I first thought they meant getting rid of abstract algebra 2 (more reasonable) but I think they mean algebra 2 in the sense of solving quadratic equations and inequalities. Honestly quite amazing...
I first thought they meant getting rid of abstract algebra 2 (more reasonable) but I think they mean algebra 2 in the sense of solving quadratic equations and inequalities. Honestly quite amazing that they think people can do statistics without learning quite basic mathematics first.
I can absolutely understand Calculus and Trigonometry being optional courses in high school. Trig is situationally useful and Calc is barely useful if you’re not a STEM major. But Algebra 2… it’s...
I can absolutely understand Calculus and Trigonometry being optional courses in high school. Trig is situationally useful and Calc is barely useful if you’re not a STEM major.
But Algebra 2… it’s pretty much the capstone of basic math. Polynomials, logarithms, exponents, functions… pretty much everyone can benefit from understanding logarithmic vs. exponential graphs shown on the news, or compound interest, or break-even points, etc. Even knowing what a “function” is would help demystify “algorithms” if you understand that it’s just inputs and outputs.
Even calculus and trigonometry are kind of essential for statistics/"data science". Some of the things which seem "too abstract" or "not practical" are (a) very often quite practical/useful (e.g....
Even calculus and trigonometry are kind of essential for statistics/"data science". Some of the things which seem "too abstract" or "not practical" are (a) very often quite practical/useful (e.g. matrices) or (b) useful in developing mathematical maturity (i.e. the ability to work out to do when you have a mathematics problem and how to proceed in solving a problem you are stuck on) or (c) foundational for other very practically useful things.
"matrices" are not typically taught in calc (they were barely touched on in pre-calc for me, which is what my school called trig plus a couple other random topics) and anyone who needs to actually...
"matrices" are not typically taught in calc (they were barely touched on in pre-calc for me, which is what my school called trig plus a couple other random topics) and anyone who needs to actually learn even the basics about their applications is going to need to take a course where the professor is at least willing to say the words "linear algebra". They are indeed very practical -- if you're going into STEM. But even if you are going into STEM, the level they're taught in high school provides you basically zero understanding, so you'd need to take a course that includes linalg in college anyway.
I work as a data scientist. I needed very basic calc, but (mostly Bayesian) statistics and linear algebra are more important. And data science is a career that absolutely requires a bachelor's and often a master's, so there's little need for someone to have taken calc in high school rather than in college. I needed a refresher course on basic calc when I started my master's anyway, and I did take it high school, because it had been years since I'd needed to use it.
The fact of the matter is that not everyone needs to be a data scientist, and most people don't ever need to use calc. A simple basic statistics course (one which doesn't require any knowledge of calc) would serve most people who don't end up going into STEM better. Students interested in STEM can still take more advanced math courses.
Funny story, but I got through high school without ever really understanding functions. The whole "one output" aspect just didn't make sense to me with how it had been explained. Got by well...
Even knowing what a “function” is would help demystify “algorithms” if you understand that it’s just inputs and outputs.
Funny story, but I got through high school without ever really understanding functions. The whole "one output" aspect just didn't make sense to me with how it had been explained. Got by well enough to pass the tests, but it just didn't click what their significance was. I went to college and passed Calc 1 without picking it up too. I majored in CS and took Intro to C++ where we were taught functions in the context of programming. Picked up the concept of functions just fine in that context but it wasn't until about a year or so later that my brain clicked and I realized function meant essentially the same thing in each context. It was like a mind blowing revelation that they had been the same thing this whole time.
I think it was similar for me. I spent so long in basic math mentally dismissing f(x) as just a synonym for y. It took science classes using other inputs besides x plus matrices with g(x), h(x),...
I think it was similar for me. I spent so long in basic math mentally dismissing f(x) as just a synonym for y. It took science classes using other inputs besides x plus matrices with g(x), h(x), etc. to really stick.
I had a similar experience with summations and for loops. Once you look at math through a coding lens, you realize that math is just another language that can be translated into many different forms.
I had a similar experience with summations and for loops. Once you look at math through a coding lens, you realize that math is just another language that can be translated into many different forms.
for me that correlation didnt really click till I learned about functional programming, because oftentimes in object oriented programming, functions are not actually mathematical functions, they...
for me that correlation didnt really click till I learned about functional programming, because oftentimes in object oriented programming, functions are not actually mathematical functions, they are stateful and the same input does not always lead to the same output.
My first thought was to agree with you since you really do need to know algebra 2 to understand what is underlying data science, but most people aren't going into a field where they get into the...
My first thought was to agree with you since you really do need to know algebra 2 to understand what is underlying data science, but most people aren't going into a field where they get into the nitty gritty of data. They still need to understand some of the concepts at a high level though, and I feel like a data science course could do a lot. People are bad at interpreting charts. People are bad at understanding risk and probability, even though it affects most of our decisions. People are bad at understanding how data is turned into conclusions. See comments on subreddits like /r/dataisbeautiful or /r/science for examples. So while I think algebra 2 is good stuff, I haven't found it useful outside the classroom except in specialized occupations (including mine, but just because I need it doesn't mean other people do). In contrast, a data science class might be more applicable to daily life, as well as a wider range of college majors.
Solving quadratic equations and inequalities are part of the Algebra I standards for California. They are expanded on in Algebra II, but students would learn the basics of those before Algebra II.
Solving quadratic equations and inequalities are part of the Algebra I standards for California. They are expanded on in Algebra II, but students would learn the basics of those before Algebra II.
It seems like the consensus here is that Algebra 2 is excessive as a requirement for college. I'm here to argue the opposite. It is a necessary enabling course to have a meaningful liberal arts...
Exemplary
It seems like the consensus here is that Algebra 2 is excessive as a requirement for college. I'm here to argue the opposite. It is a necessary enabling course to have a meaningful liberal arts education as we do it in the United States.
A little about me: I'm a tenure-track professor in Nuclear Science and Engineering at a major state university, and I believe firmly in the value of a broadly-accessible college education as a civic virtue. My background is in chemistry...and I also have a Bachelor's degree in Political Theory. I know, weird combo, but the point is I can make an argument about this as an expert while also understanding the areas that are less math-intensive.
Courses are not an abstract thing to faculty, they are concrete things that have specific goals and requirements met, such that students can achieve the goal of earning their degree. They are surprisingly complex things, and have a whole litany of constraints on them. Degrees are accredited by external bodies, and there are strict and specific requirements that are provided to then earn the right for an institution to distribute degrees. You can think about these as "licenses to learn." If you don't meet the minimum content requirements, you cannot provide the degree.
We are also limited in how many courses we can require, how many credits are too many, what each department has as its domain. Most institutions require 120 credits if on a semester schedule (8 terms, 4 years, 15 credits/term), while quarter schedules require 180. Historically, these credit counts were fairly loose. With the cost of education to students increasing, many colleges and universities have implemented strict credit caps - you will require the minimum and no more. To students, this is a good thing, but to faculty it is an optimization challenge - how do you squeeze more class into less time?
Studies of many colleges and universities have found the minimum college preparatory requirements for a long list of degrees. The consensus from data is that (depending on the study and area of coursework) being either Calculus- or Pre-Calculus-ready is a necessary pre-requisite for success. It is a sign of intellectual maturity and the ability to consider, discuss, and work through abstract thoughts. Success at the college level in the sciences and arts is not always dependent on the content of Algebra II, but it is dependent on the ability to understand the content of Algebra II.
There's a problem with this, though, and that is that success in high school often recurses back to economic stability at home. If your parents are together, if they are employed, if they are white and white collar, you are far more likely to succeed in high school and in a bachelor's education. No student comes in on their own merit, they have an "invisible knapsack" of privileges to help them along...or an invisible yoke of disprivilege to hold them back. Intellectual maturity is not simply dependent on the maturity of the student - there is much more than that.
Much has been made of the fact that a college education is more necessary today than in decades past. It has even been called "the new high school," in that it plays the same role of being necessary to get a career and stable employment that high school played. The problem is that it comes at a cripplingly high price, it is selective, and it has limits on content.
College is not for everyone immediately after graduating high school and that is not a bad thing. It is a self-motivated exercise that relies on the emotional and mental maturity of late teenagers who are newly independent, and it is the beginning of specialization for students. The value of the degree is typically in how it trains students to think, while also providing a basic understanding of how things work so that students can be armed with the knowledge to then think. It cannot be all things for all people all the time while also charging a fortune.
The problem that the policymakers at UC are trying to solve is one of cost and time for the students. It is an admirable goal. The solution proposed comes at the cost of education. If you cannot provide the minimum education needed to establish one as even a minimally-independent worker and thus benefit from that degree. If the time difference and cost were minimal, there would be no objections from any to relax requirements for entry or to have additional requirements for graduation. In a world where the desired degree can cost above a hundred thousand dollars, every additional requirement is essentially a hostage scenario for students. "You must pay more to then get a chance at a good life."
The solution is not to relax requirements and constrain credits both, these are only treating the symptoms of the problem. The solution is to remove the cost of education.
Imagine if a college education was a thing you'd want but not need to get an office job or to work in a creative environment. Imagine if college was allowed to take 5 or 6 years if that's what it needed for a specific student. Imagine if public college was free to students with continuous progress to a degree, because it was paid for by society. In such a scenario, a college would have no problem accepting students who struggled with math - there would be plenty of time to let them mature, and it would not promise financial ruination. Additional credits could be required for the degrees that needed more advanced math or statistics or technical writing classes. Higher standards could be expected of students to get degrees, since each failure does not jeopardize student's lifetime success - they could just retake it in a year.
So many of the problems of public education come from the lack of universal accessibility. Knowledge and opportunities are locked behind a paywall, one that costs more with time. The biases of our society are worsened when we require economic and social privilege to then move forward, and the crippling cost of education is just one way.
Make public education for the public good again. Let us teach what is needed. Let us require the education that is sound. Let us end the educational hostage situation.
College not being free also ironically increases costs. There are a huge number of staff members dedicated to thse things that could be drastically cut back or eliminated entirely: Most admissions...
College not being free also ironically increases costs. There are a huge number of staff members dedicated to thse things that could be drastically cut back or eliminated entirely:
Most admissions screening could be replaced with a simple marketing and waitlist/lottery system.
Financial Aid could be obliterated. A solid 15% or more of my college's funding goes towards helping make it more afforable for poorer students.
Federal/State reporting and compliance related to these
Reduced need for fundraising staff for endowments and such
Even if the costs would not decrease by that much, there are a lot of duplicated efforts. If you had a funding model based on student credit hours, you can get more cost-effective by having fewer...
Even if the costs would not decrease by that much, there are a lot of duplicated efforts. If you had a funding model based on student credit hours, you can get more cost-effective by having fewer but larger classes (which would then break into smaller studios or recitations). Some engineering colleges are considering bringing math, chemistry, and physics internal to their program so they get more student dollars - never mind that the overall cost to the institution of having duplicated classes increases.
