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[AgeEighty]

It makes sense, but common core can fuck off. I despise over-complication in all aspects of my life. For math, I always hated showing my work because I could easily and quickly do math problems in my head. I was the only kid in my class that would do math assignments in class without a calculator, and I was always the first one to turn in my papers. I'd still show my work when necessary, but it was just a waste of time for me. If I had to do common core, I probably would've dropped out, no joke. Fuck drawing diagrams to subtract two numbers. These kids are going to be lost in the real world. They're going to get paralysis by over analysis. They'll get a thousand yard stare on their face if you ask them to give you change for a 5 dollar bill because they'll be trying to visualize a damn diagram to figure it out.

You say it's ridiculous for kids to learn subtraction with diagrams they need pencil and paper for, but this:

is exactly that. It's a diagram. You can't easily do addition, subtraction, or multiplication this way in your head, lining up columns, subtracting them one by one and carrying tens digits. You'd quickly get lost. It only works with a pencil and paper, which is exactly why so many of today's adults are already "lost in the real world", as you say.

You were the type of kid who could do problems in his head, without a calculator and without using the methods they were teaching you. So was I! I feel your pain. That's because you figured out your own way for working out the math that didn't require writing it down.

And that's what this Common Core math is trying to teach all kids: the very same methods that you and I figured out on our own. That's the whole point: unlike the old methods for doing math, once mastered, these new ones don't require a kid to have a pencil and paper. Because they're the same methods you and I used in our heads.

The diagrams are only there to help the kids who aren't as instinctively good with numbers as you and I were: to help them visualize the in-your-head method for doing math and show they understand it. Unlike the one in the picture above, these diagrams aren't designed to be leaned on for life; they're training wheels.

 

[numble]

Ok, that might not have been the best example, but I think you get what I'm saying.

I don't think so, because that seems to be a real-world example of why its helpful to think in this different fashion.

 

[terribletwo]

I pity you guys. Glad that that shit wouldn't fly over here.

the system we have now where basically no one can calculate a 15% tip in their head because they don't get base 10 is definitely ideal
granted other countries have solved this problem by eliminating tipping, but that's another thread

 

[neurosisxeno]

the system we have now where basically no one can calculate a 15% tip in their head because they don't get base 10 is definitely ideal

Yea, that's a great example of how mediocre the average person understanding of mathematics is. It's a real struggle watching people try and calculate a tip these days...

 

[m3k]

Haha we teach these or similar strategies in Australia but we focus on the traditional methods as we get into highschool

 

[twobear]

i don't see what the hullabaloo over 'common core' is, it seems to me that it's more about teaching about how to mentally manipulate numbers. the 'old fashioned' way is faster, but it doesn't necessarily make it transparent how or why it works.

 

[Ayt]

You say it's ridiculous for kids to learn subtraction with diagrams they need pencil and paper for, but this:

is exactly that. It's a diagram. You can't easily do addition, subtraction, or multiplication this way in your head, lining up columns, subtracting them one by one and carrying tens digits. You'd quickly get lost. It only works with a pencil and paper, which is exactly why so many of today's adults are already "lost in the real world", as you say.

You were the type of kid who could do problems in his head, without a calculator and without using the methods they were teaching you. So was I! I feel your pain. That's because you figured out your own way for working out the math that didn't require writing it down.

And that's what this Common Core math is trying to teach all kids: the very same methods that you and I figured out on our own. That's the whole point: unlike the old methods for doing math, once mastered, these new ones don't require a kid to have a pencil and paper. Because they're the same methods you and I used in our heads.

The diagrams are only there to help the kids who aren't as instinctively good with numbers as you and I were: to help them visualize the in-your-head method for doing math and show they understand it. Unlike the one in the picture above, these diagrams aren't designed to be leaned on for life; they're training wheels.

It is amazing the number of people who can't grasp this simple concept.

 

[oti]

Common Core is used anywhere in Europe? Or rather, anywhere, but the USA?

