Mathematics - Numerical Methods

[Guest]

So, I've been getting lots of stuff on my FB wall about Common Core Math and how it sucks.  And it's always about a numerical method that they compare to the traditional method on a written worksheet.  And it's always about parents complaining that their kids don't need to learn alternative ways of doing math because it's a waste of time; time that they could spend dancing, playing the piano, playing kickball, etc.

 

Okay, first off, I do not like Common Core - I almost want to say I HATE Common Core.  But, it's not for the reason that it requires teaching Numerical Methods.  I do not like it at all because it is run like a laboratory with the kids as lab rats.  It requires certain things and neither the Feds, the Teachers, nor the Parents understand why it is required and for what purpose.  So you end up with Teachers teaching stuff they barely understand the purpose of besides "my kids need to pass this test so I can get a paycheck".  And you have Parents who are so confused they don't want anything to do with it which puts a strain between the school and the parents with the kids caught in the middle.

 

That said... all the Numerical Methods I see on my wall are stuff I learned!  These are actually really good stuff!  My kid in freshman year, for example, has Language Arts, Latin, Geometry, Science, PE/Health, and 3 arts classes.  He has 3 times more arts classes than he has Math classes.  I'd rather him have 3 math classes to an arts class.  He needs math to excel at art... visual arts requires mathematical symmetry, music requires mathematical rhythm.  Heck, even playing kickball, billiards, bowling, monopoly, yahtzee, poker all use math...

 

Anyway, I'm starting this post to see how y'all "see" this calculation in YOUR HEAD.   No paper and pen, no writing anything, no calculators, no computers, nothing.  100% completely mental math.

 

156 - 87 = ?

 

How do you see it in your head?  Can you share your mental process step by step.  Also let me know if you've had instruction on numerical methods - formal or informal.

 

Thanks!

[Jane_Doe]

Define " Common Core"....

 

As to the math thing, as a person whom works in graduate level mathematics, I will tell you up that "useful" math depends entirely where you want to go in life.  If you want to be a cashier, yes basic arithmetic is essential.  But high level mathematicians loose that skill, instead developing computer programing skills, where I can have the computer do 1billion calculations for me.

 

Just to through a wrench in your thinking 

[yjacket]

My biggest issue so far is that it teaches concepts out of order. When my son was K they were trying to teach rounding. 5+4 is about how many. 5+4 is 9 and teaching a 5 year old an abstract concept like rounding is plain stupid. If a child has a good grasp of addition then you can say 5+4 rounded in 10, otherwise you are just messing then up.

[Guest]

I see the arithmetic problem you offered as follows in my mind: I can't subtract 7 from 6 so I "borrow" from the 10's column making the next step 7 from 16 which equals 9. I'm left with 8 from 14 which = 6, so the answer is 69. I haven't had instruction on numerical methods.

[MrShorty]

Here are some of the different ways I tend to do a problem like that:

 

1) 150-90+6+3=69

2a) 156-(86+1)=156-86-1=69

2b) (157-1)-87=157-87-1=69

3) (100-87)+(156-100)=13+56=69 -- from what little I understand, this is one of the main strategies common core wants to teach.

4) 160-90+3-4=69

5) Usually, when I end up needing to do something like UT.starscoper describes, I am looking for a calculater. This one usually is the "last resort" method when I want to do these by hand.

 

As an engineer and a mathematician, I consider myself quite good at math, though I do not consider myself very good as a math educator. Much of the time, I think I understand what my children's math is trying to teach them. I try to understand the rationale behind the approach their math books are taking, and use that information. I will admit that I do not always succeed at understanding it.

Edited September 23, 2015 by MrShorty

[Guest]

I don't want to hijack the OP, so I'm very interested to see where anatess wants it to go and what remarks she makes in response to our posts. Also, I'm interested in MrShorty's post. As an adult, I'm curious enough to investigate the logic involved, and I'm interested in the practical applications--whether they would make my life easier than continuing to use the method I was taught. I can see how a typical child would be disinterested unless a skilled teacher made it interesting.

Edited September 23, 2015 by UT.starscoper

[Guest]

Ok, I'm going to tell you EXACTLY what my brain "sees" when I encounter this problem:

 

1.)  I see 87 and immediately store 3 in my head because 87 is 3 below 90.

2.)  I see 156 and immediately store 9 in my head because 156 is 6 above 150 so I add it to 3 that I already stored to .get 9.