Then there is the optimization of the credits question. Credits have to come from somewhere, and so classes get reconfigured and dumped out from the curriculum to ensure that you stay under the maximum. If you can split concepts from one class to fit in as a small subset in three other classes, that can justify its own class...and then you get a better justification but the same duplication of effort again.
The optimization requirements absolutely impact curricula and professor morale. My most vivid classroom memories of college are from science & math professors prefacing units with some variant of...
The optimization requirements absolutely impact curricula and professor morale. My most vivid classroom memories of college are from science & math professors prefacing units with some variant of “this is an irrelevant grab bag of topics shoved into this course so we can maintain accreditation to grant engineering degrees.” It’s not that they found the subjects themselves to be useless, only that they should be taught in dedicated classes instead of crammed into discrete mathematics or gen chem.
I got pushback for characterizing a class like that...but it's true. The truth is that there is far more content that should be covered than can be covered in the time allotted. It makes mastery...
I got pushback for characterizing a class like that...but it's true. The truth is that there is far more content that should be covered than can be covered in the time allotted. It makes mastery of coursework more difficult to achieve.
Algebra is not a niche field of mathematics. Algebra is used by normal people all the time in real world applications even if they are not aware of it. Algebra 2 is also a prerequisite for doing...
Algebra is not a niche field of mathematics. Algebra is used by normal people all the time in real world applications even if they are not aware of it.
Algebra 2 is also a prerequisite for doing data analysis. Sure, you can run regressions without knowing how to do the underlying calculations by hand, but you still need to know what is going on to make informed decisions when analyzing data sets.
This seems to be more of a failure of the public education system earlier in a student's education. Students should have a decent grasp of Algebra 1 by the time they finish middle school.
The University of California system requires:
Three years of college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry; a fourth year of math is strongly recommended.
If you already have Algebra 1 under your belt when you enter high school, you only need Algebra 2, Geometry, and whatever third math course you want to take. That gives you 4 years to complete two required math courses that you should be able to take straight away.
We should not allow students to enter the UC system without meeting the already fairly generous math requirements. That is not helping any student succeed. It's only letting voters, lawmakers, and educators ignore the failure of the public education system.
It’s colleges pushing to relax their standards so they can maintain enrollment. If they keep standards, the underprepared students will either never enroll or drop out with a bucket of debt and no...
It’s colleges pushing to relax their standards so they can maintain enrollment. If they keep standards, the underprepared students will either never enroll or drop out with a bucket of debt and no degree. Instead, they push to lower standards so they can keep the books balanced by meeting enrollment expectations.
California spent over a decade trying to have all 8th graders take Algebra I before reversing the policy in 2013. When it was in place, a large number of students were failing the class and it was...
This seems to be more of a failure of the public education system earlier in a student's education. Students should have a decent grasp of Algebra 1 by the time they finish middle school.
California spent over a decade trying to have all 8th graders take Algebra I before reversing the policy in 2013. When it was in place, a large number of students were failing the class and it was a significant roadblock for many students:
But at the same time, Williams and others acknowledged that 60 percent of the eighth grade minority students in Algebra I did not test proficient on the CST. Many were required to repeat the course; of those, only one in five ended up scoring proficient on the CST. And if they did get a passing grade in Algebra I, they then “hit a wall in Algebra II,” becoming discouraged or failing the course.
I understand your point that students need to be able to face and work through struggle. As a teacher that's something I try to do with mine on essentially a daily basis. However, it's entirely possible for a struggle to be unfair or unnecessary. It's also possible for a struggle to be too great for an individual and have negative effects.
I'm not saying this as a challenge or anything but more as food for thought: Have you ever burnt out on something that was too hard for you? Have you ever tried your hardest at something and failed anyway? That's what a lot of these students were experiencing. Instead of insisting that they meet a rigid and uniform requirement that was ultimately damaging their educational prospects (I mentioned in my other comment on this topic how difficulties with algebra lead to dropouts), we can instead evaluate the effects of that requirement and change it if we identify something that would work better. That isn't capitulation; it's the basis for reform.
I was one of those students affected by this policy in middle school. The way the class was taught, I basically gave up on learning math and ended up in "remedial" math classes, including...
I was one of those students affected by this policy in middle school. The way the class was taught, I basically gave up on learning math and ended up in "remedial" math classes, including introductory statistics. I did so well in statistics, that I felt much more confident with math. I went back to other math classes in high school and early college and struggled again, including taking trigonimetry twice. But calculus clicked for me, just like statistics did.
The point I'm trying to make here is that algebra is really hard if it's not taught well, so we should be enforcing better teaching styles for this essential math course, and break it up instead of teaching the full textbook in one year (or something to that effect) for students that need it to be slower paced.
I think it somewhat depends on the major. You can get by fine in plenty of fields without ever touching the majority of algebra 2. It doesn't change the fact that we have a major problem with...
I think it somewhat depends on the major.
You can get by fine in plenty of fields without ever touching the majority of algebra 2. It doesn't change the fact that we have a major problem with college being treated as the only reasonable degree because the public system outputs such a huge variance in skills.
My biggest red flag is this part of the article: I know that many factors in life can affect someone's ability to learn, but this quote says it all for me. College is hard and you often encounter...
My biggest red flag is this part of the article:
UC first approved a data science course offered by the Los Angeles Unified School District in 2013 as a substitute for Algebra 2. Other school districts followed suit, adopting data science courses that are popular among students who find mathematical theory too difficult.
I know that many factors in life can affect someone's ability to learn, but this quote says it all for me. College is hard and you often encounter topics that are not enjoyable or easy for you to learn. High school should prepare students to overcome educational challenges. If a student needs extra resources, schools should provide those, but letting people avoid challenges is wrong.
College classes don't let you skip the parts you don't like. Employers don't allow people to ignore important tasks because they are too hard. Why are high schools trying to let students skip the subjects they find difficult?
Because some people learn differently? There's all sorts of subjects you can get a degree in that don't require higher level math but might come more naturally to someone who's struggling with...
Because some people learn differently? There's all sorts of subjects you can get a degree in that don't require higher level math but might come more naturally to someone who's struggling with algebra 2.
Edit:
And now that i've got a moment, it's always been a lousy connection between "can't do it" with "giving up/lazy". It's absolutely a fallacy to just assume these are kids who would give up on everything because they've decided algebra 2 isn't for them. I get that it is a % of group, but at the same time I've seen this logic used all over the place by people who sure as shit don't change their own oil, or do all sorts of other tasks they deem "too hard".
I don't mean to sound like I am blaming the students for this. I understand that learning disabilities are a real thing that students struggle with, but we need to provide those students with...
I don't mean to sound like I am blaming the students for this. I understand that learning disabilities are a real thing that students struggle with, but we need to provide those students with tools to learn despite their different abilities. They don't need to take the class without accommodations for their disability, and they don't need an A+ to pass.
People can get accommodations for disabilities in the real world, but they can't be excused from dealing with challenging situations.
Not completing Algebra 2 doesn't even prevent someone from attending college in the first place. It prevents them from going to a UC, but the UC system is held to a higher standard than a normal university. Community colleges, other public universities, and private universities are available if you can't meet the requirements.
There's a far gap between learning disability and just different learning capacities. There are plenty of good mechanics, accountants, psychologists, lawyers, etc that I wouldn't trust to apply...
There's a far gap between learning disability and just different learning capacities. There are plenty of good mechanics, accountants, psychologists, lawyers, etc that I wouldn't trust to apply the quadratic formula let alone anything higher level.
If the UC system is supposed to be a higher standard, fine. But it seems like an arbitrary one if it doesn't relate directly to your degree.
I would argue that algebra 2 is hardly higher level math. Trig, pre-calc, and calc, sure. Even for a "lowly" marketing bachelors algebra 2 would be extremely helpful. In this age linear algebra...
I would argue that algebra 2 is hardly higher level math. Trig, pre-calc, and calc, sure. Even for a "lowly" marketing bachelors algebra 2 would be extremely helpful. In this age linear algebra and stats would also be useful, potentially more useful than calculus on its own.
I think one problem with math curricula in general is that they don't show how many different situations math can be applied to. It's always speed/velocity, train timing, and the cost of x bananas and y apples.
That’s probably because you’re comfortable with it. I am too. The vast majority of people I’ve known think it is, and the opinions of those who didn’t struggle really isn’t the point. My brother...
That’s probably because you’re comfortable with it. I am too. The vast majority of people I’ve known think it is, and the opinions of those who didn’t struggle really isn’t the point.
My brother has a degree in marketing and is a project manager. He’s used anything near algebra 2 maybe a handful of times in his career and often it’s either googling a way to apply it or asking someone who’s better at math to help.
Edit: And for clarity sake my brother is good at math as well. It just doesn't seem all that relevant, especially when you're in an industry dealing with solved problems. Apply X function to Y dataset is often the extent of understanding required for pure business applications.
It's tough, because algebra is one of those things you use if you know it. I tought math, and went and got an MBA and graduate degree in marketing. There are plenty of applications for algebra in...
It's tough, because algebra is one of those things you use if you know it.
I tought math, and went and got an MBA and graduate degree in marketing. There are plenty of applications for algebra in marketing, from modeling spend, campaign break even points, maximizing ROI, etc. Not everyone in marketing does the same thing, and big orgs always have someone to farm the math out to. Still, algebra gives you the basic ability to represent so many real world situations, that it is a huge boon to know.
That said, I think the curriculum and approach to presenting the topics needs to change, but that is different than simply doing away with it.
Yeah, I agree with your points. Mine was more about I think if it were demonstrated to be useful in more every day situations, along with appropriate visualisations and applications it would...
Yeah, I agree with your points. Mine was more about I think if it were demonstrated to be useful in more every day situations, along with appropriate visualisations and applications it would become easier to understand for a larger group of people. But when it's just very basic examples like velocity-time graphs, train schedules, and the cost of fruits I can see how a 16 year old might write that off and think it's entirely useless.
Imagine if the textbooks provided examples demonstrating of how a wannabe influencer could use analytics to calculate potential future subscriber growth, or something like that.
I got a math major at a top US college a bit over a decade ago, and somewhat recently I had to use trig in a programming project. I asked a friend who actively tutors hs students cos I don't...
or asking someone who’s better at math to help.
I got a math major at a top US college a bit over a decade ago, and somewhat recently I had to use trig in a programming project. I asked a friend who actively tutors hs students cos I don't remember anything from trig lol
(that said I am very pro math learning and pro large common core, the fact alone that one can recognize "oh haha this is a trig problem" requires pretty substantial training. I just thought this was a funny anecdote.)
on the topic of some people learn differently: Teaching styles in college and high school tend to differ wildly. If a student doesn't understand something in high school, but retakes the course in...
on the topic of some people learn differently: Teaching styles in college and high school tend to differ wildly. If a student doesn't understand something in high school, but retakes the course in college, they may understand it better. They also have a higher chance/ability to choose who teaches them so they can select the teacher and their teaching style, where in high school, that isn't the case usually.