I had never heard of this CC nonsense before this thread.

 

[Maengun1]

I keep seeing these "common core" threads here, I've honestly never heard of it anywhere else. I get (now) that it's some new teaching thing, but no matter how many times I look at these things I can never figure out what it's even asking me to do, let alone the answer. It might as well be in Greek.

Thank god I don't have kids to bring this crap home from school for me. I sucked at regular math.

 

[zoukka]

I look at this image, and I realize I haven't known how to subtract the "right" way since elementary school.

That method was never very intuitive for me, and I do something mentally that's more similar to one of the other methods that Common Core teaches (can't remember which in particular).

Yeah I solved math problems in my head kinda like that common core image, more visually I guess. I was usually faster than anyone else too.

But everyone needs to cram to the same square I guess.

 

[User 406]

These threads are essentially a testament to just how lacking American math education has been before now.

 

[sprsk]

These threads are essentially a testament to just how lacking American math education has been before now.

Right?

I don't see the problem with teaching kids all different kinds of approaches to math.

I was one of those kids who hated math because to me it didn't make sense. It wasn't until an adult I started pulling numbers apart and making things much easier for myself. It makes total sense to do it that way cause ain't no way I'm gonna keep track of all the carry the 2's and all that bullshit in my head.

What they should do though is have workshops for parents to explain to them why things are being taught this way and how they can help their children understand the systems.

I'm tired of hearing about it on my facebook from my idiot high school acquaintances.

 

[Baron Aloha]

You can't easily do addition, subtraction, or multiplication this way in your head, lining up columns, subtracting them one by one and carrying tens digits. You'd quickly get lost. It only works with a pencil and paper, which is exactly why so many of today's adults are already "lost in the real world", as you say.

That's the way I've always done it. It's not hard.

 

[crazy monkey]

fuck common core. I will teach my kid traditional way. i think it has worked out fine.

 

[Number_6]

It makes sense, but common core can fuck off. I despise over-complication in all aspects of my life. For math, I always hated showing my work because I could easily and quickly do math problems in my head. I was the only kid in my class that would do math assignments in class without a calculator, and I was always the first one to turn in my papers. I'd still show my work when necessary, but it was just a waste of time for me. If I had to do common core, I probably would've dropped out, no joke. Fuck drawing diagrams to subtract two numbers. These kids are going to be lost in the real world. They're going to get paralysis by over analysis. They'll get a thousand yard stare on their face if you ask them to give you change for a 5 dollar bill because they'll be trying to visualize a damn diagram to figure it out.

High school math teacher here. You show your work so that just in case you get it wrong your teacher will know how to help you. A teacher isn't supposed to just take your word that you understand. Evidence of mastery must be collected and documented, especially these days with teachers under fire.

As for your other points...

You say it's ridiculous for kids to learn subtraction with diagrams they need pencil and paper for, but this:

is exactly that. It's a diagram. You can't easily do addition, subtraction, or multiplication this way in your head, lining up columns, subtracting them one by one and carrying tens digits. You'd quickly get lost. It only works with a pencil and paper, which is exactly why so many of today's adults are already "lost in the real world", as you say.

You were the type of kid who could do problems in his head, without a calculator and without using the methods they were teaching you. So was I! I feel your pain. That's because you figured out your own way for working out the math that didn't require writing it down.

And that's what this Common Core math is trying to teach all kids: the very same methods that you and I figured out on our own. That's the whole point: unlike the old methods for doing math, once mastered, these new ones don't require a kid to have a pencil and paper. Because they're the same methods you and I used in our heads.

The diagrams are only there to help the kids who aren't as instinctively good with numbers as you and I were: to help them visualize the in-your-head method for doing math and show they understand it. Unlike the one in the picture above, these diagrams aren't designed to be leaned on for life; they're training wheels.

