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Anonymous wrote:AOPS isn't for most kids. They spend 75% of their time focusing on esoteric contest math tricks while skipping over basic skills.

+1 You nailed it. I'm a math teacher btw.

They are not skipping anything, they expect that kids to already know the basic skills. As many posters have said, it is not a program to build foundational skills. There is an expectation that the kids will have those skills.

Students at our location are evaluated by one of the Teachers or Administrators. DS was given a series of questions, he provided an answer and the evaluator asked him how he had solved the problem. DS would give his explanation and they would discuss different methods for solving the same problem. The problems were on grade level and meant to make sure that he had the basics down. The explanation insured that he understood the principles behind the basics.

I have been told by others that AoPS has no problem with recommending that a 3rd grader take the 2nd grade math because of where they were with their skills or holding kids back the following years because there was concern that the kid did not have a firm enough grasp of the material. We are waiting on the Teachers evaluation from this year.

There are programs that are great for kids who need to build a foundation, that is not AoPS.

Math teacher back. I never said it was for foundational skills. I said that the program is about 90% (the other poster said 75% but I think it is around 90%) quick math cheats and tricks, and 10% real, enriching mathematical and concept-building experiences. If that's what you're about then go for it.

Different math teacher here who actually teaches AoPS classes... I strongly disagree with this assessment. Most of the AoPS curriculum is focused on teaching kids how to develop deep problem solving skills of which they'll make use of throughout their life, whether they go into math, sciences/engineering, or any other field. Only a few of the classes (e.g Middle School Contests or High School Contests) have a specific math contest focus meant to help kids do very well in competitions. The majority of courses are rigorous non-contest classes and teach the basics from the ground up (without the repetition that is seen in schools), then use the basics to tackle more difficult problems. Each of these core classes cover what would be taught in a similar class in school, but with a major problem solving component built in (which is so severely lacking in school and in the way math is taught in K12).

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pettifogger wrote:

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Anonymous wrote:I have a 5th grader and a 7th grader, both in Algebra I Honors in FCPS. The 7th grader is a normal, smart kid who is similar to all of the other smart kids in FCPS. The 5th grader is way beyond that and is bored in the Algebra class. Kids who are more than one year by FCPS are pretty rare, since FCPS doesn't like skipping kids.

That’s not saying much.

Yes. If FCPS is accepting the top 25 percent of a general population. Less than 10 percent of those kids accepted are even actually gifted (top 2 percent) statistically speaking. So maybe 9 kids out of every 100 aap kids. Sometimes will do stand out.

That's the point, though. People have been arguing about whether kids need to sit in a classroom every day to learn Algebra I Honors, and whether a class like AoPS could cover all of the same material. The normal, smart kids, who are the vast majority of AAP kids, probably need to be in that classroom every day taking FCPS Algebra. AoPS would move too quickly, not give enough repetition, and make too many intuitive leaps for the regular bright kids. It still might be valuable supplementation, but couldn't stand alone for these kids.

The small fraction of kids who are at the top of AAP would be fine with just the AoPS class. FCPS will still make those kids sit in a classroom for FCPS Algebra, but it won't benefit the kid in any way. It's just another bureaucratic hoop that the kids will need to jump through. I bet the AoPS teacher posting here can tell the difference between the 4th, 5th, and 6th graders in Algebra who are highly gifted and will always be far ahead of the FCPS curriculum vs. the ones who just have pushy parents and are only ahead from all of the hothousing.

sorry to bring this thread back from the dead. I am a parent looking into AoPS for my kids because I think the other program we are using (Mathnasium) is burning them out with drilling and not enough instruction. My kids are in advanced math in FCPS but by no means are math geniuses. Would AoPS work for them? It appeals to me because it teaches problem solving/critical thinking.

Yes, this is exactly right. In general I've seen that the really young kids in our classrooms tend to outperform and/or be near the top in our classes. (Not always, but most of the time). And these are exactly the kids who wouldn't be allowed to take the equivalent class in school at the same time because of age. By the time they would let them, it would be a ridiculous waste of time for them and likely even hurt their motivation (it would be fine of course if they actually alowed them to work at their own level and pace in class but sometimes they refuse to do that due to logistics, strict rules, no computers/internet allowed, etc.) We've also regularly noticed that more frequently the kids a lot older than the average in our class do NOT do as well as expected (often they even struggle sometimes, which indicates they may possibly be struggling in school, or are just being pushed by parents against their own will). But most kids fall in the middle, i.e they're taking the same class both in school and ours. This is a common scenario and good approach since they are likely to do well (they get the basics in school) then get deeper exposure to problem solving in our class. We also have the kids who "double up" (i.e do one class in school such as algebra, and then take our geometry course at the same time). This can work, but in my experience I've found that they stretch themselves too thin and cannot handle performing well enough in our class because the two subjects do not complement each other much (and in this specific case, our geometry class is MUCH more challenging than our algebra class).

