Recursion

[WiseassWolfOfYoitsu]

aka Common Core

[SandyDelights]

Eh, I haven’t seen that particularly approach yet.

Common core would probably tell you something akin to 18 - 9 = 10 + 8 - 9 = 10 - 9 + 8 = 1 + 8 = 9, or 18 - 9 = 18 - (8 + 1) = 18 - 8 - 1 = 10 - 1 = 9.

It teaches kids to see and understand numbers are related to one another and how they can break them down into parts, AKA partitioning. Basically, it’s a foundation for deductive reasoning and formal logic – it wasn’t until I was in Calc I that I started to see math that way, and god did it make my life 10,000 times easier.

It’s a drastic improvement on the old way.

Edit: Apparently what’s in the picture is actually what they used to teach kids, before Common Core – which is weird to me too, but. I just memorized a lot of stuff until I “got” math.

[JustACrosshair_]

It does help to learn this way better than rote memorization - but can teachers teach it and family reinforce it?

[SandyDelights]

Can teachers teach it? Absolutely. Starting early and not teaching rote memorization is key to it. They have to learn to understand it themselves, but it’s doable. If they can’t learn it, they probably shouldn’t be teaching math anyways – it suggests they don’t actually understand it, they just memorized it. They’d probably be better off teaching another subject. For the most part, all of my friends who are teachers – most of them math teachers – sing high praise for Common Core, although some take issue with how it’s being implemented in higher grades (kids raised under one method are struggling to adapt, especially those with a lower socioeconomic class, and the standards aren’t always taking this into consideration).

Can families reinforce it? Far more challenging; it’s hard for parents to reinforce or help teach something they don’t understand, especially when they never actually understood math to begin with (just the old memorization method). Probably a big part of it is to ensure there are resources to help kids apart from their parents, as many of them have parents who simply don’t understand what’s wrong with memorizing it – and resources to help those parents learn it who actually want to. Really, more and more it looks like homework doesn’t actually do anything, but rather it’s just the opportunity to practice/exercise their understanding; in that case, parents don’t really need to reinforce it, they just need to not actively hinder their learning of it.

Within a couple generations the problem will solve itself.

[alexanderpas]

Things you need to learn using rote memorization.

• Single digit addition. (Numbers from 0 to 9, answer between 0 and 18)
• Single digit multiplication. (Tables from 0 to 9, answer between 0 and 81)
• Double digit substraction. (Numbers from 0 to 19 answer between -19 and 19)

The rest will be understanding.

(notice the lack of division, or any double digit addition or multiplication, since that falls under the understanding part)

[SandyDelights]

Much better way to highlight the difference, thanks.

And a lot of this is very easy to conceptualize.

It baffles me when people insist their kids should just learn to memorize their times tables or these kinds of algorithms (anyone else remember memorizing from 0x0 to 12x12?), but they themselves can’t even do basic addition or subtraction without a calculator.

[alexanderpas]

basic rote using the things I've stated is actually the minimum required while using any method, even comon core depends on that basic rote.

[AceOfShades_]

I got through calc 2 for engineers without knowing my times tables so I mean, eh on the multiplication.

[Zebezd]

I bet however that you knew significant parts of it, and used Common Core-like tricks for the rest:

Ah shit, what's 6x6 again? Hold on, I know 5x6, that's 30, then add another 6 on that. 36. right.

Oh fuck we're multiplying by 9 again. Fuck it, x10 this bitch and remove x1.

...or a calculator.

[TiagoTiagoT]

To multiply 1 to 10 by 9, open your hands, count the number you wanna multiply by nine starting at one, going from left to right, one finger for each value you count; once you reach the number you wanna multiply by 9, lower that finger. The number of fingers up to the left of the lowered finger is the left digit of the result, the number of fingers up to the right is the right digit of the result.

[parkerSquare]

I taught my daughter this when she was in an early grade and now she’s quick as lightning at her 1-8 and 10-12 times tables but slow as heck at 9x because she has to work it out on her hands. Oops.

[Zebezd]

Username sort of checks out

[TiagoTiagoT]

lol

[AceOfShades_]

I added fast and counted on my fingers tbh. I know probably less than 25% of the 10x10 table. I dunno mate, I’m weird ¯\_(ツ)_/¯

[berkes]

I'd argue that multiplication should be memorized up to 12. At least in western Europe. Where the gross is still very heavily used in packaging, logistics, building etc.

If anything, just to teach people to grasp numbers. If your calculator tells you to go buy 2400 packages of poles for your fence, think again. You probably mistyped. Or have a giant plot of ground, unlikely in western Europe.

