Let's Stop Requiring Advanced Math, A New Book Argues

Parents Forum
81

The table 7 from http://files.eric.ed.gov/fulltext/ED248142.pdf :



Course                          Percent of Schools
                                Offering Course
                (1) Advanced Level
Calculus                                10%
Analytic Geometry                       10%
High School Mathematics                 95%
    (Including Advanced Algebra,
    Trigonometry, Probability
    and Statistics)
                (2) Intermediate Level
Algebra                                 10%
Secondary School Mathematics            95%
                (3) Beginning Level
Algebra                                 80%
Plane Geometry                          20%
Advanced Mathematics                    95%
                (4) Remedial Level
Review of Algebra                        5%

There is no indication that calculus was normally considered a 9th or earlier grade (middle school in Taiwan, ROC was grades 7-9) math course.

82

Did you read the report? Only 10% of high schools offered calculus, but 95% offered math courses one would take before calculus. Post-calculus classes, like multivariable calculus, linear algebra, differential equations, were not frequently offered. I think this must be a translation issue, and maybe people are confusing high school algebra with calculus.

83

I’m a bit surprised no one has brought this in yet:

http://xkcd.com/1050

Edited to fix url

84

There is no general familiarity with or competence in calculus among the vast majority of the Taiwanese population.

And when school students have taken a basic calculus they have not “completed calculus”, any more than a French 101 student would have “completed French”.

85

One of the oft ignored pillars of the education system in some foreign countries is that it is not really open to anyone or everyone. Children are shuttled into a path based on aptitude. This type of system makes comparisons rather difficult. Many student never really go to HS, per se, as they have been deemed unworthy of the college track at an early age. This may be a perfectly acceptable system in some countries, but our generally egalitarian populous would not likely embrace that sort of division.

My core issue is more with the lack of fundamentals in the non-Stem fields. (especially economics and government). Our district (state?) only requires 1 semester of each and they are typically offered during Senior year after grades have less ‘impact’. For me, everyone needs a good understanding of these topics. Not everyone needs a good understanding of calculus.

86

Of course not. This is by virtue of the fact that you do not get better results out of students just by telling them to “work harder” and in general, this is really all that the Asian school system does (overly tedious classes by day, “cram school” by night). In general, the opposite is true - to teach students, you have to give them enough flexibility and freedom so that school doesn’t feel like a prison, and push them in meaningful ways to their full potential. Some people really aren’t made for calculus, and that’s fine - they should still be able to graduate high school with only a cursory understanding of it.

Mind you, I didn’t always know this was true. It took a fair bit of teaching to realize that most students just don’t answer the call to work harder unless they are desperate to survive in a society of scarcity, fond of being prodded like cattle, or have some higher motivation to learn and advance their knowledge. In general, the latter is the best, and the former is the worst motivation in the long term.

87

Economics and government are both very “capstone” in nature - you learn their place in the world much more effectively if you already know history and math beforehand. The fact that students aren’t interested in learning because it doesn’t impact their grades is more of a failure of how it is taught than when. Neither subject has to be boring but they often both are.

88

I never said there was, especially considering the majority end up not qualifying for the college-oriented academic high schools or the higher vocational high schools requiring advanced mathematics. Especially in the '50s and '60s.

There isn’t the mentality of most/all educational paths should lead to college/university there or in many other societies as we have here in the US. In fact, this idea wasn’t even widely accepted in the US until the late '60s/early '70s.

89

As cobrat said before:

90

It is ABOUT TIME someone spoke truth to power.

The high school graduation rate is terribly low and we need to fix this.

We need to eliminate these requirements and some other superfluous old-fashioned thinking (schools are still teaching Shakespeare, come on!). After all, it wasn’t that long ago that either shop or home economics were required. Time to more into the 21st Century.

Getting rid of this old stuff will make high school easier to graduate, then those people can go on to college and get real jobs. And yes, we need to do the same for college requirements. In an age of Google translate, why does anyone have to learn a language (and only learn it enough to pass 1 year of a language which is not enough to order a plate of dim sum in a Chinese restaurant).

This is the way to slow down this income disparity in the country!!

We keep putting up these artificial hurdles and more and more people get stuck behind them and fall further and further behind.

91

Yes, schools are still teaching Shakespeare - as well they should! And learning languages should start in elementary school and continue throughout middle school, high school and college.

Shakespeare’s plays are as relevant today as they were 400 years ago and will be 400 years from now. Properly taught, Shakespeare is not hurdle to overcome; it’s a gift to be enjoyed again and again. I’ve seen inner city 5th graders - whose first language is not English - understanding, performing and finding meaning in Shakespeare’s plays.

Learning other languages and learning about other cultures makes us better citizens of the world. Why should we be one of the very few countries whose citizens are monolingual? Why do we expect others to speak English and we not learn other languages? Certainly more useful than shop or home economics in my view…

As for slowing down income disparity, how about raising the minimum wage to a livable wage?

