I was responding only to the specific point I quoted, not speaking to the importance of learning math in general. I not need Alg 2 to understand how student loan interest works, or a mortgage, or a savings plan. That’s all.
English: Having a large vocabulary, being able to spell correctly, to be able to interpret text and write well; essential to most professions.
History: Working with ideas; things that have or have not worked, cultural literacy. When someone at the board meeting mentions the competition’s “Waterloo” you don’t want to be the only Bozo in the room with no clue what that means.
Science: Maybe not applicable to all professions,but a basic knowledge of Chem, Bio,and Physics lets one understand news events, and run a household.
Foreign Language: This one is the toughest; perhaps not applicable to all professions. Yet this gives depth and breadth to a person. I have a friend in industrial design who impressed his hirers by being fluent in French, even though it had nothing to do with the requirements of the position. They later told him that that told them that he could think in different ways and probably had cognitive and cultural insights that would be useful.
Art & Music: Makes any person more interesting, creative, lively, aware.
I do think that an educated person should have a basic knowledge of algebra and geometry. But anything above is often a waste, given the toll of homework and irrelevance in later life in proportion to the toil.
Ask your physician or attorney if trig or calculus was anything more than a hurdle for them.
However, how essential is writing literary analysis of fictional literature (what was meant by “English literature”), as opposed to general reading and writing skills (whose importance is not in dispute)?
Given the superficial coverage of history in high school, do people really know history? Lots of people seem to believe that, for example, slavery was not a major cause of the US civil war.
High school physics courses, or the equivalent preparatory/remedial physics courses in community colleges, commonly list algebra 2 or trigonometry as a prerequisite or corequisite. Even high school chemistry courses often recommend algebra 2 as a corequisite.
Calculus is useful in medicine. Indeed, one medical researcher rediscovered the trapezoidal rule instead of just applying the existing knowledge to the application in question:
http://care.diabetesjournals.org/content/17/2/152
http://care.diabetesjournals.org/content/17/10/1223.1
No doubt Calculus may come into play in some medical research. I am challenging posters to ask their physician (or attorney) if they ever use it. My father and father-in-law both worked practicing and teaching medicine. I can assure you that GPs, Pediatricians, Dentists, Dermatologists, and Veterinarians never use Calculus, ever, ever, ever.
Ask a [practitioner of some profession] if s/he ever needed to do the following for his/her job:
- write literary analysis of fictional literature.
- discuss the historical events leading up to the US civil war.
- understand why a longer wrench can be used to loosen an overtightened nut or bolt.
- use a non-English language.
- create some art or music.
And honestly, if a person can perform neurosurgery or prescribe opiates, I want them to be able to take a derivative. Realistically the details of organic chemistry aren’t directly applicable to many doctors, but someone with a medical degree should be able to problem solve even in subjects that they don’t love.
I really don’t want the person who is working out my prescription doses to be mathematically challenged.
Dentists have to deal with calculus.
From wikipedia -
In dentistry, calculus or tartar is a form of hardened dental plaque. It is caused by precipitation of minerals from saliva and gingival crevicular fluid (GCF) in plaque on the teeth. This process of precipitation kills the bacterial cells within dental plaque, but the rough and hardened surface that is formed provides an ideal surface for further plaque formation. This leads to calculus buildup, which compromises the health of the gingiva (gums). Calculus can form both along the gumline, where it is referred to as supragingival (“above the gum”), and within the narrow sulcus that exists between the teeth and the gingiva, where it is referred to as subgingival (“below the gum”).
Calculus formation is associated with a number of clinical manifestations, including bad breath, receding gums and chronically inflamed gingiva. Brushing and flossing can remove plaque from which calculus forms; however, once formed, it is too hard and firmly attached to be removed with a toothbrush. Calculus buildup can be removed with ultrasonic tools or dental hand instruments (such as a periodontal scaler).
And isn’t being current on medical research at least in principle one of the jobs of a doctor?
Medicine just so happens to be one of the fields with the least excusable aversion to math (in fact, they should have calculus and not just algebra as a requirement), given how increasingly important genetics and informatics are to the field. And it’s only going to be more important in the future.
The concepts of rates of change, inflection points, local and absolute minima and maxima, and accumulation are broadly useful whether or not they are broadly used.
But the article is about algebra, not calculus.
While I agree it sounds stupid, I suspect Hacker (possibly bad assumption: he’s logically consistent) would if they were oft-flunked on their way to a HS diploma. Beyond “it’s poorly taught,” we haven’t really discussed why Algebra I is a problem for some people. While I’ve no doubt poorly taught accounts for some percentage, I would be unwilling to stipulate that a majority of being having trouble are victims of their teacher (it’s self-servingly convenient to say so). Instead, I would look at the difference that’s arisen with all previous math–we’ve explicitly introduced abstraction. I’d argue some people have a difficult time with abstraction and Algebra I makes this visible. If you’re a teacher, I’d bet it’s easier to convince yourself little Billy understood Moby Dick when he didn’t than when he’s abysmally failed solving for X.
