claim objective knowledge of the home support of those students, after indexing all that predictive power to poverty and race.

    Consider also: is there a better way to abdicate your responsibility as a teacher than to say, “No matter my efforts, these students will not pass my class.”

  34. Many good comments. Look at the percentages of college (and community college) students who need to repeat high school level algebra classes. Many are kids who did pass algebra 2, then took no math in their senior year.
    Look at the current mess we are in after the housing bubble. How many people signed contracts with financial obligations based on math they didn’t understand? Whether it’s taught in algebra 2 or statistics or a financial math class, people in this country would be better off knowing and understanding how money works in this economy. (And that takes algebra at least through exponential functions.) Ignorance of all that is very expensive for all of us.
    Talk to community college instructors of those remedial classes. They will tell you many of their students were not yet ready for those classes in high school (Piaget again?); many of the students, according to surveys, claim they would have worked harder in high school if it had been demanded of them.
    See for more on the push to require algebra 2 as a component of “college readiness = work readiness”. Readers of this and other blogs know that the way much of what we teach is changing, and more change is needed and underway.
    I agree that for many students, stretching it over 2 years would be very helpful, but that does run up against budget troubles.

  35. India has an integrated math curriculum in most parts of the country and requires a level of Math equal to Algebra II of all 16 year olds. If you want to go to college in the “Science” or “Commerce” stream then all 18 year olds get to Calculus.

  36. Isn’t this all just speculation? How difficult is thier algebra II program – don’t know. What sorts of skill & motivation levels are we talking about for these kids that can’t pass – don’t know. Do these kids really have lack of support at home, and do the teachers really know who has a lack of support – don’t know. Do the teachers give a darn about these or any other students? Do these failing students receive the mountains of extra support that apparently should be available to them in Palo Alto? Did they mean “don’t pass even though they are trying” when they wrote “can’t pass”?

    I disagree that concluding that a student will not pass means you have relinquished responsibility for that student. I have had many students reach the point where they cannot pass for the year – doesn’t mean I stop reaching out or trying to engage them. For survival sake alone you have to show those students that you still care about them and their learning.

    I can’t see a purpose of this post.

  37. Jennifer Potier

    November 23, 2011 - 4:08 pm -

    Why do we continue to allow University systems to dictate what and how we teach? Whenever possible, I teach so that kids can think, learn, apply and transfer knowledge. Unfortunately, University admissions requirements around the world are based on ‘testing’ that offers abstract questions that have no real meaning or application in many cases.
    Furthermore, I have seen many ‘brilliant’ students, passionate in their own fields, who could not pass Algebra 2 maths (and thus dropped maths in the final years) but who did go on to become the most amazing teachers of art, physical education, and more – because they were passionate, not because they could pass ‘algebra 2’.
    I love Maths (Australia), and I try to use my passion to teach. It is passion that makes a person successful, not algebra 2.
    And coincidentally, I think that most kids, if they are taught well, by passionate teachers, can learn algebra 2. Whether or not they can pass a test (for any variety of reasons, inlcuding those related to working memory, etc) is another question.
    Shame on the University systems for using Algebra 2 as a measure into the proficiency of a student in their chosen field of study (passion).

  38. I have had kids who are 15 and have had no schooling in written language until a year ago. They can’t pass Algebra 1, but our school system will put them in algebra 1, then geometry, then algebra 2, and they will fail it all. Because of that paper (thanks for the cite) that says students will do better in college if they take higher level math, regardless of whether they pass it.
    And I do not think they are in any way stupid – they’re learning a written language, a culture, an oral language, all at the same time. Way more than I could do.
    We just pass them along so they can go to Community College and take remedial math (we aren’t allowed to do remedial math because that would be lowering the bar…). Sure it costs taxpayers more, but that way we don’t have to face reality. I suspect that avoiding this is the purpose of the PA teachers. And by the way, we do have huge numbers of students who drop out at 17 without passing a single high school math course, so evidently they do learn an application eventually.
    80% of my kids cannot reliably add and subtract whole numbers. I’m not assigning blame, I’m not saying they can’t pass Algebra 2 eventually, but I am saying that if we don’t help them learn how arithmetic works, then how algebra 1 works, they aren’t going to be able to actually pass algebra 2.
    At some point, requiring kids to complete work that every one else does on a computer program, is just cruelty.
    Unlike the English system, it’s all or nothing. You either get a high school diploma or you don’t. Most adults (including teachers) in the US would not have a HS diploma had this been in place for them. Most adults have no idea what’s in Algebra 2, they just think more is better.
    There’s a difference between requiring every kid to try algebra 2 and requiring them to pass it.

  39. I thought Dan’s main point was pretty obvious. He emphasized the word “objectively” several times. How can a group of teachers, particularly in a wealthy district, declare by fiat what a group of kids can or can’t do?

    Having worked with high school math teachers and their students in Detroit for the last three years and in other high-needs schools and districts for the last 19 years in various capacities, I’m well aware that there are kids in high schools who are ill-prepared for high school mathematics. I don’t think that’s terribly new. But I suspect that Palo Alto isn’t a district where there are schools with 40-60% special education students in math classes taught by a general education teacher and, if s/he’s lucky, a special-education co-teacher. If s/he’s MIRACULOUSLY lucky, that co-teacher won’t be math phobic and might actually be interested in and capable of co-teaching mathematics in ways that support the general education teacher and build the sort of differentiated instruction that is essential in such classrooms.

    So I, too, find the attitude implicit in that letter unfathomable. The resources available in Palo Alto would be the envy of every teacher and student I’ve worked with, including those in Ann Arbor, which is more diverse and basically middle class than the other districts I’ve been with. I’d love to be a fly on the wall when that same group of teachers is talking about the same kids regarding Algebra 1. I doubt there’s a lot of difference in tone, attitude, or belief.

