May 25, 2011

One-to-One Correspondence

Identifying numbers and rote counting are fun to teach our children, but once mastered, it  does not mean that our child understands what the value of each number is. Teaching one-to-one correspondence is a great way to teach them the unit value of a number. I have found the explanations of one-to-one correspondence to sometimes be confusing, so this post is really to clarify it for myself and hopefully for you too.

I thought that I would start with the proper definition and headed on over to Wikipedia.  This is what they had to say: "In mathematics, a bijection, or a bijective function, is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y and no unmapped element exists in either X or Y." Hee hee...You got that, right?

Okay, lets try again. My research led me to a post at A Teacher at Heart and I learned that it is fundamentally the matching of one object to one (corresponding) number or object , for example: matching the number "3" to the three bears;  or "4" to moving four spaces on a board game; matching one knife to one fork; or two socks to two shoes. The key is that the matching is to the same value.

In light of the above information, I realized that when counting with Little One (33 months at the time of this article), it is important to simultaneously touch and count the objects. In practice, this means that I may gently take Little One's hand and touch the objects that we are counting. Children tend to naturally touch objects as they count, but may sometimes skip an object or double count. A very informative article on number skills at down syndrome education online explains that children can be helped to keep track of counting by placing objects already counted in a separate pile or counting in one direction. Increasing the size of spaces between objects and using objects that are not too small to hold or roll also helps the young child in the counting process. (This website is definitely worth checking out if you would like more information about teaching numeracy.)

In an article by Rita Webb at Ezine , she points out that one-to-one correspondence also involves the skill of comparing sets to see which has more or less. She shares a variety of activity ideas to practice both matching and comparing. I won't be writing about the comparing of sets here, but you can head on over to Ezine to see what she has to say.

Earlier this year we did a mini Cats theme and I found some cat counting flashcards at Sparklebox. I wanted to try out a one-to one correspondence activity with Little One (See picture above) and was surprised at how easily he understood what was required. I would say "Can you put one block on one Kitty?" and so on. I'm on the look-out for some more easy one-to-one correspondence activities, so if you have any to share, please leave a link in the comment box.

PS. Our Touch and Count Cubes, seen in the picture above, are a great learning tool.  I highly recommend them for every household. I use them regularly during the homework session with my older son, as they have endless mathematical possibilities. They are available here in South Africa at CNA stores or through agents. Please contact me if you would like more info. 

PPS. Linking this to Show and Tell @ ABC and 123


Sarah said...

What a perfectly clear explanation of this complex cognitive skill!!! Can you believe the definitions out there? It isn't as scary as it seems!! :)

Your Touch and Count cubes are wonderful! They are great even as you work with larger numbers building a "stick" of TEN and a "block" of 100!!

I'm always fascinated at the math little ones can do when it is hands-on, fun and organized (like using cubes you can stack). They really get it! And really like it!

A Teacher at Heart

Km said...

What an extraordinary topic... Your boys are beyond blessed to have such a wise, loving and INTELLIGENT mommy to lead them on their way. I am horrible at mathmatical concepts...always have been... So thanks for this step by step info! Xoxoxoxoxxo

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