How hard should it be to pass algebra?

New York State is grappling with the difficulty of the Common Core Algebra test.  The intent is to raise the passing score to require real mastery of the material, but realistically speaking, most students are not reaching mastery.  (In fact, even with the original, very low standards, some students had to take the exam many times to pass or might not pass at all.)

The core of this issue seems to be: what is the purpose of teaching algebra?  For example:

  • If the purpose is to preserve the opportunity for all students to enter science/engineering/math, then the standard should be high.  It does no good to a student to barely scrape through algebra if they want to be a scientist.
  • If the purpose is to give everyone exposure to a beautiful subject, then the standard should be kept relatively low: it is the exposure, not mastery, that is important.
  • If the purpose is to give people access to math they need for life, then algebra should be dropped or revamped.  Many people do not need algebra in life, and a high barrier to graduation does them no good.

Right now, the grade required to pass is being used as a proxy for this kind of battle.  Those whose focus is on high school graduation want the required grade to drop.  Those whose focus is on preparing students for STEM careers want it to go up.  Without resolving this difference of goals, everyone will just keep shouting at everyone else and we’ll end up with a muddled policy that drags students in multiple directions.

Alas, that is not so unusual.

NYC’s high school selection system might be the worst system for choosing a high school — except for all the others

The New York Post published an opinion piece about the byzantine high school selection system.  As someone who’s helped well over a hundred students through this system, it really is byzantine.  There are over four hundred non-charter public high schools in the city, plus dozens of charter high schools.  In eighth grade, students can complete a “Round 1” form where they rank the high schools they are most interested in.  Each of those schools have different criteria for judging admission: some are based on your grades, test scores, or attendance; others, on the level of interest you show by attending information sessions; others, on a special test you take for admission; others on a portfolio you submit; others on an interview you do; others on geography; and finally many combine several of the above.  Just as you rank the schools, the schools rank you.  Then an algorithm is done to match students with schools.  Just imagine having to research all those schools, understand each one’s admissions priorities, and then complete all those applications!

Sound complicated?  We’re not done yet.  In a separate process, there are the specialized high schools (think Stuyvesant, Bronx Science, etc.) which have their own test, the SHSAT, which you take for admission.  Admission is based solely on this one test, and many people study for years.  (A sad waste of talent.)

No, we’re still not done yet.  Based on the SHSAT and your Round 1 form, you get a school assignment in March, which could have 2 schools (if you got into one of each, you get to choose), 1 school (if you got into one “normal” school and one specialized school), or 0 schools (if you were not placed with any of your Round 1 schools nor did you score high enough on the SHSAT).  At this point, you can complete the Round 2 form, in which the same matching process is used as Round 1, but with those schools that are left over.  (Usually, not the good ones.)

If the Round 2 process doesn’t work out, you are automatically placed into a local school that has space.  But it’s still not over.  You can appeal your choice if something went wrong.  You can also apply separately to charter schools (yes, they’re in another totally separate system), which are decided by random lottery, but the more you apply to, the better your chances.

All of which is to say, the process is truly, incredibly complicated.  (I also simplified it, leaving out LaGuardia School of the Arts, private schools, and many intricacies of appealing your placement.)  As the Post‘s opinion piece justly points out, this process dramatically favors more affluent students who have much better coaching and access to information.  (Let alone that they often speak better English.)

You might think, at this point, that I agree with the author that we should abolish this system.  After all, it clearly favors affluent students and takes a lot of time for everyone.  But there is one key problem: nothing better has been proposed.  At least the current system gives students a chance to go to a better school.  At BEAM, we can coach students on how to get into a great school that will challenge them, and we have tremendous success.  Some families find their way on their own.  Compare to a system that just places students by geography, in a city that is highly segregated (by race and income) — what chance would low-income students have then for access to these schools?

This is a subtle issue.  Maybe a system based only on geography would help, because then there might be some mixed-income schools (although I find that unlikely).  Maybe the current system has another downside, “creaming” the best students from low-performing schools, leaving them worse off.  These are interesting questions, questions that deserve study.  But it’s not worth changing a system that offers some kids incredible opportunities unless you’ve done a very careful examination of the trade-offs, and we frankly have no idea!