  40. 46 comments later, I very much agree with Dan on this. The issue isn’t whether or not all students should be able to pass Algebra 2 before graduating high school. The real issue is how will ALL students’ needs be met, understanding that their needs are as diverse as they are. If Algebra 2 isn’t an appropriate graduation requirement, then what’s an alternative path? To me, what’s lacking in their letter, is a proposed alternative of how to best meet the needs of students who struggle to pass Algebra 2. And then, what resources will be committed to meeting those needs. Finally, what role do students and their families have in the decision making process about what’s needed and best for their future. THOSE are the real questions, as far as I’m concerned.

    Although most 8th graders take Algebra 1 in Berkeley, I teach a course called Algebra Scholars which is a second year of pre-algebra. Near the end of 7th grade, I meet with all students who have scored below a certain proficiency in pre-algebra and give them 2 options for 8th grade: Algebra Scholars; or double period algebra (giving up their elective). Some of these families choose a single period of algebra, agreeing to get tutoring outside of school. By no means is it a perfect choice, but it means that students and their families choose to take a second year of pre-algebra instead of our staff making that choice.

    The issue of who makes tracking decisions is critical to me as is the issue of how to help students and their families make an informed choice with an understanding of the implications of their decisions.

  41. Everyone that posted here should read “Radical Equations” by Robert Moses. Great book that looks at mathematics as a civil rights issue. It really opened my eyes.

    But out of the 46 posts I thought 17 James McKee said it best.

    @Dan I agree, we should never make assumptions about a students ability or background. I am a big believer that all students can and do learn complicated mathematics. We need everyone to be mathematically literate and we should supply all support needed to make that happen for all students. If they are behind we need to catch them up. If they struggle with assignments because there is no support outside of school, we need to get them that support in school. We should hold nothing back because math is that important to their future success. Wether it is taught traditionally or with all the latest video technology. Absolutely every gun in the arsenal should be used.

    Remind me to never place my signed PDF documents online :)

  42. I wonder if any of the Palo Alto teachers who petitioned the school board would like to respond here? I would also love to hear from the 6 who didn’t.

  43. After browsing the websites of some of these teachers, it seems to me that one of the teachers requires each student to have both a regular calculator AND a graphing calculator. The make and model are specified. Is this part of the issue? The have students own better equipment and the have nots don’t. Are the teachers using SES to “predict” how students will do? Is it usual in the US to require students to provide this level of equipment or do some schools provide them?
    (In my limited Canadian experience, graphing calculators are a school resource at the high school level, and are not allowed at the college where I teach.)

  44. Those teachers brought this on themselves by making their letter public, but it would be nice to see a more thorough reporting of the issues before setting them up for a public beat down. Things are often much more complicated than they appear – espicially when you only have a poorly worded and tone deaf letter to go on.

    I am not sure, but it doesn’t seem like their intent was to apply “objective” criteria to pre-judge individual students and decide whether that student is capable of passing algebra II.

    It seems like they were simply trying to make the point that there are real barriers to having all kids graduate with algebra II in their current program, and expressing concern that many students will need to jump through some hoops in order to get a waiver to graduate, or they will need to lower the standards for the course.

    Some may argue that they should be able to accomodate all students while keeping the current level of rigor. This, to me, is all speculation based on the information we have.

  45. Although people are saying that Palo Alto is phenomenally wealthy, so should be able to afford nearly infinite resources, it doesn’t work that way in California. The amount of money that goes to a school district is based mainly on how wealthy the community was in 1972, not how wealthy it is now. (So Palo Alto does well relative to Santa Cruz or East Palo Alto, but not like a school district in New York with similar wealth, as Palo Alto’s switch from middle-class college town to dripping with money happened in the 1990s.)

    Even so, not everyone at Palo Alto High is wealthy–California schools tend to be more diverse with respect to wealth than those in the Midwest and on the East Coast, perhaps because the boundaries don’t correspond to tax levels and housing prices as neatly. According to the state records
    9% of the students at Palo Alto High are “socioeconomically disadvantaged”, 6% are English learners, and 9% are students with disabilities. These numbers are very low for a California school, so Palo Alto gets very high API scores overall, despite doing about the same as other school districts on the non-English speakers, the kids in poverty, and the Hispanic kids (the three groups are reported separately in API scores, but the averages make it clear that they are mostly the same kids in the three subgroups).
    Palo Alto does have a high proportion of Asian students, who are doing extremely well on the API tests and pulling up Palo Alto’s average.

    It is quite likely that some of the students with severe enough mental disabilities are “objectively” incapable of learning Algebra 2, but I’m not sure that is who the Palo Alto teachers meant, since those kids tend to get ignored in all discussions of high school graduation requirements.

    Palo Alto High is not doing particularly well for its poorer students (compare API scores on subgroups with schools like Monte Vista High in Fremont, which has similar fractions of impoverished students), so I think that there is some question about how Palo Alto High is using their resources and whether there is inequity there.

  46. Linda Gottfredson's Apprentice

    November 24, 2011 - 8:25 am -

    It seems that the “Reality-based” community has little grounding in reality. A useful reading list can be found at Linda Gottfredson’s publications page.

    At what point should we stop? Should all students be required to be proficient in calculus? How about differential geometry or vector calculus?

    What reasons would you give for not requiring calculus that also do not apply to algebra II? What is it that you think separates those who can handle calculus from those who cannot? (Hint, poverty is correlated with that hidden variable you do not want to talk about.)

  47. Is semestering common in California schools? Maybe a compromise would be to offer Algebra II as both a 1/2 semester course and a full-year course?

  48. Dear School Board,

    We are sorry when we said those disadvantaged students objectively couldn’t pass our algebra 2 class. I mean, we totes have a bunch of smart students in these classes and these Oliver Twists are getting in their way! We have heard poor kids with the same disadvantages are passing in other poorer districts but our algebra 2 is different than what algebra 2 means everywhere else. Basically our algebra 2 is calculus which is why these kids can’t pass. What’s that? Poor kids in other districts have passed calculus? Hmm…well then they must not be as piss poor at school as these kids. Also we are not used to having to teach and scaffold to diverse learners so it’s not fair! Seriously, guys, come on. Do you really expect us teachers with masters degrees from Stanford who have never been around poor people to be able to concentrate enough to ignore that they’re wearing clothes from Mervyns! That store closed down years ago! Gross! Listen, we have busy schedules because all of these smart students can’t just learn without expertise so can’t we just dump these other kids back in East Palo Alto where they belong?

