The people that want less math in school are the same people who also complain about the academic gap between high and low income students. Don’t they realize that any reduction in the level of math requirements will result in an even larger gap for them to complain about?
I have two kids who hate math. It’s been painful to watch.
Midwest- I hated math until I was admitted to a grad program which required a semester of remedial math before I could start my course work.
The professor started with arithmetic (literally- second grade arithmetic) and ended after a semester of college calculus. His thesis was that anyone who was in that class was there because they hated math- and therefore, did not understand math.
I loved it. Every single second. I had spent my life hating math and now I finally saw why people thought it was beautiful (ugh) or fun (yikes) or interesting (heck no).
I finally realized that kids who are not naturally good at math end up getting tracked so they have the worst math teachers. And then the next year. And the next year. The gifted math teachers teach the gifted math students. The wretched math teachers teach the wretched math students.
I finally broke the cycle (had to- my admissions was contingent on getting a B or better in remedial math) and while I can’t tell you that I am a math whiz I no longer hate math. I made the Dean’s list in a tough MBA program which required econ, operations research, statistics, and a bunch of other math-heavy subjects.
Can you help your math hating kids? HS was so painful for me as a math-hater. My guidance counselor begged me not to take physics. Can you imagine???
@Much2learn Although Hacker weaves those two arguments together, I (and probably many others) complain both about the education/income disparity and the undervaluing of math education.
Don’t agree about the geometry part.
Use geometry on a regular basis to plan out/navigate the shortest or longest working routes depending on whether I want to get from point A to be in the quickest manner or whether I want to extend my exercise routine.
It has also come in handy when helping an uncle with his project to build an extension to his house.
Incidentally, if one can’t do algebra…forget about doing CS programming at a level sufficient to be a decent programmer. Quite a bit of computer programming is essentially algebraic math…and if one’s program involves calculating complex problems such as vector graphics for gaming/simulations…one will need a strong grasp of geometry* and yes…even a bit of calculus**. Same with designers of computer/video gaming hardware…especially high-end graphics processor units used by hardcore gamers and those running simulations/modeling software with high graphical processing demands.
- It may have been possible to get away with poor/nonexistent geometry skills back in the '80s when graphics technology/expectations...especially in terms of real-world realism wasn't feasible or expected. That hasn't been the case in the last 15 or so years...especially if we're talking the latest and greatest graphics intensive games played by hardcore computer/video gaming fanatics.
**I.e.: Advanced simulation/modeling programs for engineering, advanced economics, etc.
If one desires to apprentice oneself as an electrician, he/she better have a decent grasp of HS math AND Physics with lab. This requirement is considered so crucial that some areas of the US require aspiring electrician apprentices to have a minimum of 15 community college credits emphasizing those areas in addition to graduating HS to ensure they have a reasonable foundation in those critical areas.
Is she the long lost twin of a friend’s ex-GF I had the dubious pleasure of tutoring?? An ex-GF of a friend was taking the equivalent of 9th grade algebra in order to fulfill the math requirement for her major in elementary ed. Despite the fact that public college allowed their elementary ed students to get away with such a lax math requirement, she had failed that very course twice and was well on her way to failing it for the third time before said friend gave up tutoring her in frustration despite being a hardcore math/STEM nerd(CS major) and both asked me to tutor her.
Quite a painful experience especially considering her issues were a mix of being socially promoted during K-12 despite not mastering prior math material and her continuing her bad habits of not taking the course seriously enough to put in the requisite time/effort to pass without a lot of prodding. She barely eked out a pass on the third try partially due to the math Prof pitying/getting sick of seeing her in class after having her 2 previous times. However, she never got her elementary ed teaching certification and is currently working as a lower-level public sector employee in her state.
You wouldn’t have had that issue in the NYC public HS system. Everyone on track for the regular or regents diploma back when I attended was required to take a semester of Econ in order to graduate.
You’d have hated attending the NY public high school and moreso my STEM-centered public magnet.
No GC would have begged off any student from taking Physics with lab as it was one of the science classes we were REQUIRED to take to fulfill the 4 year science requirement. Oddly enough, one could get away with taking 3 years of math…but student driven peer pressure was such most classmates ended up taking 4 years.
- Standard sequence was bio, chem, physics...all with labs along with taking the equivalent of another year of science electives. One of my science electives was a pharmacology course populated mostly by aspiring pre-meds and taught by a graduate of Columbia's College of Physicians and Surgeons.
** 3 years of math requirement was without regard to what level of math one started with. For instance a 9th grader who has already completed AP Calculus BC course and exam by 8th grade would still be required to take a minimum of 3 years of math beyond the level he/she ended with in 8th grade at my STEM-centered public magnet or its rivals.
You are probably not familiar with what is taught in nowdays geometry. Students spend most of the first two quarters just dealing with proofs. The reasons for this is to teach them logic thinking. Wait, why not just teach them logic, which is not harder and is more generally useful. The other two quarters are identifying shapes/ circles/surface areas/volumes. The only part that might be useful is the ratios, which is again abused everyhwere.
The basic usaful parts can not taught in one quarter. Shorten it if you can, like some schools do, and learn more if needed in the future.