sorry to bring this thread back from the dead. I am a parent looking into AoPS for my kids because I think the other program we are using (Mathnasium) is burning them out with drilling and not enough instruction. My kids are in advanced math in FCPS but by no means are math geniuses. Would AoPS work for them? It appeals to me because it teaches problem solving/critical thinking.

It's hard to say, it depends on your child's interest in math, and/or their motivation to try to tackle problems they don't initially know how to do. I can definitely tell you that there is no drilling and repetition in the curriculum. It is aimed at kids who want to have a deeper understanding of mathematics. The focus is on problem solving to gain that insight and understanding. They have a local campus which is currently virtual on Zoom, but also run classes online all year round. Not sure about the campus policies, but I know that for their online classes you can just try the first 2 weeks of a class for free as long as you drop the class before the 3rd week.

Anonymous wrote:Learning now to do math on paper vs in your head is important. At some point they won’t be able to do it on their heads and will need to know how to write their steps.

This is true, the problem is they're learning it in an unreasonable way. One step questions that many kids can do in their head (i.e mental math calculations) are not great candidates for forcing kids to write things down. It can lead to a dislike of math, as kids associate it with writing. The focus should be on the math, not the writing (save that for writing class). Requiring explanations is reasonable if the questions are interesting, such as a puzzle, informal proof, explaining why something is true, where that something is not obvious.

There are many, many great math problems that kids can try to solve and show work on, they're just not being given the chance to try and solve them. Instead they mostly get a set of calculations, which are often trivial for many of them.

No one is denying that showing work is important when it makes sense to do so. It's the "turning math into writing" that is really frustrating by forcing kids to show work to trivial questions. Teachers should know when a problem requires work to be shown, and when it does not. At the same time, teachers should be able to gauge who is struggling and may need help organizing and writing things down, vs who is really bored and is not being challenged. Forcing a kid who is not challenged to write unnecessary things in math class when they already know exactly how to do a certain calculation 1) wastes their class time, as they should instead be given more challenging problems that they won't be able to do in their head and require them to write things down 2) frustrates them to the point where they are turned off to math because they see it as pointless and boring, and possibly even worse turns them off to learning/school 3) doesn't actually teach them new math, or extends their problem solving skills.

You argument that always showing work on trivial questions in early elementary school will help kids in college calculus and science classes is not compelling at all. Teaching kids how to think, and how to organize their thinking by practicing challenging multi-step questions is what will ultimately help them tackle late high school and college math and science.

Most of the kids who are struggling in college or high school math are NOT struggling because they don't know how to write something down. They are struggling because they don't understand the problem and/or have no idea where to start, or what to do. It's having had a shaky foundation and weak understanding of math concepts, not the writing that prevents them from succeeding.

Anonymous wrote:For simple operations, it's pretty inane to ask kids to show or explain their work. The time spent demanding that in K-3 would be better spent with drilling basic math facts.

For word problems and pre-algebra equation solving, the student should at least show some steps. They shouldn't need to show every trivial operation, but there should at least be enough there for the teacher to figure out how the student arrived at the answer.

I think this example: "6x = 12 6x/6 = 12/6 x = 2" is a perfect example of the teacher being overly picky and expecting trivial steps to be illustrated. It should be sufficient for a kid to jump to x=2 from the problem statement. Now, if the problem were 6x + 3 = (-2x -13)/4, then the kid should show at least one intermediate step before listing the answer.

Spot on, 11:11. The real issue is that math class is overly focused on making a mountain out of a molehill, instead of actually solving problems. Any kid in algebra class should not need to write anything else other than 6x=12, x = 2, done. If on the other hand, the kid is in elementary and is being introduced to variables, but not the full rules of algebra (such as doing the same thing to both sides of an equation), then it would be perfectly reasonable to let them solve the problem in any way they choose. Even just saying "x = 2 because 6*2 = 12", done.