I will say, as someone who majored in IT and has worked in the field for over a decade, I've never once used algebra 2, or felt the need to use it, or higher level math in my career, which is...
I will say, as someone who majored in IT and has worked in the field for over a decade, I've never once used algebra 2, or felt the need to use it, or higher level math in my career, which is ostensibly STEM (I still have no idea why the T is even part of the other three. It has basically nothing to do with them and requires a completely different set of skills, but I digress).
However, I don't think I needed a degree for the work I've done in my field. I'm in management now, so maybe it helps a little? I learned far more about how to manage people effectively in the military than I ever did in college though.
I think college in general being a minimum requirement for any white collar job is a waste of time and resources for most people. College used to be a place where upper middle and upper class people who had no pressure to earn a living went to mingle, and become more "well rounded." I think it still serves that function far better than it does as a job training program, which is what it serves as today.
Realistically, I could have learned everything I needed to get started in the field in a year long training course, but I knew it would be tough to find jobs without a degree. Why does any IT job care that I took psychology 101, or had an elective in military history, or that I took a drawing class freshman year? Why is that a requirement?
Highschool already serves as the baseline "this is what a well rounded person in our society should know" education level. Forcing people to spend 4 years learning things they'll never need in order to tollgate a knowledge based career (which is the only way to earn a reasonable living in this county without absolutely destroying your body) is just nonsensical in my opinion.
So maybe it does make sense to continue requiring higher math in college. It doesn't make sense to require college for most jobs that require it today.
Technology, finance, communications, marketing, accounting and so on are all things that we could set up expedited training courses for that take half the time or less and teach students what they need to be effective at their chosen career. No more, no less.
And yes, I know that this exists to some degree already with AS degrees and other associates level qualifications. The issue is that for most people, that alone will not net them a job. Employers want a qualification that they can use to filter out most applicants from the very start, and for whatever reason a bachelors has become that qualification.
Is the problem entirely that students find it challenging to learn or is part of the problem that instructors have difficulty explaining it adequately? Being an effective instructor doesn't just...
letting people avoid challenges is wrong
Is the problem entirely that students find it challenging to learn or is part of the problem that instructors have difficulty explaining it adequately? Being an effective instructor doesn't just require an understanding of the topic but also an understanding of how to approach the topic from the perspective of someone who doesn't already understand it. I've sat through so many courses with instructors who have zero charisma, whose lectures are simply reading the textbook, who are more interested in students passing their tests than understanding the material, and/or who don't speak English as a first language (bless their heart, but I shouldn't have to struggle to decipher what word is being spoken before trying to understand the concept). When topics are easy, students can take on the brunt of overcoming the instructor's shortcomings, but when the topic is more complex then that task may become insurmountable. Especially when this is one of multiple classes you're likely taking, it may not even seem worth the while to put in the effort when that effort can be better used in another class.
I don't mean that students have to face hardship with no tools or resources to help them. Part of school is learning how to learn even if the subject doesn't come easily to you. If a single...
I don't mean that students have to face hardship with no tools or resources to help them. Part of school is learning how to learn even if the subject doesn't come easily to you. If a single student isn't doing well, sure that can just be their fault. If the majority of the students in a class aren't doing well, that can be the teacher's fault. If 2/3 of the State of California is not meeting math testing standards, then the whole system is to blame.
If the system is to blame, lowering the bar of minimum achievement is not helping any student improve. It may actually further harm the minority of students who were able to overcome a flawed educational system by allowing them to never challenge themselves.
In the district I started teaching in (an underfunded urban district ravaged by poverty), Algebra I was essentially a perfect predictor of dropping out. Students would take Algebra I, and, as is...
Exemplary
In the district I started teaching in (an underfunded urban district ravaged by poverty), Algebra I was essentially a perfect predictor of dropping out.
Students would take Algebra I, and, as is the case, some would pass, but many wouldn't. Those that didn't would have to take it again. Some of these would pass, but of those that didn't, there was an almost 100% dropout rate. We didn't see this same correlation with any other subject.
Around the time I started teaching there was a study done by the US Department of Education. I can't find the actual link to it, but the statistic shows up here:
In 2010, a national U.S. Department of Education study found that 80 percent of high school dropouts cited their inability to pass Algebra I as the primary reason for leaving school.
Eighty percent.
I've been on techy spaces online long enough to know that communities like ours tend to aggregate people who were very successful in math. As such, discussions tend to emphasize the importance of math -- particularly higher levels of math -- and downplay the difficulty and struggle that many people have even with lower-level concepts.
If you're good at math, it's because that is built on a lot of foundational knowledge and practice. You are fluent in a ruleset and a mindset that, to you, looks structured and logical and meaningful and applicable. Enough time in that fluency and it becomes second nature or common sense to you.
If you're someone who struggles with math, however, it is opaque and arcane and confusing and disorienting. It doesn't make sense. It's arbitrary. It's rigid. It's a brick wall that you have seemingly no way through or over or around.
Please genuinely consider this when thinking about the linked article and its proposal.
I'm a secondary school teacher in the United States and I firmly believe that most students should not have to take Algebra II. My standpoint is a bit different than the linked article, because that is specifically looking at Algebra II as a requirement for college admissions which is a narrower focus, but believe me when I say that I wholeheartedly feel that one of the best improvements we could make to American education would be to incorporate less rigid and more diverse math pathways for students.
Algebra II is not essential for all learners, and a strict adherence to it as such is likely doing direct harm to a lot of them.
I mean, I agree many people don't need to take Algebra II, but many people also don't need to go to college. This may sound harsh, but I think Algebra is simple enough even for teenagers who don't...
I mean, I agree many people don't need to take Algebra II, but many people also don't need to go to college. This may sound harsh, but I think Algebra is simple enough even for teenagers who don't like math that if someone is so far behind so as to not pass it, they probably are not suited for college anyway. There's nothing wrong with not going to college. Training people in a skill better suited to them is better than even further degrading the already tenuous value of a college degree.
While I'd agree, that's not even necessarily the question here. California has a multi-tier public university system. This editorial is arguing that the University of California system, the first...
I mean, I agree many people don't need to take Algebra II, but many people also don't need to go to college.
While I'd agree, that's not even necessarily the question here. California has a multi-tier public university system. This editorial is arguing that the University of California system, the first tier, should not require Algebra 2. Yet not going to a UC does not mean not going to college in California, or even not going to a university. There is an entire second tier system of full, public universities, the California State University system. And then there is a third tier, at a community college level, the California Community College system.
Of those three, the UC system is the smallest: the CSU system is the largest public university system in the US, and the CCC system is the largest higher education system in the US and third largest in the world. The UC system is meant to be a system of research universities for the top students in the state, not as a system for every student: under the original 1960 California Master Plan for Higher Education, before Prop 13 forced a change in the way tuition and admittance worked in the state, the UC system was meant to guarantee places for the top one-eighth of graduating high school students in the state, the CSU the top one-third, and the CCC for everyone.
The UCs have their visibility because many are top research universities at an international level, but it is the CSU system, not the UC system, that is meant to provide the most of the undergraduate education in the state.
Looking up Algebra 1, I doubt anyone who can't grasp such simple concepts is going to university anyway, even if it was removed from the curriculum. It makes sense that it's such a strong...
Algebra 1 is the second math course in high school and will guide you through among other things expressions, systems of equations, functions, real numbers, inequalities, exponents, polynomials, radical and rational expressions.
I doubt anyone who can't grasp such simple concepts is going to university anyway, even if it was removed from the curriculum. It makes sense that it's such a strong predictor, since it is non-subjective and clearly identifies people with pretty severe learning disabilities.
As someone who taught college math, I personally blame the topics included and their treatments, coupled with poor approaches to learning at lower grades. As if times tables helped anyone...
As someone who taught college math, I personally blame the topics included and their treatments, coupled with poor approaches to learning at lower grades. As if times tables helped anyone understand the importance of finding the roots of a polynomial or exponential functions.
Most math as it is taught today isn't helpful to most students, including those going into stem. Math books are written by mathematicians, to satisfy other mathematicians, rather than what best serves students.
However, there are topics buried in algebra that can be directly applied to financial literacy and many other widely applicable skills outside of STEM.
I also say this as someone who struggled with math in my youth, failed multiple math classes before dropping out, but ended up teaching linear optimizations and machine learning techniques.
I mean, there's 1000 solutions and 10000000 bad ones, and the trick is actually getting a good one through the bureaucracy without it turning into a bad one. Personally I've always felt that it'd...
I mean, there's 1000 solutions and 10000000 bad ones, and the trick is actually getting a good one through the bureaucracy without it turning into a bad one.
Personally I've always felt that it'd be a lot easier on everyone if there was a high school level focus on what you're good at, and what you're not. Algebra for "not math people" would benefit a lot because you could slow down and focus on the weak spots for the students, and also try to correlate it to experiences they might better understand.
At the same time the people who breeze through math aren't now nodding off in class because they can be in the "for math people" math classes and get the attention/curriculum they need.
This would also be better served by having more trades in schools, and getting the hell away from the "oh well you can have 60 kids per class. 10 of whom are accelerated/honors, and 15 are SPED, and 10 of whom are constant behavior issues...good luck". To the point that I feel that until you address that issue, you aren't going to get anywhere.
A potential problem with this approach is that it risks dividing students early on, potentially of the basis of factors other than ability. One traditional way of enforcing class and other...
Algebra for "not math people" would benefit a lot because you could slow down and focus on the weak spots for the students, and also try to correlate it to experiences they might better understand.
A potential problem with this approach is that it risks dividing students early on, potentially of the basis of factors other than ability. One traditional way of enforcing class and other divisions, for example, has been to choose topics and courses at different schools, or for different types of students, such that some groups will be significantly less likely, without considerable outside work, to continue on certain lines. My partner, a humanities professor, once pointed out that, while she does love her field, that she did not go into science or mathematics is at least in part because, in school, she tested well for math and enjoyed it, but was placed in 'not math people' courses for various reasons including keeping her with her friends, encouraging other students, and, probably the real reason, being at a conservative school and the wrong gender. So she was taught math with 'experiences she might better understand' rather than as something actually intellectually interesting, and while she had no trouble with the classes, tended to see the humanities as far more intellectually rewarding.
Additionally, as adding different courses increases workload compared to teaching multiple sections of the same course, without sufficient staff and light enough course loads, splitting courses doesn't necessarily make the classes better. I was in a 'math for math people' class in California. It didn't give us the attention and curriculum we needed. It just brutalized us by letting us skip to a higher year's curriculum as a result of our own independent study, then trying to keep us from causing further problems by teaching that curriculum at the same pace, just with far more assigned, repetitive work, arguably to keep us from studying at a faster pace at home. Our teacher certainly didn't have time to care about us or give us a different curriculum.
