Actually, pre-PhD economics majors may eventually take more rigorous college math (e.g. real analysis) than most engineering majors. However, the more common pre-professional pseudo-business economics majors typically take less math (calculus for business majors or no calculus, depending on the school).
Yes, discrete math and linear algebra tend to be more universally useful to CS majors than multivariable calculus.
However, most high schools treat most college prep subjects (other than art) as being sequenced, with a base sequence expected for college prep students, with relatively few branch points and options. For math, most high schools use a base sequence that leads to precalculus or calculus (or multivariable calculus if sufficiently advanced), with an off-ramp to statistics. It may require more resources at the high school, or more coordination with a local college, to offer more options at the advanced levels of high school math.
That is the PR I’m talking about. The compression course lacks important content for Calculus BC. They then said people can double up with Algebra 1 and Geometry however not every high school will let you do that. That pathway has decreased Calculus enrollment especially for Black and Latino children (I posted data and the district acknowledged this)
indeed, this math sequence poses very real negative consequences for CA and all US students. let’s put aside the issue of engaging learners of different speeds, research on the necessity of leveled instruction and SFUSD’s promise of “joyful” learning for a second and consider the equity questions: if the jo boaler-false equity approach takes hold, everyone save the rich and enfranchised will be essentially locked out of STEM education and careers. no matter what the ideologues say, this is reality on the ground. SFUSD is a case in point (my kids are also in SFUSD, so we have experienced this firsthand). insisting that “calculus doesn’t matter” and lying about its necessity to scaffold to college STEM programs doesn’t make it true. it’s not just that UC admissions are increasingly, impossibly competitive; it’s that defunding means UCs won’t have budget or scheduling space to educate outliers in foundational coursework even if they are lucky enough to be admitted (STEM and other majors are already ridiculously impacted, students struggle to get classes they need and UC strains to graduate them in four years). further, in case you were tempted to argue that UC is “elite” and therefore an outlier: CSU has already announced they hope to add a fourth year advanced math requirement. this signals that the will and funding to provide foundational high school coursework needed to access higher maths and sciences simply doesn’t exist. my graduating senior was in the second class hit by the algebra I blockade. she attends a smaller SFUSD high school where “doubling up” in algebra and geometry - the district’s preferred workaround for scaffolding to calculus - is not even possible. further, the district’s non-peer-reviewed compression course (that ridiculously folds algebra II and precalc into one torturous year) leaves out a laundry list of precalc standards needed to succeed later in calc AB and BC. delaying advanced math also reduces access to math-based sciences and makes it almost impossible for SFUSD students who don’t work around to take both calc and stats. (my D21 is a great case study: all As in math always, interested in the subject matter but already taking community college courses to fill other blanks incurred by SFUSD, finds the pace easy but forced to choose between calc and stats senior year because school wouldn’t allow both: congratulations, SFUSD – you just forced a female public school student out of STEM. just how far will the false equity purveyors go to keep moving the goalposts? first their argument was everyone should be forced to take algebra I in 8th whether they are ready or not (that went well - not). then it was, if some aren’t ready, nobody can access it. then it was here are our bizarre, not-pedagogically sound workarounds that nobody can understand without a map and extensive counseling they don’t provide (seriously - a graduating senior from lowell HS did a whole blog about it last year), let alone english learners or otherwise historically marginalized families. and now it’s “calculus is inherently toxic if explored before some peers are ready and also you don’t need it to go to either of your state public systems” (lies).
Except for CS, none of these is particularly math-heavy in its basic curriculum in college. No major at any UC requires starting in a math course more advanced than calculus 1, although some students actually do so (despite the orthodoxy on these forums that students should repeat their AP calculus in college even if they got an A and a 5).
I couldn’t agree more. There has to be a real investigation in what actually goes on at the ground level in the SFUSD instead of the superficial “look, here is a chart saying there is a path”. That chart does not reflect reality on the ground at all. The missing topics in that compression course is a lot but because pre calculus is not a requirement they were able to do it as long as all the Algebra 2 standards were met.
A couple months ago a middle school math teacher called in to the board meeting for a public comment and said just that, the compression course was not working and the high school her student got in to doesn’t allow doubling up. (not her child, her student at school and she was calling in to advocate)
San Francisco has a lottery system. Not all high schools are the same. They don’t offer the same classes.