So what should we do?  If more students had real advising on navigating the high school system, they could be vastly more successful at getting into great schools.  There are so many big mistakes that students make all the time: not filling in all 12 spots on the Round 1 form, for example, or incorrectly judging what school to apply to.  (We had a student who decided by looking at schools’ graduation rates, not realizing he’d ranked a dual-language school specifically for English Language Learners, a decision that he is now stuck with for 9th grade even though he does not speak fluent Spanish!)  Just as we need more guidance counselors for college applications, help with the high school application process might create a system that offers tremendous opportunities for all students, regardless of background.

Algebra for All in NYC

Mayor Bill de Blasio has announced a plan for every New York City middle school student to have access to algebra in 8th grade, and Chalkbeat is out with a great story discussing the challenges facing the initiative.

I work with many exceptional middle school students at BEAM, and for many, the lack of algebra in their middle schools is a tragedy.  No access to algebra closes doors; it’s as simple as that.  That’s because most people who pursue science degrees have taken calculus in high school, so you’ll be significantly behind if you don’t have that background.  But getting to calculus in high school requires taking algebra in 8th grade, unless you double up on math in some year!  There are ripple effects throughout high school and college; no 8th grade algebra makes it much harder to pursue a science major in college (which is why BEAM offers an online algebra course).

Yet simply providing some algebra classes opens a host of other issues.  First of all, algebra must be taught well, which will be hard for teachers who are not experienced teaching high school level math and who may not have the mathematical background to offer a high quality course.  Moreover, in many schools a teacher will have several classes of normal 8th grade math, and one algebra class—where would you put your prep time?  But the bigger danger is that kids who are not ready for algebra will be pushed into it.

The Chalkbeat article seems to treat this as a good thing, talking about “lower-performing students who could use the early exposure to a subject that trips up many students in high school.”  But if a student does not deeply understand earlier material, then accelerating is a mistake.  A study in California (also, paradoxically, in the same Chalkbeat article) points out that when California mandated algebra in 8th grade, those students got lower scores on 10th grade math two years later.  Really understanding algebra requires really understanding math.  Otherwise, you’re just memorizing formulas and not learning anything.

In fact, algebra is something of a debacle right now in New York.  On the old, easier, pre-Common Core Regents exam in New York City, roughly a third of students had to take the test multiple times to pass.  (And let me tell you, a pass does not demonstrate mastery.)  A quarter of students had to take it at least three times.  There were 66 students in New York City who took the test ten or more times, and half of them still didn’t pass!  Even for those students that did pass, did doing so on the tenth try really mean that they got something out of algebra class?

Fundamentally, there is a mismatch between what we are aiming for, namely that all students take algebra, and what we are achieving, which is that many students take the test repeatedly, focus on memorization, and don’t learn mathematics on a deep level.  Algebra should open doors.  There are no doors being opened by memorizing formulas, which (barring exceptional teachers) is all you can do when you don’t have the mathematical thought processes down going into the class.

It is good that algebra will be available to everyone.  It is a critical equity issue.  But for students to really take advantage of this opportunity, there is a lot more groundwork that must be put in place.

Should a test determine your high school?

In New York City, there are several highly selective public high schools called Specialized High Schools.  You’ve probably heard of some of them, like Stuyvesant, Bronx Science, and Brooklyn Tech.  They’re excellent schools.  The way you get in is by taking the test that might have the most frightening acronym I’ve ever seen: the Specialized High School Admissions Test, or SHSAT.

New York has been embroiled in a conflict over this very policy.  The SHSAT was created to provide an unbiased measure to try to combat racial discrimination in admission and to create greater diversity in the schools.  It hasn’t worked.  Out of 952 students admitted to Stuyvesant last year, only 7 were Black.  Seven.  In a city where 25.5% of the population is Black, less than 0.7% of Stuyvesant’s admitted students were Black.  (Stuyvesant had the highest cutoff scores; the results for other schools were significantly better but nowhere approaching representative.  For example, 6.9% of admitted students to Brooklyn Tech were Black.)  The situation is so bad that the NAACP has filed a lawsuit over specialized high school admissions alleging that the SHSAT is racially discriminatory.

Now, I run a program for underserved New York City middle school students with talent in math.  We work to create a realistic pathway for our students to enter into careers in science, mathematics, engineering, programming, and more.  As you can imagine, admission to a good high school is critical to their success.  It matters a lot if you have the opportunity to study calculus, to be on a math team or a robotics team, or to do independent research.  Our students are 88% Black or Latino.  Over 25% of them get into specialized high schools, and another 25% get into other highly selective schools in the city.  Getting our kids into good high schools is of primary importance to me.

