We’ve had some conversations lately with parents of children who are struggling with counting. Sharon writes: “Any tips for children with dyscalculia? My daughter has had a horrible time learning to count. She is now 7 and still has a very hard time recognizing the numbers on the abacus and counting without me. She has made some progress, but she still struggles and gets extremely frustrated when it is time for math.”
The first thing we need to address is subitizing. I know – you’re scratching your head and asking “What in the world is that?!?” Subitizing (SOO-bih-tighz-ing) is seeing the number of items without counting. Let me show you what I mean.
How many is this?
Did any of you count? Of course not. You can see it’s three!
Now how many?
Seven. You can see the five and two more. No need to count.
Young children often know the numbers from 1 to 5, if only because of their ages. The numbers from 6 through 10 can be a bit more challenging. But if the quantity is grouped in fives, just like our hands, it’s easy to learn. Here are lessons from RS2 Level A; one on subitizing 1 to 3 and the second on subitizing 6.
Always show 5 on the left hand and the additional quantities to make 6 to 10 using the right hand, like 8 shown below. The Yellow is the Sun song helps the children learn the quantities.
If a child is needing work in this area, sit across from the child. Call out a number. Display the number with your hands, having the child mirror you. Because we want the child to “read” the quantity from left to right as shown above, you use the opposite hands so that the child sees it correctly.
If the child is a bit hesitant with the quantities, show the number first and let them mirror it. Once they become more comfortable and confident, be a little slower in showing your quantities, allowing them to lead.
Start with the easy numbers: 1 through 5. Present them in random order. This is often easy. Then, move into showing the quantity of 6. Remember to have the 5 on the child’s left hand and 1 on the right. Do not show 6 as three on each hand. We want the child to see the grouping of 5 and 1 more. Seven will be five on the left and two on the right hand.
The quantity of 9 and 10 are easy; 9 is all the fingers but one and 10 is all the fingers! The quantity of 8 is the hardest to subitize, so save that for last.
To work on these quantities, play card games. Games provide the necessary practice to help the child subitize quantities and build their confidence. The Math Card Games book has a chapter on Number Sense with 46 games. Here are a couple games for you to use, along with the cards needed to play. I’ve included the bead cards which can be substituted for the finger card and tally card games.
Once the child can identify quantities on their hands, it’s time to move to the AL Abacus. Again, sit across from the child with the abacus in front of the child. Call out a number – I generally start with the number 4 – and both of you show the amount on your hands. Then ask the child to enter that amount on the abacus.
If they count it out, ask if they can do it “all in a group” on the next row. Sometimes, if the child is struggling, I will nudge the beads a bit to help the child see the quantity of 4.
Have the child slide the group to the left, followed by the remaining of the rows. If nudges are needed, make them smaller and smaller. Generally a child will only need a few nudges to see the pattern.
Once this quantity is successfully subitized, move to another number – I generally move right to 7. Clear the abacus. Have the child show 7 on their hands with you mirroring the quantity on your hands. Point out to the child that the “five hand” will be the blue beads and the “two hand” will be the yellow beads.
Have the child enter the quantity on the abacus.
Ask them to do it again on the next row, the next row, and the next. Sometimes there will be some hesitation on the sixth row where the colors switch, but just hold on to your silence and let the child figure it out. Keep going until all ten rows are entered.
Play around with other numbers, keep the quantity of 8 until last – remember this is the most difficult quantity to subitize.
So, back to the counting issue. Counting is a by-product of subitizing. It is easier for children (and adults) to subitize quantities than to count them. To foster their natural subitizing skills, children should be discouraged from counting small collections. In counting the child focuses on one item at a time. Subitizing allows the child simultaneously to see the whole and the individual items.
Counting is more of a cultural process. We tell our kids “count for Mommy” or “count for Daddy”, but why count 3 when the child can see that there are 3, with subitizing, and there’s no need to count?
With counting, it’s using a one-to-one correspondence matched with a special sequence of words. Let me show you what it looks like to a child. Since many of you don’t know Chinese, let’s look at the counting sequence words for one through ten:
You can learn the sequence. Just say them over and over. It’ll take a little bit, but you can do it. Once you have it, let’s “apply” it. How many is this? Answer in Chinese, please.
Most of us will chant “ee, are, san, suh, woo, lee-yoo, chee, bah”, while pointing to each item. Provided our one-to-one correspondence is accurate, the answer is bah!
See how the counting process can be a burdensome challenge if we don’t understand the name of the quantities and the meaning of the words? And if the quantities are not grouped for quick recognition, it’s even more frustrating.
Let’s continue using the Chinese numbers for math facts. What’s lee-yoo plus jee-yoh? Here. Let me help you with some counters.
And since we’re obviously going beyond shure, 10, you need to know that the Chinese continue numbers past 10 by saying ten-one for 11, ten-two for 12, ten-three for 13, and so on. So, let’s give this a whirl. In Chinese again, please.
“Ee, are, san, suh, woo, lee-yoo, chee, bah, jee-yoh, shure, shure-ee, shure-are, shure-san, shure-suh, shure-woo, shure-lee-yoo, shure-chee, shure-bah, shure-jee-yoh”. There’s your answer!! Clear as mud, right? And let’s not even attempt to address multiplication when we don’t understand the words and what they mean!!
That is what counting without understanding looks like to a child. Understanding is so incredibly important! Subitizing is the foundation for this understanding.
Argenta LeBlanc, a K-1 teacher in San Antonio, TX writes: “I explained to my students how important and time-saving it can be to subitize instead of counting. We have been playing games and singing ‘Yellow is the Sun.’ One day during class the week before the Christmas break, I posed a math question that required using addition or counting up as a method to complete a subtraction problem. One cute little first grader quickly without hesitation correctly answered the problem. When I asked how he got to his answer he replied, ‘I can subitize.’ I had to smile.”