View Full Version : Teaching long division

lynne

03-08-2011, 10:43 PM

So far, everything has been great with Math-U-See but now we started long division and the book teaches it differently than I learned it so now I'm trying to decide if I should use the book method or teach him the way I learned it.

The book breaks it down by place values, so if we are dividing 98 by 3, it would be 30, multiply by 3 then subtract and get 8, then put a 2 on top of the 30 then multiply and subtract with the remainder of 2. Then you have to add the numbers up.

The way I learned was to put a 3 which then subtract and get 0 of course, then bring down the 8 and put the 2 up and then put the remainder up.

The next few chapters teach this method and I'm not sure what's better. It seems like it would be confusing and harder to solve them the book way or maybe I just feel that way because it's not the way I learned it.

Any thoughts? I'm afraid if we don't use the book method we will keep running into this and won't be able to benefit from the video and teacher's manual but I think the standard way is easier to learn (to me it is anyhow).

dbmamaz

03-08-2011, 11:22 PM

The way they are trying to teach is, I think, a more intuitive way of looking at numbers. your way is an easier algorithm - a set of steps that always gets you the answer. The other way is more based on estimating first and then working your way towards the details. I think the idea is that that way helps you really understand how the different number fit together, rather than just the steps. I've never used MUS, but i assume they eventually teach the other method? Does MUS have a forum for their products?

BrendaE

03-08-2011, 11:28 PM

I struggle with "new new math" too! DSS spent a few months in2nd grade PS where they were teaching it (the point being that the children understand the concept). When I brought him back home... he was pretty much unable to do ACTUAL math problems... I am not sure how to explain that properly... He could manipulate the numbers around.. but not do the math.. or something.. Anyway.. it was all well I think maybe it is just me. I am no maths idiot nor do I struggle with math either. I can see the point of what they were trying to teach, but the end product just seems to suck. I have gone back to teaching him math old school style. Alas, manipulating those numbers like what you have stated is the exact same thing they are doing for addition and subtraction. To me, and perhaps only to me, I think this system is just not a good one.

I know when I begin teaching my DD Trigonometry and electrical circuits etc... there will be some problems requiring some VERY long (pages) division... so... yeah anyway...

Kylie

03-09-2011, 02:25 AM

Have you checked further along in the manual.....you know how they always seem to give every possible way to work things out and the first way always seems to be the longest way ;-) is it possible that they are simply doing that? I just remember with the initial addition/subtraction with regrouping problems they were shown a couple of ways that's all.

Have you been happy with MUS so far? We use it but only starting Gamma (we took a year off from it and did 'school maths' but that was terrible) so are a little behind where we should be.

I'm not a mathy but if you have been this far and it has given results and you expect to continue with it I'd be sticking to the book. However maybe it is time to consider other options?

farrarwilliams

03-09-2011, 10:27 AM

I think both systems have value. One of the problems with just knowing the algorithm is that many students never learn what they're doing. All they know is the procedure - this is how you line up the numbers, when to add, when to subtract - but not what it really means or why it works. The problem is that then those kids will be presented with a problem like 1000 / 50 and they'll think that the only way to do it is to set it up a long division problem and slowly divide the numbers - when obviously that's a problem they could do mentally if they understood what division is. In the problem you suggest, the old method is clearly the easiest, but for other problems I can see that MUS's method would work better.

I have a slight bias against MUS because my friend watched the vendor get the same problem wrong repeatedly using their materials, but I understand it's a pretty solid program. I think I would be hesitant if they didn't teach the more traditional algorithm later on. Otherwise you can end up like this poor kid who wasn't "allowed" to use the procedural method for addition:

http://www.youtube.com/watch?v=1YLlX61o8fg

Conversely, I would be worried about a math curriculum that only taught the procedure.

If you read Knowing and Teaching Elementary Mathematics it gives you some idea of how bad it can be when even teachers only understand the procedure. Of course, the point of really understanding the concepts should be to make it easier down the line to do math - if you're not allowed to use the simplest procedure, that really defeats the end goal.

lynne

03-09-2011, 02:52 PM

Yeah, I did look ahead, even before I posted here and it is the "new math" method the whole way through. We are on lesson 18 of 30. Next it goes into dividing double digit numbers and then fractional remainders, volume and Roman numerals. I'm afraid if I try to show him both ways it will confuse him more. I'm just going to take it day by day and see how he does with the traditional method. When you start dividing with 2 digits, you almost have to know how to estimate to solve the problem so he will hopefully understand it enough so that it sticks with him. I think I will still use the worksheets and tests. I also showed him the Khan academy videos and they did it the traditional way.