    Uncreative, entitled, lazy teachers who have great teaching jobs

  49. One would think that there are, in fact, objective criteria for deciding which students can pass Algebra II.

    For example, if the student can’t perform simple arithmetic, it is clear to me that that the student will not be able to pass Algebra II.

    Yet, for some reason, some people on this blog seem to believe that it is _absolutely impossible_ to _objectively_ determine whether a student can pass Algebra II without subjecting the student to said class. Worse yet, apparently, it’s about to become a _requirement_.

    What a preposterous idea.

    Yet another manifestation of the “everybody must graduate from college” idiocy that’s spreading all over.

    Oh, and Judah – how do you expect to “scaffold” a student who can’t perform arithmetic into understanding Algebra II, while still managing to teach the students who actually have the basics?

    It’s not a question of lack of money; it’s a question of lack of skills and raw intelligence.

    Oh, wait – that’s right – students are absolutely interchangeable units that do not differ in any way. Right.

  50. I personally know one of the co-authors of the letter and she’s someone who has a lot of integrity. I have no doubt there’s more to this issue then what’s written in the letter. I’d love to hear more about the factors which led to the writing of the letter and what these teachers are doing to ensure a true narrowing of the achievement gap. Maybe not enough is happening, but I hope the ‘support’ of these students is more than the straightforward goal of eliminating Algebra 2 as a graduation requirement. Hopefully Jason is right that their hearts were in the right place. It’s hard to know from this one document.

  51. Former Alg2 Teacher

    November 24, 2011 - 1:36 pm -

    I cannot help but re-ask CoQuejj’s question (post #34), but in the perspective of the (imminent) CCSS adoption. The CC standards are not organized by the de facto American course names. I am always surprised by the discourse around arbitrary course names and their ability to indicate college and/or career success.
    In my opinion, identifying “Algebra 2” as an indicator or requirement means absolutely nothing. (It would be no different than identifying English 11 or science 3 or math 10 or ‘advanced art’ or ‘math for liberal arts students’ as “the” course.) I have taught in a several states and several types of schools (each with a different belief about math progress) and no two were ever consistent.
    Until we start talking about the skills/topics for college AND career success and developing math programs from those ideas, the discourse about any arbitrary course and its ability to indicate success is impractical. By no means do I think the CCSS (or any set of standards) is the answer to the current issues of math preparation, but I do think it is a chance to reconsider–or dare I say ‘transform’–the way mathematics is taught in American high schools. I truly believe that every good math program is developed around the ideas/beliefs, essentially a set of standards, that a school or department thinks is necessary for post-secondary (college or career) success. (Check out the math programs at Phillips Exeter in NH or the Urban School in San Francisco for examples. Note there is no mention of Algebra 2 anywhere.)
    Unfortunately, I fear that schools/districts will force the CCSS standards on top of their current courses and the status quo will remain–a total exercise in futility. I just wish everyone could take one giant step backwards and inspect math education from a broader perspective and schools/districts develop programs that serve their students the best.

  52. a different eric

    November 25, 2011 - 7:42 am -

    “Unfortunately, I fear that schools/districts will force the CCSS standards on top of their current courses and the status quo will remain–a total exercise in futility. I just wish everyone could take one giant step backwards and inspect math education from a broader perspective and schools/districts develop programs that serve their students the best.”


  53. How can it possibly help a student to be in a class that they are not prepared for? This is teaching? To put a student in a class that they are hopelessly behind in from day 1? And if this is a civil rights issue then civil rights is a dead issue. Where is the progress in putting students in classes that they will fail completely.

    Reform didn’t start out this way, did it? Its goals were originally true and noble. Its goals were to make students more educated, not less. Its motives were simple and unselfish. A better education means a better life. And no teacher, and in fact no person, in their right mind would have ever suggested that a better education would involve putting a student into a situation of certain failure (I do not exaggerate, look at the test scores).

    I find this twisted version of reform, to put students in classes they have no chance of succeeding in, highly suspicious and sad. Let me ask those of you here that promote such a practice. If it was your son or daughter that had done so poorly in Pre-Algebra and Algebra 1 that failure in Algebra 2 is a certainty, would you send them forward? I know what kind of parent would do that, an entirely uninvolved and unfortunately uneducated kind of parent. But what kind of teacher would do that?

    Bob Hansen

  54. And, as many posters have already pointed out, very few people use algebra! Even the majority of teachers that teach it. They use spreadsheets and solid arithmetic in their day to day lives and careers. Be honest with yourselves and look around your workplace, even if that workplace is a university. Math past arithmetic is like music, an art. Being good in algebra does open some doors, just like being good with music opens some doors. But those doors are only a fraction of the doors out there. It seems that the next reform needs to be a reform that acknowledges that reality. That every student DOES NOT need algebra. That people don’t even use it in most walks of life.

  55. Hear, hear to many of the comments above that are appalled at this petition.

    As a graduate of Palo Alto High School, a secondary math teacher, and now a mathematics teacher educator, I had a visceral response to this post.

    I was NOT the student who found mathematics easy in high school. I had to work exceptionally hard to get mediocre grades. After a B- in Algebra I (9th grade), a B+ in Geometry (10th grade), and a C+ in Alg II (11th grade), I somehow got into the AB Calc AP class. The class prepared me so well to recognize cues in AP calc test problems and to follow memorized algorithms that I got a 5 on the AP. I couldn’t have told you what a derivative was if it would’ve saved my life (as I found out quickly in college).