I can say over and over it hasn’t worked, can point to the steep calculus enrollment decline but until there is a deep audit to show what has happened nothing will change.
d21’s compression course teacher told us that math teachers at several high schools went rogue and are using old texts instead of the bizarre mash-up worksheets the district math department authored to cram alg2 and precalc into one year. and we already know lowell HS is the only one really supporting doubling up as official policy as opposed to compression. it’s a total unstandardized free-for-all. they simply don’t care what happens after a certain point or to whom; all they care about is manifesting the appearance of not “tracking” prior to 11th grade. and if people don’t see the not-so-soft bigotry of low expectations and racist assumptions animating those policies, i give up.
While I agree with the premise that there should be a variety of paths through math, the reality is that for some sciences there is no alternative to heavy duty, and early, math. I spent one year homeschooling my daughter and we were able to spend the entire year focusing on trig. As a result, when she took Calc BC as a sophomore and the Physics C sequence as a junior, she was one of the few in the class that could actually come up with force diagrams. If these topics are all compressed into one year, anyone taking calculus-based physics for the first time in college is going to have an issue.
Right? I’ve stopped engaging with people who say nonsensical things like “it doesn’t matter”. This is actual lived experience by those of us on the ground level. For years. We’re done. I feel like the dolphins in Douglas Adams’ Hitchhiker series. “So long and thanks for all the fish”
sorry - we lived it. it is anything but clear. also, its implementation may be prohibitively problematic. remember that every SFUSD high school is different in terms of offerings, policies and politics that influence and dictate its interpretation of this pretty picture; SFUSD lacks that most basic form of equity. also, they will spring changes and blockades at a moment’s notice that render the pretty picture meaningless. for example: at our high school, this year’s seniors registered for classes as per usual last spring, only to show up in fall and be told they would be disallowed taking both calc and stats “because scheduling equity” (???). this happened too late to register for community college alternatives (CCSF is in any case also impacted in math, high school students get last dibs, and dual enrollment requires a prohibitively labyrinthine permission process that overworked counselors frequently neglect). also, last year, it was assumed that the school would continue to offer normal, full year precalc to those who matriculated from other systems or had for any reason completed algebra I in 8th (not at all unusual, right?). again, kids registered for it. again, they scrapped it on the eve of the school year, forcing those students to retake alg2 as part of compression, or scramble to find other ways to take precalc (often at CCSF, always late at night, always among older adults). further, among the dozen or so SFUSD students i know personally who have taken math courses at city college to compensate for SFUSD’s pathway elimination and math decommitment, all but two were advised to secure tutoring to fill in the blanks left by either compression or flawed pedadogy. third: doubling up in 9th or 10th grade is inherently problematic; it has to be done at the expense of another class or requirement (often an A-G, like, say, foreign language). so the unorthodox delay typically causes a cascade of delays in completing UC/CSU/district requirements at a time when these systems are increasing reqs as a culling tool, made even more important as we enter the test-optional/blind era! finally, the negative culture around math instruction generally (i.e., advanced math and science is something weird that requires you to “work around” and if you enjoy it you too are weird and elitist or worse) has functioned as a social contagion of sorts; its “success” (!!) is often cited as a justification for lowering the standards and reducing offerings in other subject areas as well. it’s sad, really.
Interesting. You’ve lived it, so far be it for me to push back on that experience and the data in SF, but here across the bay the shift (away from tracking in middle school) has been fine and I don’t think there has been a drop in Calculus enrollment at all. Perhaps the difference between a larger and more complex system and one that is smaller and has only a single high school. It feels pretty equitable.
I can never understand why math is treated so differently than reading in education. I agree with some of the goals and observations- how do we keep kids from hating math in elementary school or believing they are bad at math just because they aren’t ready for a level of abstraction in middle school that they would have zero difficulty with in high school. But a one size fit all and no one moves on is the exact wrong approach. Kids learn to read at different rates. The kid who grasped the concept with ease in 1st grade is not predetermined to have a huge advantage in high school vs the kid who figured it out in 3rd grade. There is an inherent understanding that kids learn differently and let’s just give them time to develop. I would absolutely like to see more robust support for kids in high school who could absolutely have a successful STEM career, but were convinced they were bad at math in middle school.
But I don’t see any teacher suggesting that no child can advanced until all their classmates are also ready. Can you imagine the elementary or middle school class where the kid reading at a higher grade level isn’t given access to any literature that exceeds what their classmate is ready for? Why are educators so scared of meeting kids where they’re at in math?
