Only 5 percent of students will use calculus in college or the workplace, concludes a new report on college and career readiness by the National Center on Education and the Economy. Most community college students could succeed in college courses if they’ve mastered “middle school mathematics, especially arithmetic, ratio, proportion, expressions and simple equations.” Many have not.

The report calls for providing an alternative track — less algebra, more statistics — for high school students who aren’t aiming at university STEM degrees.

In a few years, high school diplomas in North Carolina will show whether a graduate is prepared for a four-year university, a community college and/or a career.

What a strange approach, asking whether students will use a course outside of academia. If that idea were to get around, young people would be out of school a lot quicker–and a lot of us would be out of a job.

The problem with education is the academics. 😉

Wow, in just a handful of decades we’ve completely lost the concept of a “liberal education” that was built up over the course of many centuries.

You can’t possibly appreciate the world you live in without at least a grounding in mathematics. Every technical aspect of our world (electrical power, communications, modern materials, manufacturing, medicine, and so on) has deep roots in mathematics. Without at least a foundation in math, you’re at the “I flip the switch and the light comes on, what more could I need to know?” level. One would hope that those of us who are (or at least trying to be) products of a “liberal education” would aspire to more.

For those of you who would like some background on the historical ideas of a liberal education, Dr Kagan just happened to give a farewell lecture recently on that topic:

https://www.youtube.com/watch?v=fMQGDdTQImo

He’s a great lecturer, I’ve listened to his lectures on Greek History from Yale more than once. Completely old school.

“There is only one good, knowledge, and one evil, ignorance.” — Socrates

Kagan, and Bloom alike, would never insist as our public schools do that all students k-12 receive a liberal arts education, even a classics focused liberal arts education.

Also, “a grounding in mathematics” is an incredibly vague phrase. Does mastering arithmetic and basic algebra qualify as a grounding in mathematics, or is calculus necessary?

The problem with discussions of “liberal arts” education is in the definitions.

While this discussion and these comments are interesting, I really want to thank you for pointing me toward the lectures of Dr. Kagan. I’m starting on the Greek history lectures now.

“Without at least a foundation in math, you’re at the “I flip the switch and the light comes on, what more could I need to know?” level.”

Which is all 90% of people will ever need or want.

The sooner we recognize this, and give up the fantasy that everyone can and wants to be a renaissance scholar, the sooner our education system can be reformed.

And then, as electronics and technology completely takes over modern society, the 10% who do know these things will rule, while the 90% who don’t will live clueless, easily manipulatable lives.

I don’t think that this is really saying that students should only learn what they know that they’ll use later. Most of what you learn in humanities subjects doesn’t require as much of a linear progression as math, and the same content can be taught in easier and harder versions.

To get to calculus in high school, you need to be on the algebra track in middle school. I took algebra in 7th grade, and most ‘smart kids’ took it in 8th back in the 80s. Back in the 60s, my smart parents took algebra in 10th grade – their school offered trig as its highest class. Trying to funnel everybody into a math track that they’re not ready for, just to get them through calculus that they don’t need seems pointless.

lulu,

I took algebra I back in 9th grade, geometry and computer math in 10th, and algebra II/Trig as a junior (the only course left in that sequence was Analysis which was in effect calculus, but very few students, unless you were in the I.B. track, took this course).

Mind you, this was back in 1977-1981, but as momof4 points out, so many students get such poor instruction in math in ES/MS, it makes it very difficult to actually LIKE math as a subject by the time the student makes it to high school.

If I had a dollar for every time I heard the phrase:

I’m no good at math (or something along those lines)

I’d be very rich.

momof4 is also correct that a basic understanding of algebra/geometry/practical math/stats is all that is needed for most people, and even though I’m in a STEM career field, I rarely use math more complicated than Add, Subtract, Multiply, Divide, Percentages, Fractions, and Modulus (remainder portion of a integer division).

However, math is a foundation subject, so a student who is struggling with the basics above is going to have a very hard time with higher math constructs in middle school and high school.

