11–20 of 22 posts
Do we really need to work so hard to stimulate curiosity in people? Aren't people inherently very curious?
Kids are curious out of the box, but if you gently guide them, they are capable of asking amazing questions and understanding things that will blow you away. My kindergarten nephew and my two year old inspire me this way.
The comment “What an idiot I was,” I thought. “That was just an axiom, it is called commutativity. One doesn’t prove axioms.” is interesting. What's chosen as an axiom, and why, is an advanced question. Unless you get into foundations of mathematics, that question is seldom addressed. It's way beyond most pre-college math teachers. It's the sort of question that occurs to smart kids, but there's no easy answer you can give them. The usual answers are theological, and boil down to "shut up, kid". Here's a discussion on Stack Exchange of that subject: http://math.stackexchange.com/questions/127158/in-what-sense...
(If you get into automatic theorem proving, you have to address such issues head-on. Adding an inconsistent axiom can create a contradiction and break the system. This leads to constructive mathematics, Russell and Whitehead, Boyer and Moore, and an incredible amount of grinding just to get the basics of arithmetic and number theory locked down solid. In constructive mathematics, commutativity of integer addition is a provable theorem, not an axiom.
I once spent time developing and machine-proving a constructive theory of arrays, without the "axioms" of set theory. The "axioms" of arrays are in fact provable as theorems using constructive methods. It took a lot of automated case analysis, but I was able to come up with a set of theorems which the Boyer-Moore prover could prove in sequence to get to the usual rules for arrays. Some mathematicians who looked at that result didn't like seeing so much grinding needed to prove things that seemed fundamental. This was in the 1980s; today's mathematicians would not be bothered by a need for mechanized case analysis.)
Summary and table of contents at http://www.ams.org/bookstore-getitem/item=MCL-5
I believe the most important learning device used is the fact that he is sitting patiently with the kids and giving them his full attention, sending the meta-message to them that "this is important stuff and you will be rewarded with an adult's undivided interest if you work with this". All children (and most adults) crave attention, and the giving and taking of it is perhaps the most powerful tool that a parent and/…
Grrr...mixing metaphors and it's not even New Year's Eve yet.
I believe the most important learning device used is the fact that he is sitting patiently with the kids and giving them his full attention, sending the meta-message to them that "this is important stuff and you will be rewarded with an adult's undivided interest if you work with this". All children (and most adults) crave attention, and the giving and taking of it is perhaps the most powerful tool that a parent and/…
This is an exceptionally good point. I've read a lot about early child development, and I've never come across this before. It sounds very plausible though: children seek attention, so reward good behavior with attention. Of course. The same goes for schools, of course. The misbehavers earn the attention of both teachers and students alike, and if they do it enough, even that of their parents and the administrators.…
But is it? Don't we all remember that "one teacher" who seemed to give us that little extra attention or push when we needed it the most?
Good teachers (at least my good ones) all seem to understand the attention-tool intuitively, but it just became glaringly obvious to me raising my three children and seeing young children behave badly to obviously get their parents attention, and many parents obliging them without thinking.
The rather odd part, for me, was, when mentioning this to parents in social groups, I was often looked at like I was nuts...like the idea of bothering a well-behaving kids with attention was beyond the realm of reason.
If math pedagogy is your main interest any of the MSRI Math Circle Library books are worthwhile. This includes "Circle in a Box" which is a Math Circle starter kit freely available here http://www.mathcircles.org/GettingStartedForNewOrganizers_Wh...
I believe the most important learning device used is the fact that he is sitting patiently with the kids and giving them his full attention, sending the meta-message to them that "this is important stuff and you will be rewarded with an adult's undivided interest if you work with this". All children (and most adults) crave attention, and the giving and taking of it is perhaps the most powerful tool that a parent and/…
This is not uncommon now and is kind of the standard bearer for how to parent.
[1]http://www.psychologytoday.com/blog/family-affair/200809/rew... [2]http://www.fosteringperspectives.org/fp_vol1no1/articles_vol... (1997)
You could have a whole set of sessions with children exploring different arrangements of coins and noting that no matter how many you add within the hull, you don't get any 'more coin' (altering the plurality may help adults understand this problem.) If you have some button[s] and much more coin[s], can you add just one coin so that you have more coin than button? How far away do you need to add it?
don't be fooled by the title of the book. The content is beyond 7 year old kids in the US.