Hero^

 

[DerangedHermit]

I've come to the conclusion that Common Core is actually too complicated. I mean, after seeing all the self-proclaimed math savants, back in the day of course, claiming it's too hard to understand.

 

[ElectricBlanketFire]

I'm curious why you had to pay the court...

Wife changing her last name.

 

[maniac-kun]

In Germany we didnt learn this. We used math.

 

[tanooki27]

school's only there so we can "learn" our place in the socioeconomic hierarchy. common core is whatever. it's all bullshit.

 

[Sephzilla]

I absolutely love this picture and it's 100% true. Over complication to this degree would probably get you canned in the real world.

 

[AgeEighty]

I absolutely love this picture and it's 100% true. Over complication to this degree would probably get you canned in the real world.

Ffs, it's not overcomplication. Are any of the complainers actually making any attempt to understand what this is showing?

In "the real world", lots of people can't perform basic math without a sheet of paper in front of them or a calculator. How is that better?

 

[efyu_lemonardo]

The definiton that substraction is just addition of additive inverses is the one for real numbers. Trying to introduce that concept before doing real numbers is stupid or even plain wrong.

Who the fuck taught you math? That definition applies to any group including the integers.

 

[DoktorEvil]

These threads are essentially a testament to just how lacking American math education has been before now.

Every generation is like this, proclaiming that their methods were superior than the current gen.

Either way, the takeaway message should be is that math isn't difficult as a whole and that there are more than 1 way to solve a problem.

 

[CharlieDigital]

I absolutely love this picture and it's 100% true. Over complication to this degree would probably get you canned in the real world.

There's a difference between the numerical mechanics of doing the subtraction versus understanding what subtraction means. The way that many of us were raised was to do it as a mechanical operation of numbers instead of understanding the principles.

And look, some of us had no problem making that leap from the mechanical to grasping the principle. However, I think the reality is that there are many kids in the US educational system that cannot make the mental leap; not everyone's brain is wired the same way and not every kid is able to make the leap from the mechanical operation to understanding the principle.

To an adult, it is plainly obvious. But here is the thing: I have a four year old and I can tell you that to child, even if you teach them the mechanics, they don't understand the principle behind those mechanics. You naturally teach a young child mathematical principles by using physical models like having a group of objects and removing items from that group. There have been studies that have concluded that humans naturally don't think along the lines of integers, but rather logarithms so we have to be taught how to conceptually understand integers.

For many of us growing up in the last 2-4 decades, we were taught using a purely mechanical approach with the hope that eventually, we'll get it and understand integers.

Common core and Singapore math focuses on the principle and not the mechanics. Parents that focus on the mechanics assume that it's all that matters. If they can master the mechanics, why bother understanding the principle?

This thing is exactly how I was taught to perform subtraction:

But it only shows the mechanics of subtraction and certainly gets you to the right answer. But it does not demonstrate the principle of removing 5 units of 10 and 1 unit of 1.

What has shifted is that there is now a belief that kids will do better in mathematics later on in life if they understand the fundamental principles instead of just the raw mechanics of arriving at an answer.

 

[YoungFa]

Every generation is like this, proclaiming that their methods were superior than the current gen.

Either way, the takeaway message should be is that math isn't difficult as a whole and that there are more than 1 way to pay a problem.

I think all generations before and after mine used and still use the same methods as my generation did.

 

[Number_6]

Who the fuck taught you math? That definition applies to any group including the integers.

Why are you talking about groups? The guy doesn't quite know what he's saying, sure, but group theory shouldn't come into it, not explicitly. We're talking about elementary math.

Also, it's not a 'definition'. It's a property.

EDIT: Maybe you weren't talking about actual groups. Who knows?

 

[efyu_lemonardo]

Why are you talking about groups? The guy doesn't quite know what he's saying, sure, but group theory shouldn't come into it, not explicitly. We're talking about elementary math.

Also, it's not a 'definition'. It's a property.

