k******s
发帖数: 237 | 1 The Child's Conception of Number/ Piaget, Jean
Jean Piaget was a Swiss developmental psychologist and philosopher known for
his epistemological studies with children.
It is very hard to read and grasp author's idea,But still it is very good
book to understand children's psyche about numbers.
Book summary based on my poor understanding:
Stage of understanding number:
Stage 1: intuition, perceptual, no understanding of number concept (
conversation law hidden in the number)
For example, two bunch of flowers same number, identical configuration 摆的
一样
3-4 year old children judge them same, if one bundled up, or spread out,
that is spatial perception is changed, they judge different. Even some
children can count 1, 2, 3 and count them, when spatial perception is
changed, they judge different, either one more or less than another, prove
no understanding of number.
Stage 2: still influenced by perception
Stage 3: old children, doing right. understand number concept, its inherent
conversation law and more.
My own comment: The children thought is different from adult, when we
teacher, I think we should try to understand children cognitive psyche.
Sometime, they think differently than adults.
Number is at the same time both class and asymmetrical relation. Page ix
Therefore, number is seen to be synthesis of class and asymmetrical relation
. p243
meaning of this sentence:
1 apple, 1 orange, 1 pear on the table, you count them, 1, 2, 3. In this
process, you conscientiously identify those as 3 things, not apple, not
orange, not pear, but 3 things which they are belong to (that is, class
means, identical things group together), at the same time you give them
position, 1st is the apple, 2nd is orange, 3rd is pear is asymmetrical
relation which you include the number, member of number are identical but
different in position.
You can count 3 apple, but class identical meaning is not so obvious.
My own comment:I've never thought number in this angle. | k******s
发帖数: 237 | 2 不知道是否说清楚的Class意思
1 apple + 1 orange = 2 fruit
1 apple + 1 orange = 2 food
1 apple + 1 orange = 2 thing .....
In this addition process, you look for common attribute, disregard
difference, apple, orange is fruit, food, or thing, etc, but not 2 oranges,
2 apples. This process give rise to number concept, which is what author
means clas | X****r
发帖数: 3557 | 3 这个不就是朴素集合论里对自然数的定义嘛，n被定义为所有含有n个元素的集合的集合
。以前版上好像还讨论过这个。大学学过集合论和数理逻辑的应该看到过吧，当然可能
新版教材可能不讲这个古老的有问题的定义了。
,
【在 k******s 的大作中提到】
: 不知道是否说清楚的Class意思
: 1 apple + 1 orange = 2 fruit
: 1 apple + 1 orange = 2 food
: 1 apple + 1 orange = 2 thing .....
: In this addition process, you look for common attribute, disregard
: difference, apple, orange is fruit, food, or thing, etc, but not 2 oranges,
: 2 apples. This process give rise to number concept, which is what author
: means clas
| k******s
发帖数: 237 | 4 从来不知道这个，也没有学过朴素集合论。大学学化学如果学过集合论和数理逻辑，也
忘了 | a*****g
发帖数: 19398 | 5 第一个阶段的试验都已经被推翻了
for
【在 k******s 的大作中提到】
: The Child's Conception of Number/ Piaget, Jean
: Jean Piaget was a Swiss developmental psychologist and philosopher known for
: his epistemological studies with children.
: It is very hard to read and grasp author's idea,But still it is very good
: book to understand children's psyche about numbers.
: Book summary based on my poor understanding:
: Stage of understanding number:
: Stage 1: intuition, perceptual, no understanding of number concept (
: conversation law hidden in the number)
: For example, two bunch of flowers same number, identical configuration 摆的
| k******s
发帖数: 237 | 6 第一个阶段的试验都已经被推翻了
Do not understand. Do you have any scientific research. I personally feel
this book is not bad if I did not quite understand author's issue, provide
me a guidance how to teach children. Think in Children's point of view. | a*****g
发帖数: 19398 | 7 你说的那个第一个观点的试验，后来学术界认为有重大缺陷。
别的学者做了另外一个试验——
有两堆糖给孩子选。
不管实验人员把多的一堆放得靠近还是分开远一些（相比少的一堆）
孩子都会去选数量多的一堆。
所以认为小孩子是有数学 Number Sense 的，
只是小孩子不理解试验人员说的语言和问的问题——
到底是要选择“多”的，还是“少”的，
还是“宽”，“大”的、还是有变化的或者形状古怪的？
【在 k******s 的大作中提到】
: 第一个阶段的试验都已经被推翻了
: Do not understand. Do you have any scientific research. I personally feel
: this book is not bad if I did not quite understand author's issue, provide
: me a guidance how to teach children. Think in Children's point of view.
| k******s
发帖数: 237 | 8 I do not think that Piaget, Jean is so stupid, not considering 只是小孩子不
理解试验人员说的语言和问的问题. If you see this book, his experiment is
extremely well-designed, try to avoid language problem. He tried so many
different object, continuous object (like water) vs. discrete object (like
candy, bean), and other sort of consideration, I really doubt 别的学者做了另
外一个试验. e.g, for his candy experiment, he explicitly ask children, do I
have more candy to eat, or you have more candy to eat when compare my pile
of candy and your pile of candy in spite of shape of pile. |
| S*******s
发帖数: 13043 | 9 皮亚杰的贡献主要是认知发展而不是教育吧。这里的人们更多关心怎么让孩子掌握各种
技能而不是这些技能的内在学习机制。而且以现在的标准看，他的结论也嫌机械草率了
些。 | k******s
发帖数: 237 | 10 皮亚杰的贡献主要是认知发展而不是教育. You are right. But 教育家 must
understand 认知 in order to design good textbooks. I think his books is must
read for any elementary school teachers, although I found his books is very
hard to understand due to lack knowledge of deep knowledge of math, e.g, It
is hard to full understand all his tests, to me, all tests are identical.
other books like
The Child's Conception of space
The Child's Conception of geometry
very intriguing, I do not have time to read it.
现在的标准看，他的结论也嫌机械草率了些。
I do not agree. If you really read this book, his conclusion is exact
process of children number development, first 感观 then 逻辑. Some kids may
progress quicker than others, but everyone 经历这一过程. When adult can not
judge thing by logic, they use 感觉， they rol back to primitive level. | u*****a
发帖数: 6276 | 11 1 horse + 1 donkey = 1 mule
1 electron + 1 positron = two photons | S*******s
发帖数: 13043 | 12 你应该不是科班出身吧。皮亚杰的研究对于教学实践帮助不大。或者换种说法，他对教
育的影响太深远了，以致于其中被广泛接受的部分都成为今天所有老师的常识，甚至在
他出版他的著作之前。
记得当年上发心课去附近幼儿园做实验就像个笑话，原始数据很难证实他的结论。于是
就需要“解释”。这可能也是这些欧洲心理学家的传统吧，从弗洛伊德到容格到格式塔
到结构主义，每个大师都弄出一大堆语焉不详的新术语来好让学术权威随心所欲地给信
徒证明他们的理论是如何完美地反映了现实世界。
must
very
It
【在 k******s 的大作中提到】
: 皮亚杰的贡献主要是认知发展而不是教育. You are right. But 教育家 must
: understand 认知 in order to design good textbooks. I think his books is must
: read for any elementary school teachers, although I found his books is very
: hard to understand due to lack knowledge of deep knowledge of math, e.g, It
: is hard to full understand all his tests, to me, all tests are identical.
: other books like
: The Child's Conception of space
: The Child's Conception of geometry
: very intriguing, I do not have time to read it.
: 现在的标准看，他的结论也嫌机械草率了些。
|
|
