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Comment by bstar77 | Hacker News Reader

I've been home schooling my son for the past 3 years. The reason why it's "too hard" is because the traditional model of learning in public schools (in the US) translates very poorly to home schooling. Once you stop focusing on grooming for optimal test-taking, a whole world opens up.

Additionally, we don't do common core in our household, so my wife and I have no issues teaching my son math (we settled on Saxon math). I neither have the time nor energy to learn common core math in order to support my son.

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My experience with common core has been pretty awesome FWIW. I didn’t see some of the stuff our daughter did in first and second grade till the end of high school and college. No more rote arithmetic applications, it presses for actual comprehension of the material from multiple angles. Challenging, but sometimes even fun for those not mathematically inclined.

Yeah, a lot of the hate I saw for common core (I'm a high school math/physics teacher) comes from a lack of number sense on the adults trying to understand it. Like, I saw parents who were complaining about breaking 634x127 into (600+30+4)(100+20+7) because they didn't understand you can break it up like that and it makes it a bit easier to do the multiplication, then you can just sum the resuts.

Sadly, a lot of the elementary school teachers I've encountered also lack that number sense, and some even detest(ed) math. And yet we're asking them to teach it to our kids. I'm not for charter schools usually, but I'd really love to start a charter elementary school where each subject is taught by someone trained in that subject and then with, say, a MAT in elementary ed, as opposed to just a bachelors in elementary ed. I wonder how much better kids would do in math and reading especially, when they have teachers who appreciate math and who like to study literature and read for its own sake.

> breaking 634x127 into (600+30+4)(100+20+7)

For some people, this is simply too abstract. You can teach children the breakout method or normal method, their understanding doesn't change. They're just memorizing one procedure over another. The ability to analyze how to operations work doesn't improve with common core, it's just more steps.

I've seen this first hand. I taught long division to a younger family member that was struggling with whatever nonsense method common core cooked up (something about boxes and dots and circling stuff). They had literally never seen long division, I taught them to divide the same numbers they had on the page in front of them in less than 10 minutes, and they could arrive at the correct answer consistently. I asked the kid to explain the procedure of what they were doing for the common core, they had no idea and lacked the ability to articulate the process whatsoever.

> You can teach children the breakout method or normal method, their understanding doesn't change

Adults utterly confused about (600+30+4)(100+20+7) do prove that they did not understood what is going on. The follow the algorithm, but don't know how to do expressions. And they have been taught the old method.

Also, this (600+30+4)(100+20+7) not be too abstract for average intelligence adult.

I think it's quite possible that your view of 'average' is skewed. Again, you can teach (600+30+4)(100+20+7) but they're not going to understand why it works. They're just going to memorize the steps because that's what someone showed them. That's why common core is a failure. It's a more complex series of steps to arrive at the same result.

If you don't understand that 634 = 600+30+4 or don't understand how parenthesis works by the time you are 12 and you are average or somewhat bellow intelligence, your school system failed you.

The addition is simple. As soon as you tell someone that 62 * 20 is the same as 60 * 20 + 2 * 20, you lose them. Try it out and see for yourself.

Not if you draw the picture. A rectangle with height divided into 60 and 2, width 20. Then it's obvious the total area is the sum of the two parts. My kids got very comfortable early on with that notation. Switching to the standard algorithm was tough, even after they understood why it was equivalent, because the diagram just makes so much more sense.

Or you could even just build it up from basics, which is how I would expect it to be done. It's clear that 220 is the same as 120+120, then you can show that 320 = 220+120, etc etc. If they learn it that way at first, it should be clear to them that (60+2)(20) = 6020+220.

>> I've seen this first hand. I taught long division to a younger family member that was struggling with whatever nonsense method common core cooked up (something about boxes and dots and circling stuff).

Yeah, this is happening to my oldest child - they're on multiplication and division and when I showed them short and long division, they had no idea what I was doing. Common core mathematics is far more memorization and repetition. You don't derive how to actually solve the problem. It's shocking to me that this is the sole method we're teaching kids.

EDIT: And I actually like the Common Core methodology. But it's very mathematically incomplete.

wtf -- you're 100% wrong. Common Core exactly shows you how to solve problems. It precisely does not focus on rote memorization. Yes, you need to memorize "math facts", but this is limited to simple multiplication tables (and similar). The entire point of Common Core is to teach multiple algorithms by which students can solve problems for which they recognize the pattern.

Back in the 90s, when I was in school, I don't recall this kind of rigor in math at all until I got to Calc 2 and needed to actually focus on memorizing patterns & rules for solving integrals. Everything, at that time, was rote memorization.

