Your ideas for teaching the concept of infinity to children seem quite good. Certainly, I think, if you can make such an abstract concept a little less abstract and more visible, it is easier for the child to conceptual the idea. I read an interesting article written about the concept of explaining infinity to a child: http://www.googolpower.com/content/media/articles/mom-ill-love-you-til-infinity. In the article Susan Jarema offers some others ways to teach the concept. The ideas include asking a child what the largest number is they can think of and then asking them about that number plus 1 and continuing this pattern until the child realizes there will always be a plus 1. She offers approaches in terms that children could understand. I especially like the exercise with two mirrors.
In a 2006 study published by Pehkonen, Hannula, Maijala, and Soro, it was concluded that "Boys give better answers than girls in tasks dealing with infinity" (p. 351). The authors found that most primary children are very interested in the conceptof infinity, and they enjoy discussing the subject. Pehkonen et al (2006) state, "questions on infinity may also come into light. Infinity awakes curiosity in children already before they enter school: preschool and young elementary school children show intuitions of infinity. However, this early interest is not often met by school mathematics curriculum, and infinity remains mysterious for most students throughout school years" (p.345).
Studying students in a Finnish school, Pehkonen et al (2006) concluded that “students on grades 5–9 seem to have a finitist rather than a nonfinitist or an infinitist point of view in questions of infinity” and “students use intuitively the same methods for the comparison of infinite sets as they use for the comparison of finite sets. Although students have no special tendency to use ‘correct’ Cantorian method of "one-to-one correspondence," they are prone to visual cues that highlight the correspondence. For example, students tend to match set {1, 2, 3…} more easily with the set {12, 22, 32 …} than with the set {1, 4, 9 …}” (p. 346).
Though this study shows that students may not truly grasp the concept of infinity, it seems to me that if teachers are prepared for this discussion, it is a concept that would interest students and excite them. In addition, the concept of infinity could prepare students for abstract thinking in other curriculum areas as well. Playing with numbers and challenging a students’ imagination is a great way to open their minds to concepts beyond the classroom confines.
"There is no branch of mathematics, however abstract, which may not
someday be applied to the phenomena of the real world."
-- Nicolai Lobachevsky
Jerema, S. (n.d.). Mom, I'll Love You 'Til Infinity. Retrieved March 2012, from Googol Learning: http://www.googolpower.com/content/articles/mom-ill-love-you-til-infinity
Pehkonen, E., Hannula, M., Maijala, H., & Soro, R. (Eds.). (2006). Infinity of numbers: How students understand it. Proceedings 30th Conference of the International Group for the Psychology of Mathmatics Education, 4, 345-352.