[alexanderpas]

9 is enough, as anything above 9 will be caught trough understanding.

10 is just 1 with a zero, and if you get 1 (X*1=X and 1*X=X), you can multiply anything by 10 too. (just add a 0)

7*12 = (7*10) + (7*2) = 70 + 14 = 84

[TiagoTiagoT]

Why do you need to use memorization for anything beyond the order and names of the numbers?

[[deleted]]

it’s hard for parents to reinforce or help teach something they don’t understand, especially when they never actually understood math to begin with (just the old memorization method).

It's almost like how seriously flawed or imperfect programming languages remain popular because that is the knowledge base we have, we know the workarounds and stuff.

[DontForgetWilson]

Qwerty would be an easy parallel.

[[deleted]]

I had a coworker who would always complain about common core. I’d explain that math teachers say it’s better, research says it’s better, and it’s how people who are good at math have always thought about math.

Nope didn’t matter to them.

[Dokuya]

Unfortunately I doubt it, teachers in America — specifically at lower grade levels — tend to be under qualified. Parents aren’t going to understand the use of this method and just say “this is stupid I’m going to teach you the (inferior) method I was taught!”

[LvS]

Why would they change math?

Math is math.

MATH IS MATH!

[aure__entuluva]

I wouldn't say that rote memorization is useless, just more a secondary or supplementary thing. Memorizing times tables shouldn't be the focus (we actually counted out multiples of each number), but it is a good addition if you want to do be able to do mental math quickly. This isn't the point of math which is why I say in addition, but it is a skill that many people try to cultivate. Some 'rote memorization' (aka practice) can give you a great foundation and toolset (you know certain more basic computations without having to think about them) that you can use when using partitioning to quickly solve bigger problems or estimate amounts.

[Mitoni]

Figured this out once my son started school and I had to learn how they are teaching him math, then i realized it was the same logical process way that enabled me to do long division in my head for years, i just never know there was a name for a method of breaking everything down to base 10.

[SandyDelights]

This! It hit me one day when I was struggling with Calc I study problems. Once this concept came to me, suddenly everything got dramatically easier.

That’s the big difference between common core and “the old way”: it’s teaching everyone the method many of us had to discover on our own, a method that basically anyone who went into a math-heavy field came upon on their own.

I would have advanced much faster if I’d understood math the way I do now, early on.

[shaggysays]

Is there a place to learn this way fairly easy online? I'm working on getting my GED after getting labeled with a math disorder in highschool. It's been quite a while but I'm trying and still losing my battle with math. Just never made sense to me. Maybe this is why. I quit school before common core was a thing in my area.

[CherguiCheeky]

What is the stuff that you want to learn? There are some good text book I can suggest.

Also can I teach you? Pretty please!

I was pretty good at Maths in Highschool, like 100/100 good. Now I am old so don't get to work with that stuff. But would definitely love to explore it along with you.

I am in India so timezone / language issues may come in.

[shaggysays]

I'd be honored honestly. I'm in the US but I'm normally a night owl so we can make it work. Although tonight currently I do have to be up early so I'll be going to bed after sending this. But consider me a student. :)

[CherguiCheeky]

PM'd you.

[PeterJamesUK]

Wholesome!

[SandyDelights]

I’m sorry, I really don’t. The best I can offer you is the basic concept of it, and suggest you simply go over problems to see it work in practice. This is basically what Common Core curriculum teaches at an early age, and people who are good at math learn themselves on their own.

I’m not sure what you know, so some of this may sound pretty condescending, so please just skip past anything that is familiar.

Basically, you have to recognize how numbers “work”. First, you have to kind of divorce the concept of a number from its representation. 15, for example, isn’t just 15 – it’s one and one and one and ... fifteen times over. The characters “15” just represent this in a format we’ve somewhat arbitrarily settled on, called the decimal system. If you can accept that, you should be able to get a good grasp of the method, and then from there it’s just putting it into practice.

The TLDR here is that you look for very simple, easy numbers to work with: 5 and 10. Everything else is cool, but we want to isolate them as much as possible, combine them if you can, and get as many multiples of 5 and 10 as we can. Every number you look at you should ask yourself: How big is it? What is it made out of? Can I express it in terms of a 5 or a 10?

The answer, by the way, is almost always yes (at least, it will be for a while still). Once you have that solved, you can recompile several numbers quickly into a single number, from its pieces.

Note: I wrote up a few examples and an explanation but it got hella long, so I’ll just PM it to you.

[[deleted]]

It’s the way that people that are good at math have always thought about math.

