Anonymous wrote:Thanks PP. DH and I have done IT AND engineering (one as an aerospace engineer, another in operations engineering). and the path definitely depends on what our DCs eventually want to do. I’m just honestly curious on what the alternate pats are.

FWIW My friend considering opting out his DC is a SV-types by the way. He’d prefer to hire talented kids more out of HS but a lot of people are willing to take the risks of not getting the sheep skin.

My take is if a kid isn't doing lots of problem solving (whether through math, computers, puzzles, chess, ... anything really), they're kind of missing out in developing a sharp set of reasoning skills at an earlier age. Many kids only really start doing that in college (which is the first time they encounter a serious course/challenge). It's fine for those that struggle, work hard, and then are able to adapt. But an alarming number of them start a STEM major with high hopes, fail to adapt, then decide it's not for them (or even more sadly, believe that they're not smart enough which in many instances is not really the root cause... it's the fact that they're overwhelmed because they're facing a high barrier to entry in college, without having had any problem solving experiences in K-12).

A child's passion and curiosity is hard to develop (certainly even harder through the low quality way math class is taught in a typical school). The biggest reason to have them start early (i.e in elementary) is because they're natural curious, unafraid to tackle challenges, unafraid to be wrong and to fail and get back up, etc. To me an alarming number of kids who have A's in middle school and high school are actually mentally checked out (at least to math). Many parents don't realize this and think everything is well because they're doing their homework and getting good grades on paper, but have learned nothing. Some work harder and get lucky and get into a good school. A subset try out STEM because it's pretty popular in today's times, but some of them get their hopes dashed and sadly fail to get back up. And it's not their fault; their K-12 education essentially set them up for failure by not teaching any thinking or any kind of mental struggle (i.e problem solving).

None of the math classes offered in high school are mentally challenging (outside of special places like TJ, etc.) In particular they feel pretty trivial, aka an easy A, to kids who have problem solving experience. We see this all the time, the kids who played with a lot of puzzles, or did well in math contests early on, ace all high school math classes with almost no difficulty. This includes the SATs (which also feel pretty trivial when compared to harder problems found in math contests). Essentially, the kids who practiced problem solving and have developed quantitative reasoning through practice will flourish in college, no matter what major they choose.

I wouldn't honestly worry about Algebra 2, just expose your DC to interesting, challenging, creative problems and have him try to solve them (obviously start progressively with ones within their reach). The skills they will acquire by working on them will transfer to all school math classes, including Algebra 2, making those classes very easy by comparison.

In college you won't really be able to predict their path, they will decide on what drives them (perhaps it may not even be related to STEM at all). But if they have strong problem solving skills, they will succeed at whatever they choose, even the hardest possible major.

In terms of career path, a math or physics major is generally considered a very flexible option as it can open up a path to any high demand job. For example you may have read or know that top finance firms and hedge funds, don't really primarily look for finance or economics majors; they highly prefer STEM majors, in particular math, physics (or both even better). This is because they rightly realize that if the candidate went through a strong college program within those fields, they will have acquired excellent thinking skills that will be useful for them in solving new problems. But this pathway is obviously very hard, not many kids will be able to major in math and/or physics in the first place, especially at colleges with top programs. I agree that it's hard, but I don't think it's that hard if a kid is passionate about it and started a little earlier.

Thanks PP. DH and I have done IT AND engineering (one as an aerospace engineer, another in operations engineering). and the path definitely depends on what our DCs eventually want to do. I’m just honestly curious on what the alternate pats are.

FWIW My friend considering opting out his DC is a SV-types by the way. He’d prefer to hire talented kids more out of HS but a lot of people are willing to take the risks of not getting the sheep skin.

Anonymous wrote:I keep hearing that data analysis and statistics are more relevant to Algebra II and beyond even for some STEM majors. I was a STEM major, and admittedly, I was disappointed that math wasn’t used much in my field (IT/engineering) except every once in awhile. I asked some of my other STEM friends, and they had similar experiences. What those higher classes did is help us think about problems in different ways.

Anyway, as my DCs begin high school in the next couple years, I wonder what alternatives to the Algebra I - Geometry/Trig - Algebra II - Calculus path is out there.

OP you posed a great and important question, but you're not thinking about it in the correct way. Math is not necessarily a strictly linear progression like what you described (and what K12 American education tries to have you believe). The "Algebra I - Geometry/Trig - Algebra II - Calculus path" as offered in school is analogous to the "meh" tasting bread, or the plain potatoes offered on the restaurant menu which makes one feel that something is missing. There are lots of other exciting choices, not only because they are different type of dish (number theory, combinatorics, probability, statistics, contest math, and all kinds of other higher level mathematics), but also because they taste really good (because they are actually cooked well). In particular, if you select any menu item with a lot of problem solving, you will find your meal very satisfying. Note that Algebra I, Geometry, and all other K12 subjects you mentioned can be taught with a lot of problem solving, but THEY ARE NOT in the current American curriculum. That is the main reason why they are boring, tasteless, and feel empty.

