Yipes, ad hominem without having read the book! Hacker is questioning the universal value of Algebra II, not Algebra I, which would cover your example.
Hacker would agree; he questions Algebra II, Trig, Calculus.
The corn starch problem I’m almost certain I could have worked out before I had a class called “Algebra”. Yes, being able to figure out ratios is important. If the example cited above is something that is taught in a Algebra 1, then the scope and sequence of mathematics education has changed quite a it since I took Algebra 1 in 9th grade almost 40 years ago. The heart of the debate seems to be where the “everyone needs to know this” line should be drawn.
@snarlatron: You assume I haven’t read Hacker’s work? Why so?
And yeah, @mstomper, you’re right that ratios would solve the problem I presented—I was thinking of it in the way that would seem most natural to me, which would involve solving for a variable. Still, plenty of everyday uses of algebra, even in shopping or cooking or paying bills or whatever other facet of daily life you might be working in.
I have read Hacker’s arguments—not all of them, since he’s published his ideas in a number of places, but I have read a bunch of his stuff. He seems to believe that since we have to specialize in something, that we shouldn’t develop knowledge of those things we don’t specialize in—or at least that’s what I get as the overall message of what he’s saying. Of course, that comes from the point of view of a humanist who believes that the humanistic fields are being shortchanged by policymakers nowadays, and he would like to see less emphasis placed on STEM fields—and that is actually his agenda, not simply cutting math education short.
@dfbdfb First of all, you are a poster that I enjoy reading and with whom I usually agree. I assumed that you have not read The Math Myth because if you had, you wouldn’t have posted what you did. Hacker resonates with me because my father, a professor in the medical field, never used advanced math, neither did my father in law, a specialist physician. Nor have I ever in my helping run a household, raise a family, or teach any of my (non-math) classes. All HS math ever did for me was swamp me with homework and make me hate school.
@dfbdfb, if that’s the core of Hacker’s argument I don’t agree with it. I’ll have to do more research to see if I would interpret it the same way. As someone who mainly lives in gray areas, I have problems with arguments presented on both sides. Sometimes (and I’m not just talking about this thread) I don’t see a distinction made between subjects that are genuinely difficult for a student and those he/she doesn’t want to pursue deadly boring. For me, math falls in the former category. English fell into the latter. I never took physics, mostly because I knew that the math I failed to learn would probably make mastering the material impossible (my son disliked physics less than other science precisely because of the math involved). I suspect that the debate may not be quite as polarized as it initially appears.
Did the physicians ever need to understand the statistics that is commonly used in medical research papers? Basic statistics courses (e.g. high school AP statistics) tend to list high school algebra 2 as a prerequisite; more in-depth statistics courses list calculus as a prerequisite.
@snarlatron #63: I can see never using what I would call advanced math (read: calculus and above). However, how in the world would a medical professor never use algebra? It’s necessary to understand the results of pretty much any human subjects research, after all.
I do think that Hacker taps into a cultural vibe that math is difficult and that there is lots of stuff in it without any direct application—but he accepts those critiques uncritically without really making a case for it. But really, even the trades use trig all the time! (For plumbers, add geometry into the mix.)
If Hacker was saying that we need to change the way math is taught, or that we need to make it more clearly applied, then I’d be much more sympathetic to his ideas. However, in saying that we should simply jettison the whole of it, he’s providing an overly blunt solution.
Not to mention that there are plenty of subjects people don’t like and that they don’t always see the application of—English literature, for example. Hacker’s solution, taken to its logical conclusion, would have us get rid of all such requirements, and that is something that I find troubling, to say the least.
(Edited to make it clear what I was responding to.)
With the development of genetics and data science in general, along with the advances in biomedical engineering, math is only going to become more and more important over time. The opposition of most doctors I have known to math is really unfortunate and counterproductive. For a profession that is known for its heavy education requirements, medicine sure does have a lot of anti-intellectual tendencies. While I know that a lot of paths don’t require a math education (which is why some doctors have the luxury of being able to whine about how evil math is), medicine is definitely heading towards the more mathematical.
This is the problem: it’s a slippery slope from “I don’t like math” to “I will subconsciously push my life into the path of minimal mathematical resistance.” You start with deciding that algebra doesn’t matter. Then you decide that you don’t want to take physics because math (throw chemistry, physics, engineering, and even seemingly tangential occupations like flight and more technically difficult trades out the window as well). Then you decide that you really can’t do statistics because without the math you can’t really learn anything (this will hurt you pretty much regardless of what field you choose). Pretty soon, it turns into a pretty much outright rejection of any quantitative field or any quantitative approach to a field that is not necessarily so (e.g. go for medicine, but avoid any of the more math-heavy focuses like genetics or informatics). In my experience, those who fail to really come to terms with calculus tend to follow this trajectory more often than not.
Wouldn’t the pre-med process tend to select against those who take academic risks (i.e. risking a non-A grade) due to intellectual curiosity?
In a way, yes. Though the smartest pre-meds I knew could manage the GPAs they needed while taking whatever classes they wanted, everyone below that level certainly had a noticeable intellectual risk-aversion.