If any one class feels out of place in the high school curriculum, it would be geometry. The way it goes about teaching proofs is neither realistic nor helpful, and frankly there is not all that much to be gained from two semesters of proving similar, congruent, etc., angles, at least not in the way they are taught in most US schools. I wouldn’t support throwing it out, but perhaps a light introduction to discrete math would be a better way to teach mathematical logic.
Interestingly enough, the lowest math track at my public magnet back when I attended in the early-mid '90s started having us learn proofs and a bit of logic(truth tables) starting in 9th grade. Vast majority of HS classmates however already dealt with all of that in middle school so only a tiny minority of us took that track. They were further along with learning proofs in geometry, trig, pre-calc, calc, and beyond.
I’ve always felt that the problem was the way math was taught. Proofs and pointless letter juggling bore most students to tears, and that drives them away from all kinds of potential careers. Instead, students should be taught math in a way that emphasizes its uses in the real world. Along with simple finance problems like compound interest, show students how math is used in things like medical applications and computer graphics. Anyone who wants to learn proofs and derivations from that point on can do so.
Calculus is emphasized because it’s needed for probability, statistics, physics, and economics once you get beyond the most fundamental concepts. A lot of things make more sense if you know about derivatives and integrals. Algebra-based classes often require a lot of memorization and plugging things into a calculator.
I’m surprised by all this talk of proofs. They aren’t tested on standardized tests, and therefore our school has virtually eliminated them from the curriculum. I dearly wish there were more proofs being taught.
It should be possible to teach math with more real-world relevant applications but a lot of textbooks have extremely silly or unrealistic “applications”.
The problem is not with proofs per se, but with the way they are taught. Instead of using the standard prose form of proofs that I’ve seen in literally every single other situation in every theory-oriented mathematical topic ever, high schools teach with the unfortunate [two-column proof](https://dj1hlxw0wr920.■■■■■■■■■■■■■■/userfiles/wyzfiles/c7b71213-39a4-4d84-8b47-4995308fcc09.gif) format. It’s tedious, unrealistic, and not very well-liked by anyone, math-oriented or not. And it’s not like there’s anything supremely complicated about writing proofs in prose.
I wouldn’t be surprised if the two column proof format were used for high school geometry because (a) 9th-10th grade students would find reading and writing proofs in prose more difficult and make more errors*, and (b) it is easier to grade large volumes of homework and tests with two column proofs than if the proofs were written in prose.
*Of course, even college educated adults writing arguments that depend on logic in prose frequently make logical errors.
Math provides students with a toolbox of transferable skills that can prove useful for many jobs or careers: critical thinking, problem solving, logic, etc. The math that is taught in a standard high school curriculum is very basic compared to the upper-level math courses that are usually taken in graduate school. Everyone is different, therefore they will have different interests and life goals, but each of the core subjects help to reveal interests and aptitudes that were not very clear beforehand. Not everyone should be expected to be whizzes at algebra or geometry, but those subjects should not be thrown out because they aren’t “useful in the short-term.” However, I do agree that there are some problems with the way that math is taught. Common Core is awful.
This is a problem in my mind. If overemphasizing calculus is a main factor in people tuning out and winding up without strong understandings of the most fundamental elements of those concepts then I am happy to throw calculus out entirely in favor of everyone having a strong foundation in those fields.
@blossom No, I cannot help them. It’s up to them to figure out. One is going to be a senior in college, and the other a freshman in college.
Perhaps a tangent, but in my opinion, both of my kids are a bit burnt out from the grind. I wish learning in a school setting was…different. Competency based? More relevant and directional? I don’t know. Topic for another thread.
Hacker is, to put it bluntly, an idiot about what math is, or at the very least about what algebra is.
To demonstrate this, i offer you the following, and the challenge is for you to solve it without algebra:
[list][li]You want to buy something to make dinner—let’s see, it should be something totally shelf-stable, so…cornstarch. Cornstarch is, generally speaking, simply cornstarch, with no real meaningful difference between brands, so you’re just after the lowest price here. The store you go to has an astonishingly high number of cornstarch brands, but since most of them are 16 ounce boxes, you could just pick the cheapest one of those. However, there are other size boxes, too: 12 ounce, 18 ounce, 20 ounce…Since it won’t go bad sitting on the shelf, and you’ll eventually use it all so waste isn’t an issue, package size is unimportant for you. Therefore, which one is actually the cheapest, as in on a per-ounce basis?/list[/li]
Seriously, algebra (and other basic mathematics) is simply everyday life at this point in our civilization.
You won’t get a strong foundation in ANY of those fields without calculus. Probability without calculus is just some silly rules about marbles and decks of cards. Statistics without calculus is just a bunch of unjustified and nonsensical assertions about what you can do with data. Physics without calculus is… pretty much nothing.
Calculus is emphasized because it is the starting point for pretty much all fields of advanced math. Though it’s usually algebra, not calculus, that really determines whether or not you can actually do more difficult math. Calculus is just where you have to know algebra, rather than just pass it, in order to survive.
That implies that a “strong foundation” in statistics and physics is high school level statistics and physics, since that is what statistics and physics without calculus are.