How Students are “Accelerating” in Math at Aragon

Two weeks ago I posted an article requesting more information about reports regarding an increasing number of freshmen and sophomore students at Aragon who are already enrolled in calculus.  This is what I learned.

In response to my post two weeks ago, I received several replies from parents of students immediately thereafter, but had to wait for over a week to get official information back.  Somewhat surprisingly (but not too much in retrospect), every parent who responded requested anonymity.


I will summarize my findings below, but first let me start by noting that one parent replied and vigorously defended the Aragon math department, stating that the teachers are dedicated, caring, and excellent and that my “attack” was unfounded.

I replied that the article in the link above said nothing critical of the math department and was simply a request for information about how students were getting into calculus so early in high school and whether this push was causing overcrowding at the school.

Clearly in many past articles I have written critical comments about Aragon math, but I have also lauded several Aragon math teachers (recently Mr. Reiss and Shahrvini).  That said, I replied to this parent that I have not, and will not, shirk from writing constructive criticism when I think that an important problem exists, such as when the department embarked on the ill-fated CPM precalculus trial in 2016.

Teachers are constantly grading students.  They also have an important public trust.  They must be open to public scrutiny and comment.

I have also been a longstanding critic of the AP program in general, but, once again, let me make it clear that it is not the Aragon math teachers who are responsible for the AP program.  They are carrying out their teaching assignments to the best of their abilities and their students usually get good AP test scores.  My criticisms of AP are not a criticism of them.  I should also note that, in today’s (9/29/2018) San Mateo Daily Journal, a local student is speaking out about the problems with the AP system.

I deal with students and their classes on a daily basis, have an advanced science and math educational background, plus work experience in the field, as well as no need to worry about job retaliation from any source.  I am therefore one of the few people in the community able to address these issues openly.

Finally, before I get to the question of accelerating math students, I also want to note that the comment section of my blog following each article is open to anyone who wishes to post contrary opinions to mine.  I moderate it only to avoid the kind of incivility, profanity, etc., that is the hallmark of sites like Twitter.

Unfortunately, local people tend to refrain from public postings like I mentioned in the first paragraph above and instead tend to contact me privately.  My review of the CPM math textbook series (which has now been read more than 4,000 times by people around the U.S. and beyond) is one of the few exceptions and has attracted comments from many locations outside San Mateo, but even here personal details are frequently omitted.

If having to gather information from people behind the scenes is the only way to make progress, I am happy to continue to do so, and urge people to feel free to contact me privately with their concerns, e.g., through the Contact page on this web site, if they do not wish to do so publicly.

Now to the results of my inquiries…

I have heard much over the last few years about the Russian School of Math, a nationwide organization with an office in San Mateo, and wondered if it was playing a key role in accelerating students in local math placement.  Several parents have mentioned it in Nextdoor postings, at public meetings, and in private conversations with me.

While some kids who are advanced in math do attend this after school program, it turns out not to be the main ingredient.  I always had my doubts because I wouldn’t think that any public school district would offer transcript credit for a class taken at a private company.  The only way that I could see the Russian School being a real factor is if the work taken there was assisting in getting higher marks on a school math placement exam, but I have yet to hear of a student being placed into calculus by placement exam alone (this does not mean that it may not have happened; I just have not been able to get an official response to this question.)

The following block quote is the most cogent comment (the writer gave permissions to be quoted anonymously) that I received explaining how students are being accelerated.  Other parents separately confirmed various parts of the following story.  Note, however, that I have not independently corroborated the sentence beginning “Teachers have no input…”

I must admit that I am almost hesitant to publicize this quote for fear of inflaming an already overheated education “arms race.”

That said, if a student loves math and is looking for enrichment for him/herself, then it is good to know that such options exist.  However, if this is being done solely for college “resume building” purposes, I can not endorse such a practice.

Here it is:

… the middle schools are offering a zero period Geometry class, by invitation only. Students are selected by the district supposedly based on class grades and standardized test scores. Teachers have no input and do not have knowledge of the selection criteria or even who has been selected before the school year begins. These 8th grade students take Algebra I during the regular school day concurrently with Geometry before the school day starts, so two math classes at once. Some students may then apparently decide to take Algebra II at CSM over the summer, thus setting them up for Pre-calculus as freshmen and AP Calc as sophomores. Interestingly, this pathway is not shown anywhere on the SMFCSD math pathways.