> It precisely does not focus on rote memorization.

This is where the disconnect is. It may have very well been designed with that goal in mind, but common core is is memorization in another form. The form of memorization is worse than the traditional form because it involves more steps, and the steps are very unintuitive.

I don't think kids will be able to explain why it works. They might be able to recite definitions and phrases that they were forced to memorize, but they won't be able to put it into their own words. I know, because I've seen it first hand from a kid I consider to be bright. We can blame parents, we can blame teachers, but it doesn't matter. Common core is not optimized or appropriate for childhood education in the US.

> Common core is not optimized or appropriate for childhood education in the US.

Then maybe the problem is with the teachers/parents and not the Common Core? Of course the kids won't understand it if their teachers don't understand it. Just like kids won't enjoy/understand reading if their teachers don't read and talk about reading, etc.

>> recognize the pattern

>> solve problems

These are incompatible, which is what I am saying and the parent above my comment is also saying.

>> simple multiplication tables (and similar)

If you fail to memorize these, you can derive the answer using your fallback to addition, which you've been shown how to do. In Common Core textbooks and in the class my oldest is in, these are assumed facts. Breaking down how to derive multiplication and division is at least a failure of the teacher in the class, if not the methodology, though I suspect the teacher is pretty good.

Common Core relies on a lot of memorization and pattern matching. This is fine, and good for everyday use. It is not learning it from first principles, which makes it hard when your pattern matching engine isn't working properly.

Both methods should be taught in an integrated fashion. I support Common Core - and have for a long time - as an adjunct. Not as the primary method of teaching math. Most kids will find Common Core easier, I'll readily admit that. It also has better carryover to everyday use, as I've already admitted. But it lacks rigor.

>> Back in the 90s, when I was in school, I don't recall this kind of rigor in math at all until I got to Calc 2

We're likely the same age. My arithmetic classes were far more rigorous than most of my mathematics classes beyond that up until Linear Algebra.

> I saw parents who were complaining about breaking 634x127 into (600+30+4)(100+20+7) because they didn't understand you can break it up like that and it makes it a bit easier to do the multiplication, then you can just sum the resuts.

That's just a more explicit explanation of multiplication in pre-common core math. It's just a different explanation for the same thing.

That's exactly the problem though. Parents and some teachers don't realize that. They have no clue what they're actually doing, they just follow the algorithm. Which means they have no number sense either, and don't get that they can break up into easier to solve ways and play around with numbers.

> and some teachers

I guess these are third grade teachers, so maybe it's not a big deal, but WTF?

No, it's an extremely big deal as they're the ones tasked with teaching kids how to do it. Blind leading the blind, and so they just memorize whatever new algorithm there is with no explanation from the teacher as to why it works, because the teacher themselves don't know! It makes it a real pain in the ass when they get to high school and try to work with variables, as they have no clue how numbers work.

I'm unsure of what everyone's concern with common core is. It was way easier to teach my kid's once I realized that it's just what I've always been doing in my head without anyone telling me to.

It's just about breaking apart problems into digestible pieces.

I don't have a problem with common core, I like that kids gets to see all the different ways to solve a problem. The problem I see is that schools are testing all the different methods instead of asking the students to use the method to solve the problem.

There's some value in that. Not as a long term principle, but I am all for having students learn a variety of methods and have to spend some time working through those methods. But only to make sure the students are giving the different methods a shot and actually finding the one that makes the most sense to them, rather than just sticking with whatever was learned first. If they're never given the chance to just work with their method of choice after, it's pointless.

This is a great point. I found myself both admiring and hating some of my son's school work recently in that it illustrated and described mental problem solving exceptionally well, then gruelingly pushed him to repeatedly explain the model rather than simply use it. Pages upon pages of dissection and regurgitation. My son could understand the model just fine, but was perplexed as to why he had to go over it like that.

That's because public school uses memorization as a cheap stand-in for understanding. It's easy to internalize 2+2=4, but it's impossible to internalize the quadratic equation. At some point, you need to just know the procedure and it's application, and most importantly, recognize when to use it in novel situations.

It took about a one paragraph explanation to not only realize this is how I already do things in my head, but to suddenly become much better at it because I can now slow down and conceptualize the whole process when necessary.

I learned math in the "traditional" method through several levels of calculus in college (decades ago) and found a young relative's common core math curriculum to be extremely cumbersome and far more confusing for the student. In my opinion its far better to teach a student to understand a mathematical principle than to force them to absorb your prescribed method of understanding. You could know a mathematical principle backwards and forwards and be an expert in the field and still end up baffled at the nonsensical "core curriculum" methods and jargon.

a large segment of the population would have to come to grips with the fact that they didn't understand their math classes.