    Maybe Paly needs to reconsider what the kids who ARE passing Algebra II (and their other courses) are actually learning about mathematics. It wasn’t until I became a teacher that I really began to understand the conceptual intricacies of Algebra, Geometry, etc. And yes, of course parents and families are a huge part of kids being able to do well in school. But it IS also the responsibility of teachers to take the approach that ALL students can learn, and to put support in place that help students get there.

  56. I think Dan’s comment (#40 above) hits the nail on the head in several crucial ways:

    1) The fact that ANY teacher in ANY school system would claim access to objective, predictive knowledge that certain identifiable students will inevitably fail Algebra 2 strikes me as wince-worthy in the extreme;

    2) the fact that a group of teachers in a district renowned for its support of quality education would actually sign their names to such a letter says something about their institutional acceptance of an ineffective system of preparing students for and prior to Algebra 2;

    3) the clumsiness of their effort suggests a certain “learned helplessness” among these teachers, in which challenging a proposed graduation requirement is perceived to have a higher likelihood of success than an insistence that they address the underlying deficiencies of the system that leads up to Algebra 2.

    I would respectfully submit that this whole situation reveals multiple facets of dysfunction that deserve to be looked at — not just this small group of teachers. If that many math teachers felt they had no choice but to petition the Board of Ed on this matter, there’s something rotten in the state of Denmark.

    Just my two cents.

  57. To the last two posters, we are not talking about students getting by on C’s. We are not talking about minute failure, we are talking about complete failure. I think people are somewhat ignorant of just how poorly some students are doing in math. Blame who you wish, the teachers, the parents or the students themselves, or the lying bastards that rigged the lower level tests to show progress when there was none. But these students are not ready by any definition of the word.

    If a student is barely passing math then you have a talk with them, you have a talk with their parents, you suggest strongly that maybe a repeat is in order to strengthen their understanding and put them on firmer mathematical ground. If they decide to press on anyways then let them.

    But this is not the case here. These students have failed the majority of the necessary skills. They are not barely passing. They aren’t even barely failing. They are completely failing. Don’t tell me that a teacher or even a layperson cannot predict the outcome in that case. And the outcomes are dire, ridiculous even, in every state that has mandated Algebra II for every student, the same pretty much goes for Algebra I as well.

    Is pushing students to fail in a subject that few people actually use anyways, helping anyone? Only about 20% of the students in CA are making it through Algebra II as it is. You are talking about failing 80% of the students. And I will say it again, in a subject that hardly anyone uses. Why not do this with Latin instead. At least (I think) most kids would have a chance with Latin.:)

  58. a different eric

    November 25, 2011 - 2:39 pm -


    you have to be an allsum teacher.
    if you have to tutor on the side to teach them to add.
    so be it.
    if you have to tutor on the side to teach them to divide.
    so be it.

    it can be done.

    who cares if you won’t ever use it.

    i can’t think of the last time i used shakespeare in life.
    but i got something out of it.

    and i am thankful for the language arts teacher who inspired my perseverance/appreciation through/of it.

    growth mindset vs. fixed mind set.

  59. I still have this strong sense that posters are coming from this place in their heads where we MUST teach high level math to all students, or we’re failures. We’ve been sold this bill of goods by society, by the politicians, by the media, by the fear mongers with their whole sky-is-falling-USA-is-in-last-place-on-intl-math-tests-again-BS, and most of all by ourselves because we care about kids and we want them to be successful.

    I believe in the power of mathematics, and I know what it contributes to the world we live in. I believe that we should take on any and every student that’s interested and take them as far as is reasonable to do. I also believe that it is incumbent upon us to help students identify their talents and abilities, and to help them cultivate and develop those talents and abilities as much as we possibly can. If their talents and interests lie along a different path (say music, or art, or culinary arts, or learning a trade), then our efforts at dragging this kid kicking and screaming through the rigors of algebra only contribute to the perceived ineffectiveness and irrelevance of public school. We’re flogging ourselves, and I don’t do self-flagellation.

  60. Thanks James (68). Go back to Robert Hansen (61.62, 65). If you have not had a job/career/experience outside of school, you might not know that almost nobody uses Algebra 2 (dividing one polynomial by another, conic sections, normal curve distributions, trigonometric function combinations, logarithms). Mathematical models are done on computers. Nobody uses calculators either. In 20 years of engineering I never saw anybody use a calculator.
    The question is not whether it is really cool for some people to acquire this knowledge at some point in their lives, the question is whether is it sensible that these skills are a requirement for everybody to master by age 18, or be labeled as a failure by society.
    I could sort of buy the “we are teaching logic/thinking processes/how to learn” argument, but that’s not what we’re testing, and it’s surely not necessary to go to polynomial division to accomplish those goals. I believe there is logical thinking inherent in other subjects, although clearly not in the classes that teach administrators how to set curriculum.

  61. James: I still have this strong sense that posters are coming from this place in their heads where we MUST teach high level math to all students, or we’re failures.

    You and Robert and louise are missing the point of most of those comments. Definitely my own. No one here has argued in favor of teaching Algebra II to students before they’re mathematically prepared. I’ve argued against the Algebra II requirement itself. All of that is beside the point. If the Paly High School letter had concerned multivariable calculus, my point would still stand:

    The Palo Alto High School math teachers claim objective knowledge which they can’t possible have. This is arrogant. Particularly arrogant is the objective knowledge they claim of a student’s home life, her maturity, and the supportiveness of her parents. The Palo Alto High School math teachers are looking through an extremely cloudy lens having convinced themselves it’s clear and then saying that cloudy lens can objectively predict which students will pass and fail [insert any math class here]. This is wrong, both morally and factually.

  62. Former Alg2 Teacher

    November 26, 2011 - 10:08 am -

    A few rhetorical questions:
    Do ELA teachers feel the same way about teaching poetry to students?
    Do science teachers feel the same way about teaching the structure of the atom?
    Do art teachers feel the same way about exposing students to the works of the greatest artists in antiquity?
    Do social studies teachers feel the same way about exposing students to ancient civilizations?
    Is there anything we learn in high school that is arguably an absolute necessity?