Another parent writes, speaking of the San Mateo Foster City School District, (quoted anonymously by permission):

For the last few years, the district has given children in 5th grade a math placement test in the spring. This test score is combined with their Galileo test score, and their CAASPP test results to form an index, and the kids are then assigned to the regular math pathway (6, 7, 8th grade math; algebra in 9th grade), or the accelerated pathway (6 and half of 7th, half of 7th and 8th, and algebra in 8th grade).

In theory, the district doesn’t want 8th graders taking geometry. However, there are a lot of parents who demand that the district provide geometry classes for their children, because they used to under the old system, and they claim their kids are ready to take it (and some are.) . However, there is no option to advance beyond the accelerated pathway, so these kids wind up taking *both* algebra and geometry in 8th grade.  (One can see immediate problems with this, given that some knowledge of algebra is necessary for geometry, but I think in reality, the kids who sign up for geometry probably already know algebra.)

The district has held a special geometry class at district headquarters for the last year or two; this became necessary when too many kids demanded geometry, and there wasn’t room to send them to classes at the various high schools (some 8th graders did take geometry at the high schools).

Let this sink in for a minute.  Students following the pathway above are covering three normal years of math (geometry, Algebras 1 and 2) in one school year and the following short summer at CSM…

While the schools allow this pathway, I highly doubt that they endorse this practice.  In fact, all of the parental furor over math acceleration developed after the schools tried to cool things off by adopting a slower pace with the Common Core math pathway.

This is also where going to the Russian School of Math may facilitate such a demanding schedule.  Following the ill-fated adoption and then abandonment of the Everyday Mathematics program by the SMFCSD several years back, I am still dealing daily with many students, even in calculus(!), who have weaknesses with fractions and other topics covered in elementary and middle school.  If students were to attempt such a hurried schedule without first having had outside assistance such as Russian Math to remedy these elementary school defects, I would have an extremely hard time believing the outcome could possibly be good.

This explains how students get into calculus as a sophomore, but I have not been able to find out how a very small number are getting in to calculus as a freshman.

The next issue arises at the end of the above pathway.  Some sophomores manage to go directly from precalculus to Calculus BC which then sets them up for multivariable calculus as a junior, leaving them with no high school math options left as a senior!!  As I mentioned in my initial post on this topic, I was getting calls for help for some of these students.

Aragon has always allowed some top students to go from precalculus directly to Calculus BC, skipping AB.  I have strongly advised against doing this, but acknowledge that it may be OK for a few geniuses.  Sadly, this results in a tremendous burden being felt by strong students who are only “near geniuses” but want to try to keep up with their “smart friends.”

One parent told me that Aragon students are allowed to skip from precalculus to BC if they have both a 95% or higher grade in precalculus AND a teacher recommendation.  Unfortunately it appears that the school may not completely enforce that rule, and that some students got into BC without meeting this criterion.

School administrators and teachers sometimes back down in the face of a strong appeal.  Rather than fight about it, the school allows the student/parents to discover the consequences of their decision…

I agree that such cases are hard to adjudicate using a general rule.  There will always be a small number of happy exceptions who succeed in a class despite initial doubts against them.  That said, I strongly advise any student/parent who is willing to take such a high stakes gamble to line up tutoring or other help in advance, e.g., at the end of the previous school year.  Any tutor who is worthwhile will already be booked if one waits to find help until the end of the first grading period in fall semester.

It also concerns me that our education system has come to the point where paid outside tutoring help is almost a prerequisite for success.  Public schools were always envisioned as an avenue which talented people, who had the misfortune to be born into an economically-challenged situation, could take to better themselves.  The “rigor” of the AP system is making public education increasingly expensive and risks putting it out of reach of talented students of limited means.

My biggest concern about all of this acceleration frenzy remains:  Are these kids doing this because they enjoy mathematics and want to pursue it or a related STEM subject, or is this resume building for Harvard/Stanford admissions?  I am very concerned that this kind of pressure turns kids off to these fields instead of encouraging interest.  This will impact our country negatively in the long run.

That said, I have many friends who are immigrants and work in tech fields, not only from Asia but also from Europe.  They say that, in their countries, students take much more math and science than is traditionally offer in the U.S., and thrive in doing so.

For example, I was in the Peace Corps and taught in Malaysia many years ago.  That country followed the British syllabus, and the top students started calculus in the 9th grade.