I'm talking about groups because the integers are a group and the point I was trying to make is that real numbers or even rational numbers (or any structure based on more than just the group axioms) isn't required for the property of additive inverses (and closure under inversion) to apply.

Edit: which means in plain English that if you're dealing with integers it's perfectly fine to define subtraction as addition of the inverse.

 

[krameriffic]

Who the fuck taught you math? That definition applies to any group including the integers.

Most people didn't take abstract algebra.

 

[Number_6]

I'm talking about groups because the integers are a group and the point I was trying to make is that real numbers or even rational numbers (or any structure based on more than just the group axioms) isn't required for the property of additive inverses (and closure under inversion) to apply.

Edit: which means in plain English that if you're dealing with integers it's perfectly fine to define subtraction as addition of the inverse.

Yes, I get what you mean. I suppose it's just weird that we're even using the word "group" in a discussion of elementary school math.

There are some misconceptions in this thread regarding subtraction, for sure. If we're talking middle school or higher, then yes, subtraction is simply addition of the opposite. But for little kids in grade school, we're taking away puppies, or drinking bottles of beer off the wall, or something.

Deeper understanding of what is really going on with the numbers is important--the subtraction you do on paper is not meant to be the same procedure as what you do in your head. And having a good understanding of these things is important to go into the higher math classes and not be left behind. But we don't need to tell kids about abstract algebra. They're still just counting, just with bigger numbers, and eventually doing it in their heads.

 

[Two Words]

Ffs, it's not overcomplication. Are any of the complainers actually making any attempt to understand what this is showing?

In "the real world", lots of people can't perform basic math without a sheet of paper in front of them or a calculator. How is that better?

Common cores doesn't suddenly make math without paper something that you can do.

 

[AgeEighty]

Common cores doesn't suddenly make math without paper something that you can do.

Math without paper is something that I can do, and the methods they're using are the same ones I taught myself as a kid. They're not a magic formula guaranteed to work for all children, but I'll lay odds that they will be more effective than the old methods, if nitwit parents don't stand in the way.

 

[efyu_lemonardo]

Yes, I get what you mean. I suppose it's just weird that we're even using the word "group" in a discussion of elementary school math.

There are some misconceptions in this thread regarding subtraction, for sure. If we're talking middle school or higher, then yes, subtraction is simply addition of the opposite. But for little kids in grade school, we're taking away puppies, or drinking bottles of beer off the wall, or something.

Deeper understanding of what is really going on with the numbers is important--the subtraction you do on paper is not meant to be the same procedure as what you do in your head. And having a good understanding of these things is important to go into the higher math classes and not be left behind. But we don't need to tell kids about abstract algebra. They're still just counting, just with bigger numbers, and eventually doing it in their heads.

I'm not advocating teaching group theory in elementary school, was just correcting a statement that claimed it's necessary to deal with real numbers in order to treat subtraction as addition of the inverse.

If we're talking about the lower end of elementary school then indeed maybe even integers are too abstract and the discussion should be limited to the natural numbers along with zero. In such a case discussing subtraction (let alone division) would obviously require a different approach.

The reason I chose the term 'group' is because it was the only term I could think of that separated the integers from the rationals and reals. Feel free to provide a simpler/more familiar term.

 

[thecosmicfly]

Is it safe to say that common core has at last joined the upper echelon of hot topics like tipping and circumcision that cause GAF to go all skub over?

 

[MonkeyKing]

I feel like a lot of people are missing the point here. Who thought it was a good idea to divorce parents from their children's educational process? Don't we want parents to work with their children on their homework? At some point, shouldn't you have to demonstrate to the parents that this new method of teaching is superior to the old method?

We should be happy that parents are upset with this new curriculum because it means they are paying attention to the kids school work. Maybe instead of blaming the parents, we should blame the textbook writers doing a poor job explaining on paper what they so expertly do in their heads.

 

[the-pi-guy]

Most people didn't take abstract algebra.

Abstract algebra is hardly required.