Given a solid grounding in arithmetic (which most don’t get; due to awful curriculum and instruction in ES-MS), most people won’t need more than a basic understanding of algebra, geometry, practical math (interest etc) and comsumer-type statistics. As far as needing math to understand the tech world, I’d be happy if people understood that much of our electricity is produced from coal; I hate to say how many college-educated adults I’ve heard touting electric cars because they’re so clean and gaping like fish when I ask them from where the electricity comes.

I agree with those who have already commented that all are not, and never will be, interested in and/or capable of a liberal education, classically defined and we are wasting vast sums trying to do the impossible. Lulu is right that content can be taught at varying levels. Not everyone needs to read the “real” Odyssey; many will do fine with the Rosemary Sutcliff version.

” I hate to say how many college-educated adults I’ve heard touting electric cars because they’re so clean and gaping like fish when I ask them from where the electricity comes.”

This is so true, it’s scary; most people these days have no idea where the raw materials for all their modern conviences comes from, how difficult it was to make such things, etc. It’s part of the reason we’re such a wasteful, unappreciative society.

It’s not only an issue of knowing the facts and theories regarding higher mathematics, including calculus, but the deep value of the analytical skills that are developed by studying these subjects. In days of yore, calculus for engineers used to be called Engineering Analysis and was focused on developing the skill set engineers need to analyze situations. I believe all students need to develop analytical skills; many seem almost utterly devoid of the ability. Once one understands and has internalized the analytical processing, one can almost do anything. This skill applies to both STEM and liberal arts. I was never a good mathematics student but I stuck to it through 2 years of calculus, differential equations, linear algebra, probability and statisitcs and mathematical logic and I believe the skills I learned have given me not only a competitive edge in life, but also a continuing ability to comprehend and understand both technology and humanities. Finally, there’s no doubt in my mind that mathematics is literally the language of the universe.

The arguements for a liberal education are great; and I’m in TJ’s camp in that mathematics is literally the language of the universe – possibly as the handmaid of physics, but hey.

HOWEVER, given how inefficient our schools are at identifying who “needs” calculus, shouldn’t we be aiming to provide the best possible tools to the most possible students? I’d like to believe that we can provide good foundations to anybody who wants them, no matter what their background (SES, ethnicity, etc)

There is no wealth like knowledge, no poverty like ignorance.

“gven how inefficient our schools are at identifying who ‘needs’ calculus, shouldn’t we be aiming to provide the best possible tools to the most possible students?”

NO NO NO NO NO NO NO NO (and the word is No.)

No more than everyone should drive a Lexus or Lamborghini. Each student should get the schooling that is appropriate for him or her.

For me, the appropriate car is a 5 year old Toyota. For a long time, the appropriate car was none at all.

Roger: I was perhaps inelegant. What I meant to get across is that shouldn’t we make sure that everybody who is able to afford it be able to buy a Lexus? If the government is going to be in the public education space; I don’t see how we can in fairness deny anybody the right to buy whatever they please. NOW, if you ask ME to pay for your expensive tastes, I’d draw the line, but I’d pay taxes to make sure there’s a fair market where you’re able to spend your money and dealers can’t discriminate against you.

We don’t identify winners well (Solyndra anybody?) and we don’t forecast the future well; so offering more than the bare minimum seems to be in order.

I agree 100%; personally, I think that if you can’t at least pass Calculus I (derivatives and basic integrals), then you shouldn’t be able to get a Bachelor’s degree from a major University. Period.

No doubt you could pass Calculus 1. How would you feel about a requirement to fluently speak a foreign language in order to get a degree?

I am currently fighting the battle with my middle schooler. She aspires to be a speech and language pathologist and feels it is the height of unfairness to have to do the standard college prep math sequence. She thinks we should take the European route of offering separate college prep sequences for STEM and humanities students in high school.