Does anyone have a rec for a math curriculum that is traditional? I would hate to switch because we have loved it up until this point but I should probably at least consider other options for 5th grade math.

ETA: Thanks, everyone:)

dbmamaz

03-09-2011, 03:11 PM

Well, i love singapore. i hear math mammoth is similar but fewer books to buy, and goes through 8th grade.

hockeymom

03-09-2011, 03:12 PM

We love Math Mammoth (we're using grade 3). It's pretty traditional but is great about giving different ways to a solution--we call the various methods "tools for the toolbox".

Your post makes me think of my childhood; I was taught one way by my teachers (which I didn't understand), another way at home (which sometimes I thought I understood), and then mixed them both together at school to disastrous results. Math still causes me anxiety because I never did learn the "whys" behind the various methods. I've been impressed in the ways that MM guides the student through various ways to a solution.

farrarwilliams

03-09-2011, 04:26 PM

We also use Math Mammoth and I have mixed feelings about it, but the kids really like it. I feel like I would like to switch to Singapore (or go back to MEP!) but I'm not sure if that's happening for the kids. I may get Singapore for next year... we'll see.

The phrase "new math" can mean a couple of different things. On one end, you can have a program like Miquon, which was made in the 70's and focused a lot on the meaning behind the numbers. Programs like that are extremely mathy and extremely conceptual. They came about in the late 70's and were deeply influenced and even written by actual mathematicians. But the teachers rebelled. They didn't get it. There were a lot of trips down rabbit holes (such as exploring different base number systems). Teachers didn't know how to teach it. So things went "back to basics" in the 80's and 90's. But that didn't really bolster our national math scores, so now we have another "new math." This new math (which is sometimes called "new new math") is more diverse, but is probably typified by a program like Everyday Math. It was written by educators so it's super teacher-friendly, unlike the previous new math. But this go around, a lot of mathematicians have criticized it. A lot of parents loathe it. It's extremely spiral, meaning that topics are touched upon without much depth, but over and over, with the idea that it will be cumulative down the road. There's a focus on modeling solutions and doing simple algebra very young. There's also a focus on using calculators at an early age.

Personally, I kind of like the old "new math" but the "new new math" drives me bonkers. I don't know Math U See that well, but I don't think of it as being part of either of those movements really. They really have their own program and system. Yes, it's conceptually based so it's sort of like the older "new math" in some ways, maybe?

If you want "traditional" then Saxon, to me, is probably the most traditional of the popular programs. Math Mammoth is somewhat traditional, but also focused on multiple paths to solutions and has enough of the conceptual focus to keep me happy. If you don't want a program that does things in an unfamiliar way for you, don't bother looking at Singapore, MEP or RightStart.

And that was way more than I intended to write.

lynne

03-09-2011, 05:40 PM

Thanks again everyone! I think I will stick to MUS for now, get through the rest of the school year but I am going to research all of the ones mentioned. I think if we can get through the rest of the book and he seems to be learning, I will probably order the next one, which is fractions (Epsilon book, I think).

Farrar, I really appreciate all the information because this is all new to me. Thank you for taking the time to explain that to me:).

Kylie

03-09-2011, 05:47 PM

And as a MUS user it was useful tome also. Please keep us updated on this Lynne. I have a friend who's child has just begun the fractions level, mum is an accountant, I might ask her what she thinks also.

BrendaE

03-09-2011, 05:51 PM

We also use Math Mammoth and I have mixed feelings about it, but the kids really like it. I feel like I would like to switch to Singapore (or go back to MEP!) but I'm not sure if that's happening for the kids. I may get Singapore for next year... we'll see.

The phrase "new math" can mean a couple of different things. On one end, you can have a program like Miquon, which was made in the 70's and focused a lot on the meaning behind the numbers. Programs like that are extremely mathy and extremely conceptual. They came about in the late 70's and were deeply influenced and even written by actual mathematicians. But the teachers rebelled. They didn't get it. There were a lot of trips down rabbit holes (such as exploring different base number systems). Teachers didn't know how to teach it. So things went "back to basics" in the 80's and 90's. But that didn't really bolster our national math scores, so now we have another "new math." This new math (which is sometimes called "new new math") is more diverse, but is probably typified by a program like Everyday Math. It was written by educators so it's super teacher-friendly, unlike the previous new math. But this go around, a lot of mathematicians have criticized it. A lot of parents loathe it. It's extremely spiral, meaning that topics are touched upon without much depth, but over and over, with the idea that it will be cumulative down the road. There's a focus on modeling solutions and doing simple algebra very young. There's also a focus on using calculators at an early age.

