@katliamom “trade” schools are not non-university track any more btw. They are almost as difficult or more so than regular high schools because the students are required to 1) do regular high school curriculum and 2) the voc curriculum. It’s not like the old days when someone took shop class until the bell rang releasing them in June Senior year (if vocational ed was ever like that.) Trade schools are now called CTE schools for career and technical education. They often lead to AP classes. The idea is that hands-on trades now require high -level tech skills. CTE tracks are underwritten and approved by local and state accrediting agencies with more rigor than you care to imagine. STudents often graduate with not just a HS diploma – college track besides – but also a certificate in their CTE. Students have extra hours of class time each day to accommodate this rigorous track. They start school earler and end it later. Then they go home and have the same rigorous homework as regular college-prep high schools. Some schools are going even further. CTE training in some areas are taking high school through Grade 14, so that the students graduate with an AA or AS degree. Please don’t generalize that “trade” school is not rigorous and for the not-bright student. Far from it.
That was an informative post, @dustyfeathers, thank you.
I wonder to what degree deficits in spatial and mechanical reasoning are related to trouble with higher math? When I took an aptitude test in high school I was in the bottom 10% in spatial relations and the bottom 3% in mechanical reasoning. The big problem in these areas (and “higher” math as well) was that I could never tell if I understood something or not. I’d see someone put something together with a set of directions and think, “that looks easy enough.” When I tried it, I’d work on it until I was ready to hurl it across the room (I actually did that with my Algebra 2 book a few time). If the subject was anything other than algebra I could tell you within a couple of points how I’d done on a test. I couldn’t do that with algebra. I could be walked through a problem multiple times and think I understood it, but then not be able to work out an almost identical problem.
I got through college and grad school because I’m very, very good at skimming and pretty good at analyzing data. I can also, for the most part, write clearly. You know those puzzles you see on Facebook that require you to find the missing numbers in a series? I can usually get those in 30 seconds. Still, when I looked at my kids’ middle school math books they made my head spin.I don’t doubt that part of my problem was not being taught well. What gets me is when I see the suggestion that students with a deficit in mathematical thinking are not college material. Sometimes they are, sometimes they aren’t.
In my experience, it tends to be calculus that really differentiates the “can’t do math” from the “could possibly do math but didn’t learn it well” groups. Through effective instruction (the kind that most US schools fail to provide), just about everyone is capable of learning math through algebra 2/precalculus. I knew a fair few people who struggled with simple relations between problems (e.g. in noticing that “how many legs do X chickens and Y cows have in total” is the same as “how many wheels to X motorcycles and Y cars have in total” is the same problem), but could be taught precalculus if the proper effort was put into it. But calculus seemed to be truly beyond them, or else perhaps the roadblock was just so high that they mentally gave up on it.
The overall trend I’ve noticed, though, is that in most countries, it’s at calculus where some of the rather intelligent but perhaps not mathematically inclined start to lose the ability to keep up with the material.
I’m guessing surveyors are also pretty good at trig, and no one would consider that a traditional STEM job.
re #22 It may be a trig problem, but what carpenters I know do is construct the 3-4-5 triangle and then extend the lines. You can actually do most carpentry without any advanced math as long as you understand proportions. (That said, I have seen some seriously math challenged carpenters who can’t figure out how to make steps even sizes.)
My younger son who has taken no math since high school (he took BC Calc then) says you really can’t work with Excel spread sheets without understanding variables. In his work life he’s done a fair amount of planning for events and working with budgets.
Yes, the 3-4-5 triangle was the solution (using geometry, as opposed to trigonometry) to the second problem in #22. However, the carpentry problem with the A-frame does not necessarily use the angles of a 3-4-5 triangle, so it could require trigonometry. Of course, other carpentry problems could be mainly geometry.
I met a specifier last week who could not figure out the lengths he was going to need for the diagonals on a hip roof. He had asked me to draw another elevation so he could measure off the elevation. I had to explain to him that it wouldn’t help. You couldn’t measure off plans or elevations, you either had to do the math problem or draw it on the diagonal, which for what he was doing would have been fine. He just needed to be sure he didn’t order something too short.
What’s weird about OP is algebra, trig, and calculus would not only NOT be considered “advanced” in most other countries as several other posters here have said, it wouldn’t even be considered high school-level math in some societies.
For instance, algebra., trig, and even calculus would have been considered math areas to be covered in public* middle school in the ROC(Taiwan) for ALL students as tracking doesn’t start until AFTER 8th or 9th grade.
On mom’s side of the family, every one of her siblings except her managed to complete calculus by the end of 8th grade in public school which was critical if one aspired to attend an academic-prep high school which was the prereq for being eligible to take college entrance examinations/admission or some of the vocational tech high schools targeting careers for which proficiency in those math areas are critical.
One workaround if one’s family was well-off enough and willing is to send students like my mother to private remedial high schools where she completed calculus as a HS sophomore with the heavy price of high stigmatization for being an intellectual dilettante/dullard among one’s peers. Understandably, it’s still a sore subject with her after all these years.