Maybe you weren't talking about actual groups. Who knows?

I'm pretty confident he is talking about sets.


Set of integers is a subset of the real numbers.
Set of whole numbers is a subset of the integers.
Set of natural numbers is a subset of the whole numbers.

The set of natural numbers is a subset of the real numbers.
Additionally the set of real numbers is a subset of the complex numbers.

The definiton that substraction is just addition of additive inverses is the one for real numbers. Trying to introduce that concept before doing real numbers is stupid or even plain wrong.

Integers are real numbers.
You're not changing the definition, you're merely changing the domain that the definition upholds.
The calculus lectures at MIT do the same thing. They start with the domain of natural numbers. They show the derivatives the x^n (n being the natural numbers) and expand it to all reals.

 

[Jakten]

Math without paper is something that I can do, and the methods they're using are the same ones I taught myself as a kid. They're not a magic formula guaranteed to work for all children, but I'll lay odds that they will be more effective than the old methods, if nitwit parents don't stand in the way.

A number line is not a strange diagram either. It's like looking a ruler! It's not remotely complicated...

Like has no one complaining about the image in the OP had to measure something with a ruler and determine how much to cut off? It's basically the same thing.

 

[efyu_lemonardo]

I'm pretty confident he is talking about sets.

No I was talking about groups. If we're dealing with the integers specifically I could have used 'commutative ring' but despite how it came out I was actually trying not to be too obtuse...

Set of integers is a subset of the real numbers.
Set of whole numbers is a subset of the integers.

Also I believe you're mistaking integers for rationals, when they are actually the same as whole numbers.

 

[TheSeks]

Wait, you're not supposed to do it the way the parent did in that letter?

Not under common core. Common core is trying to teach the "mental math" of it which a lot of the (rightly so) criticism is coming from.

427-316 makes sense fast because you're removing one from each (4-3, 2-1, 7-6). But when you have something like 428-319 you then have to do the carry over and show your work. It's still "fast" but there's other methods of doing that and showing it mentally.

Which is what Common Core is trying to show: There's other ways of solving the problem than just one. The problem is, the way they show this with number lines and the like just confuses the hell out of people that were taught the "old methods."

 

[Aaron Strife]

Okay I get the idea behind common core being to teach complicated ideas in simpler form, but doesn't that subtraction problem just complicate things? If you write it out like

427
-316

Then you just do 4-3 (1), 2-1 (1), 7-6 (1) and lined up its 111.

If you get situations like 427-336 where it isn't as neat then yeah I'd understand reworking that but this just seems like it's over complicating things for the sake of being different.

 

[the-pi-guy]

No I was talking about groups. If we're dealing with the integers specifically I could have used 'commutative ring' but despite how it came out I was actually trying not to be too obtuse...


Also I believe you're mistaking integers for rationals, when they are actually the same as whole numbers.

Actually I am mistaking whole numbers for something else. The reason I was mistaken, is because natural numbers don't always include 0. And for some reason thought there was another set with 0, along with the natural numbers.

Natural numbers are positive whole numbers. {0,1,2,3,4,5,6.....}
Integers are whole numbers positive and negative {0,-1,1,-2,2,3.....}
Rationals are numbers that can be shown like this a/b
5/2 or 2.5 is a rational number, but it's not a whole number.

Whole numbers are rational, but rational isn't necessarily whole. Whole numbers are rationals where the bottom is 1.

I know you already know that, just demonstrating that I know that too.

 

[Cymbal Head]

Way too often, people see elementary-school level common core lessons and somehow come away with the impression that the same methods are used all the way through to high school graduation.

Let's teach young children to think flexibly and creatively about numbers, then teach them the notation that will simplify more complex operations. They'll learn the later stuff much faster if they grok the basics instead of having times tables drilled into their head with no conceptual understanding.

Another thing I see a lot in these threads are holier-than-thou types saying they'd have killed themselves if they had to use these new methods, because they had a natural talent for math and could do everything mentally.