As to the less trivial example above, I would definitely expect some sort of work, but up to each kid to decide what to show (as long as it's readable and shows some organized way of thinking). But forcing them to write specific things (like multiplication of 4 by both sides), may be misguided for the kids who are not having trouble, unless they are struggling and not getting the answers correct. Here's the minimum I'd expect to see for this one, but it can completely differ from kid to kid:

6x + 3 = (-2x -13)/4
24x + 12 = -2x - 13
26x = -25
x=-25/26

Basically I want to see a step showing they were able to handle simplifying the fraction on the right hand side, and another step showing how they combined terms, etc. Also, it's much more important for them to write in a somewhat organized fashion such that their reader (teacher) can follow what's going on. That's what really matters here, not necessarily what specific steps they have to write down, which can vary.

Anonymous wrote:I have a kid in ES in AAP math, and he's not doing well because he doesn't show his work enough. He gets the answers right, but he can do most of the problems in his head. He tries to write out his work, but he just can't do it in enough detail for her. He much prefers to do it in his head, and he doesn't do any better when he is forced to write it out. It just makes the whole thing tedious for him. I used to teach in fcps and our main goal for making kids write out their work in math was so that they would get the test questions right. The teacher tries to tell him some nonsense about how she wants to see his thinking, but she doesn't even look at the work that is turned in, and certainly has never given him even five minutes of personal attention to talk about his "thinking." Does anyone else have a kid that suffers from this rule about showing work or getting it marked wrong? I'm not happy about this, obviously.

My kid gets similarly frustrated where he finds it hard to show work or write an explanation of something that he can do in his head, or is immediately obvious. I've taught him how to handle it by finding something logical to say and succintly write it in 1 or 2 sentences max (which so far in 3rd grade aap is about as much as needed, given the low difficulty level of questions). It's been working ok and he's improved his ability to explain things but I don't force him to overdo it (and luckily neither does his teacher).

I suspect that the questions are likely simple enough given that he can do them in his head. Can you provide specific examples of questions asked, and what work he's shown, if any? Then we can figure out how much work he should show, if any, based on his level.

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Anonymous wrote:It’s part of math and will be necessary as he advances so definitely best not to fight it but instead support him developing the skill. Whatever you don’t act like getting out of showing work is worthwhile goal or that he is somehow “good at math” because he can do it in his head. Being good at math includes showing work.

Exactly. If the instructions say to show your work, that’s what you need to do. There are good reasons for it and kids don’t necessarily understand the underlying reasons now, but they will when they are older. And they will appreciate the teachers who insisted on following instructions.

OP here - I am a teacher, and I don't think our stated mission anywhere is to teach kids to follow instructions. I thought it was to teach them critical thinking, yada yada. So following instructions when it means doing something unnecessary that just make the work harder really isn't worth teaching. Like I said earlier - I was a teacher in fcps, and the only reason we insisted on them writing out the work was when we started the SOL high stakes testing and really needed them to get every answer right. There was no educational theory at all behind that.

If nothing else it’s important to be in the habit of showing work by the time he gets to 6th grade because teachers will give partial credit if the problem was done sensibly but there was a something like a rounding error or copying down 6 instead of 9. Also, the fact is even gifted math students didn’t do complicated algebra problems in their head and there are conventions around d how work is shown that even your young Einstein needs to follow. Sounds like you are not helping the situation at all with your attitude (and like you were fairly shortsighted as a teacher too.)

+1

This is part of math. There are a TON of reasons why you need to show your work in math. At some point, even the most gifted kids can't do it all in their head. Better to establish the habit of showing your work early on. Plus, the point isn't that your kid knows the answer, it's that they know how they got that answer, because the method is the same even as the problems get harder.

Please cite some educational research that shows that math achievement is in any way improved by kids being able to show their work on paper.

You can't. Because it doesn't exist.

Know what does? Research that shows that forcing kids to write down work unnecessarily (like simple problems that most kids can and do do in their heads) actually negatively impacts achievement.

When the problems are too difficult to solve without writing them out, then kids will write them out. Doing otherwise is illogical.

Spot on. "Showing work" is just a manifestation of a deeper root cause; the incredibly watered down way math is taught in elementary school (and middle/high as well!) But particularly in elementary school, where a monumental and misplaced amount of effort is spent telling the kids to "show work". The idea is that it will help them think better, when all it does is instead induce tears in a large number of kids (and ultimately makes many of them hate math, resulting in permanent mental detachment from the subject in later years). As the PP said, work will naturally be shown when a good problem or puzzle is presented which requires thinking! But we do not get problem solving or critical thinking in math class, we get a shallow and repetitive set of calculations, and an even more shallow sense that showing work on these shallow exercises will somehow lead to higher mathematical thinking. In general, it will not! Becoming better at math requires slowly spending time struggling with problems, slowly orienting oneself to the point of figuring them out, then presenting the method (proof). Showing work will happen, but teachers please at least once in a while, give your students an actual problem to solve!