    With those being asked, I do not think anyone can “objectively” determine what a student should or should not be able to accomplish academically. Furthermore, I don’t think any of us reading this blog (presumably math teachers, past and present) can “objectively” determine the usefulness of algebra after high school or college; we have all had the privilege of taken (or having taught) advanced math classes, and are therefore able make our own (subjective) judgment as to whether it is useful or not.

    I agree with Dan’s latest post–the math teachers at Palo Alto are arrogant and wrong in their intentions. Check out the description of their program and course offerings: (page 48-49).
    Their first bullet point:

    “It is our goal in the Palo Alto High Mathematics Department to place students in courses that provide the
    appropriate level of challenge. When placed appropriately, a committed student who puts in the amount of work
    required should be able to master the content of that course.”

    And the second bullet point (and the real kicker):

    For PAUSD students, readiness for a particular course is determined by the present teacher, who knows both the PAUSD curriculum and the student’s preparedness level and makes a careful, informed recommendation for placement with the student’s best interest in mind.”

    Furthermore, they offer four “lanes” of mathematics courses! They sure seem to have a predetermined conception of the capabilities of students in each lane. And their described process of transferring between lanes suggests that the structure is more rigid than flexible.
    Again, I strongly believe there needs to be a shift in the paradigm of high school mathematics education.

  63. Alg2 Teacher wrote…

    “With those being asked, I do not think anyone can “objectively” determine what a student should or should not be able to accomplish academically. Furthermore, I don’t think any of us reading this blog (presumably math teachers, past and present) can “objectively” determine the usefulness of algebra after high school or college; we have all had the privilege of taken (or having taught) advanced math classes, and are therefore able make our own (subjective) judgment as to whether it is useful or not.”

    First off, I am not a teacher, I am a software engineer, I have tutored (math) and I teach my son.

    That the majority of people don’t use algebra out of school is not subjective, it is a fact. That does not mean that I think math, including algebra and beyond algebra is not worthwhile. I personally find it to be very worthwhile like I am sure musicians find music to be very worthwhile. I just don’t see it right to push what I find to be worthwhile on students that don’t find it worthwhile, excepting of course the skills all of us use in our day-to-day lives. No one is saying to stop exposing students to algebra, that happens plenty in pre-algebra and algebra 1. And it isn’t just algebra, we should expose every student to all of the worthwhile things in life, and then trust the STUDENT to make their choice as to what is worthwhile to them. Not mandate it.

    When you and Dan question whether a teacher can objectively determine if a kid will fail, you miss the point entirely. You should be asking the students what they want. Students know what they are good at and what they are not good at. They don’t sign up for these courses and fail them because they want to be challenged. They do so because you forced them to.

  64. Robert: When you and Dan question whether a teacher can objectively determine if a kid will fail, you miss the point entirely. You should be asking the students what they want. Students know what they are good at and what they are not good at. They don’t sign up for these courses and fail them because they want to be challenged. They do so because you forced them to.

    This is an argument for a universe that doesn’t include graduation standards. If you want to make an argument against graduation standards, I’m happy to read it at your blog. This post takes place in a different universe and considers an entirely different set of constraints.

    Another feature of the universe of this post is that people don’t sign up for courses they’re already good at. They sign up for courses in things they aren’t good at, but want to be.

    No more of this.

  65. “Another feature of the universe of this post is that people don’t sign up for courses they’re already good at. They sign up for courses in things they aren’t good at, but want to be.”

    I was only talking to signing up for algebra 2, not algebra 1. I think the students know what algebra is and whether they like it and whether they are good at it after they have suffered through algebra 1.

  66. Dan and others, are you sure that the teachers signing the letter are claiming to have objective knowledge for individual students that would predict failure for those particular student? Do they mean the reasons themselves are objective (i.e. most people would agree those factors would tend to cause a student to have more difficulty) or do they mean they have objective data for individual student that would guarantee failure? It seems like they are writing about the group not passing algebra 2 collectively, not on a case by case basis. A lot of red flags went up for me as I read the letter, but I am not really sure about their motives or concerns. Have you spoken with any of them or do you have any behind the scenes information?

    The full quote shown below comes across as, “85 students didn’t pass Algebra II — some probably could do it but it is unfair to expect all of them to overcome the significant obstacles they face”. Saying that out of 85 students, some could have passed and some couldn’t is a lot different than saying Jim & Jane didn’t pass Algebra 2, Jim could do it, but Jane can’t because of her unsupportive home life & immaturity.

    Extended Quote from the Paly Letter:
    “85 Students will graduate this year from Paly without having completed Algebra II. A change in graduation requirements could probably motivate some of these students, who have the emotional ability and academic support to do so, to work harder and meet the a-g challenge. We are concerned about the others, who for reasons that are often objective (poor math background, lack of support at home, low retention rate, lack of maturity, etc) can’t pass our Algebra II regular lane course.”

  67. I guess I should apologize to Dan for ‘jacking this thread. I know my posts are off-point of Dan’s original post. The conversation brought up stuff that’s been rolling around in my head for a while that I really needed to articulate, and this thread seemed pretty close. I’ll try to control myself and stay on topic from now on. :)

  68. James I think he was directing that at me.:) I apologize Dan, so to get back to your point…

    “The Palo Alto High School math teachers claim objective knowledge which they can’t possible have. This is arrogant. Particularly arrogant is the objective knowledge they claim of a student’s home life, her maturity, and the supportiveness of her parents. The Palo Alto High School math teachers are looking through an extremely cloudy lens having convinced themselves it’s clear and then saying that cloudy lens can objectively predict which students will pass and fail [insert any math class here]. This is wrong, both morally and factually.”

