math is hard, let's get a cookie

[jeliza]

One of the things that is most challenging about helping my little kids with their math homework (beyond the age appropriate attention span issues) is that so much of what they are working on involves concepts that are so thoroughly embedded in my brain I can't explain them. Place value is just there. How skip counting relates to multiplying is just there. That reversibility of addition to subtraction and multiplication to division is just there.

But place values are HARD. Wrapping your mind around there being zeroes in the middle of numbers that aren't, say, 10, or 100, is a serious does not compute. Until it is the only thing that makes sense, and then how do you explain why it was hard?

Comments

[boonedog.livejournal.com]

What helps me with that (because I love that stuff - like hexidecimal coding or binary - where different place holders have different values) is to put it out physically. Like putting out ten pennies, one dime and a one dollar bill and explaining how the number 101, the 1 for the hundred is like a dollar bill representing 100 pennies, the 0 representing the dime (or lack of one) and the last 1 representing the one penny.

[jeliza]

Definitely the visuals can help; we have the block manipulatives, and pictures of them, but part of what's not making sense right now is if you have 4 thousand blocks, 2 ten blocks, and 6 ones blocks, why there is a zero in there. I don't think it helps that we write numbers/words in English from left to right, but numbers are constructed from right to left.

(And what really sucks is if you didn't get a really firm handle on something in, say, 2nd grade, and you get to where it is relevant in 3rd grade problems that are too big to do in your head, the frustration level is immense.)

I am so glad I am not a teacher. We really don't pay them well enough for the number of skills they have to have, and what they put up with.

[boonedog.livejournal.com]

Yeah, I'm not sure how to explain the 0 in the placeholders except maybe to explain that the numbers are like a language - they represent more than just a flat amount. so maybe showing the blocks that represent the 1000's, and 100's but a 0 for ten, then show how the mount is different if you add the 1, and showing how that 1 that is added to 99 in the tens pushes the blocks into the 100's category because one more would make the box explode cause it can only safely hold 99. Like that thin mint in the Monty Python dinner scene. Or maybe not that last analogy. I know about the teachers - I have no idea how they do it!

[dianthus.livejournal.com]

I...don't remember that being hard. But I was always that way about math until I hit calculus, and I was sometimes the only one in my grade school class like that.

[jeliza]

I don't remember it being hard, either. But partially that's a very high level of aptitude, and partly, I'm fairly sure, that I learned it in Montessori preschool so when I saw it again it was trivial.

I see a lot of kids (I volunteer at math) that can do problems, even much harder problems, intuitively, but can't explain how they are doing them, which eventually fucks you up whenever you hit the point you have to do not-in-the-head math like multiplying three digit numbers, or when you have to write it out.

[joxn.livejournal.com]

Well, you could put it this way:
four thousand, twenty, six, that is:
4000
+ 20
+ 6
------- and now, writing from right to left, and tracking across the 4000 and then down to the result digit
4..0..2..6

[jeliza]

Maybe with graph paper that would help, and if they slip again I'll try that (alignment is surprisingly non-obvious); I think we've actually mastered the place value now, it was just the most profoundly "huh" example.

[dianthus.livejournal.com]

Oh yeah. I remember the teacher having us draw vertical lines to separate the places.

[indigodove.livejournal.com]

Place value was always the first unit of the school year, and one of the harder ones to teach for me and to understand for the students. Some of this was because there is abstract thought involved, and the kids were only starting to be able to think abstractly in 3rd grade.

Expanded form can help, ex: 402 = 400 + 0 + 2, or the kind of problem above (4026) on graph paper. Actually, I made them learn regrouping for both addition & subtraction on large-square graph paper, because it was easier to keep their columns straight that way.

But honestly, math was always hard for me, so I like to think I was good at explaining it. Explaining how to write or read well was much harder for me, because those things came easily to me.

Good luck and bravo for being a concerned parent who wants to help her kids! <3

[jeliza]

Graph paper is pretty much the bomb.

Apparently place values are on the 2nd grade Common Core tests/curriculum, which seems odd to me, but a lot of what is on those tests and when doesn't make sense to me.

I think the fact that English is written left to right doesn't help, because they want to write their numbers left to right, which just doesn't work, especially once regrouping is involved.

[eub.livejournal.com]

I've sometimes found it useful to explain place values by: here's a bundle of $1-5-10-20 bills worth $27, let's lay them into a cash register drawer, and that makes an empty slot in the drawer.

Generalizing like that may be a weird way to attack the problem, I guess, but it does also make it more concrete, and dispels any mystery around the powers of ten. There's a bit of a puzzle for the teacher when the student asks "what stops us from making it as 27 $1s?", but that's a good question to have. :)

[jeliza]

Oh, I like that, because it makes the zero *VISIBLE* in a way that just lining up manipulatives doesn't, even if you just had, say $21 or $101 so the bills themselves were not complex