And did you write down your method, with the numbers crossed out and replaced by other numbers due to borrowing, and so on? Writing out the crossing-out and borrowing and boxing and so on is how the methods are taught, not how they’re actually used.
That’s because that’s part of the teaching method, representing in a written manner the thought process behind coming to the answer.
Like for 14375 - 5386. You should be able to do that in your head in a similar manner. It should be pretty quick to see that it’s 9000 - 11 (8989), but if you only were taught to do it the long way, you’d probably be lost (unless have very strong visualization skills. I know I don’t).
I’m 66, and I was taught “New Math”. What is being taught today is not called New Math, it’s called Common Core.
’
Well, finally someone posted something that is not a simple regurgitation of “It’s new, so it’s better!”
I did, in fact, think that it was the method, and not simply the teaching of the method. I would hazard a guess that a lot of people who see it ALSO think that, or there wouldn’t be such an outrage every time it comes up.
I apologize for slamming it and withdraw my objections.
(I realize this probably makes me look like an idiot, but usually I’m not)
Perhaps in the future, when this gets posted again, the response could be “Those boxes are just used for teaching the method. In practice, it’s just like you add and subtract money. No boxes or other things are used”
Are children capable of understanding that? I don’t believe I was in grade school.
Teachers taught us binary math without explaining that we might work with computers, and taught interpolation without explaining that we would need it for trig tables.
Actually, if you read what I wrote, it does not say this at all.
And I have no problem with the Common Core. I have a problem with teachers who copy worksheets from the Internet and pass them off as “teaching” and counter any complaints about the curriculum with “Sorry, it’s Common Core!” And parents who rail against Common Core because they think Obama started it.
But that’s another issue.
I’m not one of those two, but I’ll answer anyway. (Traditional around here, isn’t it? :D) I’m in my early 60s, and New Math was a new thing when I was in grade school. And Tom Lehrer’s song came out in '65.
That song involved doing subtraction in base eight. I’m pretty sure it was in fourth grade (definitely no later than sixth) that we learned how to convert from base ten to any other base, and vice versa. Thus I was shocked when twenty years later no one else in my class at SubScol had any idea how to even convert decimal to binary.
And one last question, if I may, those of you who are math teachers, do you teach the “box” way (whatever it’s called)? Do you also teach the “borrowing” way? And the 3rd way that I can’t remember the name but someone linked to a video on it?
You teach all 3 ways when you are teaching subtraction?
Quoted for truth.
This belongs here:
EDIT: Credit where credit is due:
I swear, I read the thread and looked real hard before posting a second Tom Lehrer link.
Who said you have to tell students why you’re doing what you’re doing? :dubious:
For my high school students, yes, I tell them what the potential value to learning something is (it’s the only thing that gets them to bother learning how to factor polynomials, for example). But for elementary school children, do you think that telling them that something they are learning in second grade is going to make sixth grade math soooooooo much easier is going to be of some value? :rolleyes:
I don’t teach elementary school, so I cannot speak to teaching subtraction (or addition or multiplication or division) with integers.
However, if you look at the Common Core standards, they include being able to do both “traditional” subtraction, as well as subtraction by other methods, such as estimation, use of grouping techniques, etc. So if the elementary school teacher is doing her/his job, yes, they are all being taught.
If it were up to ME to sequence this, I’d sequence the “figure it out through backwards addition” first (since that’s an operation they are familiar with). Then, I’d introduce more traditional methods, probably the same way I learned them, by using popsicle sticks to do grouping by ten exercises, and then showing how borrowing works visually/kinesthetically, before moving on to doing it via a pencil and paper algorithm. But I did my substitute teaching in elementary school prior to the implementation of the Common Core, so I’m not sure how elementary teachers sequence it.
One of the troubles with Common Core teaching is not the Core itself. It’s the fact that elementary teachers don’t really understand math (for the most part). So they are often simply doing what some textbook/workbook combo tells them to do, and then figuring out ancillary materials on their own. It’s quite common to see worksheets that take a method for approximation and using it to determine an exact answer. That, of course, is silly, and leads to precisely the objection you had earlier: it’s faster to do it the “normal” way. But the teacher doesn’t KNOW that the point of the method is estimation, so … <sigh>
DSYoungEsq, I was taught Set Theory in the sixth grade, though I didn’t USE it for another 20 years. Why did Sister Mary Ellen think I needed it? What was the bloody point? I might suspect you are an inadequate teacher if you are not prepared to explain to children of eleven WHY you are teaching them what appears to them as nonsense.
I would have like to known why I was learning binary math or interpolation instead of playing on the monkey bars or something I understood the reason for, like grammar or history. Hmmm…History may be doubtful for some students.
FTR, it was the first year of the New Math and Sr Mary Ellen was probably trying to stay one chapter ahead of us.
What do you tell them is the value of learning to factor polynomials? I’m having trouble telling my kids what the point is besides “It will help you in later math classes”
For one thing, it provides one way of solving polynomial equations.
Yes, of course it does. But so what? How is that useful? I have to admit, I don’t use solving polynomial equations in my job. Is there any benefit other than “It will help you in later math classes”?
I’m not saying they shouldn’t learn it, but they honestly want to know why they have to. What the point of it is.
I just want to add the observation that the supposedly frustrated kid in the OP’s pic has already successfully solved the problem!