    Why do you think this is not possible? I mean why is it not possible to judge a student’s probability of success in algebra 2 based on their performance in algebra 1? I can understand borderline cases, but I have seen the scores, these are not borderline cases, and the actual resultant number of failures bares that out. It’s a bit out of order (logically) to say “predict” when they already did intact fail. But when did teachers lose the ability to perceive when a student was ready for the next course or not and advise them accordingly? Is that part of the “universe” also? If this were music and the student, after a year, was still unable to string 6 notes together into a melody would you still say that we can’t predict total failure in advanced music? That doesn’t seem very cloudy.

  69. Robert: An individual student really can surprise you from year to year, or from 9th grade to 12th grade. Most don’t, but some do. I would be concerned if a poor algebra I performance prevents a student from ever taking algebra 2 (i.e. they are put on a lower track with no possibility of getting off). I am not sure if that is the case at Paly or not.

  70. Former Alg2 Teacher

    November 26, 2011 - 2:22 pm -

    @Robert (post #72)

    I don’t think Dan nor I are suggesting to force students into a course that they do not want to take. I believe Dan has already stated that in a previous post (#6, for one example) and my comments about shifting the paradigm were meant to imply the very same thing (see last sentence of my post #58). Also, I believe Dan’s track record, especially when he was teaching full time and posting his WWYDWT lessons, speaks for itself. And I have too seen the TED talk by Sir Ken Robinson that James posted in comment #17, and feel the same sentiments. (Actually, an animated version of this talk is also cool to check out:

    Why do you think this is not possible? I mean why is it not possible to judge a student’s probability of success in algebra 2 based on their performance in algebra 1? I can understand borderline cases, but I have seen the scores, these are not borderline cases, and the actual resultant number of failures bares that out. It’s a bit out of order (logically) to say “predict” when they already did intact fail. But when did teachers lose the ability to perceive when a student was ready for the next course or not and advise them accordingly? Is that part of the “universe” also? If this were music and the student, after a year, was still unable to string 6 notes together into a melody would you still say that we can’t predict total failure in advanced music? That doesn’t seem very cloudy.

    Your comment about teachers losing the ability to perceive when a student is ready implies subjectivity. (And just for the record, I am not arguing that this should be stripped from any teacher nor discounted as irrelevant.) The Paly letter references these as objective reasons: poor math background, lack of support at home, low retention rate, lack of maturity. What is the objective measure of ‘lack of support at home’ and ‘lack of maturity’? I can almost agree that the closest thing to objectively determining success is an Algbera 1 grade (math background/retention rate); however, even that is dictated by a school or teacher’s belief about how students should perform. (And a personal note: my Algebra 2 grade was significantly better than my Algebra 1 grade, so I don’t necessarily think that is a sure-fire method either.)

    (Off the main topic, but IMO, I think we need to eradicate the Algebra 1-Geometry-Algebra 2 structure and start offering high school math programs that are congruent to the needs of 21st-century students. One of the reasons for the status quo math curriculum is largely due to the fact that university mathematics programs traditionally started with calculus. But as we all know, there are now many different math classes that are offered to first- and second-year university students. There is no need to prepare everyone for calculus any more, and we should provide high school courses that can prepare an individual student for which ever path he or she chooses.)

  71. ” how do you expect to “scaffold” a student who can’t perform arithmetic into understanding Algebra II, while still managing to teach the students who actually have the basics?”

    Seriously? That is the whole point. Scaffolding in this type of situation is an essential skill and pretty much the norm for any school of lesser means. With some obvious exceptions nearly any student is “capable” of learning Algebra.

    Regarding others speculating that we are arguing that it should be a requirement to graduate, you are mistaken. I agree that there is a frustratingly dumb notion to send everybody to college, take Algebra 2, etc. But the problem here is the letter is not questioning “why” in the letter but rather it shows a strange breed of entitlement that some elitist folk have.

  72. Robert: Why do you think this is not possible? I mean why is it not possible to judge a student’s probability of success in algebra 2 based on their performance in algebra 1?

    It is possible. Performance in Algebra I is a reasonable predictor of performance in Algebra II, though different teachers will evaluate “performance” in different, highly subjective ways.

    You’ve either misread their letter, my post, or both, if you think prior mathematical performance is what this has been all about.

  73. Wow, this is a harsh crowd. Dan, I’m a huge fan of your pedagogical work, but I think you’re being overly uncharitable to the authors of the letter. OK, granted, they wrote a tone-deaf letter that could have been worded better. But it feels to me like you’re reading an awful lot into a few sentences. Perhaps this is just personal preference, but I prefer to try read letters like this charitably, under the assumption that the author is conscientious and concerned and passionate and acting in good faith, and see where that takes me. What would a charitable reading say?

    You keep pushing on this word “objective”. That’s one word in a two-page letter. What if that was a clumsy word choice that doesn’t accurately convey what the authors were trying to express? Sometimes we all have experiences with poor wording choice that comes out wrong. Or at least I do; maybe you have better communication skills than I do. What if that word “objective” had never appeared in the letter? What if it had been replaced by something like “quantifiable” or “measurable” or “beyond the control of the high school”? Would you still be criticizing these teachers so harshly

    I could easily imagine a situation where teachers who have a lot of experience with students who are blatantly failing Algebra I could form the kind of views expressed in this letter — without acting in bad faith, or being arrogant, or abrogating their responsibility.

    Dan, I feel you have a better point when you suggest, instead of treating everything before Algebra II as a given and getting caught up on whether to mandate Algebra II, maybe Palo Alto should also be examining the entire math curriculum that leads up to Algebra II to see whether it meets the needs of all students. But I find that the attacks on the authors of this letter make me wince in sympathy for the authors.

  74. @Dan

    “You’ve either misread their letter, my post, or both, if you think prior mathematical performance is what this has been all about.”

    I find the wording (in the snippet of the letter you posted) odd, dumb even yes, but I haven’t seen the whole letter, your pdf link doesn’t work. Do you have another link? I am assuming that they are talking about kids that are at a very real risk of failing.