To your gripe about not seeing enough mathematics despite being a STEM major... I suspect that you suspect that your experience may not generalize to other STEM majors. Sure, there are many who do not use it even at all (certainly many in IT especially), but you have to agree that there must also be many jobs that use an incredible amount of math and engineering concepts. I mean SpaceX/NASA just launched its first manned mission to the ISS, which hasn't happened for 10 years! This was no easy feat at all, and many many incredible people had to solve many many difficult design, engineering, math, science, etc. type of problems.

But I digress... I'm also not saying the extremely linear K12 pathway offered to us by schools is worthless. There is a reason it's set up like that, namely that algebra is required to understand calculus, and calculus is required to understand pretty much anything in science and engineering. And geometry is also not only fundamental to our world, but it's the gateway to thinking about problems in a mathematical sense, i.e learn how to prove things for one's self (that is if they actually teach it properly, which they do not... very far from it). See here if you're curious how they screw it up: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

You can't get out of learning algebra and geometry, and studying calculus. These are just the basic fundamentals needed to be successful in STEM. And by STEM I not only mean your typical IT job (which may admittedly not require much math as you related), but many of the exciting (and high paying) engineering jobs out there (i.e all the tech companies in Cali, and the other spots in the country). And if you're interested in doing research, then having a good mathematical understanding is even more critical (this includes a really solid grounding in statistics, in order to even be able to write up an experiment).

You should supplement all the K-12 above classes with real problem solving. If there is no thinking going on, then you're not doing mathematics. If there isn't a problem to solve in the classroom, then there is no point memorizing a bunch of formulas. You should be aware that many school students taking AP calculus classes have almost no problem solving ability. If they were to be asked to solve some elementary math problems (such as found in a middle school competition like MATHCOUNTS, etc.) many would have no idea even where to start. Yes, the situation is that dire.

Luckily you have endless amazing enrichment opportunities outside of the classroom and it's just a matter of choosing some. Others mentioned AoPS, which is obviously pretty amazing in terms of teaching problem solving in a challenging environment. There are lots of Youtube channels that give you a taste for cool mathematical topics (3blue1brown, Numberphile are some of the best). There are lots of high quality courses on the MIT OCW site that are completely free, and you also have many MOOCs that teach pretty much any STEM class you can think of. All of these will have ample amount of problem solving.

Remember the most important point: if you're not struggling solving a problem that you don't initially know how to do, then you are NOT doing mathematics. I will once again recommend Lockhart's Lament which I linked above, as he explains all of this in a much, much more eloquent fashion than I could even begin to.

Anonymous wrote:OP here — my DCs are in advanced math / honors now, and aren’t struggling. We’re in FcPS. DH and I have engineering degrees. A couple of friends who are hiring directors have even said Algebra II is a waste of time, and we’re looking for alternatives for their own DC. One is going as far as possibly pulling their DC out to take GED after 10th, and do their last two years of “high school“ at NoVA. Not sure he’ll find away around Algebra II And I haven’t asked.

Algebra II is not a waste of time if they are in advanced math and want to take any additional math classes, including statistics. Some people will tell you all math is a waste of time. Most colleges will require a minimum of algebra II for admission. I believe statistics is very applicable to most fields and is a useful course to take. Look into statistics offerings, but algebra II should be taken before AP Stats.

I’ve been following the topic loosely for a couple years now, but it’s getting real, real fast as our Dc are almost in HS.

Since your kids aren’t struggling, I’d keep them in the normal course pathway just to check the boxes for college. Perhaps an interesting math elective could be considered. AOPS has some interesting advanced number theory stuff, or perhaps they could take a math elective at a community college, or extend math learning via MITOCW. There’s so much more to math than the standard pathway and it’s great you are realizing that. But, you kind of also need Algebra II. There’s a lot in that course.

OP here — my DCs are in advanced math / honors now, and aren’t struggling. We’re in FcPS. DH and I have engineering degrees. A couple of friends who are hiring directors have even said Algebra II is a waste of time, and we’re looking for alternatives for their own DC. One is going as far as possibly pulling their DC out to take GED after 10th, and do their last two years of “high school“ at NoVA. Not sure he’ll find away around Algebra II And I haven’t asked.

Some high schools offer AP Statistics but Algebra II would need to be taken as a prerequisite.

If your child struggles in math, see if Algebra Functions and Data Analysis is offered. This would be a good alternative if they do not want to take algebra 2 and want more real life applications or to strengthen math skills. It is not as rigorous.

What does your kid’s high school offer? What does he want to major in college if that is the goal? How much does he struggle with math (Is he on track to take calculus, if so take the lowest calculus). If he’s already on that track and it is too hard, maybe see if he can take Alg 2 for two years then precalc, or statistics senior year. If math for your child is really very very hard I would suggest consumer math or the like if that option exists.

I keep hearing that data analysis and statistics are more relevant to Algebra II and beyond even for some STEM majors. I was a STEM major, and admittedly, I was disappointed that math wasn’t used much in my field (IT/engineering) except every once in awhile. I asked some of my other STEM friends, and they had similar experiences. What those higher classes did is help us think about problems in different ways.

Anyway, as my DCs begin high school in the next couple years, I wonder what alternatives to the Algebra I - Geometry/Trig - Algebra II - Calculus path is out there.