Good for you, you're one of the lucky ones, and I hope you made the best use of your gift. But education should work for everyone, not just the future engineers.

I feel like a lot of people are missing the point here. Who thought it was a good idea to divorce parents from their children's educational process? Don't we want parents to work with their children on their homework? At some point, shouldn't you have to demonstrate to the parents that this new method of teaching is superior to the old method?

We can't exactly do this until the new curriculum has been implemented and we have data to show. You're proposing a catch-22 wherein we need parental consent to obtain data, but we need data to obtain parental consent.

 

[not psycho]

Ffs, it's not overcomplication. Are any of the complainers actually making any attempt to understand what this is showing?

Are you attempting to understand what it is showing? I notice nobody has answered my multiple choice question:

A. Jack misread the 316 as 306 but otherwise did the problem correctly
B. Jack was on acid and hallucinated he was hopping over 3 large pits and 6 spike traps.
C. Jack forgot to subtract 10. Holy shit, that's some pedagogical value right there! He forgot! God damn. He forgot.
D. Jack doesn't exist, the problem is trivial, the number line is scaled incorrectly just to fuck with the kids, the lack of scale destroys any visualization benefit, the method is painfully unnecessary for the given problem, the "write a letter" gimmick gives an inappropriate air of gravity that conflicts with the intended stupid answer, but I'm drunk and tired and the kids won't know any better, and Common Core cheerleaders won't say shit about it.

A, B, C, or D?

Let's teach young children to think flexibly and creatively about numbers

Thinking flexibly and creatively about numbers.

By literally telling them what to think, drilling the fuck out of it, and testing the taste out of their mouths.

Yet again, we see that Common Core defenders are recognizing a technique they like, which they did not learn from Common Core, and becoming so ecstatic that every other aspect of Common Core slips past them like an assassin in the night.

This is narrow-minded shit that stifles creativity and discovery.

You don't trust teachers or kids. In fact you think kids are dumb as rocks, so that they won't notice a stupid beyond belief trivial problem, won't notice how needless a technique is on that problem, won't notice absurd vocabulary or wording, and need to be spoon fed exactly what to think (even though there is plenty of room for actual creativity here).

 

[Brakke]

Kids are dumb as rocks. That's the whole thing. That's why we send them to school.

Your whole "but what about creativity!" thing is so hollow. What if a kid just never has the bolt-from-the-blue you think is so valuable?

 

[ZdkDzk]

Math without paper is something that I can do, and the methods they're using are the same ones I taught myself as a kid. They're not a magic formula guaranteed to work for all children, but I'll lay odds that they will be more effective than the old methods, if nitwit parents don't stand in the way.

The problem with common core is that it's used to teach kids about the relationships between numbers before and sometimes in lieu of teaching them basic mathmatic principles.

Looking at a lot of Common Core worksheets is like looking at a diagram of how I (someone who understands that relationship between numbers and knows the fundamentals) would do it in my head, except sans context, potentially out of order (in relation to my own process), and being tought to someone who doesn't understand the relationship between numbers and is still trying to nail down basic math. It's often best to break the rules you're taught and find workarounds, but these kids don't know the rules intimately enough to do that, and the way CC goes about it is both confusing and misleadding.

I'm all for alternative ways to solve problems; I tutor kids in math, and if there is a way for met to help them better understand what they are actually doing. But often CC methods are roundabout and run counter to what you are intended to do. Sometimes they're outright teaching them the wrong thing in order to get simple concepts across, without making the distinction between the correct method and the intermediary method. Like, I was trying to help my younger cousin with rounding, and her worksheet wanted her to round traditionally for the top half of the page; but the bottom half wanted her to round the one number, and then add the difference to the second number, but the worksheet made no distinction between either questions other than one being written horrizontally and the other vertically. I don't know what it was intended to teach, but it was her first week learning about rounding and they were telling her to do a process which wouldn't give the intended aswer had anyone else asked. I just took away the page taught her how to round 1s - 100s, reworked the questions for that method and had her write the answers they wanted. She had o turn something in and I didn't want to confuse her.