92

oops - I posted before I finished…

In addition to raising the minimum wage to a livable one, greater distribution of wealth will slow down income disparity. Why should Mitt Romney pay an effective 13.9 percent tax rate? Why is Warren Buffet’s tax rate still lower than that of his secretary? Why to CEOs in this country earn over 300 times as much as the average worker while in England and France and Germany CEOs earn 22, 15 and 12 times the median workers’ rates, respectively?

As for advanced math, again, I think that, like Shakespeare, it has as much to do with how it’s taught rather than the subjects themselves. We are not taught to appreciate the beauty and wonder of mathematics. One fitting analogy – from a book written by a high school math teacher – would be that if music and art were taught the way we teach math, it would be like teaching students how to read and play music without ever having heard a symphony or how to mix colors and learn brush strokes without ever having seen a painting.

Oh, and why don’t we cut the arts in education too while we are at it? (oops, we’ve already done that…and we see how far that has gotten us…sarcasm duly noted, I hope)

93

“This is the way to slow down income disparity in the country!!”

I’m not entirely sure if your post was sarcastic, @skyoverme. If it wasn’t, then:

It’s also the way to make sure you that the next generation is filled with uneducated idiots. Not sure about you, but I want the next generation of doctors, politicians, academics, and yes, even garbage men know how to reason effectively (something you learn from logic, philosophy, and advanced math), to communicate effectively (which is something you learn from picking up a foreign language or studying Shakespeare), and to lead effectively.

Now, if you really want to fix the high school graduation rate, here are some suggestions:

  • Let's move away from the system where district funding is often based on property taxes which in turn are determined by property values, leaving preschools in poor districts severely underfunded relative to their counterparts in more affluent districts.
  • Let's move away from thinking that "those who can't do, teach" and decide to recruit highly talented and accomplished people to teaching.
  • Let's make sure that those highly talented and accomplished teachers are distributed evenly so that gasp poor people can have good teachers!
  • Let's get refuse to uphold the common core standards that have kids take standardized tests as early as elementary school.
  • Let's stop the school-to-prison pipeline. Black kids are suspended at twice the rate of the their white counterparts and five times the rate of their asian counterparts starting, quite literally, in pre-K.
  • Let's start giving academic counseling to help kids in high school stay on track to graduate.
  • Let's make sure students have access to mental health and drug counseling.
  • Let's raise the minimum wage and disability security so that students don't have to work full time on top of their studies to support their families.

I think that the 5th graders performing Shakespeare that @LoveTheBard (nice username, btw – I totally agree!) mentioned are the Hobart Shakespeareans. In Hobart Elementary School in East Los Angeles, over 90% of the students live in poverty and most are kids of Mexican or Korean immigrants and learn English as a second language. The students put on an annual production of one of the Bard’s works under their teacher, Rafe Esquith, who has recently been facing some unfortunate legal/ethical allegations. The students use original text, not adaptations. They understand every word they say and are proud to say them. It’s absolutely beautiful to watch.

And guess what? Years later, Mr. Esquith helps them with standardized test prep while simultaneously teaching them the works of Shakespeare are the other great writers. The vast majority of Hobart Shakespeareans graduate high school, and former Shakespeareans now attend, among many other fine universities, HYPS, WASP, other Ivies and NESCACS, and basically every other acronym you can think of.

So do you really think Shakespeare has a negative effect on high school graduation rates?

94

According to Andrew Hacker’s outlook, the high school graduation rate in California (now 81%, https://www.google.com/search?q=high+school+graduation+rate&ie=utf-8&oe=utf-8#q=high+school+graduation+rate+California) will rise if the requirement for algebra is ended. (California requires two mathematics courses, being specific only about one - algebra, for high school graduation, http://www.cde.ca.gov/ci/gs/hs/hsgrmath.asp). A numeracy course as he describes it, as an allowed alternative to algebra, provided that it involves many and varied problems to solve, for high school graduation likely would do more good than harm.

It’s a different matter for people going on to college.

95

I think Hacker’s publisher knew that the book would be so controversial that they’d make a mint on a short run. Must be the only reason it was published.

The Math Myth: Another strategy to insure a permanent American underclass.

This has got to be one of the worst ideas of the century.

96

I just read this book, and while the writing style was absolute garbage, and I disagree at many details,
the overall notion is worthy of consideration. What one should consider basic education required by all is a
matter of opinion, not fact. What is the purpose of education ?

Master basic skills necessary for daily life.
Explore possible talents for potential higher education and careers.

I do not think geometry is a necessary skill for daily life, for all.
Problems solving yes, geometry is not the only way to accomplish that task.
Now these classes should be encouraged and offered, so kids can figure out if this
is of interest to them and pursue further.

