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Steven Gubkin
Steven Gubkin
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I think that actually trying to get students at this age to contemplate infinities in a rigorous way is probably ill advised.

I do think that exploring counting from both an "ordinal" and a "cardinal" point of view is probably a good idea.

Example for a 5 year old: Something you could do is have 20 stuffed animals, only 18 of them wearing hats. You can ask: are there more hats or stuffed animals? Get them to explain theretheir reasoning: How could you know there are more stuffed animals than hats without counting them? These kinds of questions introduce them to the ideas of injection, surjection, etc, at a level appropriate to the age.

I think that actually trying to get students at this age to contemplate infinities in a rigorous way is probably ill advised.

I do think that exploring counting from both an "ordinal" and a "cardinal" point of view is probably a good idea.

Example for a 5 year old: Something you could do is have 20 stuffed animals, only 18 of them wearing hats. You can ask: are there more hats or stuffed animals? Get them to explain there reasoning: How could you know there are more stuffed animals than hats without counting them? These kinds of questions introduce them to the ideas of injection, surjection, etc, at a level appropriate to the age.

I think that actually trying to get students at this age to contemplate infinities in a rigorous way is probably ill advised.

I do think that exploring counting from both an "ordinal" and a "cardinal" point of view is probably a good idea.

Example for a 5 year old: Something you could do is have 20 stuffed animals, only 18 of them wearing hats. You can ask: are there more hats or stuffed animals? Get them to explain their reasoning: How could you know there are more stuffed animals than hats without counting them? These kinds of questions introduce them to the ideas of injection, surjection, etc, at a level appropriate to the age.

Source Link
Steven Gubkin
Steven Gubkin
  • 26k
  • 4
  • 63
  • 112

I think that actually trying to get students at this age to contemplate infinities in a rigorous way is probably ill advised.

I do think that exploring counting from both an "ordinal" and a "cardinal" point of view is probably a good idea.

Example for a 5 year old: Something you could do is have 20 stuffed animals, only 18 of them wearing hats. You can ask: are there more hats or stuffed animals? Get them to explain there reasoning: How could you know there are more stuffed animals than hats without counting them? These kinds of questions introduce them to the ideas of injection, surjection, etc, at a level appropriate to the age.