 

[Yoritomo]

The problem with common core is that it's used to teach kids about the relationships between numbers before and sometimes in lieu of teaching them basic mathmatic principles.

Looking at a lot of Common Core worksheets is like looking at a diagram of how I (someone who understands that relationship between numbers and knows the fundamentals) would do it in my head, except sans context, potentially out of order (in relation to my own process), and being tought to someone who doesn't understand the relationship between numbers and is still trying to nail down basic math. It's often best to break the rules you're taught and find workarounds, but these kids don't know the rules intimately enough to do that, and the way CC goes about it is both confusing and misleadding.

I'm all for alternative ways to solve problems; I tutor kids in math, and if there is a way for met to help them better understand what they are actually doing. But often CC methods are roundabout and run counter to what you are intended to do. Sometimes they're outright teaching them the wrong thing in order to get simple concepts across, without making the distinction between the correct method and the intermediary method. Like, I was trying to help my younger cousin with rounding, and her worksheet wanted her to round traditionally for the top half of the page; but the bottom half wanted her to round the one number, and then add the difference to the second number, but the worksheet made no distinction between either questions other than one being written horrizontally and the other vertically. I don't know what it was intended to teach, but it was her first week learning about rounding and they were telling her to do a process which wouldn't give the intended aswer had anyone else asked. I just took away the page taught her how to round 1s - 100s, reworked the questions for that method and had her write the answers they wanted. She had o turn something in and I didn't want to confuse her.

This mirrors my own experiences and frustrations with my 3rd and 4th graders math curriculum.

 

[Number_6]

Abstract algebra is hardly required.


I'm pretty confident he is talking about sets.


Set of integers is a subset of the real numbers.
Set of whole numbers is a subset of the integers.
Set of natural numbers is a subset of the whole numbers.

The set of natural numbers is a subset of the real numbers.
Additionally the set of real numbers is a subset of the complex numbers.



Integers are real numbers.
You're not changing the definition, you're merely changing the domain that the definition upholds.
The calculus lectures at MIT do the same thing. They start with the domain of natural numbers. They show the derivatives the x^n (n being the natural numbers) and expand it to all reals.

Nah, he meant groups. A group is a set, coupled with an operation with four main properties:

Associativity
Closure
Identity element
Inverses

So the integers are a group under addition. However, they are not a group under multiplication, for example, because the set of integers does not have all its multiplicative inverses. The rationals are a group under multiplication, though.

No I was talking about groups. If we're dealing with the integers specifically I could have used 'commutative ring' but despite how it came out I was actually trying not to be too obtuse...


Also I believe you're mistaking integers for rationals, when they are actually the same as whole numbers.

Some books differ on this, but here is the heirarchy:

Natural Numbers: 1, 2, 3, 4, ...
Whole Numbers: 0, 1, 2, 3, 4, ...
Integers: ...-4, -3, -2, -1, 0, 1, 2, 3, ...
Rationals
Reals

There are also the irrationals, which are the complement of the rationals within the reals.

 

[MonkeyKing]

We can't exactly do this until the new curriculum has been implemented and we have data to show. You're proposing a catch-22 wherein we need parental consent to obtain data, but we need data to obtain parental consent.

I am proposing something much simpler to begin with. I am proposing something much simpler to begin with. Something along the lines of "hey parents we have looked at how they do math in country X and country X produces a lot of people that really understand math. We will now emulate how they do things and here is how it looks. We will send home worksheets for parents, and or have workshops at school, so that parents can understand what their children are doing."

See, now you have buy-in from the parents! We want our kids to succeed. It's fine if the new method is unfamiliar. What's not okay, is leaving parents out of the process, then becoming indignant when they call bullshit on your new methods.