數(shù)學(xué)基礎(chǔ)認(rèn)識(shí)與理解.ppt

1、數(shù)學(xué)基礎(chǔ)認(rèn)識(shí)與理解Mathematical Literacy and Understanding,數(shù)量的認(rèn)識(shí)和數(shù)數(shù),兒童從多大開(kāi)始有數(shù)量的觀(guān)念呢? 數(shù)量的認(rèn)識(shí)是怎麼? 是先天的還是後天培養(yǎng)的? 兒童對(duì)數(shù)量的認(rèn)識(shí)是是透過(guò)聽(tīng)覺(jué), 視覺(jué), 還是其他呢? 兒童何時(shí)懂得加數(shù),減數(shù)? 他們懂得做多大的數(shù)量的加減? 兒童何時(shí)懂得數(shù)數(shù)? 數(shù)數(shù)過(guò)程中包含什麼概念?,Humans are born with a fundamental sense of quantity?,Same number of marbles?,4/5 years old: Left, yes; Right, no. they can a

2、nswer correctly until 7-8 years.,Younger children do not posses a conceptual understanding of numbers and that any number re-related activities are learned by rote?,2 1/2 years to 4 1/2 years olds,Take the row you want to eat, and eat all the M&Ms in that row.,Children understand more than and less

3、than.,Numerical Competencies,Numerosity (數(shù)量感): 對(duì)數(shù)量的認(rèn)識(shí) Ordinality(序列感): 對(duì)順序的認(rèn)識(shí) Arithmetic: 基本數(shù)學(xué)運(yùn)算,思考問(wèn)題,你以為兒童能否認(rèn)識(shí)簡(jiǎn)單的數(shù)量呢? 如果可以, 他們可以認(rèn)識(shí)到多大的數(shù)量? 這種能力是與生俱來(lái)的(Innate)還是後天學(xué)習(xí)得到的? 如果你是一個(gè)研究人員, 你將怎樣設(shè)計(jì)你的實(shí)驗(yàn)以找出這些問(wèn)題的答案呢?,Numerosity,Habituation procedure: dishabituation means notificaiton of number of presented dots c

4、hanged. 4 months to 7 1/2 months: discriminate 2 from 3 items but not 4 from 6 itms. 10 - 12 months: 2 from 3, not 4 from 5 infants: look longer when 2 dots presented with 2 drum bits, (abstracts codes for numerosities up to 3 or 4 items),Infants abilities in numerosity,Not dependent on a specific m

5、odality not influenced by factors such as: whether dots or household items are presented, whether the presented items are static or moving, density of the displays,Ordinality,Infants sensitive to numerosity implies they understand larger than or less than? Ordinality before or after numerosity? Why?

6、,思考問(wèn)題,Ordinality,Infants represent numerosity do not imply they can rank the representations. Developed during the first 1 1/2 years of life.,討論問(wèn)題,兒童懂得加數(shù)和減數(shù)嗎, 何時(shí)開(kāi)始懂得呢? 如果他們年紀(jì)這麼少便懂得加減數(shù), 這顯示了什麼呢?,Arithmetic,Infants have a preliminary sense of addition and subtraction at 5 months of age.,Objects take o

7、ut or add in,Infant looks in this direction,討論題目,你怎樣看出一組物件的數(shù)目?,Development of Early Numerical Abilities,Subitizing Counting Estimating,Reaction Time Patters for Making Numerosity Judgments,討論題目,試解釋上圖背後的原因,Error Rates,Rare for arrays with 4 or fewer items 50% for arrays with more than 7 items,討論題目,兒童

8、何時(shí)開(kāi)始數(shù)數(shù)? 什麼原因令他開(kāi)始? 數(shù)目有什麼特質(zhì)? 數(shù)數(shù)是什麼? 包括什麼過(guò)程? 兒童要懂得什麼才能開(kāi)始數(shù)數(shù)? 數(shù)數(shù)過(guò)程中包含許多概念, 兒童是先有概念才數(shù)數(shù),還是從數(shù)數(shù)中學(xué)習(xí)概念?,Properties of Number System,Each number word is unique and represent a unique quantity numbers are serially ordered each number reflects a group of smaller numbers.,Counting: basic skills involved,One-to-one

9、 correspondence between number names and the counted items order the number names in the correct sequence the last number named in the count (the cardinal number) represents the total number of counted items.,Cardinality and Ordinality,Cardinality: number word assigned to the last counted object can

10、 be used to represent the total number of the counted objects Ordinality: successive number words represent successively larger quantities.,Cardinality and Last-word Rule,Test of cardinality: A child is asked to count his or her fingers asked, “How many fingers do you have?” understand the concept o

11、f cardinality or just use the Last-word Rule? Cardinality is always confused by how the items are arranged.,Ordinality,Refers mostly to the childs knowledge of equivalence and greater than and less than. Children as young as 2 1/2 years of age have an understanding of ordinal relationships.,Developm

12、ental Mechanisms for Counting and Number Knowledge,Most researchers agree that a sensitivity to numerical information is, at least in part, inborn, there is considerable disagreement over the relative importance of this innate sensitivity. Tow general positions: principals-first: innate principles g

13、uide the development, procedures-first: first count by rote and gradually induce counting concepts.,Principles-First,Behavior of young children guided by 5 principles: one-one correspondence: one number word one counted object stable order: same sequence of number words for counting cardinality: the

14、 number word associated with the last counted item has a special meaning. Abstraction: awareness of what is countable (skill at counting mixed sets too) order irrelevance:,The principles guide and structure the childs counting behavior, serve as a reference against which the child can evaluate this actual counting behavior, and m