I should note, however, that many of these Asian countries were in a race to develop their countries technologically, and it was a national goal to quickly develop a technological elite.  Malaysia and other similar countries succeeded in this quest, but what does not get mentioned is the number of people who fell by the wayside in pursuit of this goal.  I also think that authoritarian governments realize that keeping students focussed on technical subjects may keep them out of politics!

In the U.S., our goal has been to educate all students through high school to be participants in a self-governing society.  This means providing a broad-based high school education in many subjects instead of focusing just on STEM.  Specialization does not start until college.

My tech friends will reply that they do not want their kids to fall behind in the competitive global race, and this is very understandable.

Many of my clients are also of Chinese descent.  One told me previously that older Chinese people would always say that “life is hard” and that, if you don’t work unceasingly, you will be crushed.

I can understand how such an attitude developed, particularly in the case of China which went through unfortunate struggles with colonialism, overpopulation, and famine at times.

My grandparents also immigrated to the U.S. from Europe.  They, as do most immigrants, came here to find a better life.

Nonetheless, I always remember, when I was a child, listening to them sometimes talk nostalgically about “the old country” and how things were done there.  I also remember them being irrationally influenced by the prejudices that they brought with them from Europe.  For me, it was almost a sense of relief to finally move to California in the 60s and leave that behind.

When I lived on the east coast in the 50s and early 60s, people always asked about your ethnic heritage.

I would reply that I was an American.

It is exciting, albeit expensive, to live near Silicon Valley, where the future is being made. A consequence is that we are a crossroads of the world with many cultures and ideas intermixing.  This impacts many aspects of our lives, including our education system.

Although parts of California have some of the worst poverty in America and one hears often about hunger in our country now, deprivation has not shaped our world view since the Great Depression (I still remember my grandparents being extremely careful about not wasting food).

We have to ask ourselves what kind of society we really want to build, because our education system reflects those desires.

If we direct all of our efforts into cutthroat competition due to a fear that resources are limited and that only the strong will possess them, that is exactly the kind of society that we will create.

We are already well down that path.  In that society a few will do quite well, but many of lesser ability will fall by the wayside.  We are already seeing some of the results, for example, in the recent highly publicized snatch-and-grab raids on Apple Stores.  In the long run the system could become top-heavy and collapse.

It doesn’t have to be that way, but if we stick solely with “old country” thinking, that is what we will get: a school system that is focussed on standardized exams and cramming for the test instead of one that promotes the love of learning and develops people’s potentials.

This is not to say that everything we are currently doing is for the best and that we have no reason to listen to other inputs.

It is saying that we need to be open, listen to each other, and evaluate ideas in the light of logic, not solely because “this is the way it was done where I came from.”

That is why I continue to try to facilitate this discussion through this forum.  

Unfortunately it saddens me that parents are fearful of retaliation, and school administrators and teachers tend to circle the wagons any time someone tries to say that there may be a better way of doing things…

Lastly, I was concerned that the push to accelerate kids in math might be leading to overcrowding at Aragon.  Apparently the freshman class this year is around 500.  I was also told that Aragon currently has three classes of Calculus AB and three classes of Calculus BC, the most it has had in some time.  I was not able to get precise class size information, but parents who commented tended to put their students’ classes at “a little over 30.”

I was not able to get from the school itself precise numbers on freshmen and sophomores in AP Calculus.  I was told only that this year it was “very few” and that the year before there were “more.”   I also still do not know the path that would allow a freshman to take calculus (a placement test?  Even more summer school than mentioned above?)

I would think that this should be public information, and would really like to hear these statistics/information.

Teacher class sizes are capped by contract at 35 (which in my opinion is pretty large).  I remain concerned that directing too many students to Aragon in accelerated math will lead to overcrowding and extra stress for the math teachers.  This could then backfire by leading teachers to make their classes even more difficult at the start of each year in an attempt to quickly wash “excess” students out of the classes and reduce class size.  These kids already have enough demands placed on them, not to also have to start the school year off under this kind of discouraging burden.

As I have stated repeatedly, precalculus and AP Calculus already cover far too much material far too quickly.  We don’t need to add pressures and make matters worse.

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Author: David Kristofferson

Retired scientist, teacher, bioinformatician, IT director, software product manager, AAAS Fellow, avid cyclist (7690 miles and 724,300 feet of climbing in 2015), backpacker, you name it! Current avocation is tutoring high school students near San Mateo, CA in mathematics, physics and chemistry. Please see the Bio link in the right sidebar for my detailed background information.