Yes, and no. I once taught an "Algebra 1A" course, which was a slower course for students with learning disabilities. It was essentially the first half of Algebra I spread out over the course of a...
Yes, and no.
I once taught an "Algebra 1A" course, which was a slower course for students with learning disabilities. It was essentially the first half of Algebra I spread out over the course of a year.
My students did great. They needed the extra time and different instruction to be able to pick up on the concepts. They would have been completely cooked if they'd been in a regular Algebra I class. It would have moved too fast, and they likely wouldn't have been able to pick up the concepts from the type of instruction given.
But, to get at what @Eji1700 said in their comment, can we institutionalize this and make it a genuine solution? Well, that's much more difficult. I'd love more diverse pathways for math (and everything else really) but I have to acknowledge that it sounds great in theory but becomes essentially unworkable in practice. Making shifts like that add substantial complexity and often have unintended knock-on effects.
For example: my students that took Algebra 1A had their entire high school trajectory changed because of it, because it technically was a half-credit course even though it took up a whole year. That completely changes how they have to allocate credits elsewhere, and creates its own opportunity costs.
Another example issue: teachers are already strapped and we don't have enough of them -- if you then told them that they were teaching a different subject (or a different form of a given subject) every single period, they'd balk. It would simply be too much work. Much of education policy is based around a uniform efficiency not because it's what's best for kids but simply because it's what's workable.
Problems in education are so complicated they're nearly intractable. There simply are no quick fixes.
I 100% agree with this. I think Algebra II is fairly simple now, but I got a C+ the first time I took it in high school. Because I didn’t do well, my school put me in pre-calc the next year which...
If you're good at math, it's because that is built on a lot of foundational knowledge and practice. You are fluent in a ruleset and a mindset that, to you, looks structured and logical and meaningful and applicable. Enough time in that fluency and it becomes second nature or common sense to you.
I 100% agree with this. I think Algebra II is fairly simple now, but I got a C+ the first time I took it in high school. Because I didn’t do well, my school put me in pre-calc the next year which was mostly review for me. It wasn’t challenging, but I was given more exposure to the topics I struggled with the previous year. The next year, I was able to take AP Calculus A/B and do well.
Another time in middle school, I slacked off in Algebra I and got a C on the final. I still passed with a B, but the teacher recommended I go to summer school.
I am confident in my math abilities and my ability to learn more math because I know that having trouble doesn’t mean you’re stuck forever. You just need some extra practice and guidance to get back on track.
Does your school have any free or low cost summer programs to help students get back on track?
I know that lots of times the resources aren’t available, but it seems like falling behind is a big issue for math students. If someone is failing Algebra I because they lack some prerequisite knowledge, it makes sense that taking it again won’t work unless the gaps in knowledge are patched.
To answer your question, I'm going to sidestep a bit. Since this topic is focused on California, let's look at their data for a moment. That's from their standardized state testing for 2023....
To answer your question, I'm going to sidestep a bit.
Since this topic is focused on California, let's look at their data for a moment. That's from their standardized state testing for 2023.
States start testing their students in third grade, so that's where we can start. Take a look at the math proficiency of third graders for last year.
It is less than half.
So, our first data point regarding math ability, for eight- and nine-year-olds statewide, is that over half aren't proficient. I know we're not focused on third graders, we're looking at algebra here, but in order to understand why people can't do algebra, we have to consider the antecedents.
The point of me bringing this up is that the problem isn't one of a few lagging students who need some extra help. It is a systemic issue embedded into math pathways starting at least in third grade (and almost certainly earlier). 2023 isn't an outlier in the data, by the way -- nor is California. You can look at most states, for the years going back to when schools first had to start reporting this data, and you'll see similar numbers. According to standardized testing, large portions of students -- often a majority -- are starting out their educational careers behind.
This goes in to what I was talking about in my other comments: is this failure simply people not meeting the bar, or have we set the bar incorrectly? I firmly believe it's the latter. I think we have a duty to change that.
(Side note: I also believe that the testing industry has a vested financial interest in creating the perception of the continued "failure" of American education and so their data will continue to support that even if we do make changes, but that's an entirely different and much more pessimistic rabbit to chase.)
One of the legitimate criticisms of Common Core was that its early elementary curriculum was far too fast. Too much content was covered and the students retained none of it. Math, especially,...
One of the legitimate criticisms of Common Core was that its early elementary curriculum was far too fast. Too much content was covered and the students retained none of it. Math, especially, falls apart when cramming for the exam. Most other subjects can paper over missed steps, but math presents the hard wall you describe.
IMO, Algebra I is the failure point because it’s the first time the students must be proficient to pass instead of being socially promoted or squeaking by because it would otherwise be cruel to hold them back. IIRC, the trouble with Algebra isn’t that the students can’t substitute x for a number, it’s that they never mastered arithmetic with fractions. The fix lies in the elementary levels.
To address your aside, the numbers are validated by comparing them to prior year results. Any curriculum improvement with immediate efficacy would show up in a state board of education meeting as “those lazy testing companies something up BAD this year” instead of “wow, I can’t believe this already worked.”
One thing I wonder is if the intervention needs to go back even further. I know we don't make students repeat grades in elementary school anymore because there were some studies that found it to...
One thing I wonder is if the intervention needs to go back even further. I know we don't make students repeat grades in elementary school anymore because there were some studies that found it to be harmful in some ways even if the student can catch up academically. Remedial classes starting back in elementary school could be the solution.
Students can stay with their core social groups for most the day, but when it's time for math, one teacher can teach normal track math and another teacher can teach remedial. They can swap the students into the class they need for that subject, then move back to their normal teacher for the rest of the day.
Also, if you look at the disparities in math achievement between different races, my intuition would be that the Black and Hispanic families that have lower math test scores have higher rates of single parents. The data actually backs this up. Single parents may have to spend more time working to survive than a two parent household. Single parents also may have less time to spend monitoring their child's performance in school. I know many of us have memories of doing math homework with dad and crying at the kitchen table, but that was probably beneficial for our educational outcomes. For students without dads that can yell at them about multiplication tables and fractions, I think a restructuring to math education in elementary school would help a ton.
I agree that it's the system that is causing these failures and not particularly the students. I think that lowering the bar is doing a disservice to students. These students on average are capable of more, but there are barriers in society and the educational system that gets in the way. Lowering the bar is telling them that they are not capable of improvement when it's actually society's fault for not doing more to even the educational playing field among all students.
I'd say the answer is simple: Algebra shouldn't be required to pass high school. It could be replaced with something more basic but useful if students can't cut it, like basic budgeting. But it...
I'd say the answer is simple:
Algebra shouldn't be required to pass high school. It could be replaced with something more basic but useful if students can't cut it, like basic budgeting.
But it should still be considered mandatory for entering into college, which was my impressions for this situation.
Perhaps there should be a mandatory intermediary learning between high school and college, ideally seperated from home life a bit A 50/50 split between smoothing out any educational gaps part time, and doing a kind of 'temp job service duty', giving exposure to a wide variety of careers.
High school does a real shit job of helping show the kinds of jobs available in the world, and I think that's half the problem of listless students not using the degrees they earn.
Something like say 5 years of this vocational service/post-secondary prep from 18 to 23 gives some time to mature and figure out 'what they really want' and 'who am I outside the context of my childhood.'
I think that would give mass improvements to performance in post-secondary and be able to eliminate a lot of 'fluff.'
Emphasis added (but still not strong enough). They especially fall short at prepping boys in the middle of the ability scale without nepotism connections. Here’s a stereotypical list of the...
High schools do a terrible job explaining what careers exist
Emphasis added (but still not strong enough).
They especially fall short at prepping boys in the middle of the ability scale without nepotism connections. Here’s a stereotypical list of the categories of options a white-collar HS senior may think of (that aren’t pure wishful thinking like astronaut or YouTuber)
Prestige careers: physician and, formerly, lawyer
Technical specialties: research scientist, architect, professor
Engineers & brogrammers (their own category halfway between the first two)
Careers they use to threaten the disruptive kids: military, ditch digging, checkout clerk
(girls only): teacher, nurse, MD
Note how the only options that aren’t targeted at the tails of the bell curve are the pink-collar careers. Despite probably providing an order of magnitude more jobs than the technical specialties, the following are totally absent from discussion
Being in higher ed, having computational math as one of my early degrees, and having taught and tutored math, the subject of what math should be required for the general student population is one...
Being in higher ed, having computational math as one of my early degrees, and having taught and tutored math, the subject of what math should be required for the general student population is one I have been close to for many years.
Much of the debate seems to invariably come down to those who believe universities should deliver a traditional, broad education, while others think it should be more vocational based on the job markets requirement for four year degrees.
When it comes to algebra 2, I generally take the view that the topics should be required, but are often taught poorly or in ways divorced from their broad applicability.
I've seen some schools start to break apart math tracks based on degree path, so that the content can be a little bit more tailored. This helps avoid the "fourth year weedout" of real analysis for folks that thought they wanted to be math majors, by allowing for earlier classes that focus on theory, and one or more separate tracks that focus on applications to business or humanities.
It is also a little bit of a referendum on education that most people with four year degrees lack the tools to calculate their own retirement portfolios, projections, or needs. Some of that material is in algebra 2, but buried in treatment that satisfies the mathematicians in the room, but poorly serves most students.
Since it doesn't seem like anyone has mentioned it yet, here are some of the subjects covered in Algebra 2: Complex numbers Roots of quadratic polynomials The binomial theorem Division of...
Since it doesn't seem like anyone has mentioned it yet, here are some of the subjects covered in Algebra 2:
Complex numbers
Roots of quadratic polynomials
The binomial theorem
Division of polynomials
Reasoning about inequalities
Modeling exponential, logarithmic, polynomial, and linear behavior
Linear equations of two variables
Introductory statistics
Conic sections
Some of these topics are admittedly pretty basic (e.g., arithmetic with complex numbers) while others are fairly arcane (when was the last time you thought about hyperbolas?). I personally don't have much of an opinion about whether Algebra 2 should be a requirement for college (I'm way too deep in STEM to be generalizing about other majors), but I am genuinely curious:
For which majors could you get by without knowing any of the above topics? Don't most (all?) majors have at least one science prerequisite? I can't think of an introductory science course that wouldn't mention logarithms, for example.
Or is the first question misleading? For instance, are most of these topics already covered in Algebra 1 (or some other class)?
I think complex numbers are fun but, outside electrical engineering, it’s hard to find practical situations where you need them or could even use them.
I think complex numbers are fun but, outside electrical engineering, it’s hard to find practical situations where you need them or could even use them.
