Heh, ditto. I don't think I got any new info that I didn't get in high school calculus, but it is a well done review of things I hadn't seen in a couple of decades
I got calculus in college, from mathematicians. :-(
We spent about 15 minutes (well, ok, one lecture) on series, then a couple weeks on limits, then limits and differential calculus, then the rest of differential calc. (throwing the limit stuff away), then limits and integral calc., and finally the rest of calculus.
Limits are a horrible way to learn calculus if you're trying to understand it at the same time as doing the algebra. :-)
My argument has always been that making unmotivated (it's remedial and annoying work for them), math experts, ie people that probably have never struggled with math in their life, teach entry level math to lots of people who don't "intuitively" get things like the teacher did 20 years ago, has been a huge mistake. These professors never seem to understand what it's like to NOT understand calculus.
The anecdote I always reach for is find someone who has been taught a higher level math subject by both a university professor, and an adjunct or local community college professor who might not have higher level knowledge of math. Many people prefer the "less expert" teacher.
Consider if you have been in software development for a long time, and how hard it is to remember what NOT understanding a variable was like.
Yea, it has gotten worse in the US thanks to the common core bullshit. My daughter’s math education has been eroded with shitty ed tech apps like the ones from MHM[0]. I’ve been able to support her but there’s many kids that are not so fortunate.
Most of the hate seems to stem from the changes in mathematics teaching. Instead of focusing on rote memorization, the curriculum wants students to understand the concepts, thus it teaches more ways to tackle a smaller pool of topics. I believe this idea comes from the way that mathematics is taught in countries whose students outperform Americans. A friend of mine who was schooled in eastern Asia claims his daughter is learning the same methods he did growing up.
FWIW, I learned some cool techniques that I didn't know about when my friend showed me his daughter's homework. But I can see how parents of fifth graders who aren't able to help their kids with their homework because they don't understand it / never learned that way would be angry.
States all had their own standards, which were largely the same, but just kind of different enough. Prior to Common Core, private companies sprang up to fill the need of mapping all of the different state standards to a common standard.
Modern "teaching" practices are just pretending to teach concepts; they're mostly based on the expectation that the students will somehow "rediscover" everything on their own. You can't truly understand concepts without doing quite a bit of solid practice. Many teachers will fail to provide the needed guidance, if only because they often never properly learned the subject themselves; and "Common Core" ends up being used as an excuse for substandard teaching.
It could be worse but one thing that constantly bothers me is the stupid new vocabulary. One of the worst examples: "number sentence". It means what you, an adult, might guess it does (well, it means one of the things you might guess it means) but why use it at all? They introduce it before the kids have a decent idea of what a normal sentence (what, a "word sentence", I suppose?) is. Many of the symbols in them aren't numbers (+, -, =). They don't really act like sentences or serve the same purpose. It's misleading as hell and the kids don't even have the context that might, even hypothetically, make it useful for scaffolding, when they introduce it in kindergarten.
They do this for lots of stuff. There's a whole Common Core Math jargon the motivation for which I just can't grasp.
Also, much of the approach is effectively what you do with kids who are struggling in math—you shower them with techniques and explanations for the same thing, hoping one will stick. The "show 5 different ways how you could have solved this" worksheets drive gifted kids, at least, batty, and that's most of the work. "I fucking solved it, I've already shown you a hundred times I understand this other technique (which I'll never use because I also know several better ones), why are you still bothering me?" They'll have them do two problems with all that extra stuff, in the time and space the kids could have practiced ten problems. It's making my kids hate math in early elementary. Wonderful. Just wonderful.
[EDIT] To illustrate by example why I find "number sentence" in particular so deeply stupid: would anyone think a good approach to introducing sentences to very young children, in language classes, might be to label them "word equations" or "word formulas" or "word algorithms" or anything like that? Would anyone think that would be an improvement? God no, it's plainly a bad idea—but that's exactly what someone, somewhere, decided to do, in reverse.
> One of the worst examples: "number sentence". It means what you, an adult, might guess it does (well, it means one of the things you might guess it means
Specifically, it means “equation or inequality”.
