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That's not 8th grade algebra "50/x = 25, what is x?
That's graduate level linear algebra, where "X" stands in for entire expressions. Similar to matrix math, where you do operations on matrices and then open out the matrix to what it consists of. So, multi-dimensional calculus operations applied to expressions which, themselves, are stand-ins for expressions. NOT the stuff of eighth grade algebra.
Well, I guess I"m not really clear what your point was. The discussion started out as "if you throw a ball you're using algebraic concepts" as justification for 8th graders learning algebra (8th grade algebra, not graduate level math-major complex algebra), versus the people with math-fright who think that children should be excused from learning anything that's difficult and the end-use isn't immediately apparent. So I'm not sure where complex algebra taught in grad school has anything to do with this.
Frankly I think justifying the teaching of mathematics by reference to throwing balls (and the like, I've heard lots of these kinds of discussions, it's not just balls) is a very weak argument. I prefer to think of the collection of things one is SUPPOSED to learn in high school, which has now been demoted to the first couple years of college in many cases, as a set of tools. To be a fully functioning adult in Western society, you need to come out of the chute into adult life (whether that be defined as the transition from high school to college, or leaving college, or leaving high school without college following) with a certain set of tools. You may or may not end up using some of them in the future and you can't guarantee that. I really oppose the idea that normal kids be allowed to opt out of some of the tools as early as 8th grade. Because learning and knowledge builds progressively, you simply can't jump into third-year college material (whether it be in the humanities or sciences) without the prerequisites.
We've chewed the algebra thing pretty thoroughly, but consider the student who hated and did poorly in English in early high school and never took another course. Then he decides he wants to be - say, a lawyer - at age 20. Surprise, surprise! Law is all about reading and writing and parsing out the various shades of meaning in written material. You can't suddenly decide to acquire the knowledge of that without scuffling to catch up to all your classmates who've been learning and applying those skills to written material, being graded on the quality of their work, for years.
Well, I guess I"m not really clear what your point was. The discussion started out as "if you throw a ball you're using algebraic concepts" as justification for 8th graders learning algebra (8th grade algebra, not graduate level math-major complex algebra), versus the people with math-fright who think that children should be excused from learning anything that's difficult and the end-use isn't immediately apparent. So I'm not sure where complex algebra taught in grad school has anything to do with this.
Frankly I think justifying the teaching of mathematics by reference to throwing balls (and the like, I've heard lots of these kinds of discussions, it's not just balls) is a very weak argument. I prefer to think of the collection of things one is SUPPOSED to learn in high school, which has now been demoted to the first couple years of college in many cases, as a set of tools. To be a fully functioning adult in Western society, you need to come out of the chute into adult life (whether that be defined as the transition from high school to college, or leaving college, or leaving high school without college following) with a certain set of tools. You may or may not end up using some of them in the future and you can't guarantee that. I really oppose the idea that normal kids be allowed to opt out of some of the tools as early as 8th grade. Because learning and knowledge builds progressively, you simply can't jump into third-year college material (whether it be in the humanities or sciences) without the prerequisites.
We've chewed the algebra thing pretty thoroughly, but consider the student who hated and did poorly in English in early high school and never took another course. Then he decides he wants to be - say, a lawyer - at age 20. Surprise, surprise! Law is all about reading and writing and parsing out the various shades of meaning in written material. You can't suddenly decide to acquire the knowledge of that without scuffling to catch up to all your classmates who've been learning and applying those skills to written material, being graded on the quality of their work, for years.
Above you wrote........
"Algebra is a high school course. Typically in grades 8, 9, 10. (depending on curriculum). It needs to be out of the way BEFORE college admission. If for some reason you don't have algebra already completed before college you need to take remedial classes at the junior college."
My point is large slices of algebra are way beyond high school.
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Functional geometry, algebra etc. should be well covered for interested high school students with strong foundations earned before college. We agree on that.
However, the farmer with a 5th grade education estimating the size of a pond because he knows via visual perception how large 100 gallon tanks are is using algebra. His inability to explain the algebraic processes applied is a separate matter.
I tend to agree with you overarching point(s). That said most college students never sniff a calculus based statistics class.
Not all colleges are alike. My history major son was required to take a calculus based statistics and a macroeconomics class.
Ideally, students come from a decent high schools with AP courses. Then students can test out of some of the general education courses and foreign language requirements. However. at a good college, general education courses are NOT basic courses. Basic, high school level courses are remedial classes.
At my college - general education courses were electives like pick one science, social science, one history, literature, math, foreign language course. There were no assigned courses. I could pick biology, botany or physics or any other science that fulfilled that requirement. You would have messed up SAT/AP's to be assigned to a general education redo of basic writing or math. The other option is its a less rigorous college with lower requirements.
Last edited by YorktownGal; 11-16-2022 at 02:49 PM..
Algebra is a high school course. Typically in grades 8, 9, 10. (depending on curriculum). It needs to be out of the way BEFORE college admission. If for some reason you don't have algebra already completed before college you need to take remedial classes at the junior college.
Too many people go to college. That's why costs are so high. If you can't do high school level math, you don't belong in any college.
I just looked to be sure. The University of Texas has at least 4 algebra based gradate level courses and at least as many upper division undergrad classes within the math department alone. For certain it has algebra based physics, econometrics, and statistics as well.
An upper division undergrad course or a graduate level course with "algebra" in the title is probably something like linear algebra or abstract algebra. Not the algebra that is taught in high school.
That's why you take algebra in high school. What is the point of retaking it in college as a gen ed?
Maybe not algebra, but a lot of freshmen classes are more designed to weed students out than to teach. Students won't be taught anything more than what they already learned in high school, and they won't be allowed to AP out of it regardless of AP score. But the students will be given a draconian workload of mostly busywork, an exam worth half your grade will be at 10 PM the Wednesday night before Thanksgiving (when the dorms closed hours earlier), you get a 0 for any exam missed, even if it's for a funeral or a hospitalization, exams focus on trivia that was never taught and are too long to finish anyway, and you are penalized for any absence from class, even if for a funeral or hospitalization. And if you dare point out that the professor is violating university policy, they just remind you that they have tenure and can do whatever they want, and there is nothing we can do about it.
Not all colleges are alike. My history major son was required to take a calculus based statistics and a macroeconomics class.
Ideally, students come from a decent high schools with AP courses. Then students test out of some of the general education courses and foreign language requirements. However. at a good college, general education courses are NOT basic courses. Basic, high school level courses are remedial classes.
The issue is that there is a wild variance in what is offered. I have a friend who used to be a superintendent in a rural Midwestern school district that had a total of 450 kids! As you can imagine, that’s not enough to support any AP classes. I think administrators (including my friend) were also teaching positions and everyone had a course load. IIRC, she taught 2-3 classes a semester. A few of those kids probably want to go onto college, but they are probably not going to be at the same level as kids from the state’s larger districts that have a full array of offerings. State universities are there to serve state residents, and in rural states, they’re just going to have to do more remediation to make up for the lack of offerings in many rural schools.
An upper division undergrad course or a graduate level course with "algebra" in the title is probably something like linear algebra or abstract algebra. Not the algebra that is taught in high school.
I don't disagree. My point is that a student does not get far into algebra in high school.
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