Do you mean to suggest quantum field theory is not practical? Let me introduce you to the highly troublesome sign problem! Just kidding. By "basic" I meant relatively simple, not necessarily...
outside electrical engineering, it’s hard to find practical situations where you need [complex numbers]
Do you mean to suggest quantum field theory is not practical? Let me introduce you to the highly troublesome sign problem!
Just kidding. By "basic" I meant relatively simple, not necessarily useful (poor wording on my part). I'm sure there are plenty of students who have no trouble with complex numbers but struggle with linear systems, for example, so I think it does the students a bit of a disservice to assume that the folk struggling with Algebra 2 are struggling with the former when they might just be struggling with the latter. That's all I meant to suggest.
Edit: oh right, but yes, you probably wouldn't need them outside a STEM major. But maybe you would need them for a science prerequisite?
Higher education is an interesting thing to put a price on because while some classes can provide economic benefits to people who get a higher education, many classes provide more of a societal...
Higher education is an interesting thing to put a price on because while some classes can provide economic benefits to people who get a higher education, many classes provide more of a societal benefit.
A history class doesn't help an engineer make a jet turbine, but it can help them be an informed voter. College campuses mix people of different races, genders, origins, and socioeconomic classes with each other. The general education courses expose students to different concepts that can help them in their civic lives.
College graduates also have many economic benefits to society. On average, college graduates pay much more in taxes than they take in government benefits over their lifetimes. High school graduates also contribute, but only a modest gain where college graduates contribute 4-5x what they take. Governments invest $28,000 per college student on average, but gain $335,000 in net monetary benefit over their lifetime.
I get that many people are opposed to courses that don't directly apply to a career because they have to pay a lot of money out of pocket when the course may only provide a benefit to society. Why can't the government provide loan forgiveness to anyone who graduates? It would take pressure off students and still provide a net benefit to society over having them not graduate.
I don't disagree with the value of a liberal education, but it's worth pointing out that in European countries tertiary education tends to be more specialized and they don't seem to be worse off...
I don't disagree with the value of a liberal education, but it's worth pointing out that in European countries tertiary education tends to be more specialized and they don't seem to be worse off for it. For instance, in Germany there is a distinction between Universität (basic research, e.g. physics), Fachschule (applied sciences, e.g. engineering), Kunsthochschule (art school, e.g. architecture), and Berufsakademie (vocational school, e.g. social work). A typical university in the US would have all of these programs.
I did a little poll with my social circle, which includes a handful of writers, an artist, a marketing executive with experience in several big-name companies, a couple lawyers (one for a massive...
I did a little poll with my social circle, which includes a handful of writers, an artist, a marketing executive with experience in several big-name companies, a couple lawyers (one for a massive media company, one public defender) and myself (a teacher who is significantly less financially successful than everyone above).
None of us have ever had to think about any of this outside of school. Most of the people I asked don't know remember anything they learned after PEMDAS. I know that I took Algebra 2 once upon a time, but like my Russian classes that I needed for my BA, I forgot pretty much all of it sometime around 2015. That list you made might as well have been in Cyrillic.
I’m rather torn on this. I think not every kid should go to college and many jobs unnecessarily require a college degree. I’m reminded of what happened with air traffic controllers - a stressful...
I’m rather torn on this.
I think not every kid should go to college and many jobs unnecessarily require a college degree. I’m reminded of what happened with air traffic controllers - a stressful job that not everyone can do, and new hires get a lot of training before they go to work. But it didn’t require a college degree until they decided to do that, and I don’t know why they did that. It seems good and unusual that they rolled it back, though it was a mess how they did it and unfair to the students who did go to college.
Meanwhile, many college majors do legitimately require heavy math, and without getting the preparation, there’s little chance of being ready for them. And you can’t know far in advance what a kid will want to do.
There are some kids who get really into math at young ages, or at least that’s what I heard from the parents. Schools are not always catering to them well either.
So it seems like there should be college-track math, not every kid should do that, but every kid needs multiple opportunities to get on that track, in case they bounce off the first time. Also, maybe there needs to be less stigma about trying something and failing the first time? What matters is that you get there, not how you got there.
I’m reminded of how learning musical instruments worked when I went to school. In third grade, there was a chance to sign up to learn an instrument after school. I picked trombone for not very good reasons, which turned out to be a bad choice. I dropped out after a few weeks. The case was big and heavy, I had a hard time playing anything, taking the late bus home was annoying, and I was already taking piano lessons.
Maybe if they had signups more than once, I would have given another band instrument a try? Even at the time, I thought maybe I should have tried the sax instead. In retrospect, the clarinet seems like it would be worth a try, certainly more portable, but mostly girls chose it, and that made me wary for some reason.
Sometimes the whims and insecurities of a third-grader have more consequences than I think they should.
It seems like it would be even more the case if math were treated similarly? Kids learn to hate math if it’s not done the right way. How do you try hard to teach them in case they take it up, but not too hard?
And then you get the nonsense now that because "everyone" has a college degree, to weed out further candidates, some companies are requiring master's degrees when it's not needed either. I agree...
And then you get the nonsense now that because "everyone" has a college degree, to weed out further candidates, some companies are requiring master's degrees when it's not needed either. I agree with you that not everyone needs to go to college. Continuing education should be the norm for all people, even if it's a simple "updated tax/retirement math course" or something like that, but I agree that we're focusing on college being essential for the wrong reasons.
I first thought they meant getting rid of abstract algebra 2 (more reasonable) but I think they mean algebra 2 in the sense of solving quadratic equations and inequalities. Honestly quite amazing that they think people can do statistics without learning quite basic mathematics first.
I can absolutely understand Calculus and Trigonometry being optional courses in high school. Trig is situationally useful and Calc is barely useful if you’re not a STEM major.
But Algebra 2… it’s pretty much the capstone of basic math. Polynomials, logarithms, exponents, functions… pretty much everyone can benefit from understanding logarithmic vs. exponential graphs shown on the news, or compound interest, or break-even points, etc. Even knowing what a “function” is would help demystify “algorithms” if you understand that it’s just inputs and outputs.
Even calculus and trigonometry are kind of essential for statistics/"data science". Some of the things which seem "too abstract" or "not practical" are (a) very often quite practical/useful (e.g. matrices) or (b) useful in developing mathematical maturity (i.e. the ability to work out to do when you have a mathematics problem and how to proceed in solving a problem you are stuck on) or (c) foundational for other very practically useful things.
"matrices" are not typically taught in calc (they were barely touched on in pre-calc for me, which is what my school called trig plus a couple other random topics) and anyone who needs to actually learn even the basics about their applications is going to need to take a course where the professor is at least willing to say the words "linear algebra". They are indeed very practical -- if you're going into STEM. But even if you are going into STEM, the level they're taught in high school provides you basically zero understanding, so you'd need to take a course that includes linalg in college anyway.
I work as a data scientist. I needed very basic calc, but (mostly Bayesian) statistics and linear algebra are more important. And data science is a career that absolutely requires a bachelor's and often a master's, so there's little need for someone to have taken calc in high school rather than in college. I needed a refresher course on basic calc when I started my master's anyway, and I did take it high school, because it had been years since I'd needed to use it.
The fact of the matter is that not everyone needs to be a data scientist, and most people don't ever need to use calc. A simple basic statistics course (one which doesn't require any knowledge of calc) would serve most people who don't end up going into STEM better. Students interested in STEM can still take more advanced math courses.
Calculus is used all the time in business in terms of calculating marginal cost and various other common financials. It’s not just stem.
Funny story, but I got through high school without ever really understanding functions. The whole "one output" aspect just didn't make sense to me with how it had been explained. Got by well enough to pass the tests, but it just didn't click what their significance was. I went to college and passed Calc 1 without picking it up too. I majored in CS and took Intro to C++ where we were taught functions in the context of programming. Picked up the concept of functions just fine in that context but it wasn't until about a year or so later that my brain clicked and I realized function meant essentially the same thing in each context. It was like a mind blowing revelation that they had been the same thing this whole time.
I think it was similar for me. I spent so long in basic math mentally dismissing
f(x)as just a synonym fory. It took science classes using other inputs besidesxplus matrices withg(x),h(x), etc. to really stick.I had a similar experience with summations and for loops. Once you look at math through a coding lens, you realize that math is just another language that can be translated into many different forms.
for me that correlation didnt really click till I learned about functional programming, because oftentimes in object oriented programming, functions are not actually mathematical functions, they are stateful and the same input does not always lead to the same output.
I could see ditching calculus. Not algebra.
Especially for higher education. There's enough remedial math needed as-is.
My first thought was to agree with you since you really do need to know algebra 2 to understand what is underlying data science, but most people aren't going into a field where they get into the nitty gritty of data. They still need to understand some of the concepts at a high level though, and I feel like a data science course could do a lot. People are bad at interpreting charts. People are bad at understanding risk and probability, even though it affects most of our decisions. People are bad at understanding how data is turned into conclusions. See comments on subreddits like /r/dataisbeautiful or /r/science for examples. So while I think algebra 2 is good stuff, I haven't found it useful outside the classroom except in specialized occupations (including mine, but just because I need it doesn't mean other people do). In contrast, a data science class might be more applicable to daily life, as well as a wider range of college majors.
Solving quadratic equations and inequalities are part of the Algebra I standards for California. They are expanded on in Algebra II, but students would learn the basics of those before Algebra II.
It seems like the consensus here is that Algebra 2 is excessive as a requirement for college. I'm here to argue the opposite. It is a necessary enabling course to have a meaningful liberal arts education as we do it in the United States.
A little about me: I'm a tenure-track professor in Nuclear Science and Engineering at a major state university, and I believe firmly in the value of a broadly-accessible college education as a civic virtue. My background is in chemistry...and I also have a Bachelor's degree in Political Theory. I know, weird combo, but the point is I can make an argument about this as an expert while also understanding the areas that are less math-intensive.
Courses are not an abstract thing to faculty, they are concrete things that have specific goals and requirements met, such that students can achieve the goal of earning their degree. They are surprisingly complex things, and have a whole litany of constraints on them. Degrees are accredited by external bodies, and there are strict and specific requirements that are provided to then earn the right for an institution to distribute degrees. You can think about these as "licenses to learn." If you don't meet the minimum content requirements, you cannot provide the degree.
We are also limited in how many courses we can require, how many credits are too many, what each department has as its domain. Most institutions require 120 credits if on a semester schedule (8 terms, 4 years, 15 credits/term), while quarter schedules require 180. Historically, these credit counts were fairly loose. With the cost of education to students increasing, many colleges and universities have implemented strict credit caps - you will require the minimum and no more. To students, this is a good thing, but to faculty it is an optimization challenge - how do you squeeze more class into less time?
Studies of many colleges and universities have found the minimum college preparatory requirements for a long list of degrees. The consensus from data is that (depending on the study and area of coursework) being either Calculus- or Pre-Calculus-ready is a necessary pre-requisite for success. It is a sign of intellectual maturity and the ability to consider, discuss, and work through abstract thoughts. Success at the college level in the sciences and arts is not always dependent on the content of Algebra II, but it is dependent on the ability to understand the content of Algebra II.
