Translated from this post by Jane Kats.
I would love to know the source of the very prevalent idea that counting on your fingers is bad.
Our school is currently teaching counting and basic arithmetic using a ruler, i.e., a number line, which doesn’t seem like a great or logical solution to me.
The students are told that 6+2 is a grasshopper that hops 2 steps to the right of the number 6. Look, see, we stopped at the number 8, so 6+2 is 8. And when it’s 6-2, the grasshopper hops to the left.
From my experience, this method doesn’t add any visual value and it’s not terribly convenient for kids who confuse left and right (and there’s quite a large percentage of young kids who do!)
If we instead took craft sticks (or any other counting manipulatives) and took 6 red sticks and added 2 blue ones, the result is much more visual and much clearer than a ruler.
You can do this same problem on your fingers and there’s nothing bad or harmful about it. Show me 6 fingers (by the way, can you show me 6 fingers not as 5+1? How many ways can you think of?) Now lets do 6 of your fingers and 2 of mine – how many does that make in total?
The important thing is not to memorize, but to understand that I can figure out the correct answer by myself (even if it’s through the help of my fingers)!
Show the same number of fingers as I am showing. How many fingers are we showing altogether?
You three showed the same number and got 23 fingers in total? Count again please!
Can you figure out another way to show 16 fingers between the two of you? How do you show 16 fingers if there are three of you?
With five year olds, we use not only counting on their fingers but also many other manipulatives, such as these bright stickers.
Glue as many petals to each flower as the number in the center tells you. Then roll a die and add leaves to the stem based on the number that you rolled.
Now lets use base 10 blocks. We have small cubes that are ones, sticks that are 1 x 10 blocks that are tens and big squares 10 x 10 that are hundreds. The kids like to count and check that there are indeed 100 little ones blocks in the big square.
I am going to give you a stick and 3 blocks and you have to draw that in your notebook and write what number that is. How about 3 sticks and 2 blocks? Can I have one hundred square please? And it’s completely ok if some kids need to count every block in each stick to be sure of their answer.
Others work with hundreds with no problems. But for me, it’s not important to figure out who can count better or worse. I want to give them a chance to get a feel for the numbers. What does 10 look like? And what about 100?
There is also a big 10x10x10 block in this set of blocks. One six year old girl was recently examining it during class. She counted all the faces – 100 on each side, 100 on the top and on the bottom, and then exclaimed, “I know, this block is 600!”
Sometimes we also take rubber bands and tie wooden matches into batches of 10. It’s tricky for some kids to count out exactly 10 matches and then tie them up. And now the manipulatives look different, so some kids need to count every matchstick again to get exactly 23 matches.
The following is a great story from my colleague. A five year old in one of her classes asked what “five squared” means. She explained and, at the end of class, he wrote out a problem on the board for her as he interpreted it.
What materials do you use with your kids and students at school and at home?