Gifted Issues Discussion homepage Forums Learning Environments Math curricula and confusion

Hi everyone,

Some odd things have been happening with DD6's math lately. I've been afterschooling her a bit, and her teacher has reported that she's having trouble with some of the concepts. After spending some time looking over the math curriculum, I wonder if the problem is the curriculum and not the child. Thoughts welcome!

For example, I "taught" DD how to add with regrouping a while back. I put that word in quotes because I was partway into the explanation when she said, "I get it! I get it!" and intuited most of the rest. A few minutes later, the lesson was done and she had it down pat. We've practiced from time to time without problems.

Then, last week, her teacher reported that she was having trouble with it. ????? She gave me a workbook page full of problems that looked like this :

  __
|__||
____|____
    4 | 8
       |
  + 3 | 5
_________
       |


My daughter said she didn't get what she was meant to do with "all those lines and boxes." I can see that.

I looked at some of the other exercises, and they're all mixes and mashes of manipulatives, lines, pictures, grids, and so forth. Some of methods are downright confusing. Yet the concepts are so simple. I was struck by how her book (and others I checked) turn simple ideas into complex messes. Teaching the same concept in six or seven different ways seems unnecessarily involved when all the kids really need is a bucket of Cuisenaire rods.

I'm now seeing a lot of this stuff as wasted time spent "teaching" the same thing over and over in confusing ways. And the worst part is that the connections must seem so obvious to the adults, that I suspect that many don't conceive of why kids might not get that the boxes, cubes, lines, pictures, grids, digits, and manipulatives all stand for the same thing. What happened to simplicity? Arithmetic is SIMPLE and INTUITIVE!!!

Val

Relating arithmetic to patterns, cubes, etc is important for today's students.

I personally don't get the grid example - please explain. However, figuring out codes and recognizing patterns is very important to higher math. Starting this early will pay off.

Relating numbers to geometrical figures is a weird concept for the brain and building this will help in science and other fields.

It is the same topic - over and over again - but different areas of study.

I, like you, was skeptical at your child's age. However, my daughter is now 13 and is great at estimating and especially in science.

The example appears to be an attempt to make sure that the child recognizes that the carrying is occurring from one register to the next higher one, and to focus the child's attention on the proper place for the carried digit when writing it. The extra horizontal line seems to be an attempt to make sure the child sees the carried digit(s) apart from the original ones.

I can see that the notation would be a bit confusing at first glance. Still, it's nothing your daughter can't handle. I guess it's good that she learn to be able to deal with different types of notation, although I agree with you that simplicity is often best.

ETA: I think it seems suboptimal, but it is hard to portray things with just typography and it might not be as bad as it seems. If the column lines were in light gray, for instance, they'd serve the useful purpose of keeping things lined up (which is something kids tend to have trouble with in my experience) without being so obtrusive and potentially confusing. I definitely think, though, that the line separating the carried digits from the rest is unnecessary, since the little box is there.

I agree with the two prior responses, although I am not convinced this is the intent of the educators actually presenting the material or the school districts adopting it, or if it is appropriate for children struggling with the basics. I say this because if a child is struggling with the basics of elementary school math they probably aren't going to need to be adept at figuring out codes and patterns and dealing with different types of notation. Hopefully, my kids will so I think there is some value in it for them.

I don't think it's the most efficient approach to teaching math but at worst it's a form of brain exercise, like suduko or a crossword.

I have to admit, I overlooked the age of Val's daughter. I can't interpret the expample, I don't know what they are trying to show, but if it's for a 6 y.o. it seems very strange.

The concepts they're trying to express visually include that the carried digits are not part of the original problem (I guess), that the numbers for each place should be kept strictly aligned, and that the carried digits have to be aligned with the columns they're carried into.

This seems like an attempt to give kids more guidance, based on knowledge of how kids typically screw these problems up. The real problem is that there isn't a universally accepted great way to teach math; there are a lot of opinions, some of them based on solid research or knowledge. When a district, school or teacher puts some of this stuff in place, I can see that it could easily become a mishmash.

So the problem is 48 + 35 and the little box is to carry the 1?

It's hard to judge based on a a typed representation, but what's here looks pretty bad to me.

Val - what's in the workbook? Is it lines and a square or is it really all those little dashes, segments, whatever?

I found the example confusing, but actually applaud the carrying the digit. In Everyday math, they use a slanted grid to teach and not "carry" but they cannot continue this method into middle school -- so, why are they doing that?

I already taught DD6 to carry and she can do any number of digit numbers of addition and subtraction using the same, old, tried method of carry. Though with the handwriting of a 6 year old, the columns get messy when she writes them herselves and does 6 or 7 digit numbers.

Ren

I agree with this, it's how I emphasised place value at first. And having pictures of manipulatives is helpful, too. That's how we started with division. And I'd kill to have my daughter putting the new value for a number above it where it's supposed to be. My husband used a crazy technique where you don't write anythign down, so she won't be able to show her work, instead of the proper way where you borrow 1 from the tens column, cross out the 4 and write 3 there instead, then change the number where you've brought the ten, too. he rhas her writing a 1 in the place where you'd write something you're carrying.


But you need all six mothods to make sure all the kids in the class get it. What if the one method they chose made no sense to you at all?

eta: I just reread your OP, and you have the opposite problem, they're writing the carrying number where a borrowed number should be!

But you need all six mothods to make sure all the kids in the class get it. What if the one method they chose made no sense to you at all? [/quote]

I expect that the other methods I looked at don't make much sense. I admit I could have described them!

One of the regrouping ones I mentioned but didn't describe was like this:

A picture showed 28 + 16 as two sets of ten blue blocks and 8 green one blocks for 28 and the same idea for 16. Then they regrouped the tens in groups of five and recolored stuff: two blue tens, 14 multicolored ones in two groups of five and one of four, and one ten. A subsequent step showed everything in blue again as tens, except they showed three tens and six ones as the answer.

I'm going to stand by my original idea that a lot of this stuff is unnecessarily confusing and that Cuisenaire rods demonstrate the concept much more effectively than a lot of other presentations. Arithmetic is straightforward, and the explanations about it should be too.

My eldest son's first school used Everyday Mathematics and he used to complain about how much he hated it, that a lot of the exercises were too confusing, and that adding was much easier.

Sometimes it's hard to tell fads from good stuff.

Val