How do children learn about infinity?

This is a post in response to a research article titled: INFINITY OF NUMBERS: HOW STUDENTS UNDERSTAND IT:

"Consider the sequence of natural numbers 1, 2, 3, … and think of continuing it on
and on. There is no limit to the process of counting; it has no endpoint."

We know this to be true and that a child could in theory never run out of numbers that they could possibly make up. But because we've already been through our formative and grade school schooling we know that this is true and we have a name for it. Its called infinity and we accept it to be true. On dictionary.com the definitions of infinity are:

infinity

in·fin·i·ty

1 .the quality or state of being infinite.

2.something that is infinite.

3.infinite space, time, or quantity.

4.an infinite extent, amount, or number.

5.an indefinitely great amount or number.

We know and accept this but do children? Can they understand this? This is an incredibly hard concept for children to wrap their heads around but at the same time a very intriguing one. Many students may struggle with this concept. The author of this study notes that "previous research has identified typical problems and constructive
teaching approaches to cardinality of infinite sets." With that being said how do we teach the concept of infinity?

 

That question may not lie in the application of lesson plans or in the way it is taught. It may lie more introducing this key mathematical concept at a stage in the child's cognitive development when they can truly grasp and grapple with it.  We know from research that as child age and gain more life experience that they increase their capabilities to understand mathematical concepts. The research in this report backs up that claim of development psychologists. In the article data reveals the best time to introduce the concept of infinity to be when they are older and they also found a gender difference stating "Boys give better answers than girls in tasks dealing with infinity."

 

So reflect on when you first were dealing with the concept of infinity. Who told you it was true? When did you first believe it to be true? Did you ever test it? And if so how high of a number did you go before you believed it to be true?

 

Feel free to explore this interesting article for yourself: 

http://www.emis.de/proceedings/PME30/4/345

 

And if you would like further proof of the existence of infinity truly check out this article on infinity:

http://plus.maths.org/content/does-infinity-exist