  75. Another few phrases that keep popping up are things like a math curriculum that “meets the needs of all students,” graduation standards, etc. Is there one math curriculum or set of standards that can meet the needs of all students? Or does each student have individual needs that can’t be met with one document/plan/curriculum?

    As I ruminate the impending implementation of Common Core State Standards in Montana I keep having the thought that as soon as we point to *any* document and start with the words “every student will” we’ve pointed a loaded gun at our own heads and started pulling the trigger.

    Not only do I think that any one math curriculum/set of standards/etc. is going to be too “high” for some and too “low” for others, but just plain the wrong stuff for many.

    Which begs the question: How do we develop a flexible set of standards that helps each student obtain the education that they need as individuals?

    Here’s a heretical thought: does a set of math standards need to be “rigorous?” I’m not sure I believe in rigor for rigor’s sake. I think that a kid that wants to be a musician should take rigorous music courses, but if they can do the arithmetic needed to function in their daily lives we should leave well enough alone. Are we obligated to challenge this kid mathematically? Why? How do we then identify kids that we should let be and ones that should take a rigorous mathematics curriculum?

    Other random thoughts: Is it imperative that we make every aspect of a student’s life (meaning every subject they take) rigorous? Can some things just be easy? Can we provide rigor in a few areas that interest and are appropriate for the student and will that serve them just as well?

    Okay. Too many questions. I’m now lost in my own head. It’s too late for this kind of deep thinking. Somebody throw me a life jacket. Or a large gin and tonic. Either one.

  76. Thanks LL, my bad, I missed that dan’s post had two links, it looked like one long link.

    I agree, a poor choice of words or just a clumsy way of explaining why kids do poorly in school. As soon as I read “brain theory” I knew this letter wasn’t going to enlighten me. But the message in the (whole) letter is pretty plain. There is a group of kids that will not be able to meet an algebra 2 requirement for graduation.

    According to the California STAR results last year, 81% of the students at Palo Alto took Algebra 2 (the remaining 19% are the 85 students in the letter) resulting in 58% of the students being proficient (71% of the Algebra 2 takers). For the whole state, 58% of the students take Algebra 2 resulting in 19% being proficient (33% of the Algebra 2 takers).

    My point here is that 71% of the students that take Algebra 2 at Palo Alto score proficient on the CST, 29% do not. I do not think that is being overly selective.

    While we are talking about a requirement for algebra 2, The full proposal also adds two years of a foreign language! Yuck! That is probably what the Algebra 2 requirement looks like to some kids.

  77. I read the whole letter and it paints a picture of teachers with their heads in the sand. They are a huge piece of what is wrong in that school. Everyone from administration to the parents need to be educated about what it means to be a 21st century learner. To come from an “affluent” family does not mean that you have a natural ability or motivation to do well in school. This I have seen first hand. After 11 years in an urban school where 75% of the students qualified for free or reduced lunch to 4 years in an independent school whose students come from more affluent backgrounds, I see little difference in the learner as a whole.
    Students at this age do NOT know what they are good at. Isn’t that point of middle and high school? I know that I (and I know that many of you) have changed the mind of a student who thought they were dumb in math. It’s why we teach.
    Algebra I and Algebra II content is way too cumbersome to be taught properly in the school year. The pace that some teachers employ insures failure. There is a better way to teach math.
    I believe that the countries who integrate the math curriculum are doing the best job of engaging students and showing them the true meaning and application of math concepts.
    We adopted this approach to math curriculum two years ago and the students are more motivated, work harder, see the “why” of math more clearly and are more successful on assessments. There is no gap between Alg 1 and Alg 2. All strands of math are taught every year. We teach basic trig in Alg1 and the students are geeked. Statistics runs through the curriculum from 6th grade on to Pre-Calc. We are seeing more high schoolers interested in Stats courses as juniors and seniors.
    My students are girls, who either from their parents, elementary school teachers or society, assume that they could never be good at math. They can put up so many barriers and so many excuses that it would be easy to give up on them. Some come with little number sense and panic at the thought of a story problem.
    For me to say “objectively” that they were unable to learn and be successful at math…. wow, I can’t imagine.
    Carol Dwek needs to visit and work with the whole community on the growth mindset.

  78. @Eileen, do you have any links to your curriculum or results? I said most people don’t use algebra, which is true, but when people do use it, it is the full technical and analytical version of it. iPhones, iPads and software are not designed nor built using statistics. How many women have you seen present the newest gadgets and technology that we see today? I’m just being honest here. There is a big question making the rounds as to what happened to the girls. There are actually less now in these fields than there were, say, 10 or 15 years ago, and female mathematicians are on the endangered list. It could be that they found other things that they like better, life sciences and such, which is cool. My theory is that they were taught too much damn statistics, which has almost nothing to do with the technical and analytical attributes that define most of the STEM fields. Just a thought.:)

  79. My point eileen is that if you girl-proof your entire math curriculum then you are not exposing your girls to all the paths, specifically not the analytical and technical paths. I am not saying you did girl-proof your curriculum, I haven’t seen your curriculum. But I have seen the phenomena and it is my theory that is partly why we are loosing the girls in these fields. The other reason is simply that they find things they like to do better, which is fine.

    I will stop hogging Dan’s blog now, I apologize. Thanks for putting up with me Dan, I will return the hospitality, some how.

  80. “iPhones, iPads and software are not designed nor built using statistics.”

    Having been a computer engineering professor for many years, I can say quite definitely that a lot of hardware and software does require statistics. Computer engineers are required to take at least one probability course, and recent developments (particularly the rise of machine learning and data mining) have made Bayesian statistics highly recommended for computer science grad students (required for bioinformatics).

    Google looks for statistics knowledge as well as programming knowledge, and both more than algebra.