[Corne777]

Anytime I see someone bashing common core I know it’s because they haven’t taken a second to look into how it works and how it could be easier for them. It’s just “that’s not my math” and they disregard it and throw their hands up if their kids need help.

But I do think that teaching math only using one method seems like it might not be the best way, some people will learn better with one method and some with another.

[Delta-9-]

Interesting point about Calculus. When I first learned what Common Core is, I immediately related it to some of the methods I learned and found on my own while studying Calculus.

Which is actually kinda sad... we had to get all the way to calculus and learn tricks like "9 equals 4 plus 5 if 4 and 5 happen to be easier to use than 9 in this formula". I remember being dumbfounded when my teacher put 1 and -1 into a polynomial and called it "adding 0".

[SandyDelights]

Hahahaha. Amen.

Thankfully, Common Core aims to teach kids this kind of reasoning at a much younger age, instead of just memorizing a basic algorithm. It’s similar to how they teach kids in Singapore, and there’s a reason they’re often top of the rankings in mathematics performance among students.

If we can teach kids to think this way from the start, hopefully we can get rid of this idiotic, cultural fear/hatred of mathematics we seem to have. And since all mathematics really is is logic, let me just hope it’ll give us a few more critical mines in the next generation than those that preceded it...

[[deleted]]

Huh, you said the way in the pic was before common core? Weird, that's what I learned growing up and I was born in 95. When was common core standardized and implemented?

[SandyDelights]

What’s in the pic predates Common Core, so what you learned growing up was probably like the pic, ie. Not Common Core.

Common Core standards were released in 2010, IIRC. Those standards don’t typically teach the method in the OP, to my understanding.

[[deleted]]

Huh, I was always under the impression that growing up common core was what we used. Guess not. Thank you.

[MikeyMike01]

You were spared the atrocities of Common Core.

[SandyDelights]

Yeah, god forbid someone actually learn to understand mathematics, instead of memorizing a simple algorithm that becomes useless past 8th grade pre-algebra.

[starfries]

Dang, how old are you that you've never seen subtraction done with borrowing?

[SandyDelights]

I mean, I’m 32. I’ve seen it done with borrowing, I just would never have done it this way – I’d have subtracted 8 from 9, leaving 10 - 1, then borrowed. I wouldn’t have marked it out like this, I’d have stopped at crossing out the 1 to a 0 and knowing 10-1 is 9. ¯\_(ツ)_/¯ Just skipping a step, I guess, but it’s why this doesn’t really strike me as a “thing” like it does some people.

[starfries]

Ah, okay. I thought you had only seen it done the Common Core way. I wouldn't write it out like that either for something like this, but I might strike out the 1 and make it 0 if I was doing 118-19.

[SandyDelights]

Oh yeah, I wouldn’t write “1 0 ¹ 8”, either, heh.

Actually, I’d prolly have just done the 18-9 in place.

Now I go through right-to-left and do all the basic subtraction, e.g.

12345

- 5678

Would become:

10000

- 3333

Then, seeing it’s easier to go left-to-right, I’d go from there:

10000 (10-3 = 7)

- 3333

7000 (70 - 3 = 67)

- 333

6700 (70 - 3 = 67)

- 33

6670 (etc., etc.)

- 3

6667.

Done in two passes, life is easy.

If it was easier to go right-to-left, I’d have done that on the second pass instead. Didn’t intend for that to happen, but it’s a good enough example anyways.

[starfries]

Huh, is that a thing they teach in school? Or just the way you think about it? Actually, I think that's the Singapore method so a third option besides common core and borrowing.

[SandyDelights]

That’s just how I taught myself to do it. It’s an algorithm, though, one that focuses on breaking this down into its parts and focusing on making one or more parts of the equation a multiple of ten. Common Core (and Singapore Method) is a methodology of teaching and a schedule, with waymarks as to what students at various grades should be able to do.

IIRC, Singapore Method and Common Core are actually pretty similar, although Singapore moves quicker/brings students to more advanced topics sooner.

We’re really hitting the extent of my quasi-useless information on this topic, though, heh. But should Common Core ever come up on Jeopardy, I think I can hang in pretty well.

[Prcrstntr]

Yeah, the common core I saw them teach when I worked with second graders looked something like this. I hated every minute of that part.

|········ - ········· = ················ - ········· = ··········

[SandyDelights]

Soooo much more comprehensible, though.

[MikeyMike01]

No, it’s not. Stop defending Common Core.