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pettifogger wrote:

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Anonymous wrote:I went to an excellent public school system in New England, and we had no differentiation or G&T in elementary school. Honors classes (for a couple of subjects) started in middle school (7th grade), with expanded honors/AP options in high school. I graduated in 2002.

However, the parent population was pretty well educated and kept tabs on their kids. Not many behavioral issues or disruptions to distract the teachers. And class sizes were ~22 kids. Everyone was taught the same lesson though. I felt I received a good education (later went to HYP for undergrad)

I completely agree. I think AAP is ridiculous and over utilized. I have a good friend who is an AAP teacher and she put it this way, which I agree with: an AAP/GT program is not for the truly advanced when half of the grade level is in that program. Then it's just to brag that "my kid is advanced." Most are not, and that's in her experience in a highly rated AAP center school. There are so many ways to press your way into AAP, at this point. I know people who've done it.

My kid did not do AAP. DC was not selected for advanced math in ES (but should have been, but I didn't complain). DC is in 8th. All honors 7th and 8th. Straight A's. And our principal says that the kids taking all honors are taking the same curriculum as AAP kids. So DC is successfully doing AAP work.

I have no gripe with my kid not doing AAP in ES as DC didn't want to do it. I didn't care to push hard. DC was succeeding. And now exceeding most of DC's peers. Hopefully that will continue, but who knows?

I believe ES AAP is not necessary based on our experience and my interactions / knowledge with AAP at our ES. It's a waste of resources. It should be eliminated.

Irrespective of AAP or not, I would urge you to consider checking in detail what your child actually knows vs their gaps. Per your bolded statements it seems that you overly trust what school admins are saying. Doing well in middle school classes does not necessarily translate into doing well high school classes, as there are so many kids who get A's in middle school and end up struggling in high school.

There are so many more factors you need to consider; i.e is the teacher appropriately challenging the kids vs giving them easy assignments, is your kid actually working hard and getting A's or just coasting, is the school and teacher known for academic excellence or just average... etc, etc. The only way to find out all this is to investigate, as well as check your kid's understanding. Peruse the homeworks; is there critical thinking going on, or just basic memorization? Can your kid think independently and do they have some amount of problem solving skills? What do some of the tests they took look like? Are they very basic, or does earning an A on them involve being able to do more than that? Give them logic questions, or some easy math contest questions, or even some SAT type questions... can they figure it out? Or do they quit almost immediately saying something like "we weren't taught that" ? If the latter, and if it's something you believe they should know how to figure it out, then that should raise a red flag with you. These type of things will let you directly glimpse into how they are thinking and approaching problems. To be successful in high school, an 8th grader should be able to display a reasonable degree of problem solving and willingness to figure out something that they don't initially know how to do.

I'm not just saying this; I've tutored many high schoolers in math who were really struggling despite having been good students in middle school, and even having good grades in general in high school. Parents are always shocked and don't know what happened. I work with their kid and pretty quickly by far the most common patterns are a combination of: 1) They don't really understand basic fundamentals, i.e manipulating fractions, or basic algebraic skills, or 2) They cannot think beyond the examples the teacher gave in class; if a problem is even a little different they just shut down, which signifies a lack of any kind of problem solving ability.

Agree (I'm the person you're responding to). That's why I said "hopefully it will continue." I'm well aware that HS is more difficult. But, that doesn't really change that DC is excelling and had no benefit from AAP in ES. Or are you saying only if they were AAP they'll do well in HS? That, I would take issue with.

My child also has a math enrichment tutor precisely b/c it is a HS level class and I was concerned the online would be an issue. I've listened to the class recordings and, by and large, DC's teachers are doing an outstanding job. My one concern is English. But, I've had concerns about how FCPS teaches that for the entirety of my child's time in school.

Nope, not at all, irrespective of AAP. Too many people on these forums are getting a bit too distracted by the AAP program, when they should be more concerned about the lack of rigor and challenge/enrichment fading from the classrooms, across both AAP and not.