... these 2 steps seem to run instantaneously in my brain.  I can't explain it, they just happen fast because my brain is very comfortable with 6+3.

3.)  I then take 90 out of 150... this is effortless in my brain because I'm comfortable with multiples of 10... I immediately see 60.

4.)  I then add the 60 to the 9 that is already residing in my brain to get 69.

 

This happens lickity split.

 

Now, say, I was talking on the phone so my brain is only half-way focused, I would grab the closest paper and pen and do the math on paper... and, for some reason, when I'm writing out the stuff, I immediately go to the traditional method that UT.starscoper described.

 

I learned numerical methods in grade and high school and then again in college (went to engineering).  My brain just automatically chooses the easiest method for whatever I'm doing at the time - a lot of times coming up with my own method that my brain is most comfortable with because what I learned in numerical methods is that there are a jillion ways to skin a cat... so what they teach in numerical methods is not the steps to skin the cat, but rather they teach what in the world is a cat and what are you going for when you're skinning it, so that you can come up with your own steps to get that skin off.

 

That's why I'm very surprised at all the "What the heck is this???  This is stupid, this is a waste of time!" comments I read in all the Common Core posts on my FB wall.

Edited September 23, 2015 by anatess

[Guest]

Okay, I asked my son and this is how he processes this in his head:

 

1.)  He splits 87 into 80 and 7.

2.)  He takes 156 and take out 7 to get 149.

3.)  He takes 149 and takes out 80 to get 69.

 

He says this is effortless in his head.

 

I'm thinking about it and my brain rankles on 156 and 149... my brain naturally wants to round those out.

 

I taught my kids numerical methods growing up as I help them in homework or just for fun.  I'm starting to notice that my older kid has a more powerful brain than I have.

[Guest]

... That's why I'm very surprised at all the "What the heck is this???  This is stupid, this is a waste of time!" comments I read in all the Common Core posts on my FB wall.

This fascinates me. It also illustrates that there's more than one way to get from "hither to yon". It reminds me to take care before rejecting others' methods out-of-hand and to self-analyze to try to avoid rejecting truth because of my pride, my impatience or my narrow mindedness.

[MrShorty]

so what they teach in numerical methods is not the steps to skin the cat, but rather they teach what in the world is a cat and what are you going for when you're skinning it, so that you can come up with your own steps to get that skin off.

Much of the "propaganda" for the common core tries to emphasize this as one of the advantages of these teaching methods. IMO, this is a good goal, in theory. The better we understand the mathematical concepts and principles, the better we will be at applying those concepts, principles, and algorithms to the real world.

 

In practice, my daughters still complain about "the teacher/textbook insists that I solve the problem this way, when I think this other way is easier", so I sometimes wonder if the implementation of the new math curriculum is going to end up being just a different flavor of the same old math curriculum. Sometimes, I can see where there is value in learning the methodology the text is trying to teach, even if I can see a different, maybe easier, way to solve that problem. Other times, I just cannot see what the "new math" is trying to teach.

 

I guess only time will tell if the new common core will do a better job of teaching our kids math, or if it will just do a different job of teaching our kids math.

[Guest]

Okay, I gave my other son a different expression... 125-99.

 

This is how he thought this out:

 

1.)  He climbed up to 100 by 1... stored 1 in his head.

2.)  He climbed up to 125 from 100... added the 25 to the 1 that is already in his head to get 26.

 

Another different method.

 

Really, really cool.

[MrShorty]

Okay, I gave my other son a different expression... 125-99.

 

This is how he thought this out:

 

1.)  He climbed up to 100 by 1... stored 1 in his head.

2.)  He climbed up to 125 from 100... added the 25 to the 1 that is already in his head to get 26.

 

Another different method.

 

Really, really cool.

This is the way they used to teach us to make change. I think there is real value in learning how to apply this kind of reasoning to other subtraction problems.

[Guest]

Much of the "propaganda" for the common core tries to emphasize this as one of the advantages of these teaching methods. IMO, this is a good goal, in theory. The better we understand the mathematical concepts and principles, the better we will be at applying those concepts, principles, and algorithms to the real world.