Personally, I kind of like the old "new math" but the "new new math" drives me bonkers. I don't know Math U See that well, but I don't think of it as being part of either of those movements really. They really have their own program and system. Yes, it's conceptually based so it's sort of like the older "new math" in some ways, maybe?

If you want "traditional" then Saxon, to me, is probably the most traditional of the popular programs. Math Mammoth is somewhat traditional, but also focused on multiple paths to solutions and has enough of the conceptual focus to keep me happy. If you don't want a program that does things in an unfamiliar way for you, don't bother looking at Singapore, MEP or RightStart.

And that was way more than I intended to write.

agreed, agreed, and agreed again! I believe youre the very first person I havent had to explain new new math to! :D

dbmamaz

03-09-2011, 11:39 PM

I actually wrote Farrar once to tell her that sometimes I forget she even has kids, she seems more like the board's educational consultant. Isnt she awesome?!

farrarwilliams

03-10-2011, 08:25 AM

I like to summarize things and spout opinions. Really, not always good. :p But thanks.

lynne

03-10-2011, 09:36 AM

Well, it's been really helpful to me. I respect your opinions, all of you!

Update: Nick is doing much better with his division problems this morning. I think I made the mistake of working off a sheet that had 2 and 3 digit problems and it was too much for him to even think about bringing two numbers down at separate times. Today he is doing great sticking with only 2 digit problems. I jumped ahead, not thinking. I feel better about his ability to learn this now:).

Kylie

03-10-2011, 06:05 PM

Excellent Lynne, and I second that Farrar, thank you for your input in general on SHS :-)

higgledypiggledy

03-15-2011, 06:32 PM

On the new, new math idea--research of large numbers of elementary school students using Everyday Math showed that while children made consistent gains in k-3, in grade four, the study groups levels and by grade 6 students using everyday math were behind their peers in the control group. I've got the study somewhere in my files, but can't seem to locate it at the moment. We are using Singapore which teaches a variety of methods to solve problems. I like that uses pictures and place values to help my kids understand why a procedure works. I also like some of the ideas in the old new math. My husband is an engineer and was one class shy of a double major in math. He is our go to guy on math and he always comes back to how he was taught math in uni. He feels like he had lots of catch-up to do because higher math is largely about how one thinks about numbers and he wants our kids thinking about numbers.

lynne

03-15-2011, 07:03 PM

I think we're going to try Singapore Math for our first grader in the fall. It seems like a good fit for us. I may still use MUS for my soon to be 5th grader because, aside from the way they taught long division, he really likes it. Trying Singapore for the younger one will give me a chance to compare them too.

AddlepatedMonkeyMama

03-15-2011, 09:25 PM

We're using Singapore for both kids and I like it so far. I feel like it's giving them a good foundation. As higgledypiggledy said, I think it's great at helping kids understand how the math works, not just how to get the right answer. It also shows kids how to do math mentally, which is a good skill. I don't have experience with other programs, so I don't know how Singapore compares, but we're happy customers so far. BTW, you can probably get by with just the workbook and textbook. I bought one instructor's guide and picked it up maybe three times, mostly for game ideas.

lynne

03-15-2011, 09:52 PM

BTW, you can probably get by with just the workbook and textbook. I bought one instructor's guide and picked it up maybe three times, mostly for game ideas.

Thanks for the tip. I was wondering about that.

ocitrus

03-19-2011, 10:16 PM

We use MUS and just finished the Delta book which teaches all the division... I have selectively followed along with the manual teaching. It started with long multiplication in the Gamma edition when they were multiplying by place value using the blocks. I myself just couldnt grasp that teaching. So since then I have my children watch the video and then I also present the way I learned. They then choose which way is easier for them.

By the way, we love MUS. Sometimes I worry that the kids arent learning enough bc the program doesnt jump from one subject matter to the next. I then realize that they are learning each step in its entirety and I relax. They love it and that makes it a good fit for us.

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