I wish that changing the SHSAT could possibly address the problems faced by our students, and students like them across all of New York.  It won’t, and we shouldn’t change the system without a viable alternative.

Why?  Because the SHSAT is just reflecting a stark reality: minority students in New York City are less prepared, and they are not given a chance to excel.  If we drop the SHSAT, we might see an increase in diversity.  But it will stratify the schools, creating two tiers of students, those with adequate preparation (who will be taking advanced classes) and those without it (who will be taking more basic classes).  Can you imagine a school with such obvious racial segregation?  This would send the wrong message to the students, the teachers, and the outside world, and it would paper over the truth, which is that these incredibly brilliant, incredibly promising kids are not getting the education they deserve at a much younger age than high school.

Let’s see if we can understand just how stark this difference is.  There is a test called the National Assessment of Educational Progress (NAEP).  It is a low-stakes test given every few years to a nationally representative sample of students, with sub-samples in major cities.  Because it is low stakes (nothing depends on the outcome), no one studies for it.  It’s just a measure of what they’ve learned.  While there might be biases—some curricula might be more closely aligned with it than others, for example—within one city it’s a good measure.

NAEP has a wonderful online tool where you can run queries on its data, so I did.  So let’s see what percentage of students score at the Advanced level on this low-stakes test in New York City in 8th grade.  Asian students?  26.20% score at Advanced.  White students?  17.72%.  Black students?  1.40%.  Hispanic students?  0.93%.  That’s not a typo.

No one is studying for this test.  There are no cram schools for it, no tutors.  Much as I dislike tests, as far as measures of what the students have actually learned, this is pretty good.  And what we find is stats which, when scaled for city population, match the overall specialized high school admissions pretty well. (*)

Now imagine that you artificially admit more underrepresented minority students.  What happens?  They are not as well prepared.  Obvious differences appear in the student body.  And it doesn’t fix the real problem, the one that no one seems to want to address, which is that the students are not adequately prepared when they are younger.

I’ve worked with a lot of our alumni who go on to specialized schools.  It’s a tremendous opportunity for them.  It’s also very, very difficult adjusting to a much more rigorous academic experience than what they had in middle school.  We provide a lot of support and tutoring, like what more affluent students would be able to get.  Broadening admissions simply does not address the real issues.  Moreover, there are several great schools in the city (such as Bard High School Early College, or The Beacon School) which are not based only on tests, but consider grades, interviews, portfolios, and more.  We recommend each student to the school that is the best fit for them both for admission and for attendance.  There are other options.

There are serious, legitimate questions to be asked about the SHSAT.  The test should be properly validated.  It should be examined for racial bias.  We should consider other admissions mechanisms that might be more fair—but not jump to them willy-nilly!  Right now, there is no serious alternate proposal that looks likely to accomplish the goals of the specialized schools, and there is no evidence that the SHSAT is discriminatory given the prior academic achievement of the students who take it.

Now can we please, please, please support the very promising students in elementary and middle school who are ready for more math in their lives?


(*) It does seem like a higher than expected percentage of admitted students are Asian, and lower than expected percentage are White, but this could be due to any number of factors: extra studying on the part of Asian students, data based on city-wide demographics instead of based only on school-age children, NAEP’s “Advanced” ranking is in the wrong place on the bell curve, or because a larger fraction of White students go to private schools.

A Reminder That Personal Relationships Matter

I wanted to briefly point you all to an article by Atul Gawande in a recent New Yorker.  Gawande is writing about the adoption of medical advances, but his remarks about teaching rural nurses in less developed nations are as relevant as anything to education.

Gawande asks: what drives a nurse to internalize that hand washing or warming the baby are important for safe childbirth?  He has a fascinating description about how one nurse was able to persuade another nurse to change her practices by becoming her friend.  Not because the mentor nurse’s training was impressive, nor because she had the force of law behind her.  Because the two of them sat down to tea.