 

In practice, my daughters still complain about "the teacher/textbook insists that I solve the problem this way, when I think this other way is easier", so I sometimes wonder if the implementation of the new math curriculum is going to end up being just a different flavor of the same old math curriculum. Sometimes, I can see where there is value in learning the methodology the text is trying to teach, even if I can see a different, maybe easier, way to solve that problem. Other times, I just cannot see what the "new math" is trying to teach.

 

I guess only time will tell if the new common core will do a better job of teaching our kids math, or if it will just do a different job of teaching our kids math.

 

 

I see what you mean!  Yes, yes.  I can see your point.

 

The way I learned is first, I learned to count using objects - fingers, toes, marbles, sticks, lines on the paper (we called this "monkey math") and then we learned the traditional method that UT.starscoper showed.  I think the traditional method gives you a thorough understanding of the mathematical concept.  Then, I learned other methods or short-cuts and other ways to slice and dice numbers.  This is another math class that builds on the previous class.  This enhances the understanding of the numbers so that we're not just learning to Do the Math, we are actually learning The Math itself.  Make sense?

 

So yes, teaching one method and only one method and being graded on that one method is no better than the math they already have.  Because, it still just promotes "Doing the Math" instead of "Understanding the Math" and doesn't really empower them to be creative with their unique brain capacity.

[Vort]

I think the idea of centralized control, which is at the heart of "common core", is a bad one, designed to centralize power. This is the main reason I deeply disagree with "common core".

 

As for the specifics of how math is presented, my wife and I have always hated how the schools teach math. That is the one subject we will not let our kids take in school. We teach them math at home, so they avoid all the foolishness of school-taught math. But from what I have seen of the "common core" stuff, especially what gets presented on FB and the like, it looks like those who oppose common core are cherry-picking outstandingly stupid examples, and many times just bad teaching of what otherwise might be fine techniques. (It astounds me how unbelievably bad most public school teachers are at math -- including the math teachers.)

Edited September 23, 2015 by Vort

[Guest]

VORT the mathematician!  I wanna know how you work 156 - 87 in your head!  I'm intensely curious!

[Vort]

VORT the mathematician!  I wanna know how you work 156 - 87 in your head!  I'm intensely curious!

 

Mathematician? Heh, heh. No. Math-lover, maybe.

 

I subtract 90 and add 3.

[classylady]

156-87=?
 

First of all, I can't figure it out in my head.  I have to write it down on paper.  I could estimate in my head to get an approximate answer, but I don't trust that estimation, so I write it down to figure it out.

 

156

- 87

------

 

I borrow from the 5 to make the 6, 16.  The 5 then becomes 4.  Then minus 7 from 16 which is 9

Then I borrow from the 1 to make the 4, 14. Then 14 minus 8 equals 6.

So, the answer is 69.

 

Math has never come naturally to me.  I struggle with it.  But, I can eventually figure it out.  To me, if I know the formula, and I can plug in the numbers, then it is just like a puzzle in figuring out the answer.  And, I love puzzles!

[Backroads]

I subtracted 56 from 87 and that from 100.

I'm teaching Common Core. I like much of what is taught in this particular curriculum, but I'm not at a point where I can say I like the whole thing. It's new to our school, my second graders are lacking many skills the program assumes (meaning we are not very far into the program at all because a good quarter of my kids barely know their numbers and I'm not exaggerating.)

There are strategies I think are very good to know, but I'm not in a good place to say yay or nay yet.

[Backroads]

To note, my team hardly forces the strategy of the day beyond the whole class lesson. I believe kids will find what works. I'm for learning a variety of strategies to the end of understanding.

[clwnuke]

VORT the mathematician!  I wanna know how you work 156 - 87 in your head!  I'm intensely curious!

 

I change the problem to 160-90 and then subtract one because 6-7= -1

 

Maybe not the most efficient but it works.

[Jamie123]

I would start with 90 and count down nine tens from 156 to get 66. But I need to subtract 3 less than 90, this so the answer is 3 bigger than 66, so 69. (This is not the way I would teach anyone to do it though.)

[Blackmarch]

Mathematician? Heh, heh. No. Math-lover, maybe.

 

I subtract 90 and add 3.

that's the first thing i thought of too lol.

[Guest LiterateParakeet]

Antess, I agree with you - about math and Common Core.

I can't do that equation in my head at all, which I think is a shame. I have over the years been able to retrain my brain to do some math in my head. I can figure out how much a tip should be, or prices after a sale %.

But your question reminds me that I still have a large gap.