8 thoughts on “How Students are “Accelerating” in Math at Aragon”

  1. 3 comments on your article:
    1: First parent quote:”Interestingly, this pathway is not shown anywhere on the SMFCSD math pathways.” Since the SMFCSD recommends for the majority of students to finish middle school in 8th grade Math. They won’t recommend/advertize to take additional classes during the summer at CSM.

    2: Second parent quote: “However, there is no option to advance beyond the accelerated pathway, so these kids wind up taking *both* algebra and geometry in 8th grade. (One can see immediate problems with this, given that some knowledge of algebra is necessary for geometry, …” The teacher who did the 0 period in Borel actually supplemented the geometry curriculum with Algebra curriculum when needed. His curriculum was similar to a European Math curriculum where an Algebra lesson was taught prior to a Geometry lesson when the content was needed. He even covered some Algebra 2 concepts.

    3: Yes RSM is an add-on of the regular Math class in elementary and middle school. It provides the right foundation for a student to succeed in HS (I’m not affiliated to them!!). It also provides for some students some challenges that they are not getting in their elementary school. Again, when a teacher has a 6th grade class with 25-30 students, with some students who don’t know their multiplication table and can’t multiply or add fractions, the teacher’s priority is to put those students at level. There is no time to teach and challenge the more advance students. And yes it means that students with family with the means to pay RSM have a better chance for college and it starts in elementary school!

    Finally, The last level provided in the RSM is (I might be wrong) Algebra 2. It shows that there is a high demand on elementary and middle school Math classes, which I let everyone conclude the obvious….


  2. When we live our lives from a place of fear … of having or being less than, of not being good enough or having to be better than … we set inauthentic goals & promote a “me/us vs them” mentality. The end result is never good. Not for an individual, a community, a country, or the world. Thank you, David, for asking great questions, doing the research, and providing your thoughtful perspective. It may not be popular with some … especially in the Bay Area … but it’s profound, and … I believe … provides a glimpse of changes to come.


  3. Part of the problem seems to be the inflexibility of their system. I have a freshman taking geometry and he finds it painfully boring. He wishes he had started at the next level of math, the combined geometry/algebra2/precalc program. I was leery of shoving all that material in too quickly so had him take the ‘slower’ path and now he has a 99 in the class and is chomping at the bit to move faster. The school won’t even talk to me about how to let him move up, or how to judge how hard the following years will be. He seems to be stuck in this lane even though it’s barely second semester of his first year. This isn’t a case of ambitious parents hoping for a math prodigy, it’s a student who loves math who is getting no chance to learn more. Shouldn’t there be some path for the kids who find they love it and want to go faster?


    1. Kaaren, you are exactly right. It is getting painfully apparent to me that the regular stream is too slow and the accelerated stream is too fast for many students in the middle to upper middle. This will be the topic of my next blog article and I am unfortunately going to have to revise some of my past recommendations about the regular stream. It is a complicated topic though and that is why I haven’t composed it yet. However, with next year class sign-ups happening probably next month, I have to do it before then.


  4. Enjoyed reading the article and agree with the overall conclusions. One additional data that I would like to bring up about immigrants is this. There is a component of “how it is back there” like you have described. However, another big component is that many of these immigrants who work really hard in the Silicon Valley tech companies, quickly realize one thing in their career – even when they work twice as hard as their white, male colleagues, success (as measured by promotions or assignments or bonuses and pay etc.) does not come to them equally. They respond with the only way they know, which is to ensure that their kids are also working as hard as they are – because the world they experience in their daily corporate life isn’t fair and they see the results every day. I would add that the US is (or was up to 2016) probably the country that has made the most progress in this area, but the reality and statistics point to the need for more work to be done in this area. So an immigrant from Europe will have a very different experience than an immigrant from Asia in their tech career. If you are a woman, the challenges are compounded. The only ones that break through the barriers are the truly exceptional ones – and hence the drive to make their kid into an exceptional one.


    1. You make a good point, though I am also glad that you mentioned progress on this front in the U.S., at least prior to the ascendency of Trump. I have worked overseas and this issue is universal. We are much more open about it in this country, but I am also concerned like you are that things are heading in the wrong direction here. Sadly similar “populist” movements are sweeping the world now in Europe as well as in Asia. With all of the uncertainties in the air, people tend to “circle the wagons.”


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