A Child Thinking About Infinity (2001) [pdf]
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A Child Thinking About Infinity (2001) [pdf]
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Re: A Child Thinking About Infinity (2001) [pdf]
#2Some guy brags about his son..
Re: A Child Thinking About Infinity (2001) [pdf]
#3Some guy brags about his son..
Maybe, but it's interesting because I had quite a few discussions with my kids about infinity. It came up when playing the "how much do I love you" game. I introduced infinity, and from there I was able to teach them a little about it. They were very young and I am still impressed with how easily they grasped some of the concepts.
Re: A Child Thinking About Infinity (2001) [pdf]
#4Interesting read. Though Socratic method much? The writer uses leading questions[1] as a primary expository method, directing the kid towards conclusions that "should" be made within the proposed system, rather than merely exposing a small set of rules and letting the child freely explore their consequences. All the talk about the different infinities felt that way.
This leading style may be good for teaching the history of mathematics, i.e. introducing concepts that have been relevant to solve problems in the past. But for teaching math skills I prefer methods where a problem is stated, and the student is left to build their own abstractions about it; the IOUs and thermometer examples were more in this line. This competence will prove more useful when solving new problems than merely following the trodden path of already invented mathematics.
Re: A Child Thinking About Infinity (2001) [pdf]
#5Some guy brags about his son..
Maybe, but it's interesting because I had quite a few discussions with my kids about infinity. It came up when playing the "how much do I love you" game. I introduced infinity, and from there I was able to teach them a little about it. They were very young and I am still impressed with how easily they grasped some of the concepts.
Young kids easily grasping things is interesting. It is also commonplace...
Re: A Child Thinking About Infinity (2001) [pdf]
#6Interesting read. Though Socratic method much? The writer uses leading questions[1] as a primary expository method, directing the kid towards conclusions that "should" be made within the proposed system, rather than merely exposing a small set of rules and letting the child freely explore their consequences. All the talk about the different infinities felt that way. This leading style may be good for teaching the his…
I think it's noteworthy that the article you point to pertains to common law and testimony, rather than to philosophy, pedagogy, or education. When a student freely explores a concept, that clearly demonstrates a higher ability or skill in mathematics. But "leading questions" are scaffold to show the student how to explore and build abstractions, and most will have to learn how to do that from example.
Re: A Child Thinking About Infinity (2001) [pdf]
#7Some guy brags about his son..
It seems that you may not be the target market for this information if that's all you have to contribute.
Re: A Child Thinking About Infinity (2001) [pdf]
#8I know this isn't the point of the article, but did anyone else LOL at the bottom of page 3 when the difference of 10^100 - (ninety nine 9's) was given as 1? The author seems proud to attest "There really are ninety nine 9s!" The problem though is that this doesn't equal 1. You would need to subtract a number with one hundred 9's in a row to get an answer of 1.
Re: A Child Thinking About Infinity (2001) [pdf]
#9Some guy brags about his son..
Maybe, but it's interesting because I had quite a few discussions with my kids about infinity. It came up when playing the "how much do I love you" game. I introduced infinity, and from there I was able to teach them a little about it. They were very young and I am still impressed with how easily they grasped some of the concepts.
Do you think it's possible that they accepted your ideas of infinity in a dogmatic sort of way, similar to how many young children accept god? I remember first having discussions with my father about infinity as young as 6, but I didn't really start exploring infinity for myself until my mid teens. It would be interesting to see how your kids thoughts change as they mature.
Re: A Child Thinking About Infinity (2001) [pdf]
#10I would like to see fMRI studies on how human experience the infinite or perhaps near infinite. There is an instinctual appeal of vastness (near infinite, perceptually infinite?) - mountains are climbed, sunsets into far away horizons over seemingly infinite oceans, skyscrapers are built and their height and subsequent view are valued,... - These are times when humans first experience vastness which may trigger pathways in the brain related to comprehending / thinking about the infinite. I would like to see is the parts of the brain associated with self-awareness are active during these experiences.