As one who loved math and computers, I took all offered in my HS growing up,
and in fact more than offered, self teaching advanced computer skills that our math
dept could not teach ( I was teaching my HS math/comp sci teacher).

But I acknowledge this is not for everyone, should be available but not forced.

This is more of an economic constraint. To have a free public education, one must
have a one size fits all curriculum to a large extent. Only the richest high schools are going
to have lots of options as electives.

How much more useful would it be to offer plumbing and electrical contracting skills than geometry,
for some people ? The question is at what age is one ready to make such decisions ?
I think it’s a bit younger than 18, maybe not much. The standard forced curriculum should probably
end around 15 or 16, last couple of years of HS should be electives to focus in on what you enjoy
and would motivate you to graduate.

But since there will never be funding for such flexibility, one has to figure out what truly needs to be
in the one size fits all curriculum. Yes one must communicate in one’s own language, verbally
and in writing, but Shakespeare analysis ? Yes you need arithmetic and maybe statistics, but
why geometry for all ? Earth science, biology, chemistry maybe, but physics for all ?

97

Geometry helps you understand the area and volume of various geometric shapes and volumes. Geometry and trigonometry help you understand the relationship between angles and dimensions of triangles.

Physics helps you understand how you can more easily loosen the overtightened lug nut/bolts on your car wheel when you have to change a flat tire.

98

There is a compulsion felt to subject our young to rigorous mental exercises. Educational policymakers seem to want to see their own extensive, traditional educations reflected in the educations of their “charges.” And nations seem to be running some kind of Sputnik-reminiscent competition with each other in regards to education rigor as if it were emblematic of national worth.

Algebra may be attractive to policymakers because it is well defined - what students have to learn is predictable, easily made consistent across schools and school districts, and, even though abstract, seems to be basic.

But the nagging question is why not have content that is useful conveyed in the mental exercises? Do the nation’s 3.4 million cashiers, 6.9 million food and beverage serving workers, 3.8 million protective service workers, 3.8 million janitors, maids and building cleaners, 6 million “personal care and service workers” and 2.7 million truck drivers (http://www.bls.gov/emp/ep_table_102.htm) in the course of their work or general lives ever have to factor quadratics? NO. But they do have to manage complicated money situations.

All decisions are sensibly made on the basis of benefit vs. cost. If there were no cost to having a certain level of mastery of algebra prerequisite to a high school diploma, it wouldn’t matter. But there is a cost. Academic difficulty definitely figures among the reasons for dropping out of high school (http://sgo.sagepub.com/content/3/4/2158244013503834.figures-only). And algebra is specifically cited. From http://www.districtadministration.com/article/solving-our-algebra-problem: “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.” Should we be sacrificing these people so that we can have a feel-good-about-our-standards curriculum that’s easy for us to administer?

(I’ve focused on algebra, because in my state, California, it’s the only specific kind of math beyond arithmetic stipulated for high school graduation.)

99

Again, I submit that part of the problem is how math is being taught that makes it – for many students – tedious at best and impossibly difficult at worst.

I alluded earlier to a book/article written by a high school math teacher, Paul Lockhart, who likens present-day math instruction to mandatory music instruction consisting of having students study musical theory and notation, doing transcriptions, etc. without ever having listened to music or heard a symphony. A similar analogy would have students learn art by studying color theory, examining brushstrokes, and doing paint-by-numbers without ever having visited a museum, seen a painting or confronted a blank canvas. One could make a similar analogy about how Shakespeare is taught in schools.

Lockhart’s piece is called “A Mathematician’s Lament.” Here’s a link:

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

Perhaps if we exposed students to the beauty of mathematics rather than subjecting them to rote memorization of times tables and formulas, we would not be having this conversation.

And, yes, it does come down to funding, and education should never be a “one size fits all” proposition. Perhaps if we spent more on hiring and training the most competent people to teach our kids, and perhaps if we began to truly value education in this country – as we should – we would not need a “feel-good-about-our-standards” or a “make-money-for-textbook-and test-creators” curriculum that teaches to the test and thwarts the love of learning in our students.

Edited - Sorry. My brain was hurting to see someone with the screen name LoveTheBard use the phrase “eluded to”.
ED

100

I read “A Mathematician’s Lament” a few years ago, and I think it does encompass most of the problems with math education.
I was lucky in that my geometry teacher actually did teach the way that Lockhart teaches. My Algebra II class, however, was everything that Lockhart hated about the system.
I tutor math, and I can tell that most students learn math in the disjointed, illogical way that “A Mathematician’s Lament” describes. Especially with geometry, I try to focus on why formulas work, because that makes it more interesting, and because that makes the formulas easier to remember.
Memorizing multiplication tables is not mathematics, actually creating math for yourself is mathematics.