Monday, May 22, 2006

Counting On Your Fingers - arithmetic part zero of several

An Anonymous reader asked about teaching children how to add on their fingers. Adding and subtracting on one's fingers undisciplined can lead to off by one errors - in either direction. This leads to a reliability (getting the right answer) of less than 33%. In the world of math, off by one is as good as off by a million - it is just as wrong. The student is discouraged, then afraid of failure. No wonder we're so bad at math. One of my high school peers walked out of the SAT exams unfinished. It was so sad. Not a damned thing to do about it then. Maybe this will help now.

Correcting simple counting isn't anything magic, it's just being careful. I won't attempt a description. What follows is a description of a technique with the power of rocket science, brought down to the simplicity of a kindergartener. It isn't dumbed down. Instead, it is broken up into consumable chunks for the student. The goal is seven second lessons. Each post is a lesson. I won't go further than partial differential equations with boundary value problems (the math that is rocket science).


Q: How high can you count on the fingers of one hand? Five?

A: You can count from zero to nine on the fingers of one hand.


Each of the four fingers are worth one. Make a fist. That is zero. For now, use your right hand. Count to four with one finger each. Some people find it easier to put the pinky up first. I use the index finger first. It doesn't matter.

Make the fist again, and stick out your thumb. The thumb is worth five. Five is just with the thumb out. You can think of this as five and zero. Add a finger with the thumb - that's six. Count from there until you have the thumb and all the fingers out. That's nine. You've just counted from zero to nine on one hand.

Now, every day for a week, perform this exercise. Don't hurry. Don't skip ahead. Stay with this exercise longer if you need to.

Start with a fist, say 'zero'. Say it out loud.

Add a finger. Say 'one'. I can't hear you.

Add a finger. Say 'two'. Shout if you must.

Add a finger. Say 'three'.

Add a finger. Say 'four'.

Make the fist again, and stick out the thumb. Say 'five'.

Add a finger. Say 'six'.

Add a finger. Say 'seven'.

Add a finger. Say 'eight'.

Add a finger. Say 'nine'.

Extra credit. Count down from nine to zero.

An aside. Zero is a number. It is perhaps the most meaningful of the numbers. After all, nothing is more important than math. We will return to zero again and again for infinity, and beyond.

6 comments:

John Branch said...

Ah, clever. If you use the right hand for the so-called ones place as described, and use the same method for the left hand but regard it as the tens place, one can then count to 99 by using two hands. Perhaps you mention this in a later post.

Stephen said...

Later posts cover addition and subtraction with two digits. Multiplication is planned.

Anonymous said...

Actually, if you count in binary with your two hands (finger down is zero, finger up is one) then you can count to 1023 on two hands. Throw in your two big toes, and you can get up to a whopping 4095.

Stephen said...

I would count finger or toe down as "1" in binary. That way, tactile feedback lets you do it in the dark.

Cooking Vegan With Soul said...

Awww, thanks for posting this!!! It's just what I needed! Mwah!

Stephen said...

I just found my soroban. It's been missing for a year. Apparently, i'd cleaned off the dinning room table in a hurry. It to start the next bits, and with pictures.