Gawande says that success at getting nurses to adopt improved methods—especially those (like hand washing or warming the baby) whose effects are only visible after the child has left the hospital—come from personal connections formed by mentor nurses.  Otherwise, no matter the law, no matter what classes or informational videos or glossy handouts you offer, change comes slowly if at all.  To me, this sounds a lot like convincing kids to learn mathematics or to want to go to college.

Indeed, I think that these observations, hardly a surprise to anyone who’s seen the success of individual tutoring and mentoring, have implications across education.  I suspect that a difference between successful charter schools and unsuccessful ones is while both shout “college! college! college!” from the rooftops, only successful schools forge persuasive personal relationships.  While MOOCs make great resources available, they still have to persuade people to invest time in their classes.  How much did you learn from your best teachers because you felt like they knew you personally, or because you admired them and wanted to be like them?

Anyway, it’s a great article.  Read it while thinking about teachers—especially the difference between great teachers and merely good teachers—and it will give you provocative new thoughts about education.

The Latest Updates from SPMPS

I periodically send update e-mails to our supporters.  Here’s the latest:

Dear friends of SPMPS,

What happens when almost 40 middle school students from low-income backgrounds get to learn mathematics topics like Logic, Number Theory, and Combinatorics?  Amazing, amazing things.

In Group Theory, instructor Ben-Blum Smith invented a dance.  As Ben played on his guitar, the students responded to calls like “East-West Switch”, “LAX to JFK”, and “Jam in Place” to learn about symmetry groups.  In Proofs, Shelley taught her students about the pigeon hole principle and how to phrase a formal mathematical proof.  In Numbers, Sets, and Mappings, Marcus helped students prove that the quantity of natural numbers is the same as the quantity of even natural numbers, but that the real numbers are a higher order of infinity.  In Circuit Design, Sage helped her students construct circuits to add two numbers in binary.  In Digital Communications, Taylor’s students designed their own methods of sending images across a room using nothing but sound.

Thirty-nine students came to the program and got their first entry point to advanced mathematics.  Of course, the summer is just the launching-off point: over the coming year we will be connecting students with selective high schools and summer programs, the New York Math Circle, math contests of all kinds, and other opportunities that will open a new world up to them.

We’re still crunching the data, but here are a few outcomes that we’re already seeing:

  • Students took the AMC-8, a contest given to advanced students nationwide.  By the end of the program, the average of our students’ nationwide rankings grew by 21 percentile points!  Six of our students, exposed to serious mathematical study for the first time, saw their scores rise by 40 percentile points or more.
  • Students reported huge changes in their dispositions towards mathematics and challenges.  97% agreed that the program “showed me that I can learn more than I thought I could”, and 82% strongly agreed.  Students also learned the importance of hard work (not just natural brilliance) and of frustration and challenges: every student agreed that “Working can improve one’s ability in mathematics”, and 95% agreed that “time used to investigate why a solution to a math problem works is time well spent”.
  • Students raved about the program in their summer evaluations.  “A life-changing thing,” wrote Edson.  Math is “the best subject in the world” wrote Faith, who also said that she learned to “stop being shy”.  “I find math as a more common language than the language I speak”, said Seth.  Tiffany summed up something that many students said: “I want from liking math to loving it.”

Next year, SPMPS is looking to grow to a second campus.  We’ll be able to serve twice as many NYC-area students.  This expansion is possible thanks to a three-year grant from the Jack Kent Cooke Foundation which expires after next summer.  We’re fundraising now to raise the difference to make the second site possible next year, and also to help us transition smoothly as this grant concludes.  If you are able to contribute or you can make an introduction to someone who might be able to, please do let me know!  We are working to raise an additional $150,000 over the next twelve months to help support summer 2014 and summer 2015.

There are two other ways you can help us out:

  • We’re seeking meeting space in NYC on evenings and weekends.  This year, we will be greatly increasing our year-round programming to help students enter future programs for advanced study, and space costs may become an issue.  If you have access to free or low-cost space, please get in touch.
  • We are also looking for someone to help redesign our website to match our growing profile.  Please drop me a line with any connections!

Finally, you might enjoy this Bard news article about this summer:

Thank you so much for all your help and support with the program!  Until next time,


There are lots of exciting things in the coming year with much stronger year-round programming and connections to other mathematical offerings.  (What this post doesn’t tell you, for example, is that we’ve seen an explosion in SPMPS alumni registering for the NY Math Circle.)  This is a very exciting time for SPMPS!