Math from Three to Seven: Chapters One and Three [pdf]
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Re: Math from Three to Seven: Chapters One and Three [pdf]
#2Absorbing tales, most likely for those of us with young children in the aforementioned age bracket. First time I'd read about Jean Piaget too. Was reading through @tokenadult's[1] site earlier and didn't see much mention of Piaget, so another good reference to add to the list.
This is the probably the most insightful part of the AMS narrative:
>OK, if it is so hard to teach kids the notion of a number, what am I trying to do? What is the point of my lessons? I said it many times and I am going to say it again: the meaning of the lessons is the lessons themselves. Because they are fun. Because it’s fun to ask questions and look for the answers. It’s a way of life.
Re: Math from Three to Seven: Chapters One and Three [pdf]
#3Absorbing tales, most likely for those of us with young children in the aforementioned age bracket. First time I'd read about Jean Piaget too. Was reading through @tokenadult's[1] site earlier and didn't see much mention of Piaget, so another good reference to add to the list. This is the probably the most insightful part of the AMS narrative: >OK, if it is so hard to teach kids the notion of a number, what am I tryi…
More direct link to his homeschooling site (because his profile is quite lengthy and filled with links): http://learninfreedom.org/
Re: Math from Three to Seven: Chapters One and Three [pdf]
#4Do we really need to work so hard to stimulate curiosity in people? Aren't people inherently very curious?
Re: Math from Three to Seven: Chapters One and Three [pdf]
#5Do we really need to work so hard to stimulate curiosity in people? Aren't people inherently very curious?
I think his point is that we need to work hard to avoid discouraging curiosity. Often it is replaced with rote memorization or knowing things because an authority figure says it is so.
Re: Math from Three to Seven: Chapters One and Three [pdf]
#6Do we really need to work so hard to stimulate curiosity in people? Aren't people inherently very curious?
I think his point is that we need to work hard to avoid discouraging curiosity. Often it is replaced with rote memorization or knowing things because an authority figure says it is so.
This is particularly true in math, as it is presented in many schools.
Re: Math from Three to Seven: Chapters One and Three [pdf]
#7Do we really need to work so hard to stimulate curiosity in people? Aren't people inherently very curious?
Serendipity does happen, and children will have some fascinating observations suddenly all on their own. But while they may be curious, they may not know that there's something to be curious at. Contriving a situation to foster that can help, perhaps.
I really loved his note about Dima who asked everyone to swap chairs around. The group had one more person than there were chairs, yet with each shuffling he was bewildered to find they were still short one chair. The child wasn't dumb, and in fact is occasionally clever, but this isn't the sort of problem to be curious at - it's baffling. (Though that's not to say Dima didn't reflect on it at a later date - I'm only halfway through.) The fact Dima didn't quite understand the problem is the part of the interesting point being made; something seems off, but Dima didn't understand to dig into it and figure out right then why this situation felt wrong, at least not yet. Indeed, shortly after on page 28 he notes that this sort of misunderstanding could happen to an old person, too, despite their longer lives and observations.
I think part of the lesson here is that the lessons don't even really stimulate curiosity. Rather, it gives the children more information, more opportunities to have that special serendipitous 'aha!' moment. To your point, it's more akin to bringing the child to a curious place and letting them do their natural thing, rather than foisting stimulation onto them.
Re: Math from Three to Seven: Chapters One and Three [pdf]
#8I 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/or teacher has in the arsenal.
I've always thought a lot of parents do it totally wrong...they give the misbehaving kid lots of (albeit negative) attention while the quiet, well-behaved one they ignore.
My parenting style was the exact opposite...I always stroked good behaviours and tried my best to ignore bad ones.
Re: Math from Three to Seven: Chapters One and Three [pdf]
#9Earlier quoted context omitted.
I think his point is that we need to work hard to avoid discouraging curiosity. Often it is replaced with rote memorization or knowing things because an authority figure says it is so.
This is particularly true in math, as it is presented in many schools.
Math is a weird topic. It can be completely wrong when teachers don't understand maths, and even with teachers that do convey the goal and added values of math, it's still off to me. The algorithms are too complex and learned without any real clues (you basically program pupils as biological Turing Machines / Arithmetic Units.. very sad).
Re: Math from Three to Seven: Chapters One and Three [pdf]
#10I 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. The promising students, on the other hand, are often expected to do their work in near-monastic solitude: usually, the only reason for special attention is if a student is performing weakly.
This is necessarily the case given that a teacher having to divide their attention between twenty students and the current priority structure of our schools. Regardless, that's a clear area for improvement.