2025年2月16日 星期日

Jean Piaget(1896–1980 )兒童發展心理學《皮亞杰對話錄》 (劉玉燕譯);比較了「在學校中學習」、以及「在市場工作」的孩童數學能力。Gustave Doré (18321883)法國版畫家和插畫家

最早知道心理學家Jean Piaget是1978年英國Essex 大學的電腦科學的學生之報告----要了解智慧型電腦. 似乎該深入了解Jean Piaget的百科全科式的兒童發展心理學
我在1985-95 之間才讀了許多皮亞杰Jean Piaget的著作

皮亞杰對話錄 (劉玉燕譯)的台灣版本的一小段是我大力促成的


......研究以印度的孩童為對象,比較了「在學校中學習」、以及「在市場工作」的孩童數學能力,發現兩者的數學能力有巨大的差異,而且他們的數學技能幾乎無法互相轉移。

動態消息貼文

東海物理晨間劇場(開學了QQ):早安科學新聞 其之24
中小學的數學老師在上課時,最容易碰到來自學生的質疑就是:「我們學了一堆這種數學,到底可以拿來幹嘛?」這時候老師經常要抬出各種大義名分,生活中有太多地方會用到數學了,別的不說,平常買東西的時候就經常要用到。
不過真的是這樣嗎?最近麻省理工學院的一項研究顯示,要把課堂上學到的數學用在生活中,還真不是那麼直接的事。
這項研究以印度的孩童為對象,比較了「在學校中學習」、以及「在市場工作」的孩童數學能力,發現兩者的數學能力有巨大的差異,而且他們的數學技能幾乎無法互相轉移。在市場工作的兒童能夠閃電般的算出交易的金額,但是面對學校的數學題時無能為力;而學校的學生能精確地解出標準化的數學問題,站在收銀台前面卻錯誤百出。
研究團隊招募了 1,400 名市場工作的兒童以及 471 名學校學生,並讓他們分別解決兩種不同類型的數學問題。
第一種是「模擬市場交易」問題,例如:馬鈴薯與洋蔥單價分別是每公斤20與15盧比,購買800g馬鈴薯與1.4kg洋蔥要多少錢?客戶用200 盧比鈔票付帳時,應該找回多少錢?這類問題模擬市場交易的情境,測試兒童如何應對現實中的金錢計算。
第二種則是「教科書式數學」問題,例如三位數除以一位數的除法,或是兩位數的減法計算,完全依照學校的標準測試模式來設計,以測試學生的計算能力。
研究結果顯示,市場工作的兒童在市場交易的計算測試中表現極為優異,正確率超過 90%。這些兒童能夠迅速且準確地計算總額與找零,並且主要使用「直覺性的心算策略」,例如將複雜的計算拆解為較簡單的步驟。例如,當他們遇到 19 乘以 7 時,他們可能會先計算 20 乘以 7,再減去 7,如此一來能夠更快得到答案(這種方法老師在課堂上都有教,但是學生後來通常都不會用)。他們也會使用近似計算,例如將 49 盧比視為 50 盧比來進行概算,然後再修正誤差,以此減少心算的負擔(我們每年都有家長抗議「概算」這個單元的題目)。這些策略讓市場兒童在交易時能夠迅速反應,且不需紙筆輔助,就能完成日常交易的計算任務。
然而,當這些市場兒童面對學校標準的數學測試時,情況卻截然不同。雖然就數學計算的內容而言,本質上跟市場上算的東西差不多,但是他們此時的正確率驟降至 32%。這是因為學校的數學題目與市場的計算的「情境」完全不同,市場兒童習慣於基於實際應用來計算,而非根據學校教授的標準化演算法來解題。因此,當問題沒有市場的情境與脈絡時,他們就不會啟動熟悉而有效的計算策略。
另一方面,學校學生在標準數學測試中表現優異,能夠準確運用筆算與固定演算法來解決問題。然而,當這些學生被要求進行市場交易模擬時,他們的表現卻極為糟糕,在部分測試中,正確率甚至僅有1%!這樣做生意會賠死吧!
學校學生的數學學習依賴固定的計算步驟,這些步驟在面對動態且多變的市場環境時,顯得僵硬而不靈活,甚至在學校裡,用那種「先靠直覺抓個大概,第二階段再把精確性補回來」的算法可能還會被老師罵咧。學校的學生習慣逐步計算、確保每一步的精確性,卻缺乏市場兒童那種靈活應變的能力。因此,當問題無法直接對應教科書上的標準解法時,他們便顯得無所適從。
這項研究結果顯示,數學能力的學習與「情境脈絡」高度相關,學校上課時的情境,導致所教授的數學知識很難自然地轉移到現實應用的情境,而市場中的計算技巧也無法適應教科書的題型。
不過即使是在「市場交易」的情境下,若逐步把交易問題變得更複雜,市場中的孩子的表現會開始下降,可能是因為直覺式的算法已經難以處理太複雜的問題;使用標準化解法的學生則會迎頭趕上。
目前的數學教育現場,經常還是照著教科書進行標準化的解題方法,並且強調筆算的精確度,將數學學習限制在固定的演算法與計算步驟內。學生如果使用教科書外的方法解題,可能會受到老師的質疑,甚至被要求改回「標準解法」。這種過度標準化的教育方式,可能限制了學生在現實世界中的應用能力,使他們難以靈活應對實際情境中的數學問題。
這項研究突顯了一個關鍵問題:如何讓學校數學教育更加貼近現實,並提升學生的數學遷移能力?本文作者班納吉(Abhijit V. Banerjee,他是2019年諾貝爾經濟學獎得主,沒有在駕駛獨角獸鋼彈…)認為,學校應該改變「只有一種正確解法」的教學方式,而是幫助學生培養估算能力,理解數學問題的本質,而非單純依賴固定算法。
「我們不應該責怪老師,因為這不是他們的錯。」另一位作者Esther Duflo補充,「教師被要求嚴格遵守課綱與固定的教學方法。」
在教學現場中引入更多的應用情境,而非只有「坐在座位上以標準的算法進行紙筆計算」,讓學生習慣於在不同的情境與脈絡下切換思考與計算的模式,是一個可能的改善方式,當然這又面臨教學時數與所需資源的拉扯,所以教育真的是很難……
這個研究,發表於2025/02/06的「Nature」期刊。
超中二物理宅雜記
話都給我說就好 其之496
可能是 1 人和文字的插圖