There's a problem with this, though, and that is that success in high school often recurses back to economic stability at home. If your parents are together, if they are employed, if they are white and white collar, you are far more likely to succeed in high school and in a bachelor's education. No student comes in on their own merit, they have an "invisible knapsack" of privileges to help them along...or an invisible yoke of disprivilege to hold them back. Intellectual maturity is not simply dependent on the maturity of the student - there is much more than that.
Much has been made of the fact that a college education is more necessary today than in decades past. It has even been called "the new high school," in that it plays the same role of being necessary to get a career and stable employment that high school played. The problem is that it comes at a cripplingly high price, it is selective, and it has limits on content.
College is not for everyone immediately after graduating high school and that is not a bad thing. It is a self-motivated exercise that relies on the emotional and mental maturity of late teenagers who are newly independent, and it is the beginning of specialization for students. The value of the degree is typically in how it trains students to think, while also providing a basic understanding of how things work so that students can be armed with the knowledge to then think. It cannot be all things for all people all the time while also charging a fortune.
The problem that the policymakers at UC are trying to solve is one of cost and time for the students. It is an admirable goal. The solution proposed comes at the cost of education. If you cannot provide the minimum education needed to establish one as even a minimally-independent worker and thus benefit from that degree. If the time difference and cost were minimal, there would be no objections from any to relax requirements for entry or to have additional requirements for graduation. In a world where the desired degree can cost above a hundred thousand dollars, every additional requirement is essentially a hostage scenario for students. "You must pay more to then get a chance at a good life."
The solution is not to relax requirements and constrain credits both, these are only treating the symptoms of the problem. The solution is to remove the cost of education.
Imagine if a college education was a thing you'd want but not need to get an office job or to work in a creative environment. Imagine if college was allowed to take 5 or 6 years if that's what it needed for a specific student. Imagine if public college was free to students with continuous progress to a degree, because it was paid for by society. In such a scenario, a college would have no problem accepting students who struggled with math - there would be plenty of time to let them mature, and it would not promise financial ruination. Additional credits could be required for the degrees that needed more advanced math or statistics or technical writing classes. Higher standards could be expected of students to get degrees, since each failure does not jeopardize student's lifetime success - they could just retake it in a year.
So many of the problems of public education come from the lack of universal accessibility. Knowledge and opportunities are locked behind a paywall, one that costs more with time. The biases of our society are worsened when we require economic and social privilege to then move forward, and the crippling cost of education is just one way.
Make public education for the public good again. Let us teach what is needed. Let us require the education that is sound. Let us end the educational hostage situation.
College not being free also ironically increases costs. There are a huge number of staff members dedicated to thse things that could be drastically cut back or eliminated entirely:
Even if the costs would not decrease by that much, there are a lot of duplicated efforts. If you had a funding model based on student credit hours, you can get more cost-effective by having fewer but larger classes (which would then break into smaller studios or recitations). Some engineering colleges are considering bringing math, chemistry, and physics internal to their program so they get more student dollars - never mind that the overall cost to the institution of having duplicated classes increases.
Then there is the optimization of the credits question. Credits have to come from somewhere, and so classes get reconfigured and dumped out from the curriculum to ensure that you stay under the maximum. If you can split concepts from one class to fit in as a small subset in three other classes, that can justify its own class...and then you get a better justification but the same duplication of effort again.
So the cost of education makes it less effective.
The optimization requirements absolutely impact curricula and professor morale. My most vivid classroom memories of college are from science & math professors prefacing units with some variant of “this is an irrelevant grab bag of topics shoved into this course so we can maintain accreditation to grant engineering degrees.” It’s not that they found the subjects themselves to be useless, only that they should be taught in dedicated classes instead of crammed into discrete mathematics or gen chem.
I got pushback for characterizing a class like that...but it's true. The truth is that there is far more content that should be covered than can be covered in the time allotted. It makes mastery of coursework more difficult to achieve.
Algebra is not a niche field of mathematics. Algebra is used by normal people all the time in real world applications even if they are not aware of it.
Algebra 2 is also a prerequisite for doing data analysis. Sure, you can run regressions without knowing how to do the underlying calculations by hand, but you still need to know what is going on to make informed decisions when analyzing data sets.
This seems to be more of a failure of the public education system earlier in a student's education. Students should have a decent grasp of Algebra 1 by the time they finish middle school.
The University of California system requires:
If you already have Algebra 1 under your belt when you enter high school, you only need Algebra 2, Geometry, and whatever third math course you want to take. That gives you 4 years to complete two required math courses that you should be able to take straight away.
We should not allow students to enter the UC system without meeting the already fairly generous math requirements. That is not helping any student succeed. It's only letting voters, lawmakers, and educators ignore the failure of the public education system.
It’s colleges pushing to relax their standards so they can maintain enrollment. If they keep standards, the underprepared students will either never enroll or drop out with a bucket of debt and no degree. Instead, they push to lower standards so they can keep the books balanced by meeting enrollment expectations.
This is about the UC system though. Not only are they state schools, their enrollment has been growing like crazy.
California spent over a decade trying to have all 8th graders take Algebra I before reversing the policy in 2013. When it was in place, a large number of students were failing the class and it was a significant roadblock for many students:
I understand your point that students need to be able to face and work through struggle. As a teacher that's something I try to do with mine on essentially a daily basis. However, it's entirely possible for a struggle to be unfair or unnecessary. It's also possible for a struggle to be too great for an individual and have negative effects.
I'm not saying this as a challenge or anything but more as food for thought: Have you ever burnt out on something that was too hard for you? Have you ever tried your hardest at something and failed anyway? That's what a lot of these students were experiencing. Instead of insisting that they meet a rigid and uniform requirement that was ultimately damaging their educational prospects (I mentioned in my other comment on this topic how difficulties with algebra lead to dropouts), we can instead evaluate the effects of that requirement and change it if we identify something that would work better. That isn't capitulation; it's the basis for reform.
I was one of those students affected by this policy in middle school. The way the class was taught, I basically gave up on learning math and ended up in "remedial" math classes, including introductory statistics. I did so well in statistics, that I felt much more confident with math. I went back to other math classes in high school and early college and struggled again, including taking trigonimetry twice. But calculus clicked for me, just like statistics did.
The point I'm trying to make here is that algebra is really hard if it's not taught well, so we should be enforcing better teaching styles for this essential math course, and break it up instead of teaching the full textbook in one year (or something to that effect) for students that need it to be slower paced.
I think it somewhat depends on the major.
You can get by fine in plenty of fields without ever touching the majority of algebra 2. It doesn't change the fact that we have a major problem with college being treated as the only reasonable degree because the public system outputs such a huge variance in skills.
My biggest red flag is this part of the article:
I know that many factors in life can affect someone's ability to learn, but this quote says it all for me. College is hard and you often encounter topics that are not enjoyable or easy for you to learn. High school should prepare students to overcome educational challenges. If a student needs extra resources, schools should provide those, but letting people avoid challenges is wrong.
College classes don't let you skip the parts you don't like. Employers don't allow people to ignore important tasks because they are too hard. Why are high schools trying to let students skip the subjects they find difficult?
Because some people learn differently? There's all sorts of subjects you can get a degree in that don't require higher level math but might come more naturally to someone who's struggling with algebra 2.
Edit:
And now that i've got a moment, it's always been a lousy connection between "can't do it" with "giving up/lazy". It's absolutely a fallacy to just assume these are kids who would give up on everything because they've decided algebra 2 isn't for them. I get that it is a % of group, but at the same time I've seen this logic used all over the place by people who sure as shit don't change their own oil, or do all sorts of other tasks they deem "too hard".
I don't mean to sound like I am blaming the students for this. I understand that learning disabilities are a real thing that students struggle with, but we need to provide those students with tools to learn despite their different abilities. They don't need to take the class without accommodations for their disability, and they don't need an A+ to pass.
People can get accommodations for disabilities in the real world, but they can't be excused from dealing with challenging situations.
Not completing Algebra 2 doesn't even prevent someone from attending college in the first place. It prevents them from going to a UC, but the UC system is held to a higher standard than a normal university. Community colleges, other public universities, and private universities are available if you can't meet the requirements.
There's a far gap between learning disability and just different learning capacities. There are plenty of good mechanics, accountants, psychologists, lawyers, etc that I wouldn't trust to apply the quadratic formula let alone anything higher level.
If the UC system is supposed to be a higher standard, fine. But it seems like an arbitrary one if it doesn't relate directly to your degree.
I would argue that algebra 2 is hardly higher level math. Trig, pre-calc, and calc, sure. Even for a "lowly" marketing bachelors algebra 2 would be extremely helpful. In this age linear algebra and stats would also be useful, potentially more useful than calculus on its own.
I think one problem with math curricula in general is that they don't show how many different situations math can be applied to. It's always speed/velocity, train timing, and the cost of x bananas and y apples.
That’s probably because you’re comfortable with it. I am too. The vast majority of people I’ve known think it is, and the opinions of those who didn’t struggle really isn’t the point.
My brother has a degree in marketing and is a project manager. He’s used anything near algebra 2 maybe a handful of times in his career and often it’s either googling a way to apply it or asking someone who’s better at math to help.
Edit: And for clarity sake my brother is good at math as well. It just doesn't seem all that relevant, especially when you're in an industry dealing with solved problems. Apply X function to Y dataset is often the extent of understanding required for pure business applications.
It's tough, because algebra is one of those things you use if you know it.
I tought math, and went and got an MBA and graduate degree in marketing. There are plenty of applications for algebra in marketing, from modeling spend, campaign break even points, maximizing ROI, etc. Not everyone in marketing does the same thing, and big orgs always have someone to farm the math out to. Still, algebra gives you the basic ability to represent so many real world situations, that it is a huge boon to know.
That said, I think the curriculum and approach to presenting the topics needs to change, but that is different than simply doing away with it.
Yeah, I agree with your points. Mine was more about I think if it were demonstrated to be useful in more every day situations, along with appropriate visualisations and applications it would become easier to understand for a larger group of people. But when it's just very basic examples like velocity-time graphs, train schedules, and the cost of fruits I can see how a 16 year old might write that off and think it's entirely useless.
Imagine if the textbooks provided examples demonstrating of how a wannabe influencer could use analytics to calculate potential future subscriber growth, or something like that.
I got a math major at a top US college a bit over a decade ago, and somewhat recently I had to use trig in a programming project. I asked a friend who actively tutors hs students cos I don't remember anything from trig lol
(that said I am very pro math learning and pro large common core, the fact alone that one can recognize "oh haha this is a trig problem" requires pretty substantial training. I just thought this was a funny anecdote.)
on the topic of some people learn differently: Teaching styles in college and high school tend to differ wildly. If a student doesn't understand something in high school, but retakes the course in college, they may understand it better. They also have a higher chance/ability to choose who teaches them so they can select the teacher and their teaching style, where in high school, that isn't the case usually.