The data really does speak for itself in terms of how much money is being poured into tutoring, not just during COVID (which makes sense) but during normal years. If the tutors are mostly doing enrichment, then it's great; it indicates the child is interested and wants to learn more, or perhaps overly agitated parents (hopefully the former). But if the hiring of tutors to help keep up with homework is a pervasive thing in the area, it really says that something is not working correctly in the school and classroom.

Anonymous wrote:

Anonymous wrote:I went to an excellent public school system in New England, and we had no differentiation or G&T in elementary school. Honors classes (for a couple of subjects) started in middle school (7th grade), with expanded honors/AP options in high school. I graduated in 2002.

However, the parent population was pretty well educated and kept tabs on their kids. Not many behavioral issues or disruptions to distract the teachers. And class sizes were ~22 kids. Everyone was taught the same lesson though. I felt I received a good education (later went to HYP for undergrad)

I completely agree. I think AAP is ridiculous and over utilized. I have a good friend who is an AAP teacher and she put it this way, which I agree with: an AAP/GT program is not for the truly advanced when half of the grade level is in that program. Then it's just to brag that "my kid is advanced." Most are not, and that's in her experience in a highly rated AAP center school. There are so many ways to press your way into AAP, at this point. I know people who've done it.

My kid did not do AAP. DC was not selected for advanced math in ES (but should have been, but I didn't complain). DC is in 8th. All honors 7th and 8th. Straight A's. And our principal says that the kids taking all honors are taking the same curriculum as AAP kids. So DC is successfully doing AAP work.

I have no gripe with my kid not doing AAP in ES as DC didn't want to do it. I didn't care to push hard. DC was succeeding. And now exceeding most of DC's peers. Hopefully that will continue, but who knows?

I believe ES AAP is not necessary based on our experience and my interactions / knowledge with AAP at our ES. It's a waste of resources. It should be eliminated.

Irrespective of AAP or not, I would urge you to consider checking in detail what your child actually knows vs their gaps. Per your bolded statements it seems that you overly trust what school admins are saying. Doing well in middle school classes does not necessarily translate into doing well high school classes, as there are so many kids who get A's in middle school and end up struggling in high school.

There are so many more factors you need to consider; i.e is the teacher appropriately challenging the kids vs giving them easy assignments, is your kid actually working hard and getting A's or just coasting, is the school and teacher known for academic excellence or just average... etc, etc. The only way to find out all this is to investigate, as well as check your kid's understanding. Peruse the homeworks; is there critical thinking going on, or just basic memorization? Can your kid think independently and do they have some amount of problem solving skills? What do some of the tests they took look like? Are they very basic, or does earning an A on them involve being able to do more than that? Give them logic questions, or some easy math contest questions, or even some SAT type questions... can they figure it out? Or do they quit almost immediately saying something like "we weren't taught that" ? If the latter, and if it's something you believe they should know how to figure it out, then that should raise a red flag with you. These type of things will let you directly glimpse into how they are thinking and approaching problems. To be successful in high school, an 8th grader should be able to display a reasonable degree of problem solving and willingness to figure out something that they don't initially know how to do.

I'm not just saying this; I've tutored many high schoolers in math who were really struggling despite having been good students in middle school, and even having good grades in general in high school. Parents are always shocked and don't know what happened. I work with their kid and pretty quickly by far the most common patterns are a combination of: 1) They don't really understand basic fundamentals, i.e manipulating fractions, or basic algebraic skills, or 2) They cannot think beyond the examples the teacher gave in class; if a problem is even a little different they just shut down, which signifies a lack of any kind of problem solving ability.

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Anonymous wrote:Gawd some people's comments are so ignorant and uncaring. For some people (yes, that includes Asian and Eastern European immigrants), advanced/gifted/whatever you want to call them programs which judge fairly by merit are their refuge from the discrimination they'd otherwise be facing. It's also a refuge for the kids who have an IQ which is multiple standard deviations above the norm and who, as a result, get consistently misunderstood by society at large. I can't emphasize enough how unacceptable it is for people to even think that "who cares?" applies to this situation.

It’s a refuge for kids who are taught to game those tests too

Yes they game the test because the test is easy and a low bar filter. If you can't game the test in style by studying minimally for it, you don't belong in TJ. But once you get to TJ those type of tests mean nothing. You get to play with stuff that most kids don't see, even in college.

Such a stupid response. Gaming the test is all the tiger mom/dads excel at and teach their kids ! Glad the admission process is being changed. The amount of prepping that starts from Grade 1, the lobbying with teachers, the child being in every possible activity and class (music, art, dance, soccer, chess, school clubs) - its crazy ! lets kids be tiger parents. You being able to spend 1000s of dollars to prep your child and make him "excel" in every way does not make your child the brightest. Some of the AAP parent questionnaires are hilarious - one would think the child is gods gift to mankind and a miracle - excellent in every thing on earth !