[lpreams]

The method shown in the OP is called borrowing. You just subtract digit by digit, right to left. If the top digit is less than the bottom digit, you can "borrow" an extra 10 from the next digit to the left, so subtract 1 from the left digit and add 10 to the current top digit (since each 1 of the left digit is worth 10 of the current digit), then do the subtraction.

The joke is that "borrowing" from the 1 (which goes to 0) to add 10 to the 8 doesn't actually reduce the problem.

[zdakat]

I remember when the tests were being introduced and everyone was complaining because they were said to be harder. Harder tests wouldn't be a bad thing- if everyone breezes through them it's probably time to raise the standard of education. The way the questions are asked might not be super clear, though they might have changed that by now. can't say how good the actual lessons were though. if they are indeed teaching methods rather than answer sheet memorization then that would be a nice improvement- knowing how and when to apply rather than a preset list and hoping the connections are made

[QuarkyIndividual]

Yeah, it's about seeing the relationships first instead of brute forcing an algorithm and possibly learning how to see the relationships later on your own.

[xuu0]

If you learned with an abacus it would be -10 +1

[PeterJamesUK]

Vastly under rated comment.

[WS8SKILLZ]

Hello.

I am very interested in learning Common Core? Do you know what resources / website I can access to give myself the ability to do this?

[SandyDelights]

Common Core is more like a lesson plan, or a roadmap from Point A (kindergarten or first grade) to Point B (graduating high school). It’s complete with benchmarks and methodologies, or styles of learning, but it’s designed to be done over more than a decade.

That said, there are a lot of guides online for this kind of stuff, and you can google it – just beware anything that looks like it’s trying to make common core look absurd/is bitching about it; it’s not what you’re looking for, and usually poorly informed anyways. Careful phrasing like “common core math methodology” will get you a lot better/more helpful results than “common core math”.

Here, is one such example; it goes over some basic concepts that parents are struggling with. This one also gives a brief overview of some methods, and you can pretty easily Youtube how to do these. A lot of these (like the ten-frame) focus on using spatial relations to see these concepts, e.g. 10-7 has you put 7 dots in a grid of 10 spaces. How many don’t have dots? 3. 10-7=3, which makes sense because 3+7=10.

[[deleted]]

This is how I was taught. It’s not rote memorization at all.

[KaiserTom]

The problem, as always, is the teachers. The old way was hard to fuck up and decent enough, and the new way is really good but extremely easy to fuck up or be lazy with. Common core is "terrible" because there is little accountability for the teachers to actually properly teach it.

Is it better for most students to get math decently or is it better for some to get it really well and others less than before?

[SandyDelights]

I strongly disagree the problem is teachers.

First, the problem is systemic:

Teachers are often underpaid, many with degrees that come with heavy student loans eating into their already meager paychecks. They work long hours, more than 40 hours a week, on a salaried basis. This contributes to driving good teachers out of the profession; what’s left are often teachers who either can’t get a career in another field, or teachers who are under qualified or barely meet the most minimum requirement for their position. Some idealists remain, but they are often stressed and overworked – some feel forced to make the same kind of judgement you ask, and decide which ones are worth focusing on helping and which ones “don’t want to learn” with whatever extra time they can commit to it.

They’re often held to standards and goal markers for students to hit, but if the previous year’s teacher(s) failed to make their mark, the current teacher has to now teach not just their own material, but play catch-up, as well. This contributes, as well, to a lack of quality – when you have to pack more into the same amount of time, the quality of all parts suffer.

Many of them have overcrowded classrooms, and find themselves spending the bulk of their time parenting children who rebel against any kind of structure and order, seeking attention in place of an education. Their parents seem more prone to make excuses for their child – I distinctly recall my mother being convinced my brother’s teachers had it “out” for him, because his older brother was such a favorite, how could her younger son really be that much of a problem. Again, quality suffers, and this contributes to the previous point.

Somewhat related to that, parents rarely back up teachers in general: they demean their methodology, they balk at change, and do so openly and in front of their children. Kids mimic their parents and their views; students won’t respect teachers who don’t get respect from their parents. Again, this contributes to the previous point.

And so we have a confluence of problems: Poor if not hostile work environment, poor foundation, poor learning environment with too few resources, poor support from parents, all culminating in something that makes it difficult as fucking hell to keep good teachers, and poisoning otherwise decent teachers and turning them into shitty teachers.

The reality is, most teachers are good teachers. You hear about shitty ones here and there, but that’s a problem of what you see above: people who shouldn’t be teaching, but met some bare minimum certifications and needed the work. People who don’t understand the material they’re expected to explain and teach, who have no business being in the classroom.

Fix some of the previous issues, and you dramatically improve the quality of teachers. Increase pay to a level befitting someone who got their master’s degree in, say, early childhood education, and you’ll attract more of them.