I will say, as someone who majored in IT and has worked in the field for over a decade, I've never once used algebra 2, or felt the need to use it, or higher level math in my career, which is ostensibly STEM (I still have no idea why the T is even part of the other three. It has basically nothing to do with them and requires a completely different set of skills, but I digress).
However, I don't think I needed a degree for the work I've done in my field. I'm in management now, so maybe it helps a little? I learned far more about how to manage people effectively in the military than I ever did in college though.
I think college in general being a minimum requirement for any white collar job is a waste of time and resources for most people. College used to be a place where upper middle and upper class people who had no pressure to earn a living went to mingle, and become more "well rounded." I think it still serves that function far better than it does as a job training program, which is what it serves as today.
Realistically, I could have learned everything I needed to get started in the field in a year long training course, but I knew it would be tough to find jobs without a degree. Why does any IT job care that I took psychology 101, or had an elective in military history, or that I took a drawing class freshman year? Why is that a requirement?
Highschool already serves as the baseline "this is what a well rounded person in our society should know" education level. Forcing people to spend 4 years learning things they'll never need in order to tollgate a knowledge based career (which is the only way to earn a reasonable living in this county without absolutely destroying your body) is just nonsensical in my opinion.
So maybe it does make sense to continue requiring higher math in college. It doesn't make sense to require college for most jobs that require it today.
Technology, finance, communications, marketing, accounting and so on are all things that we could set up expedited training courses for that take half the time or less and teach students what they need to be effective at their chosen career. No more, no less.
And yes, I know that this exists to some degree already with AS degrees and other associates level qualifications. The issue is that for most people, that alone will not net them a job. Employers want a qualification that they can use to filter out most applicants from the very start, and for whatever reason a bachelors has become that qualification.
Is the problem entirely that students find it challenging to learn or is part of the problem that instructors have difficulty explaining it adequately? Being an effective instructor doesn't just require an understanding of the topic but also an understanding of how to approach the topic from the perspective of someone who doesn't already understand it. I've sat through so many courses with instructors who have zero charisma, whose lectures are simply reading the textbook, who are more interested in students passing their tests than understanding the material, and/or who don't speak English as a first language (bless their heart, but I shouldn't have to struggle to decipher what word is being spoken before trying to understand the concept). When topics are easy, students can take on the brunt of overcoming the instructor's shortcomings, but when the topic is more complex then that task may become insurmountable. Especially when this is one of multiple classes you're likely taking, it may not even seem worth the while to put in the effort when that effort can be better used in another class.
I don't mean that students have to face hardship with no tools or resources to help them. Part of school is learning how to learn even if the subject doesn't come easily to you. If a single student isn't doing well, sure that can just be their fault. If the majority of the students in a class aren't doing well, that can be the teacher's fault. If 2/3 of the State of California is not meeting math testing standards, then the whole system is to blame.
If the system is to blame, lowering the bar of minimum achievement is not helping any student improve. It may actually further harm the minority of students who were able to overcome a flawed educational system by allowing them to never challenge themselves.
In the district I started teaching in (an underfunded urban district ravaged by poverty), Algebra I was essentially a perfect predictor of dropping out.
Students would take Algebra I, and, as is the case, some would pass, but many wouldn't. Those that didn't would have to take it again. Some of these would pass, but of those that didn't, there was an almost 100% dropout rate. We didn't see this same correlation with any other subject.
Around the time I started teaching there was a study done by the US Department of Education. I can't find the actual link to it, but the statistic shows up here:
Eighty percent.
I've been on techy spaces online long enough to know that communities like ours tend to aggregate people who were very successful in math. As such, discussions tend to emphasize the importance of math -- particularly higher levels of math -- and downplay the difficulty and struggle that many people have even with lower-level concepts.
If you're good at math, it's because that is built on a lot of foundational knowledge and practice. You are fluent in a ruleset and a mindset that, to you, looks structured and logical and meaningful and applicable. Enough time in that fluency and it becomes second nature or common sense to you.
If you're someone who struggles with math, however, it is opaque and arcane and confusing and disorienting. It doesn't make sense. It's arbitrary. It's rigid. It's a brick wall that you have seemingly no way through or over or around.
Please genuinely consider this when thinking about the linked article and its proposal.
I'm a secondary school teacher in the United States and I firmly believe that most students should not have to take Algebra II. My standpoint is a bit different than the linked article, because that is specifically looking at Algebra II as a requirement for college admissions which is a narrower focus, but believe me when I say that I wholeheartedly feel that one of the best improvements we could make to American education would be to incorporate less rigid and more diverse math pathways for students.
Algebra II is not essential for all learners, and a strict adherence to it as such is likely doing direct harm to a lot of them.
I mean, I agree many people don't need to take Algebra II, but many people also don't need to go to college. This may sound harsh, but I think Algebra is simple enough even for teenagers who don't like math that if someone is so far behind so as to not pass it, they probably are not suited for college anyway. There's nothing wrong with not going to college. Training people in a skill better suited to them is better than even further degrading the already tenuous value of a college degree.
While I'd agree, that's not even necessarily the question here. California has a multi-tier public university system. This editorial is arguing that the University of California system, the first tier, should not require Algebra 2. Yet not going to a UC does not mean not going to college in California, or even not going to a university. There is an entire second tier system of full, public universities, the California State University system. And then there is a third tier, at a community college level, the California Community College system.
Of those three, the UC system is the smallest: the CSU system is the largest public university system in the US, and the CCC system is the largest higher education system in the US and third largest in the world. The UC system is meant to be a system of research universities for the top students in the state, not as a system for every student: under the original 1960 California Master Plan for Higher Education, before Prop 13 forced a change in the way tuition and admittance worked in the state, the UC system was meant to guarantee places for the top one-eighth of graduating high school students in the state, the CSU the top one-third, and the CCC for everyone.
The UCs have their visibility because many are top research universities at an international level, but it is the CSU system, not the UC system, that is meant to provide the most of the undergraduate education in the state.
Looking up Algebra 1,
I doubt anyone who can't grasp such simple concepts is going to university anyway, even if it was removed from the curriculum. It makes sense that it's such a strong predictor, since it is non-subjective and clearly identifies people with pretty severe learning disabilities.
As someone who taught college math, I personally blame the topics included and their treatments, coupled with poor approaches to learning at lower grades. As if times tables helped anyone understand the importance of finding the roots of a polynomial or exponential functions.
Most math as it is taught today isn't helpful to most students, including those going into stem. Math books are written by mathematicians, to satisfy other mathematicians, rather than what best serves students.
However, there are topics buried in algebra that can be directly applied to financial literacy and many other widely applicable skills outside of STEM.
I also say this as someone who struggled with math in my youth, failed multiple math classes before dropping out, but ended up teaching linear optimizations and machine learning techniques.
Could we instead rectify that by making it slower paced or incorporating alternate teaching methods for Algebra?
I mean, there's 1000 solutions and 10000000 bad ones, and the trick is actually getting a good one through the bureaucracy without it turning into a bad one.
Personally I've always felt that it'd be a lot easier on everyone if there was a high school level focus on what you're good at, and what you're not. Algebra for "not math people" would benefit a lot because you could slow down and focus on the weak spots for the students, and also try to correlate it to experiences they might better understand.
At the same time the people who breeze through math aren't now nodding off in class because they can be in the "for math people" math classes and get the attention/curriculum they need.
This would also be better served by having more trades in schools, and getting the hell away from the "oh well you can have 60 kids per class. 10 of whom are accelerated/honors, and 15 are SPED, and 10 of whom are constant behavior issues...good luck". To the point that I feel that until you address that issue, you aren't going to get anywhere.
A potential problem with this approach is that it risks dividing students early on, potentially of the basis of factors other than ability. One traditional way of enforcing class and other divisions, for example, has been to choose topics and courses at different schools, or for different types of students, such that some groups will be significantly less likely, without considerable outside work, to continue on certain lines. My partner, a humanities professor, once pointed out that, while she does love her field, that she did not go into science or mathematics is at least in part because, in school, she tested well for math and enjoyed it, but was placed in 'not math people' courses for various reasons including keeping her with her friends, encouraging other students, and, probably the real reason, being at a conservative school and the wrong gender. So she was taught math with 'experiences she might better understand' rather than as something actually intellectually interesting, and while she had no trouble with the classes, tended to see the humanities as far more intellectually rewarding.
Additionally, as adding different courses increases workload compared to teaching multiple sections of the same course, without sufficient staff and light enough course loads, splitting courses doesn't necessarily make the classes better. I was in a 'math for math people' class in California. It didn't give us the attention and curriculum we needed. It just brutalized us by letting us skip to a higher year's curriculum as a result of our own independent study, then trying to keep us from causing further problems by teaching that curriculum at the same pace, just with far more assigned, repetitive work, arguably to keep us from studying at a faster pace at home. Our teacher certainly didn't have time to care about us or give us a different curriculum.
Yes, and no.
I once taught an "Algebra 1A" course, which was a slower course for students with learning disabilities. It was essentially the first half of Algebra I spread out over the course of a year.
My students did great. They needed the extra time and different instruction to be able to pick up on the concepts. They would have been completely cooked if they'd been in a regular Algebra I class. It would have moved too fast, and they likely wouldn't have been able to pick up the concepts from the type of instruction given.
But, to get at what @Eji1700 said in their comment, can we institutionalize this and make it a genuine solution? Well, that's much more difficult. I'd love more diverse pathways for math (and everything else really) but I have to acknowledge that it sounds great in theory but becomes essentially unworkable in practice. Making shifts like that add substantial complexity and often have unintended knock-on effects.
For example: my students that took Algebra 1A had their entire high school trajectory changed because of it, because it technically was a half-credit course even though it took up a whole year. That completely changes how they have to allocate credits elsewhere, and creates its own opportunity costs.
Another example issue: teachers are already strapped and we don't have enough of them -- if you then told them that they were teaching a different subject (or a different form of a given subject) every single period, they'd balk. It would simply be too much work. Much of education policy is based around a uniform efficiency not because it's what's best for kids but simply because it's what's workable.
Problems in education are so complicated they're nearly intractable. There simply are no quick fixes.
I 100% agree with this. I think Algebra II is fairly simple now, but I got a C+ the first time I took it in high school. Because I didn’t do well, my school put me in pre-calc the next year which was mostly review for me. It wasn’t challenging, but I was given more exposure to the topics I struggled with the previous year. The next year, I was able to take AP Calculus A/B and do well.
Another time in middle school, I slacked off in Algebra I and got a C on the final. I still passed with a B, but the teacher recommended I go to summer school.
I am confident in my math abilities and my ability to learn more math because I know that having trouble doesn’t mean you’re stuck forever. You just need some extra practice and guidance to get back on track.