> They don't really act like sentences or serve the same purpose.
They act exactly like sentences, and serve exactly the same purpose, because they are declarative sentences about the relationships between numbers.
> It's misleading as hell land the kids don't even have the context that might, even hypothetically, make it useful for scaffolding, when they introduce it in kindergarten.
The idea is that they are mutually reinforcing, not sequential, concepts.
It also, as a sibling comment notes, has nothing to do with Common Core, its an orthogonal development in pedagogical approach to the Common Core standards.
> The "show 5 different ways how you could have solved this" worksheets
... also have less to do with the Common Core standards thablazy development of the particular materials (demonstrating proficiency with different articulations of operations and ways of solving problems is part of Common Core, to an extent, but even where it is doing it by using them all on the same problem, in the same assignment, and doing that for a substantial number of problems on one assignment, is just bad exercise design.)
> To illustrate by example
What you offer there is an analogy, not an example. Analogies don't really act like examples and don’t serve the same purpose.
> They act exactly like sentences, and serve exactly the same purpose, because they are declarative sentences about the relationships between numbers.
"Exactly" is simply incorrect in both occurrences, here.
> It also, as a sibling comment notes, has nothing to do with Common Core, its an orthogonal development in pedagogical approach to the Common Core standards.
All this hit alongside Common Core. Ask teachers and they won't quibble with lumping this practice in with Common Core, since that's how it's expressed in practice, though some might be aware that it's not in the standards. Source: I know a lot of teachers.
> What you offer there is an analogy, not an example.
It's both, so you're technically wrong, which I gather you think is the worst kind of wrong. Analogy's probably the better word here, though, sure, if I was only going to use one.
> Analogies don't really act like examples and don’t serve the same purpose.
They act exactly like them. Using your sense of "exactly" from above.
Well, if you take Montague semantics seriously then a "word sentence" is precisely a very broad generalization of a "number sentence", mostly differing by modality (accounting for "possible worlds", time, epistemic state, indexicals, attitudes etc. etc.) The basic "algorithmic" approach to language and words was already known to the ancient Indian grammarian Pānini. It's incredibly sad how few in the supposedly advanced West are aware of the countless innovations India brought to so many fields of science, art and culture.
If something isn't part of the formal Common Core standard, but is part of the "reference implementation," then practically speaking calling it part of Common Core is usefully descriptive.
We use this kind of synecdoche all the time when we do things like say Blub is a high performance programming language. If you want to be pedantic it's actually the Blub language, the Blub compiler, and the Blub runtime as a whole that determine whether or not Blub programs execute performantly. Sure it's useful to be aware of the distinction, but it's annoying and even disruptive to get caught up on it when everyone knows what is meant.
Number sentences existed prior to Common Core, so saying that number sentences is part of Common Core is not usefully descriptive and simply serves to confuse the issue.
Most people's complaints stem from assuming their local schools implementation of common core, and who they purchased the teaching materials from === "Common Core"
There are some SERIOUSLY garbage work books available for common core curricula. Some of them are obviously trying to touch on the understand that common core is trying to push, but seemingly written by someone who never understood that concept themselves, so they are basically nonsense word salad.
I remember when I was a kid, our state pushed a different direction in math education about helping students understand how to turn situations and problems into a mathematical equation to solve. Local parents decried the situation as "New Math" (importantly this stuff was distinct from the actual 70s era "New Math"), and that it was terrible and blah blah blah the same thing that happens any time you have poorly educated parents struggling to understand their children's educational material.
Of course, we children did absurdly well in education terms, literally a stand-out class of students in terms of educational outcomes, maturity, flexibility, and standardized test scores. Unfortunately it would be difficult to tell what the heck caused the improvement because there were MANY weird things to happen to my class (we were called the "Guinea pig class", we had second language schooling from first grade, our middle school scheduling was changed up to give us more specialized teachers and more classroom variety, and we always got brand new curricula to test out, along with just plain notable demographic changes happening in the area at the time)
