Gifted Issues Discussion homepage Forums General Discussion Supplementing Common Core Math with Traditional

As someone who always asked 'why' and got the 'this is how we do it' response, I wish I'd been taught the why better, not just how. I appreciate that my kids have a strong number sense and can explain their maths. It's interesting to me, even their use of terminology that is beyond what I would have expected from kids so young, is cool to me. I never used baby talk with my kids, so why not teach terminology like decompose, number model, mental math, estimating, etc, from the get go, to take away the potential scariness of the big words before you get into abstract math? It might make math less intimidating later.

That said, it is how spiraling (which isn't CCSS specific) affects gifted kids that I struggle with, because my kids want to keep going to master it deeper, not stop and pick it up next year. So they might truly get it right away, beyond the instruction level, and then feel like they aren't learning anything new 1-2 years later when circling back. Whole to part, vs step by step.

The drawing can be frustrating -- DS has asked why he had to draw a picture to explain, and his teacher said it was to show his reasoning and that he's fluent enough to have more than one way to solve a problem. Sometimes that seems tedious, and yet, I find I do that myself when I'm trying to process something, and I've actually learned a few things that I didn't really get (or forgot) from my own education. It also is handy for figuring out where misunderstanding might be occurring.

To have that 'I never thought of it quite like that' moment is pretty cool. And there's this sense that the way you do it isn't wrong, you don't HAVE to do it like I do. It's not just memorizing the chart, pattern or algorithm; it's learning how to do calculations mentally and having a back up mental process for when your memory fails you on that quick answer. Rounding and estimating help you confirm your long work, in case you made a simple calculation error.

I think they're good habits to form, if you can allow for those who show mastery initially to do something beyond the class, rather than forcing too much repetition. The CCSS, from my observation, have given a framework for teachers to differentiate at least a grade above -- they can look at the next year's rubric in that standard and work toward that level of mastery with the top cluster in class.

My understanding is that CCSS Math doesn't spiral unlike the math program they were using previously. At least for my state. It used to be that 4th & 5th grade math were nearly identical, just 5th grade math went deeper. Making it easy for the 'gifted' or high performing math students to skip 4th grade math. While with Common Core they need to implement "compression" instead.

That said.. since Common Core is a set of STANDARDS. Not all states/school districts teach it the same way.

I think that this is the essential problem with the Common Core. The list of standards is only a start, with the most important step being making curricular materials. Every single standard is open to a wide interpretation, and given that textbook authors are underpaid and on tight deadlines, it was completely predictable that things wouldn't work out as planned. So the very laudable teach them that addition means combining things has turned into decomposing numbers and number bonds. It's a farce.

I've done a lot of grant application review in the education field. People who propose a new way of teaching something without providing concrete examples AND samples of their curriculum tend to get heavy criticism. In the end, the most important thing is the product, not the idea.

The CC authors failed by not producing textbooks. Worse, I can't even find a small set of examples for each math standard (maybe I've missed them?). How hard would that have been, to at least give Pearson a starting point? Maybe they saw that as too much or not their job or whatever, but the result is that we end up with a bad stew that looks like Everyday Math on LSD.

I was initially in favor of Common Core math, and now I'm dubious. The K-5 standards are okay (though 6-8 are not, IMO), but that fact was always irrelevant because the plan was always to drop the ball as soon as the game got going.

A lot of the problem people associated the Common Core math is the problem of the reform math. Unlike Val, I am quite okay with decomposing numbers and number bonds. That is how I do mental math and it feels natural to me. The reform math comes in when the kids are required to draw everything, explain everything and that is really annoying. The bad text books and bad test questions exacerbate the issue.

I always find it interesting that American teachers found Singapore Math hard to teach. I happen to love it.

Wrt SG Maths - what is there to teach? Most kids I know that did it just followed the books and basically taught themselves by following the examples in the book.

The problem is that it’s important to see a concept through the eyes of someone who’s never met it before. Not doing this, I think, is a stumbling block in a lot of American math education programs. Number bonds is a good example. It’s abstract, and abstraction doesn’t mix well with 6-year-olds. The concept needs to be as obvious as possible, and this just isn’t the case with number bonds. That they work for a gifted adult as an algorithm isn’t honestly relevant to teaching a concept to a little kid.

It’s much easier to have the teacher put 3 blocks on her right and two on her left. “Okay kids, how many blocks here (pointing)?” “THREE!” How many here? “TWO!”

“Now I put them together. How many blocks?”

“FIVE!”

“See? I combined 3 and 2 and got 5. Addition means combining things.”

What do number bonds offer that this simple demonstration doesn’t? IMO, bonds are unnecessary and may turn a simple idea into something confusing. Why use an abstract concept on six-year-olds when a simple concrete one will do the job better?

Decomposing numbers has the same basic problem. The idea is obvious to an intelligent adult, but that doesn’t make it so for a kindergartner. Again, it’s too abstract. Think about little kids who tear a piece cheese into several pieces and tell you that they have more cheese now. They decomposed the cheese, but didn’t see that they still have the same amount of cheese, because the idea is too abstract for them.

What you described is the first step of introducing addition. Number bond basically is just how many different addition problems give you the same answer. Decomposition is the natural extension of that. Very naturally these skills lead to adding numbers great than 10. My first grader never had a problem doing any of these. Maybe the words are big, but the concept is not tripping up the kids. It might be tripping up the parents who grew up in a different environment, but the kids don't have any issues with this concept if this is how they are taught.

It is an astonishingly good curriculum/text book, isn't it?

That's not what I've seen. But either way, why add a layer of complication to simple process?

Extend the demonstration and move a block from the group of two to the other group. Now you have four on one side and on the other, yet when you combine them, there are still 5 blocks. "See? There are different ways of making a group of five." Next: hand out blocks ask the kids how many ways they can combine things to get a group of 4 or 6 or 7 or whatever. Bonus: see who can put all their blocks on one side and none on the other.

This idea, once ingrained, can be extended naturally and logically to writing out sets of sums that equal a single number. It can also extend to the commutative property without using that term explicitly (e.g. four blocks on the left vs. four blocks on the right).

Again, why use abstraction when concrete will do? Kids need a solid foundation in concrete ideas and basic operations before they can move to the abstract and truly understand topics like algebra.

As for decomposition being a natural extension, it starts in Kindergarten. There's nothing to extend from when you're at square one. Plus, kindergarten is an age when kids think they have more cheese when they tear the cheese into pieces.


Okay, that's a bit insulting, and there's no need for that. That said, this accusation has been used frequently by people defending poorly thought-out math programs: you just don't understand it. Yes, I understand it. The engineers complaining about Everyday Math understood it, too. Etc. I also understand that in teaching concepts of basic arithmetic, simplicity wins over abstraction.

What you described is exactly how number bond is taught in Singapore math. From concrete to pictures and to abstract. Maybe you just don't like the name/jargon, but kids need some definition as a short hand at some point, right? I don't see how what you described is any different than the number bond teaching is in Singapore math. Once the kids figured out all the number bonds up to 10, they can easily decompose a number to make 10s for hard addition and subtraction problems.

Sorry if I offended you, I did not mean to be insulting anyone. I do hear parents complain about this method. I am just trying to point out this is really not that different than what you are doing. Also I am not sure whether Everyday math uses number bond. Singapore Math does. This happens to be what I like about the current math education. I can do away with the explaining the answers in words part.