Does your school have any free or low cost summer programs to help students get back on track?
I know that lots of times the resources aren’t available, but it seems like falling behind is a big issue for math students. If someone is failing Algebra I because they lack some prerequisite knowledge, it makes sense that taking it again won’t work unless the gaps in knowledge are patched.
To answer your question, I'm going to sidestep a bit.
Since this topic is focused on California, let's look at their data for a moment. That's from their standardized state testing for 2023.
States start testing their students in third grade, so that's where we can start. Take a look at the math proficiency of third graders for last year.
It is less than half.
So, our first data point regarding math ability, for eight- and nine-year-olds statewide, is that over half aren't proficient. I know we're not focused on third graders, we're looking at algebra here, but in order to understand why people can't do algebra, we have to consider the antecedents.
The point of me bringing this up is that the problem isn't one of a few lagging students who need some extra help. It is a systemic issue embedded into math pathways starting at least in third grade (and almost certainly earlier). 2023 isn't an outlier in the data, by the way -- nor is California. You can look at most states, for the years going back to when schools first had to start reporting this data, and you'll see similar numbers. According to standardized testing, large portions of students -- often a majority -- are starting out their educational careers behind.
This goes in to what I was talking about in my other comments: is this failure simply people not meeting the bar, or have we set the bar incorrectly? I firmly believe it's the latter. I think we have a duty to change that.
(Side note: I also believe that the testing industry has a vested financial interest in creating the perception of the continued "failure" of American education and so their data will continue to support that even if we do make changes, but that's an entirely different and much more pessimistic rabbit to chase.)
One of the legitimate criticisms of Common Core was that its early elementary curriculum was far too fast. Too much content was covered and the students retained none of it. Math, especially, falls apart when cramming for the exam. Most other subjects can paper over missed steps, but math presents the hard wall you describe.
IMO, Algebra I is the failure point because it’s the first time the students must be proficient to pass instead of being socially promoted or squeaking by because it would otherwise be cruel to hold them back. IIRC, the trouble with Algebra isn’t that the students can’t substitute x for a number, it’s that they never mastered arithmetic with fractions. The fix lies in the elementary levels.
To address your aside, the numbers are validated by comparing them to prior year results. Any curriculum improvement with immediate efficacy would show up in a state board of education meeting as “those lazy testing companies something up BAD this year” instead of “wow, I can’t believe this already worked.”
One thing I wonder is if the intervention needs to go back even further. I know we don't make students repeat grades in elementary school anymore because there were some studies that found it to be harmful in some ways even if the student can catch up academically. Remedial classes starting back in elementary school could be the solution.
Students can stay with their core social groups for most the day, but when it's time for math, one teacher can teach normal track math and another teacher can teach remedial. They can swap the students into the class they need for that subject, then move back to their normal teacher for the rest of the day.
Also, if you look at the disparities in math achievement between different races, my intuition would be that the Black and Hispanic families that have lower math test scores have higher rates of single parents. The data actually backs this up. Single parents may have to spend more time working to survive than a two parent household. Single parents also may have less time to spend monitoring their child's performance in school. I know many of us have memories of doing math homework with dad and crying at the kitchen table, but that was probably beneficial for our educational outcomes. For students without dads that can yell at them about multiplication tables and fractions, I think a restructuring to math education in elementary school would help a ton.
I agree that it's the system that is causing these failures and not particularly the students. I think that lowering the bar is doing a disservice to students. These students on average are capable of more, but there are barriers in society and the educational system that gets in the way. Lowering the bar is telling them that they are not capable of improvement when it's actually society's fault for not doing more to even the educational playing field among all students.
I'd say the answer is simple:
Algebra shouldn't be required to pass high school. It could be replaced with something more basic but useful if students can't cut it, like basic budgeting.
But it should still be considered mandatory for entering into college, which was my impressions for this situation.
Perhaps there should be a mandatory intermediary learning between high school and college, ideally seperated from home life a bit A 50/50 split between smoothing out any educational gaps part time, and doing a kind of 'temp job service duty', giving exposure to a wide variety of careers.
High school does a real shit job of helping show the kinds of jobs available in the world, and I think that's half the problem of listless students not using the degrees they earn.
Something like say 5 years of this vocational service/post-secondary prep from 18 to 23 gives some time to mature and figure out 'what they really want' and 'who am I outside the context of my childhood.'
I think that would give mass improvements to performance in post-secondary and be able to eliminate a lot of 'fluff.'
Emphasis added (but still not strong enough).
They especially fall short at prepping boys in the middle of the ability scale without nepotism connections. Here’s a stereotypical list of the categories of options a white-collar HS senior may think of (that aren’t pure wishful thinking like astronaut or YouTuber)
Note how the only options that aren’t targeted at the tails of the bell curve are the pink-collar careers. Despite probably providing an order of magnitude more jobs than the technical specialties, the following are totally absent from discussion
There's a reason I swore in this instance. Words cannot express how poorly aware of the world at large high school seniors are.
Being in higher ed, having computational math as one of my early degrees, and having taught and tutored math, the subject of what math should be required for the general student population is one I have been close to for many years.
Much of the debate seems to invariably come down to those who believe universities should deliver a traditional, broad education, while others think it should be more vocational based on the job markets requirement for four year degrees.
When it comes to algebra 2, I generally take the view that the topics should be required, but are often taught poorly or in ways divorced from their broad applicability.
I've seen some schools start to break apart math tracks based on degree path, so that the content can be a little bit more tailored. This helps avoid the "fourth year weedout" of real analysis for folks that thought they wanted to be math majors, by allowing for earlier classes that focus on theory, and one or more separate tracks that focus on applications to business or humanities.
It is also a little bit of a referendum on education that most people with four year degrees lack the tools to calculate their own retirement portfolios, projections, or needs. Some of that material is in algebra 2, but buried in treatment that satisfies the mathematicians in the room, but poorly serves most students.
Since it doesn't seem like anyone has mentioned it yet, here are some of the subjects covered in Algebra 2:
Some of these topics are admittedly pretty basic (e.g., arithmetic with complex numbers) while others are fairly arcane (when was the last time you thought about hyperbolas?). I personally don't have much of an opinion about whether Algebra 2 should be a requirement for college (I'm way too deep in STEM to be generalizing about other majors), but I am genuinely curious:
I think complex numbers are fun but, outside electrical engineering, it’s hard to find practical situations where you need them or could even use them.
Do you mean to suggest quantum field theory is not practical? Let me introduce you to the highly troublesome sign problem!
Just kidding. By "basic" I meant relatively simple, not necessarily useful (poor wording on my part). I'm sure there are plenty of students who have no trouble with complex numbers but struggle with linear systems, for example, so I think it does the students a bit of a disservice to assume that the folk struggling with Algebra 2 are struggling with the former when they might just be struggling with the latter. That's all I meant to suggest.
Edit: oh right, but yes, you probably wouldn't need them outside a STEM major. But maybe you would need them for a science prerequisite?
Higher education is an interesting thing to put a price on because while some classes can provide economic benefits to people who get a higher education, many classes provide more of a societal benefit.
A history class doesn't help an engineer make a jet turbine, but it can help them be an informed voter. College campuses mix people of different races, genders, origins, and socioeconomic classes with each other. The general education courses expose students to different concepts that can help them in their civic lives.
College graduates also have many economic benefits to society. On average, college graduates pay much more in taxes than they take in government benefits over their lifetimes. High school graduates also contribute, but only a modest gain where college graduates contribute 4-5x what they take. Governments invest $28,000 per college student on average, but gain $335,000 in net monetary benefit over their lifetime.
I get that many people are opposed to courses that don't directly apply to a career because they have to pay a lot of money out of pocket when the course may only provide a benefit to society. Why can't the government provide loan forgiveness to anyone who graduates? It would take pressure off students and still provide a net benefit to society over having them not graduate.
I don't disagree with the value of a liberal education, but it's worth pointing out that in European countries tertiary education tends to be more specialized and they don't seem to be worse off for it. For instance, in Germany there is a distinction between Universität (basic research, e.g. physics), Fachschule (applied sciences, e.g. engineering), Kunsthochschule (art school, e.g. architecture), and Berufsakademie (vocational school, e.g. social work). A typical university in the US would have all of these programs.
I did a little poll with my social circle, which includes a handful of writers, an artist, a marketing executive with experience in several big-name companies, a couple lawyers (one for a massive media company, one public defender) and myself (a teacher who is significantly less financially successful than everyone above).
None of us have ever had to think about any of this outside of school. Most of the people I asked don't know remember anything they learned after PEMDAS. I know that I took Algebra 2 once upon a time, but like my Russian classes that I needed for my BA, I forgot pretty much all of it sometime around 2015. That list you made might as well have been in Cyrillic.
I’m rather torn on this.
I think not every kid should go to college and many jobs unnecessarily require a college degree. I’m reminded of what happened with air traffic controllers - a stressful job that not everyone can do, and new hires get a lot of training before they go to work. But it didn’t require a college degree until they decided to do that, and I don’t know why they did that. It seems good and unusual that they rolled it back, though it was a mess how they did it and unfair to the students who did go to college.
Meanwhile, many college majors do legitimately require heavy math, and without getting the preparation, there’s little chance of being ready for them. And you can’t know far in advance what a kid will want to do.
There are some kids who get really into math at young ages, or at least that’s what I heard from the parents. Schools are not always catering to them well either.
So it seems like there should be college-track math, not every kid should do that, but every kid needs multiple opportunities to get on that track, in case they bounce off the first time. Also, maybe there needs to be less stigma about trying something and failing the first time? What matters is that you get there, not how you got there.
I’m reminded of how learning musical instruments worked when I went to school. In third grade, there was a chance to sign up to learn an instrument after school. I picked trombone for not very good reasons, which turned out to be a bad choice. I dropped out after a few weeks. The case was big and heavy, I had a hard time playing anything, taking the late bus home was annoying, and I was already taking piano lessons.
Maybe if they had signups more than once, I would have given another band instrument a try? Even at the time, I thought maybe I should have tried the sax instead. In retrospect, the clarinet seems like it would be worth a try, certainly more portable, but mostly girls chose it, and that made me wary for some reason.
Sometimes the whims and insecurities of a third-grader have more consequences than I think they should.
It seems like it would be even more the case if math were treated similarly? Kids learn to hate math if it’s not done the right way. How do you try hard to teach them in case they take it up, but not too hard?
And then you get the nonsense now that because "everyone" has a college degree, to weed out further candidates, some companies are requiring master's degrees when it's not needed either. I agree with you that not everyone needs to go to college. Continuing education should be the norm for all people, even if it's a simple "updated tax/retirement math course" or something like that, but I agree that we're focusing on college being essential for the wrong reasons.
Mirror, for those hit by the paywall:
https://archive.is/ExvmC