Math education in the U.S. is notoriously behind the rest of the world. It's about time. Speaking as someone who barely passed undergrad calculus and still has nightmares from that 7 problem 4 hour final exam.

Honestly, a lot of it is because of elementary school teachers in my opinion. I don't want to bash them too much, but they often struggle(d) with math. They don't have much of a number sense, and now we're asking them to teach our kids how to have number sense (which is what common core does; it shows that 65+37 = 70+32, etc etc). I actually remember my 6th grade math teacher specifically for this reason. She explained things to us in a way that gave us number sense, instead of just memorizing rote steps. It made my math skills so much better, and I'm still thankful for that today. Sadly, it was only one teacher at the entire school.

I'd love to start a charter elementary school (as much as I generally dislike the concept of a school getting state/federal funding with no testing accountability) where each subject is taught by someone who actually studied the subject, not just "elementary education". Then you might see kids enjoy math and understand it, as their teachers understand and enjoy it and can teach that; it's infectious. I wouldn't be surprised if reading scores also raised when kids are taught by people who clearly enjoy reading and are passionate about reading.

I think math is taught too slow in the U.S.. I remember learning to add, then once I got whatever score on the flash card assessment I got to learn to subtract, then multiply, then divide. Slowly, painfully, and in a way that leaves you bored early, causing you to checkout and fall behind, then you are left wondering why you suck at math later in life.

I think we could stand to move the math curriculum up 3-4 years. Geometry and trigonometry can be taken in 5th grade instead of 9th, algrebra 1-2 in 6-7th grade, then calc in 8th grade, instead of waiting until high school to take these courses. Then in high school, you could offer advanced courses and an actual course progression in statistics, rather than solely AP stats.

Tone down the difficulty, maybe, but there is no reason why these concepts shouldn't be introduced a lot sooner. Basic algebra is pretty intuitive, and in geometry classes you are kinda just plugging and chugging sines and cosines with your calculator anyway. This is coming from someone who sucks at math and wishes they didn't.

In the 6th grade, you were mentally developed enough to understand some of the basic concepts of algebra. Someone (most) in the 3rd or 4th grade isn't developed enough to understand those concepts. This would be analogous to teaching elementary school students latin roots, it just doesn't make much sense, and their ability to dissect particular words is of little to no value at that stage in their development.

This isn't true. Kids start learning algebraic concepts in roughly 2nd grade, and are well-acquainted with the concept of variables, algorithms, order of operations, roots & exponents, converting fractions to decimals & vice versa, etc before they get out of 5th grade. The only fundamental key concept I don't think they're taught, that is critical in algebra 1, is how to solve systems of equations.

> (which is what common core does; it shows that 65+37 = 70+32, etc etc)

I did automatically 90+12 and I am old. How would common core improve my mathing?

It wouldn't improve yours if you're doing that, but the point of it is to teach the kids number sense and how numbers work and can be manipulated to make problems easier.

Do you both work?

I've seen parents try to work from home remotely, while also taking care of and schooling their kids, and it seems like a nightmare.

Nightmare is a strong word, but it is very hard. We have a 3yo, a 3rd grader and a 5th grader. If it weren't for the 3yo we'd probably be in decent shape because our kids are generally pretty mature and well-adjusted, and academically competent. That said, they've had to not just focus on continuing to learn the curriculum, but also learn a bunch of new tools (with little help), and also learn to type because handwriting isn't really an option anymore. They're struggling through the "this is the first time I'm alone with a computer" growing pains. The toddler is the real monkey wrench, to the point where I've started trying to split the older kids' schedules so one focuses on school in the morning and the other in the afternoon, and they split time interacting with their little sister. It's not remotely fair to anyone and I feel horribly guilty about it, but it's where we are right now and everyone's making the best of it.

A 3 year old doesn't need self-directed on-computer lessons...

Right. The older ones do but their little sister is running amok in everyone's business. That's the real challenge.

Yeah, that's where I am at. My partner works full-time (1-2 days in the office, the rest remote), and I work two full-time jobs (my company + another FT job) remotely, with no childcare.

Our lives/schedules were built around 20 hours of childcare/school per week, and without it, it's been a nightmare. Productivity is at an all-time low. Not really sure what to do about it.

No. I'm a remote software developer and my wife is a mom. We optimized our life to be able to do this effectively and have complete freedom. Took a while to get to this point, but we're there and enjoying the rewards.

Its a pain, but it can be managed, specially if the teaching methods are adapted to the situation.

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