As far as I can tell, these two changes (dropping the math requirement and adding a diversity requirement) aren’t directly related. They both happen to be part of a [new plan](http://wayne.edu/engaging-gened/documents/overview_of_proposed_gened_revision.pdf) for general education at Wayne State. [This article](https://www.insidehighered.com/news/2016/06/16/debate-over-whether-all-undergraduates-should-take-mathematics-course) makes it sound like they’re dropping the requirement because most incoming freshmen have already learned the material:
The [math requirement](University Advising Center - Wayne State University) is essentially basic algebra and can be met by scoring 25 or higher on the ACT math section. According to Wayne State’s [Common Data Set](http://budget.wayne.edu/institutional-data/cds) for 2015-2016, however, 97% of incoming freshmen submitted ACT scores and 57% scored 23 or lower on the math section. It doesn’t seem like the requirement has become redundant yet.
Wayne State appears to be replacing the math general education requirement with a “quantitative experience” general education requirement that would allow courses in other departments that include some quantitative work to fulfill it.
I’m voting with Neo here.
There isn’t a chance in hell that an innumerate doctor is going to have a fighting chance once Big Data/Analytical Science gets its hands on meta analyses which can quickly assess huge numbers of patient outcomes. Do you want to be treated by the oncologist who reads a few medical journals every week and goes to a conference once a year to stay on top of the field, or be treated by the oncologist who can evaluate tens of thousands of patient outcomes, slicing and dicing the results by demographic group and other co-morbidity/pre-existing conditions?
When it’s my life at stake, I think I’ll head for the doc who makes a recommendation based on thousands and thousands of outcomes, and not a few dozen. The days when a doctor took the free pen and started writing prescriptions based on the say-so of an attractive pharma rep are over.
Let’s just make it simple. When my life is at stake I would prefer to deal with a doctor who was at least smart enough to pass Algebra II.
Immediate bias disclaimer: Math major entering a Ph.D program in Economics
Math is absolutely important, and I didn’t really get it until Calculus, but it truly holds a lot of meaning about life in general. The philosophical aside (I could go on and on about this), math classes are used as a screening process in higher education now because there isn’t another subject that can test you both empirically and abstractly. Why are higher and higher levels of math being added as graduation requirements for majors like Philosophy to Horticulture? It’s because they want to see students stretch their thinking in areas where they might not be as strong, not be be in their comfort zone their entire student career.
Do Geometry, Trig, and Algebra II feel like a useless chore while you’re learning them in middle school or high school? Absolutely. Does that mean we should stop teaching it to students? No, because it will inevitably result in students going for an easier route that will lock them out of the inevitably STEM focused career trajectory of this planet.
I also truly believe the reverse to also be true, STEM majors shouldn’t be allowed to exempt themselves out of History, Economics, English, Foreign Language and so on. You don’t want those students to be in their comfort zones forever either.
I guess my question for Hacker is: What is the purpose of education?
One would hope so. But maybe not, if the pharma reps upgrade their offerings to free meals.
https://www.ucsf.edu/news/2016/06/403306/free-meal-pharma-doctors-are-more-likely-prescribe-brand-name-drugs-study-shows
http://archinte.jamanetwork.com/article.aspx?articleid=2528290
To me there is a vast difference between saying “math doesn’t matter” and choosing career paths that match one’s aptitudes. If I never learn to hit a 75 mph fastball in high school, I’m not going to play pro ball. I took a stats class that focused on interpreting research findings, and I do use it every time we look at student data. I definitely pick up on patterns many of my colleagues don’t. I actually got my best grade ever in a math/quantitative course. Does algebra matter? Yes, virtually everyone needs to be capable of solving for a variable. I see nothing wrong with choosing a career path where I utilize my strengths and where my weaknesses don’t limit my effectiveness. I have even more of a problem with mechanical things and spatial relations than I do math. As a result, I often have to pay others to get a job done properly. Back in the days when search engines were less likely to easily provide the most relevant results someone told me they’d spent an hour trying to find the answer to a question. I found the answer in 30 seconds. My point is that, unless mastering a subject is necessary to do your job well, it shouldn’t keep you out of the profession. I have no problem with someone who has great difficulty mastering a subject relevant to a given educational or career path out of that path.
You don’t need calculus to understand probability and statistics. The only calculus I remember from my statistics classes (Elementary Statistics, Scientific Sampling, Experimental Analysis and Design) was looking at the area under a curve, which is a simple enough concept to not need calculus to understand it.
@mstomper
What would you say is an unreasonable job requirement? Often, the ability to do advanced work does hinge on the ability to understand the theoretical considerations, and math plays no small part in that. A university education is more than just a job qualification, it’s an introduction to the advanced and theoretical aspects of a field that, paired with natural ability, lead to the ability to do difficult and unusual tasks. If someone demonstrates that they are truly incapable (either by work ethic or ability) to think beyond the basics of their job, then they shouldn’t be accepted into the profession, or at least not at an advanced level.
My personal experience is that usually a math aversion is a mental block rather than a lack of ability. Algebra II and calculus come easier to some than others, but with enough effort most can learn at least algebra. Calculus, I’m not so sure, but few people advocate that as a hard requirement.