- One other difference is that unlike in the US where private schools/colleges are often deemed superior, it's the exact opposite in ROC and other societies as public run schools/colleges are considered much more academically rigorous whereas with few exceptions private schools/colleges are at best regarded as academic fallbacks and at worse with the same skepticism we reserve for for-profit colleges.
There’s a firm line between arithmetic and mathematics. When we talk of quantitative skills, 97 percent of that is arithmetic. Mathematics is what starts in middle school or high school, with geometry, algebra, trigonometry, precalculus and calculus.
FALSE. I’m not even sure where he got this idea from, but it is completely false. Arithmetic is the OLDEST branch of mathematics. It might be the most basic, but that doesn’t mean it’s different from/separate from mathematics, and there’s no “firm line” between arithmetic and the other branches. In fact, arithmetic dovetails quite nicely into algebra.
But even if that’s the case, why would the solution be that we should stop teaching math? I mean, if we said “anatomy is the hardest part of a nursing curriculum” would we then have our nurses stop taking anatomy? No, because you need that class to be a nurse. Algebra is such a basic part of living in this world - you need algebra to figure out the second question he poses, for example, the one about the three coins. Maybe you don’t realize that you’re using algebra, but you are - the coins are clearly variables.
It’s especially shameful that a political scientist is saying this, as political science is a quantitative social science. If nobody learns algebra in high school (let alone geometry and calculus) then no one does the kind of higher-level analysis necessary for poli sci.
I do agree with him on the STEM shortage. It’s not that I don’t think we need scientists (we do) but I think the “need” has been greatly inflated by companies that want to lower the cost of software engineers.
THAT’S ALGEBRA. Does he think his students would be able to answer that question if they didn’t advance beyond 5th grade arithmetic in school?
A biography of John Adams I have on the shelf claims he was required to take calculus for a degree in the mid 1700’s.
Beyond that, we built a chicken coop for my parents. In looking back on it, judicious use of trig, geometry and algebra let us cut the parts cost roughly in half. We didn’tneed those things to build the coop! but we saved a bunch of money.
Maybe the author would be more accurate to posit that while certain of those math skills are not strictly necessary, using them can be an attractive alternative to poverty.
Edit: s/we/let us/
I’d replace calculus with statistics. I took three semesters of calculus and analytic geometry and hardly ever used it, while lots of public policy discussions dealing with everything from climate change to public health require an understanding of statistics to recognize what’s bs and what isn’t.
Seems to me that the area between everybody needing Algebra and nobody needing it is pretty sizeable. Also, we learned how to do things that were technically algebra long before high school. What I have a problem with is the insistence of some to make Algebra 2 a dividing line between “college material” and everyone else.
We are already teaching the average student less math than almost any other country. Why lower it even more?
"The overall trend I’ve noticed, though, is that in most countries, it’s at calculus where some of the rather intelligent but perhaps not mathematically inclined start to lose the ability to keep up with the material. "
I think you hit the bulls eye here. We do not write standardized tests and I used to wonder how the colleges decide who to admit to their most competitive programs. Then a friend told me her prof once let slip that our senior calculus course is the “invisible schieve”.
Out of curiosity I decided to look into all the highly competitive programs in the province at that time and I did not come across one that did not ask for that calculus course. In short, they looked at the “pre-requisites”, and the grades.
Algebra is not advanced mathematics. I don’t think everyone needs calculus but everyone can and should take algebra. Kids in other countries pass algebra. Maybe instead of dumbing down our education system we should take a look at what everyone else is doing to get their kids to pass simple classes like algebra.
Math is important in teaching students how to think logically. It has nothing to do with whether they use it on a daily basis when they are adults.
let’s stop requiring advanced math, science, SAT’s, recommendations for college(the one thing I support getting rid of) or anything else for that matter. let’s dumb down schools down to the lowest common denominator.
it will be perfect… as other countries push harder and harder to advance themselves we can keep going the other direction!
You keep repeating this - what exactly did your mom’s siblings take for math in high school? Can you give the actual names of the courses? Does it really matter if you take calculus in 8th grade versus 12th grade if it’s the last math class you take?
Oh please…Americans are already dumb as it is. If anything, we should require advanced math courses to be completed in high school so that colleges don’t end up accepting a bunch of no-potential losers. If students can’t even handle high school math, how are they going to demonstrate the work ethic required in most colleges?
After 8th or 9th grade, the course one takes beyond calculus depends on what academic/vocational track they are placed into and what specialization within those tracks. Among those on the academic track aspiring to universities, students are placed/choose to specialize in the arts/social sciences/humanities track or the STEM track.
However, specialization even in the arts/humanities/social science track at an academic high school doesn’t necessarily mean one stops taking more advanced math courses or going into STEM as shown by one aunt who ended up majoring in bio related field at NTU and later finishing undergrad and nursing degrees at an Ivy. Her sibling who went on to major in Foreign Literature at NTU ended up qualifying and working as a CPA accountant here in the US.
Within the vocational institutes…including some which are vocational high school combined with a type of community college, some targeting students for careers requiring heavy math like some training highly technical specialists will have math requirements which likely require proficiency beyond calculus. Others, not so much.