Something clicked for me this weekend, and it clicked for Ella too.
All this time, I was frustrated with her counting - HAH! What was I thinking? Ella's problem had nothing to do with difficulty counting, or understanding the relationship between the number of objects with the numeral or the name of the numeral.
She had shown interest, the last time we did math, in trying to match two number rods to make the length of a third. So, using the first five rods we did a little bit of introductory addition. There was no frustration, no "I'm to tired's", no I don't want too's."
Up at my Mum's later while visiting with my visiting siblings, "Uncle" asked Ella, "If you had three kitty cats, and I gave you two more kitty cats, how many kitty cats would you have?"
"Five," said Ella, in a tone of voice which added the feeling that she was thinking, "Isn't that obvious? What a silly question!"
Uncle posed a few more addition problems, all which she answered promptly and correctly, until he asked two plus four, to which she answered "Five!" He cocked his head to one side and look at her, to which she responded, "No, no! Six!"
Earlier today, as we were still at my Mum's, and as a result of visiting aunties and uncles, we hadn't had "school" in a while, I noticed her playing with a group of her "Little People" animals. I laid down in front of her and told her we were going to play a little game. Since "little zebra" is her favourite, he and she were going to be on one team and they were going to figure out the mysteries I made.
I started with four little people in one spot, and one separate from them. I made up a little ditty and sang something along the lines of "How many animals do you see?" while pointing to the four animals together. She and zebra sang back at me, "Four, four, we see four!" Then I sang the same ditty while pointing to the solo animal. Zebra and Ella sang back "One, one, we see one!" Then I slid them all together while singing, "So four plus one makes ____." Zebra and Ella sang right out on cue, "Five!"
We did this for quite a while, when she began asking for harder "mysteries." We went through 2+3, 5+1, 5+2, 6+1, 3+4, 7+1, 3+5, and 4+4, when she (and zebra) asked for a really tough one. So I put out 6+6, which at first she said was 11, but when I said, "You'd better check again," she figured out it was 12.
So, now I'm going to have to buy/make the next stage of math materials, such as the mathematics bead material (now there's a huge project!), the teens and tens boards, and a second set of number rods. I'm really glad now that I received the Montessori Research & Development Mathematics Manual. (In fact, I got quite a few Montessori R&D Teacher's Manuals, and I'll be writing about them at length in a future post.)
I doubt my math woes are completely over, but at least now I know it wasn't that the material was too hard, but that it was too boring. I have a funny feeling that when it comes to making/buying Montessori material, I'm really going to have to work to keep up with Ella!