Momof4,

Here is something your daughter might want to look at in terms of requirements for getting a bachelor’s degree in speech and language pathology:

http://www.towson.edu/asld/undergraduate/speechaudiology/degreerequirements.asp

Here is the pre-major requirements (so she can be admitted to the major) for math:

MATH 111 Algebra for Applications (3) or MATH 109 Transition to Algebra for Applications (3) or MATH 115 Basic Mathematics for the Sciences (3) or MATH 119 Pre-Calculus (4)*

Given that she wants to do this field, perhaps she should look into the coursework sequence, since she will be required to take anatomy and physiology in college (which is very difficult class, I had it in high school, and the teacher taught it at a college level pace).

The fact that she doesn’t want to do the traditional math sequence might make her reconsider if the highest level math in order to be admitted to the major is pre-calculus.

Mind you, this is from Towson University, but i’d imagine that if the program a GPA requirement of 2.80 for 5 of the pre-major courses, it’s not a stretch to think that if she can handle the standard prep sequence for math in high school, she should have absolutely no problems completing the math requirements for the speech pathology major at any university.

The local Cal State has a SLP department that includes an undergrad major in Communicative Disorders. The only required math is a single course in statistics. However, to get accepted to CSU in the first place she would need at least 3 years of high school math through Algebra 2 at minimum.

She is a decent math student so I have confidence that she can handle a normal H.S. college prep sequence. She just dislikes the subject and resents being forced to study it when she has no interest in going into a STEM-heavy field.

It’s not clear to me how you can study statistics without knowing any calculus. I’m taking a seven-week basic stats MOOC and we’re integrating in only the second week of lectures.

Discrete vs continuous probability, maybe?

I took basic stats for social science when I was in college and there definitely was not any calculus in it. I actually had taken a year of calculus but the stats class required for my biopsychology major was not the same stats class required for my husband’s engineering major.

So I looked up the descriptions in the current course catalog of my alma mater. Here is the one I took:

“Introduction to statistical methods for social scientists. Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, regression, analysis of variance and chi-square tests, computer statistical packages.Here is the one my DH took for engineering:

“Introduction to statistics for engineers and physical scientists. Topics: descriptive statistics, probability, interval estimation, tests of hypotheses, nonparametric methods, linear regression, analysis of variance, elementary experimental design. Prerequisite: one year of calculus.”I would imagine that the stats class required for the Communicative Disorders major is similar to the one I took.

There’s a big difference between a practical statistics course and a theoretical one. You need calculus for the latter but not for the former.

Have her read Xenophon’s account of the _Symposium_ (free in Kindle form), then ask if she agrees with Socrates. From there, you’ve got her. It’s funny how all this stuff was a slam dunk a hundred years ago…

Again, personally, I think that if you can’t handle Algebra I, Geometry, and Algebra II (at least pass with a ‘D’ Algebra II), then you shouldn’t be able to get a High School diploma in the Western world. Period.

Given this topic, some might find it interesting to look at the current article on the Washington Post education section (look under local news) about the very low pass rates on Montgomery County, MD’s countywide various end-of-course math tests. Even though the county schools have had had a strong reputation (heavily influenced by demography, which has changed significantly) and have made a big push to get more kids through high-level HS classes, the current results are not stellar. The link doesn’t show it, but I’m pretty sure the pass numbers, especially at the upper end, are likely to correlate with the usual student subgroups, which also correlate with specific schools.

I’m enormously in favor of improving the ES-MS math curricula and instruction and in offering more – faster, deeper etc – to whomever has the necessary background and the desire. I am opposed to requiring the same HS sequence for everyone.

However, I have observed that many colleges do require math, at least through calc, even for non-STEM majors. Also, as more people avoid math, those who understand it have an employment advantage. Even though finance is not math, it’s mathy enough that many (non-finance) majors in the undergrad business schools do not do well at it. My DD (in the b-school but not finance major), was a 3-semester TA in finance and it’s been a BIG advantage ever since. I wasn’t surprised when she was a new grad, but even 6 years out, both of the new jobs she was offered specifically mentioned her finance background and she was able to get them to bump up the numbers because of it.