  81. This kind of nonsense makes me not want to be a high school teacher anymore. I’m a freshman in college and I’m working towards a double major in physics and secondary education, but now I’m just considering getting a physics major. In my area these standardized tests are becoming a huge priority in our school districts. I know from experience; as an advanced placement calculus student I had to do what was the equivalent an algebra 2 review packet to ensure I would do well on this standardized test. We took valuable class time to review this packet because my teacher felt pressured by the administration to make us review.
    It’s ridiculous. I may just become a research scientist until I can get a master’s degree so I can be a college professor and not have to worry about all this BS.

    This is so discouraging. A college student with a dream, being deterred by stupid standardized tests.

  82. Suzanne – This is the ugly side of teaching math for sure, but do not get discouraged. Teaching math is the greatest!! Right now mathematics education is going through some growing pains. The classroom is still the same. The students are still the same. I love being with my students. I wouldn’t do anything else. As teachers we whine and complain. In the end teaching Algebra 2 to every student may not be possible, but some of the topics covered in this class are essential for students to understand in order to take part fully in our society. For instance, I would argue that the housing crises could have been avoided if more Americans understood the exponential function. Many had no idea that a variable rate interest would make that big of a difference in their 30 year mortgage payment, or that y = mx + b occurs in almost every aspect of our lives. It is our jobs to show them these connections. It is our jobs to give them the tools to not be taken advantage of mathematically (finance). Show me a job that could possibly be better?
    We get to be the advocates to those who the rest of society has given up on. We get to make a difference in the lives of students that are told by other teachers/parents/society they can’t do it. We get to prove the arrogant naysayers wrong. There is no greater feeling in the world than to hear that student who you yourself had almost given up on say, “Wow, Mr./Mrs._______, I get it!”

  83. Most kids can learn Algebra II. Most kids should learn Algebra II, and too many don’t.

    Algebra is a skill used to develop higher level thinking, analytical thinking. It teaches students to work hard, to seek understanding, to push themselves to succeed. But, not if the teachers don’t valuse these traits that make the learner sussessful.

    Too many of the above are basing there ideas on insufficiant data – why – cant those kids learn? Why dont they learn? Is it cognitive ability? Do you even know what you are talking about, or is all you research on “why” they can’t learn based on your own beleif system, based on what you are conditioned to believe, based on ignorance and the inability to critically read research and develop lesson plans and tests that are significant.

    Most of the above comments are based on personal ideas and lack in critical analysis. Maybe, perhaps if we had more teachers that could look past thier own simple ideas – kids could and would learn.

  84. I would like to bring family educators into this conversation. At every homeschool meeting I visit, parents discuss decisions: “My kid will do these projects and subjects areas, and will not do those projects and subject areas.” These discussions never get to the level of drama and strife presented here, though of course, sometimes there are disagreements between kids and their parents, resolved within each family. These conversations and decisions, in family educator communities, are normal and non-controversial and very much a part of the daily routine of education. And yes, many delay Algebra II beyond the age of 18 years (possibly forever, as the case may be).

    One size does not fit all.

    But who will act in loco parentis for kids whose parents don’t?

    My kid told me this Summer she does not want to do any math for a while, other than what comes in her freelancing. I don’t know what “a while” means. She’s doing that Stanford free programming course this Spring, though – because she’s inspired by Cory Doctorow’s work of programming as a social change force, and is doing a project with friends Cory though was a good idea, etc. I would rather she did this – or any number of other things – with love, than whatever math course is “next” without love.

    Yesterday, I had a relevant conversation with a public school student I tutor in Algebra II. He loves math ideas and has beautiful insights, but he’s not good at computation by hand or paying attention to where the minus has to go. He would be brilliant in any computer-based math activity; as it is, he’s in the least demanding Algebra II class in his elite magnet school. He shared the fact both kids and the teacher in the class got so depressed this Fall that the teacher is quitting the profession over it. This isn’t right.

    The point: this discussion can be about unique personal interests, desires and strengths of children.

  85. Suzanne,
    Daniel has a lot of good reasons not to give up. I would like to add that, in spite of the ugliness of the bashing of teachers, public education in general, etc, there has never been a better time to be teaching math (thanks iPad). The blog we are reading and responding to is part of a terrific guerrilla network of the best professional development anywhere. Finding these resources online has benefited me enormously as a teacher, and benefited my students as a result.
    The state tests are focussed on minimums, and teaching problem solving skills beyond them is the best strategy – it’s the best preparation for those who continue in math and the best preparation for problem solving on tests, whether state or SAT.
    You can find ways to connect math to all kinds of social issues and debates as well as science and finance connections. There is much that is poorly understood about important issues because people generally lack the necessary foundation in math. Kids appreciate being in on the know – because you brought them in.

  86. I am 64 years old. I have always been very good at basic mathematics and finance but have a complete blank with Algebra and was a complete failure at scholl with it. I even went to adult classes for g.s.c.e maths qualifications, raced away from the rest of the class in general maths , then algebra starts……result , after one term of it , well I just gave up !! My job before I retired was as an engineer, everyone came to me for advice on finance and to work their calculations out, nobody remembered the Algebra they did at school and nobody ever needed to !! In UK children are leaving school unable to do even basic maths. Why not concentrate on teaching things that the average person will actually need in life, learn about avoiding getting into debt, mortgages, banking, how to get best value shopping etc and lastly basic maths. In my opinion Algebra should be an optional class, it spoilt my chances of getting qualifications as I could never understand it . Lastly a true story that happened to me . When I was studying as a mature student for my city and guilds in engineering, we had a gearing reduction question which the teacher worked out in algebra, everyone else followed, accept for me , I worked it out using fractions. Of course the answer he came up with was different to mine but I could not see where I had gone wrong, all the young students laughed at me !! So I said to the Teacher if he had an answer book …..and he looked the answer up……I was right and he and the rest of the class was wrong !! So he was very astonished, sent the class home while I stayed back and showed him how I had worked it out. He took my work, phot copied it and handed it out to the class next week to replace the wrong answer done by algebra. Problem is he had got it wrong and because the students did not understand algebra they just copied what he said was right !! I passed the course with top marks and was given the award as student of the year.
    But I still cant do Algebra !!