I think we’re conflating two things in this thread:
- Hacker’s assertion that Algebra I isn’t necessary for HS graduates.
- What role does math play in a well-educated individual? And, by extension, what curricular requirements should there be for colleges to support this role?
I’d ask if anyone believes the first one is a reasonable position to take. Personally, I believe Algebra II should be the minimum bar for HS graduation as I’ve observed many people don’t get the implications of exponential growth rates as (IIRC) this is where non-linear functions enter the curriculum.
@fragbot’s mention of the centrality of abstraction in mathematics is intriguing, since one of the critiques (both from the left and the right—you get this from neoliberal educational reformers, but also from, say, Arne Duncan) of American pedagogical methods is that we have too much abstraction, and not enough application. (And that’s not just in math, but perhaps particularly so there.)
Of course, the one thing the US K–12 system excels at (at least for those well-served by the system) in ways that many other systems it’s often negatively compared to in this way (e.g., Singapore, China) don’t, is that it produces pretty good critical thinkers. You have to start to wonder if maybe there’s a connection there.
For those well-served and who take advantage of educational environments where critical thinking is encouraged…
However, the more cynical side of me wonders if this is something we Americans like to tell ourselves to feel better about the state of our K-12 educational systems when they are shown to be caught short compared with those of other nations.
It also sounds particularly absurd considering if our K-12 system produces pretty good critical thinkers…how do we explain aspects of US society/life outsiders find absurd/dumb…such as the state of our current political elections which privileges celebrity, “says what I feel”*, and “can go have a burger/beer with him” while willfully ignoring the obvious hype and demagoguery of some candidates.
From Inside Higher Ed today, not taking math out but teaching it differently.
https://www.insidehighered.com/news/2016/07/06/michigan-state-drops-college-algebra-requirement
It was probably earlier on this thread that I remarked that the state of Michigan requires four years of high-school math, to include Algebra 1, Algebra 2, and Geometry. Most Michigan State students are in-state. The out-of-state students tend to be quite strong, so if their home states do not require Algebra 2, it is a moot point.
High school students in Michigan can substitute a year of a “Career-Technical” course for a year of math. The university expects students to have completed Algebra 2, though.
The issue arises because students who have credit for Algebra 2 from their high schools may not be able to pass the math placement test–this probably occurs at many large universities. I take this as a sign that Michigan State is throwing in the towel on trying to get them to understand Algebra 2, and hoping instead to at least guarantee some level of quantitative capability. It will be interesting to watch the news on this.
Re the point raised by dfbdfb that high school (and college) math is often criticized as being too abstract, and fragbot’s mention of the centrality of abstraction to mathematics: I think that most mathematicians would say that all of high school algebra as well as math through multi-variable calculus is quite concrete, rather than abstract–that is, concrete, though not applied.
In my opinion, the difficulty with math arises when the instruction outpaces the natural curiosity of the students, or their ability to really “get” it. Then the students adopt all sorts of maladaptive strategies, mainly memorizing how to solve problems of each specific type, rather than developing a general understanding, so that they could solve the problems for themselves. The slower pace of math in the US as opposed to a number of other countries may reduce the counter-productive adaptations, and encourage students to think about the problems for themselves.
Given that a lot of those countries with more stringent math standards seem to produce many of the best mathematicians (who do work in their own countries and often in others, like the US) and also have quite high general competence in math among the population, while Americans as a whole have a lot of trouble with math, I would hesitate to call the US system better.
@QuantMech: Well, abstract and concrete often do mean very different things to mathematicians and non-mathematicians, so it may just—very literally!—be semantics. 
@NeoDymium: I don’t know that anyone praising the US system is calling the US system better across the board—rather, that it’s better at particular things that other systems aren’t nearly so good at.
(Maybe it’s all tradeoffs, with no perfect system? Nah, then we’d all know we have to compromise, and we can’t have that, can we?)
I’m finshed with trying to argue my earlier points, but now I have a question for those more knowledgeable in mayth than I am (pretty much everyone reading the thread, in other words). Despite my problems with algebra, I was often able to work my way backward on standardized tests and get the correct answer. My SAT and ACT math scores were, while lower than my other scores, still respectable. There certainly wasn’t a big enough dfference to produce any red flags. Any ideas?
Plugging the answers back into the problem is a test taking technique that can be used on many multiple choice math and other questions to solve them more quickly and easily than solving them the usual way. It would not be surprising if it were well known among those who have taken test-preparation courses or read test-preparation books, but less well known among others, though some may figure out this method on their own.
I.e. in some cases, verifying that an proposed answer is correct or incorrect is much easier than finding the answer to the problem. (CS majors may recall a similar concept from their theory courses.)
Plugging the answers in just seemed to me the logical way to go. This was in the early eighties; I’m sure there were test taking books then, but I wasn’t aware of them. For me it was a matter of getting the best result with the least time/effort. The same skills made me a good reference librarian later.