Other than a full scale lottery, removing the test will not change the tiger behavior you described. In fact I would argue it will work in their favor for precisely the reason you described; i.e they will be gaming the subjective questionnaires (essays) replacements, which are clearly more gameable and BSable than a test.

Anonymous wrote:Hi, I’m doing a project and I was wondering if any teachers would like to chime in.

What are key curricular issues you have seen or feel exist nowadays in our area in particular or our country as a whole?

Bonus points if you also include issues that also affect learners with special needs.

I’m supposed to create a presentation to speak to the school board about specific curricular issues. Thank you in advance for your sweet and altruistic collaboration!

The main curricular issue (not just in high school) is the lack of proof and sound logic when forming an argument. This is especially true in math class where formulas are almost exclusively presented as cold hard facts without enough motivation, with derivations/intuitive justification happening very rarely. As one might expect, this leads the students (and teacher) into believing that math is all about math facts (hence the overused term "math facts", "learn your math facts", "we need to drill those math facts", etc.), when it's really about imagination, intuition, patterns, and creativity. Most students follow this line of gospel into adulthood, some decide to become teachers and propagate the "math phobia" to the next generation in an endless cycle.

Pedagogically, math is taught in a very sterile way, again using facts but offering very little key insights and justification for *why* the presented facts are actually true, how they fit together as a whole, and how they are connected to other parts of mathematics. Geometry, a critical and wonderful part of mathematics, is woefully absent from the curriculum; what passes for it in the one year students get to see it, is a dumbed down approach which instead of using the natural free form essay argument structure relies on an artificial "2 column proof" format, pigeonholing kids into believing that coming up with an argument/proof is akin to following a recipe, step by step. None of the delightful geometry proof problems that could be given to students are ever given, mainly because those problems would require too much of them according to the "educators", (or whoever created the silly curriculum), and they wouldn't nicely fit into their 2 column proof format. As a result students spend the bulk of their time unintuitively filling in blanks (in you guessed it, 2 column format), instead of actually learning how to form coherent geometrical arguments.

Calculators are used exclusively as a crutch instead as a tool for further exploration or to even check work. Students end up relying on them for everything, which over a long period of time reduces their natural number sense abilities. This is akin to walking around with a physical crutch all day despite your legs working perfectly fine. After a while of doing that, the gait and posture permanently change for the worse. This wonderful impact of calculators is nicely highlighted in AP calculus class (in high school considered as the highlight of math status and achievement, for some opaque reason), when juniors and seniors are taking the class but can barely do arithmetic at a high school level (and would certainly have no idea how to solve the most elementary problems given in modern middle school math contests).

I could go on and on, but if you really want a full picture said in an infinitely more elegant way than I could muster writing, you may want to consider spending two hours reading Lockhart's Lament. It is probably the most spot on summary assessment of the state of math education in the U.S that I have had the pleasure (and sorrow) of reading:

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

P.S: A whole essay could be written just on the ills of geometry class. This is even alluded to in a well known problem solving book with a chapter aptly titled "Geometry for Americans". https://ibb.co/KFRPZtP

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.

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:

Anonymous wrote:I am kind of concerned about this too, but then I ask myself “how did people think about grades during the Spanish flu pandemic?”

I think a sense of normalcy is important, but so is perspective. These are weird times. If we are healthy, we are okay. Nothing else matters that much.

Millions of people were dying dying the Spanish flu.

Only 3,000 Americans have covid 19. Do you know anyone dying? Do you know anyone critically ill? My guess is no.

That's because until now the "doubling" portion of the exponential curve has resulted in small totals (1, 2, 4, 8, 16, etc). But now that we've reached critical mass, each doubling will rapidly lead to millions and more. The current doubling rate seems to be about 2-3 days. I'll let you do the math, but under this same rate (assuming the social distancing doesn't work, or people don't follow it and this rate doesn't change), we'll hit a million in about 20-21 days, which is 3 weeks. I'm not taking into account the actual number of infections (which we don't know since testing so far has been minimal, but could be logically estimated at 10x or more).

Let's hope that everyone in the country assumes the level of individual responsibility they need to in order to put a dent in this curve.

Anonymous wrote:We have tried two and find them to be a marketing gimmick.

This is unhelpful without some specifics.