Last semester Astroboy was on a counting spree. By the end of the semester, we’d kind of covered the end of “counting” as it was presented in my album. But he still wanted to count. How much does he like to count? On our drive to swimming, he’d suddenly start counting from 1 to whatever he can get to. He managed to get to 300 with very minimum help for me. When we do any other math materials (addition, multiplication, operations), you can see what he really enjoys is counting the beads. I did not see this before with Thumper. It’s fascinating to watch a child at work in their sensitive period.
But what materials can I use in the classroom? I was at a loss as to what to do until I bought the bead cabinet for Thumper to learn skip counting since she’s doing multiplication. During my research of the bead cabinet arrows, it finally dawned on me that I should introduce linear and skip counting because the beads are way longer. Now, if you read the Australian Montessori Council and their National Curriculum guide, or even Info Montessori it’s spelled out right there, Counting or Continuation of Counting. I don’t know why it didn’t occur to me other than the fact that linear and skip counting is all the way at the end of my album and I was told during my training that kids don’t really get to linear and skip counting. Plus, it’s all the way at the end of my album! Somehow I thought that meant it’s the end of the sequence. We rushed through these presentations during training since it was the last day. If you look at the album though, it says age of introduction is 4. Maybe the instructor was really talking about the concept of squaring and cubing.
Anyways, so now I know if someone were to ask me. For counting, after the intro materials, teens and tens, hundred board, use the bead chains.
During prep week, Astroboy said he was bored and was happy to do the 1000 bead chain work when I suggested. Now, before Christmas break, we played a lot of Hundred Board games. He got really good at reading up to 100, 200, and 1100. It doesn’t mean he knows what comes before or after a number, how to count that high, he’s just good at reading them. However, I’m glad we did all this prep work because he didn’t have to learn how to read the numbers on top of counting the numbers. This is why I suggested the 1000 bead chain. Thumper wanted to join in as well. Which turned out to be a good thing.
Because the classroom is a mess, I had the kids lay out the beads in a circle over two rugs. The kids had fun laying out the beads together. Once I dumped the bead chain arrows out, Astroboy got discouraged. Too many arrows. Thumper on the other hand, got right to work sorting them. It’s obvious she has a better grasp of the numbers and their relationship with each other. After showing Astroboy laying the arrows for #1-#9, #10, #20, he and Thumper worked together to lay out the rest. He laid the arrows for the first few 10’s then got tired. That’s what he says when he doesn’t want to do a long work. So I gave him sets of numbers in hundreds (110, 120, 130, etc) and had him find them in order to give to Thumper, who for some reason really wanted to lay them out.
When they were done, we admired their handiwork and counted backward. Though he found the work of laying out arrows from 1-1000 tedious, he painstakingly walked and counted backward along the chain.
I wanted to talk about Thumper’s counting and counting in Chinese. You’re supposed to introduce that huge cube to count to 10000, or was it 1,000,000 in Elementary. We haven’t gotten to it because I haven’t had time to make the material. But Thumper’s been showing her sensitive period for counting as well, in a not as noticeable and different way. Several times, she counted spontaneously in the car to measure how long it takes, in seconds, to get home from swimming. She goes along with Astroboy when he counts and goes higher. Both kids like to use big numbers, even though they have no concept what they mean when they say “I love you 100,000,000 times.” What was evident though, through a bit of assessment last semester, was that Thumper didn’t have a firm grasp of reading and counting in the 1000s nor does she know how to count to 10000. 10,000 is actually the highest number you count to in Chinese before the counters “repeat”.
The amazing thing about 7 year olds (and why sometimes I wonder what’s the point of learning so early) is how fast they get a concept. One night, while Astroboy was counting his 100s, I asked Thumper to count to 10,000, in 10s. So she started with 1010, 1020, 1030, 1040, etc, all the way to 10,000. She didn’t want to in the beginning but got egged on by Astroboy and really got into it. All the way driving home from Ranch 99, through getting ready for bed, she was counting and counting. She even pulled up some papers to remember where she’d counted to since she had to take a shower (while counting). In the beginning, she kept getting confused. After 1090 she’ll say 10,000! It’s always that turning between 9 and 10 that gets kids. I was so proud when she got to 10,000 by herself. Next up, counting backwards!
In any case, about counting in Chinese. In Chinese, we say, one thousand zero one ten when we count. It’s very clear to the kids when they count in Chinese because you state the number in each place value. Of course we also take short cuts. Like we will say, one zero one zero (1010), when reading numbers. I think this way of counting makes it easier to see numbers and their relationship with each other. Ten is read as “one ten” and twenty as “two ten”. This is actually how math counting is done in Montessori presentations anyway. But makes so much more sense when the language reflects it already and the child doesn’t need to do that extra step of connecting “two ten” with “twenty”.
Next up is counting in English for Thumper. I wonder if it will confuse her. Because in English, you would say “one thousand AND ten”. You don’t mark the zero.
What I learned
It’s important to have two children work together in long work. Even though the kids are 3 years apart, it helps to have someone advanced to help push the younger one along and maintain focus. The younger child also pushes the older child along when they think something is easy and not worth doing.
I am also reminded of something I learned from a Montessori teacher once. She told me how if a child doesn’t want to finish their lunch (let’s disregard making kids finish lunch, which is really about parent vs teacher) she would “divide” the plate in half and say, “It’s not much, just finish half”. Usually the child will then finish the whole thing. Similarly, when a child thinks something is “too hard” it usually means because they think it’s too big, too much, too something. Breaking up the problem, helping them along a bit, often does the trick. I remember the first time I saw the hundred board presentation in training and realized “Oh! you divide the numbers into sets of 10s so the child doesn’t get discouraged looking for one number in 100! D’uh!” It’s really hard for me though, I very much like to throw a child with a material and expect them to just work it out themselves, be persistent.
