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Today, he said he did the 100's board, which is a step up from the 50's board he's been talking about. He explained that this is where you line up the numbers in order, which I remember someone saying last year was debatably Montessori. I asked if he ever did Math with beads or spindles and he said no.

When ds was 21/2, he was developing the concept of addition and subtraction, not by rote but by figuring out the concepts with small numbers. Today, he still can't count to 100 reliably, even though this seems to be what he has been working most on, by his report, and even though he is fully capable. When he is counting with me, we talk about the pattern of the 10's, but I don't drill it.

The other day, he was practicing writing his numbers and "quizzing" us  what's 1+1? 11, what's 5+3? 53. And another time, he took some our numbers and made 479+625 and added all the numbers together (4+7+9+6+2+5) using little tokens we had. I didn't jump in and give a lesson on decimals and hundreds because 1) I'm not sure where he is working in Math and don't want to jump ahead, 2) I don't know how to teach it appropriately, and 3) I didn't have beads/hundred squares available.

So my questions are: What is the progression of Math works in the Primary cycle? I understand that developing the underlying concepts is most important, but what point should a bright enough child be working at at this age? Are those types of math errors due to a developing curiosity/emerging understanding, or is he somehow stagnating/regressing?

The 100 board comes before addition and the bead cabinetN so the answer that 5+2 is 52 seems right from what he is learning now. He is identifying 2 digit numbers so when you ask about putting them together, he thinks about what he is working with. He might even understand the concept of addition, but not the terminology. Try asking him instead, "If I have 2 apples and I buy 1 more, how many will I have?". Putting it in a full sentence might show he understands the idea, but not the symbols + and = or the words that go with them.

Not to hijack the thread, but Matt...where would a job such as the 45 lay out come in? Is that after the hundred board? My DD has pretty much mastered the hundred board and I just had a lesson by the teacher on the 45 lay out and had never seen it before. I was impressed!!

Here is a picture:
http://3.bp.blogspot.com/_rsgetwotaj.../45layout.jpg The right side has unit beads, from 19 with the numeral cards. Next to that are the tens...then hundreds...then thousands. It's called the 45 lsyout or decimal layout. (45 is because each decimal place has 19. 1+2+3+4+5+6+7+8+9=45). 
Okay, I've seen that before; I just didn't know what it was called. Thanks!
So where does it fall in the progression? I ordered a copy of the Parent's Guide to Montessori. I'm looking forward to it. I seem to have a lot of questions arising these days, and I'm starting to wonder if M. is really the best for ds. Can't really think of a better alternative for him, though. 
I guess then, the question to me would be, "What are you trying to get out of his education?"
We're probably the only parents in our son's class who don't quiz the teachers on his academic progress during conferences. We ask about what he enjoys, and his social interactions, because we have faith that he will learn everything he is expected to learn. it might be on his own timetable, but it is obvious to us that he can learn and that he enjoys learning. We figure that the Montessori approach is giving him a tremendous luxury: the luxury of time, of space and of opportunity. He is only ahead or behind if we compare him to other children. As long as he's at a Montessori school, he won't be compared to other children, so he's developing on his own schedule. He probably could be pushed to do some things that he is academically ready for (like reading) but he is not yet emotionally ready for them (he tells us, "I can read, but i don't want to because I want you to read the books to me!") I am sure at some point, he will be pushed or led a little more than right now, but it seems to me we owe all of our children at least a few years of school where they aren't compared to others, where they aren't pushed to meet standards, and where they are free to explore and develop their own interests based on their own timetable. 
Another question: What are the prerequisite skills/works to play the Snake game or Bank game? Ds told me he's finished the 100's board. When we were talking about works, he said he wanted to learn the Bank game and the Snake game. I didn't want to encourage him to ask for a lesson if they were just going to tell him he wasn't ready. Maybe I'll suggest it and prompt him to find out what he needs to learn first, so that he can set a goal to keep him on track. I wonder if the mystery of the progression is as frustrating to him as it is to me...

Thanks for the information, Matt. I met with the teachers a couple of weeks ago and told them he's been asking for the Banker's game and Snake game. They said he wasn't ready for the Snake game but that they'd invite him to a lesson of the Banker's game the next day. They also gave him the 45 layout. I think it's a lot more interesting and motivating for him now.
That looks like a good book. Does it take you into elementary years, also? And this is fantastic  the seller is a bookstore in my city! 
Matt, I bought it today. Haven't had a whole lot of time to look at it yet, but it looks like they go into some higher level math. They've talked about how Montessori teaches the addition, multiplication, subtraction, and division, and then proceding to the memorization of math facts. A lot of it seems more geared for children beyond primary.
Also, that bookseller has several copies, so if you're interested in getting another (or anyone else is), you could probably order one without problem. 
From what I have read, is the order she is being taught reversed? should she have learned counting through 99 first before doing addition/subtraction? I understand that montessori emphasizes on concrete to concrete, then concrete to abstract (doing math with beads and writing out the problem on paper or reading a problem on paper and solving it with beads), and finally abstract to abstract (paper only). Usually, what age or how long will it take to reach the abstract stage? DD is 4y2m now.


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