“Given a solid grounding in arithmetic (which most don’t get; due to awful curriculum and instruction in ES-MS), ”

This really isn’t true. Students are doing very well in 4th and 8th grade national tests, as well as statewide tests. Everyone likes to say that elementary school math teachers are weak, but in fact kids are learning fine.

It’s amazing how many people repeat utterly nonsensical truisms.

And of course we don’t need calculus. But it’s not about need, it’s about signaling. And we can’t admit that learning calculus is not about your bad teachers, but cognitive ability.

Want to know WHY a gas plant can’t just jump in and compensate for a solar power array that has suddenly gone cloudy? You’ll need calculus and vector analysis. Want to know WHY the positive your mother just got on a cancer screening may not be the end of the world (or even important at all)? You’re going to need to understand Bayes Theorem.

Sure, you don’t HAVE to understand math, it’s only important if you want to understand your world and its issues. If those aren’t your priority, then go blissfully, ignorantly ahead.

RoB:

I don’t need to know any of those things. I rely on people I trust to know those things and explain them to me, when and if I ever do need to know them. It is almost like that’s their job…..

When my kid was 3 months old, I had to take her for a chest X-ray. I overheard two nurses with a calculator discussing a dosage for her. They made an error in their metric conversions. Being familiar with both math and the metric system; I eventually got them to see the error and my kid was OK. That’s part of their job, and I’d like to trust them, but hey; at least my kid is alive and healthy.

Trust, but verify.

I’ll bet that all of those nurses had been required to take and pass Algebra 2 at some point. Anyone who understands Algebra 2 can easily make a metric/English conversion. In fact, a good understanding of fractions (pre-Algebra!) will do it.

This suggests that we may have the worst of both worlds:

1. Too many people take advanced math they are not interested in and never use.

2. Too many people don’t understand basic math. They are passed on because they can remember enough to pass a test soon after they have practiced–but they “forget” after a while.

3. There is a non-trivial overlap of the first two groups!

It’s your right to live as you see fit. My point all along has been that the whole point of a liberal education is to inspire you to more. What a shame that we’ve lost that.

I think we’ve veered a bit off of the original question, which seemed to be ‘what can we reasonably expect most students to learn?’. I think it’s great when people want to understand complex issues, and having taught bio to nursing students, problems with dosage calculations are way too common. That being said, the idea that everybody is going to learn a lot of complicated information so that they can understand all sorts of complex systems isn’t realistic.

My husband and I both have PhDs (computing and genetics). He can explain how the chips on a computer work and is teaching binary to our kid. I just trust that the computer will come on when I push the button. I worry about any lotion that claims to ‘increase production of X’, and he trusts me when I babble about epigenetics. I sometimes read Alton Brown for fun, but usually just trust that the recipe will work without knowing the biochemistry behind it. While we need a group of very trained people working on problems, and lots of informed people keeping up with what they’re doing, we all have our bit of the world that gets most of our attention.

Are you seriously trying to suggest that it is preferable, or even possible, for someone to know everything?

I’m not disputing that a certain level of IQ is necessary for real HS math, increasing with each course, but poor preparation removes kids who should be able to be successful.

Recent national testing trend aside (most state tests are a joke), my kids’ old district is transitioning from a solid curriculum to a spiral math curriculum, while pushing as many kids as possible to finish geometry (or “geometry”) by HS entry. I know the knowledgeable teachers my kids had in math have been retired for at least a decade. I’m also reading teacher comments in the WaPo that many kids are entering HS without ES-level foundations and that many teachers are forced to teach classes “beyond their comfort zone” because of the push to accelerate. There’s been an increase in the tutoring centers in our old area, and I don’t think it’s an accident.

I know what I see locally – different state; HS grads unable to calculate sales tax with a calculator, unable to calculate 1/3 of a pound on a digital scale, unable to calculate proper change etc; they don’t have understanding and they don’t know the algorithms and it’s not that they lack the IQ; they’ve never been taught properly. Good curriculum and effective instruction are necessary for most people.

