Conclusions

Instead of a pure abstraction, infinity has become something the students have created, experienced, and manipulated.

The children have

• experienced how a proper subset can have a 1-to-1 correspondence with the whole set,

• reasoned about countability of the set of all rational numbers,

• understood why no sequence can be constructed for the real numbers or the set of all infinite sequences.

Difficulties that we didn't address:

• a reluctance to use one-to-one correspondences that weren't in ascending order
• a confusion resulting from the same number being in both sets being compared.

title | why | what | why toontalk | activities | rationale 1 | activity 1 | findings 1 | rationale 4/5 | activity 4 | activity 5 | findings 4/5 | rationale 8 | activity 8 | findings 8 | conclusions