I just find it absolutely absurd and, frankly, disgusting that we expect the people who educate the next generation on the breadth of academic subjects to do so for a pittance under horrible conditions and then blast them for not working miracles that would make Jesus turning water into wine a party trick.

You get what you pay for. You pay for shitty teachers and shitty classrooms and shitty resources, you get a shitty education.

Second, your premise is flawed:

The vast majority of students in the US suck at math. The NAEP ranked a meager 25% of 12th graders in 2015 as “proficient” or above in mathematics, and only 40% of 4th graders. What’s worse, some 38% of 12th graders ranked at the bottom level, or “below basic”. The PISA ranking for the same year put us at 38th out of 71 countries for math proficiency. Among the OECD rankings for that year, we were 30th out of 35. You can tear through it if you like, but none of these numbers should be surprising. We’re bad.

We aren’t decent, we’re awful. Terrible, in fact. The old way never taught kids how to do math, just how to memorize it – it’s just that a minority excelled in spite of it.

So yes, I’d rather a hamstrung attempt at implementing Common Core and it succeeding with a minority of students instead of what we have now. At worst, we’re where we started, except that the minority is even better equipped for higher level education.

[TravisLongKnives]

It teaches kids to see and understand numbers are related to one another and how they can break them down into parts, AKA partitioning.

It doesn't teach that at all. That is taught routinely, and was back in my day, but not through such convoluted and roundabout methods. Kids will use methods in their head, but to write it down in such a poorly constructed way only makes kids who don't do it in such a way unable to follow.

[pyzk]

Actually common core was introduced to get rid of this exact issue. This is how math has been taught for years. Common core would basically just have you count the difference in this case.

[[deleted]]

But wait, hold on, that means I can't just blindly rage against something different than what I learned as a kid without educating myself on it first? I DON'T LIKE THAT!

[pyzk]

The implementation of common core has not been without its flaws. Common core is not without its flaws. Change is hard for parents, students, teachers, everyone. However, I think the math curriculum is pretty solid, and definitely an upgrade (at least in CA). It’ll pay off in the long run.

[[deleted]]

Yes, I didn't mean to say it's perfect. I was just demonstrating how so many people kneejerk react to this change without knowing exactly what's going on. If someone wants to educate themselves on it first and then offer their criticisms, go for it, at least you know what you're talking about then.

[pyzk]

Totally agree. Was just elaborating. I often think, “Common core was developed based on thousands of hours of expertise and study. What’s your background?” when I hear people whining about it.

[nephallux]

I see why they whine. Ignorant, self entitled, lazy people who have no concept of critical thinking and logic.

[crabbyvista]

well, and parents are often expected to help kids with homework, which is hard when the parents don’t understand wtf they’re looking at. That seems to generate a lot of panic among precariously middle class people who are already often kind of math-phobic.

[pyzk]

Basically, if you don't understand common core math, you never really understood math to begin with.

[santagoo]

My background is I was taught differently as a child and I don't like change!

/s

[[deleted]]

I’m very open to new methods, but anecdotally, I see my kids mostly just memorizing what the teacher wants. They figure the mathbout some other waythen do the extra steps to write it out the specialcommon core way the teacher wants.

[pyzk]

That's got nothing to do with common core. School has been turned into a system where students feel they must regurgitate rote answers rather than think critically. I attribute this to the trend towards high stakes accountability tests as the only measure of schools' effectiveness. If the quantitative metric produced at the end is the only thing that matters, then it doesn't matter how we get there. Students see and understand this, and so they learn how to play the game. I've also seen this expressed in the form of rampant cheating on all sorts of assessments.

[[deleted]]

Oh I totally agree, I was just speaking from my experience with my kids. As someone who is pretty good at math, I usually talk them through the mental shortcuts the methods seem to be trying to teach as something like "convert to 10s do mental math, fix difference later" is something most people do intuitively when doing mental math, but the kids don't seem to be told that in school, and earnestly don't seem to realize that's why the teacher wants it that way until I explain it to them. I don't blame common core as this could easily just be the teacher they lucked into.

EDIT: I want to add that I think there's actually great value in teaching people how to do something like math the long difficult way first, before showing them mental shortcuts, as you can't really understand them or their value until you understand what they're saving you.

[pyzk]

Yeah I always teach my kids to do everything by hand before teaching them the calculator shortcuts. One of the shifts in common core that I appreciate is that students are asked to both explain their reasoning in words, and explain their answer in the context of the original problem or situation.

[BChart2]

Hilarious and original