And finally that condensed pathway posted above is utter insanity. The idea that more kids will be successful if the only option for Calculus is to cram an extra year in high school just makes absolutely no sense to me - particularly when the pace in elementary school for some students is painfully slow.
Not only did we live it, we all had to navigate college applications. Like you said, saying it’s not necessary and making odd excuses even when the colleges say it is necessary is a luxury for theorists even if reality doesn’t agree.
I’m just so happy my children are done and both of them are in college (I can’t believe my son is graduating college, I have my graduation ticket and my plane ticket in hand).
20 years ago I would have been on the front line as a proponent. We are a k-12 sfusd family too. We went to a title 1 elementary when people would flee the district because of the lottery and they were assigned there. We were also pre feeder middle which meant another lottery and I toured middle schools and the inequity of class offerings were breathtaking. Same with the high schools.
I have since come to the realization that while aspirational language is needed it’s hollow unless there are results to back it. Boaler misrepresents the data in what happened in SF and if anything comes out of this, I really hope finally there will be a conversation about what happened here and how to better prepare all students.
I wonder how much of this is driven by how hard it is to find qualified math teachers.
We fled an East Bay school district for many reasons, but math instruction was high on the list. We felt privileged to be in the school district- it was the reason we moved here. But the reality on the ground in middle school was deeply dysfunctional and counterproductive. Kiddo hasn’t experienced the public high school math, but he has friends who have. One in particular- super mathy - had to fight his way to Calc AB for next year. If he were at kiddo’s school, he would have finished Calc BC as a junior. I am not advocating for speeding ahead just for bragging rights, but some kids need the enrichment, just like special ed kids need enrichment.
There was a line in the proposal about how all kids are “gifted”. I disagree; it is more accurate to say all kids are special ed - everyone benefits from a tailored educational program. By trying to serve everyone with one program, they serve no one.
Wrong. The language in math education is IMPORTANT. Studies of how math is taught have demonstrated that the attitude of the teacher matters, the language in the book matters, the photos in the text books matters.
Also, you are wrong.
Math isn’t reality.
Math is a philosophical framework which was developed to help us model the real world.
Gravity is real.
g = GM/r2 is an attempt to describe the relationship between the estimate of the gravitational constant, the mass of an object, and the shape of the object. However, it isn’t “real”, and if somebody developed a better formula, that would replace this one.
This formula isn’t reality, it is a model of reality.
2 + 2 = 4 is true because we have defined 4 as being the sum of two twos. We use this formula to describe a limited set of phenomena. However the use of this formula is limited in use in the real world to discrete objects with clear boundaries.
For example, two matches + two matches match = four matches. So far, so good.
However, in many cases, two clouds + two clouds = one cloud. So this supposedly universal model is not actually all that universal.
So the universe does not work that way, except in very specific conditions.
Again, math is a method that humans use to describe reality. It, however, is not reality, but a model for reality. It is the most useful and reliable method that we have, but it often makes no sense.
You tend to think that 1 + 1 = 2 is somehow a universal truth because you can envision it and use it to describe part of the reality that you perceive around you. However, the best models of subatomic realities use i, or the square root of -1. What sort of reality does that describe?
It is VERY easy for people who grew up as part of the same cultural, ethnic, and racial group who has been determining education in the this country to assume that, because this education meshes with their own background, that it is, therefore, free of cultural, religious, or racial biases.
Math education seems to many to be free of cultural biases because it fits within their own framework of cultural biases.
It always reminds me how nobody ever seems to think that they have an accent…
Jewish immigration from Europe was limited because people made the same claims that you are now - based on math tests that were used for immigrants, and on which Jews from Eastern Europe scored poorly. So the people in charge claimed that Jews evidently were not that good at math, and would therefore be a drag on the USA economy and should not be allowed in.
After all, “Math was universal”, and if the people couldn’t do basic math, they must simply lack the ability.
Yes, the tests were probably administered in a completely foreign language, which would account for the poor showing in test scores; I’m sure that if those tests were administered in their native languages, very different outcomes would have occurred. And, yes, after those immigrants lived here and learned English, they probably did much better – especially those who had a prediliction – natural gifts and talents, if you will – towards mathematical concepts already.
The problem with math education is racism and other things, too.
The forced choice in designing a curriculum is what I am truly bothered by. It isn’t either address systemic racism or address the needs of kids who are accelerated. We have to do BOTH.