Joanne, the last paragraph of your community college spotlight piece is: “However, the path to 12th-grade calculus usually starts with eighth-grade algebra. At 12 or 13, students would have to decide whether they’re aiming for a university degree in engineering or science. Imagine a STEM-prep track for 5 percent of students — or even 20 percent — with everyone else preparing for a low-tech university degree or a community college job training program. The future engineers and physicists are likely to predominantly Asian-American, white, middle class and male.” (I don’t know how to quote on this platform.)

Sixth grade is too young. Our affluent public school district has remarkable success with female students aspiring to STEM careers. Any sorting mechanism which tries to predict student success rates based on the patterns of the past will artificially restrict access to STEM careers to women and non-asian minorities.

The local system does teach Algebra in middle school. There are two tracks of algebra. Some students are able to succeed in math and science, but aren’t as successful in the humanities. There are also mothers with STEM careers who encourage their daughters and their daughters’ female friends to consider STEM careers.

Medical school is already at parity, or slightly more female than male, if I recall correctly. Not that long ago, people might have said, “well, doctors always have been mostly male, so it would be most efficient to steer girls to nursing careers.”

In addition to which, much of the top 5% in ability don’t want STEM careers. The Ivy League has very strong math SAT/ACT averages, but their graduates don’t stream exclusively into STEM fields. A strong system would allow students to choose.

Regarding medical school, the coursework required for entry has changed significantly over the last 20-30 years. I have heard med school faculty and staff specifically say that the math/science requirement changes have been influenced by a desire to attract more women and URMs. I had pre-med friends – male and female – in college (60s) and it was extremely science-heavy. There are now med schools that do not require any undergrad sciences for entry – a friend’s kid is in one. I’m pretty sure he didn’t have to take calc undergrad, either.

I would like to see as many kids as possible get through a real calc course in HS, but the foundation starts in ES. If you have to play catch-up in HS, you’re in big trouble and it’s not much better if you’re significantly behind in MS. I think that MoCo is seeing that; they’ve been pushing kids into MS algebra and geometry and too many are in “algebra” , “geometry”, “algebra II”, “pre-calc” etc and the countywide end-of-course exam failure rates show it.

Cranberry, it’s true that 8th grade is too soon to predict what each student will want/be capable of. But it’s equally true that our current systeme is pushing pretty much all students through a college-prep math sequence, only it’s not sticking for a fairly substantial number of kids. The opportunity cost, for them, is that since they didn’t spend enough time on K-8 basics, and have no access to a more technically-oriented math curriculum even if it matches with their desires or plans, we are in essence giving those kids NO math.

EB, what guarantee is there that a system which doesn’t advance people beyond college Algebra I in high school will do a better job teaching “a more technically-oriented math curriculum?” I think if it’s bad at the current model, it would be even worse in the proposed model, if only because no one’s tried teaching students who have not been labeled as struggling with school a “math-lite” curriculum. And it would be a math-lite curriculum.

Here we go again.

Which kids in K-6 need calculus and which ones do not?

Which ones even need algebra II?

The problem is that the decision is made starting in the earliest grades that NOBODY needs it. The top PARCC PLD level level 5 (“distinguished”) specifically excludes STEM curriculum needs. Their top level translates into being able to pass a college algebra course – i.e. no remediation – hopefully. This training starts in the earliest grades. They do not deal with the needs of those kids who could get to a STEM career. It’s all over by 7th grade unless they get help at home or with tutors. People see that some kids get to calculus and think that everything is ducky-fine, but they never ask us parents what goes on at home.

Sure, IQ matters, but like always, many just can’t seem to separate the variables and calibrate the level. Do teachers, curricula, and expectations matter or not? Why teach kids at all if IQ is such a dominant variable? Just put them in a room and let them figure it out themselves. Oh yeah, that’s what they are doing now with the teacher as the guide-on-the-side. Differentiated Instruction is just a form of IQ sink or swim.

Many people see only what they want to see. Low expectations and talk of IQ are such horrible things. Nobody can look at El Sistema and not see it. The IQ curve might still be there, but their level is so much higher, with many kids coming from the barrio. The only solution is more choice for parents. They see individuals where many educators see only a statistical bell curve.