Some guy brags about his son..
You're being downvoted, but you're right. This article was somewhat silly.
A Child Thinking About Infinity (2001) [pdf]
11–20 of 41 posts
Re: A Child Thinking About Infinity (2001) [pdf]
#12Some guy brags about his son..
The guy is David Tall: https://scholar.google.com/citations?user=IV1rmyEAAAAJ&hl=en...
Re: A Child Thinking About Infinity (2001) [pdf]
#13I 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 pathw…
Mathematical concepts like nothing, straight lines, circles, are also abstractions that have no complete reference in nature - is it just infinity that you consider needs self-awareness? I'm not quite sure what you're hinting at?
Re: A Child Thinking About Infinity (2001) [pdf]
#14Interesting 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.
The Wikipedia article may be primarily written about legal cases, but leading questions appear in many other contexts. In psychology and interviews they're often advised against, as they induce a precise answer and thus make it hard to learn about the subject of study, instead reinforcing the interviewer preconceptions; in user interface design they can produce the wrong conclusions about how easy an interface is to use.
Leading questions have their use in education, but as the other commentator below points out, the child might be giving the answer that the questioner wants to hear, rather than showing a true understanding of the topic. Having a stated problem to solve may prevent that, as the child can instead answer the question in a way that solves the problem.
Re: A Child Thinking About Infinity (2001) [pdf]
#15Earlier quoted context omitted.
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.
I do think they accepted it in a dogmatic way. Incidentally, I am raising our children Catholic so it's an idea that fits pretty well with the idea of God, the Holy Trinity, and all that. Three in One, yet one is the Father and the other is the Son? Yes, dear. Oh, ok.
Re: A Child Thinking About Infinity (2001) [pdf]
#16Earlier quoted context omitted.
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...
I agree. I am not claiming my kids are geniuses. They are smarter than me I feel, but that's not saying much. :)
Re: A Child Thinking About Infinity (2001) [pdf]
#17I vaguely recall having a "night terror" centered around infinity when I was very young. I think I was trying to truly grasp how tiny and insignificant I am and how immensely huge everything else is and it just freaked me out.
Re: A Child Thinking About Infinity (2001) [pdf]
#18I 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 pathw…
Mathematical concepts like nothing, straight lines, circles, are also abstractions that have no complete reference in nature - is it just infinity that you consider needs self-awareness? I'm not quite sure what you're hinting at?
I was just musing, no concrete connections at the moment. I don't know if infinity needs self-awareness, but I was thinking that it could prompt one to call into question his/her self relative to the infinite that is being experienced, and in that perhaps adjust one's concept of self through comparison. Or even just thinking about how one can conceptualize such a thing based upon all life experiences where almost everything encountered is finite.
Re: A Child Thinking About Infinity (2001) [pdf]
#19Earlier quoted context omitted.
Mathematical concepts like nothing, straight lines, circles, are also abstractions that have no complete reference in nature - is it just infinity that you consider needs self-awareness? I'm not quite sure what you're hinting at?
I was just musing, no concrete connections at the moment. I don't know if infinity needs self-awareness, but I was thinking that it could prompt one to call into question his/her self relative to the infinite that is being experienced, and in that perhaps adjust one's concept of self through comparison. Or even just thinking about how one can conceptualize such a thing based upon all life experiences where almost eve…
In my experience, children (and most people) just conceptualize infinity as a very large set, just as they perceive a tire a "circle", and think a square drawn on paper is made up of "lines".
It requires years of thinking about these mathematical entities before people get a first glimpse of what they really mean, beyond a simplistic qualitative experience.
To most people, children included, infinity is conceptually no different from the amount of sand on a beach. They just allow that it is simply not quantifiable. That turns off the brain.
The more interesting thing to test, I would argue, would be the human mind conceptualizing a very, very large but ultimately finite set of something. That requires that we make a distinction between the discreteness of something and our ability to quantify it.
That is a much more difficult concept to comprehend, and it must be understood before we can even begin to think about teaching a child about mathematical entities like infinity, circles, or lines.
Re: A Child Thinking About Infinity (2001) [pdf]
#20Just a few days ago I had an interesting conversation with my 4 year old son that went something like this:
"Daddy, what's the biggest number?"
"There is no such thing as the biggest number; numbers keep getting bigger and bigger forever. This is a concept called infinity."
"Which number is the biggest?"
And so on; he's only 4, so I don't expect him to grasp the concept of infinity, but I was impressed that he's already asking about it.
My son is in his first year of Montessori education, and has learned to count into two digit numbers already, and understands zero, but doesn't yet understand negative numbers. Montessori is fairly interesting because they teach math in a different way, by learning powers of 10 and using a bead system similar to an abacus, so Montessori educated kids can actually do simple arithmetic with large numbers (in the thousands) by around age 5.