* 書緣:川瀨先生講談會、皮亞傑發生認識論精華譯叢;total book ...

mypaper.pchome.com.tw/2adigoxl/post/1260832545Translate this page
Nov 10, 2005 - 然後我太太劉玉燕根據日本和英文翻譯『皮亞傑對話錄』(Bringuier, J-C. (1980). Conversations with Jean Piaget. Chicago: University of Chicago ...
 
 Jean Piaget, 1896–1980,(簡稱JP)是我20年前醉心的科學家(知道他是在1978年英國的電腦科學博士生推薦的)。我還到加州大學Davis 校園找過資料。然後我太太
劉玉燕根據日本和英文翻譯『皮亞傑對話錄』(Bringuier, J-C. (1980). Conversations with Jean Piaget. Chicago: University of Chicago Press),我幫點小忙。



JP的主要著作大陸已翻譯十幾本。沒想到大陸教育界發揚光大,繼續弄「
皮亞傑發生認識論精華譯叢」,今天買到:
※走向一種意義的邏輯
※關於矛盾的研究
※可能性與必然性
※心理發生和科學史
(我會讀它們嗎?)

他的作品約2/3有英譯本 中國有翻譯



September 17, 1980
OBITUARY

Jean Piaget Dies in Geneva at 84

By ALDEN WHITMAN
Jean Piaget, the Swiss psychologist whose study of child development has often been compared to Freud's work in its vast influence on the science of human intelligence, died in Geneva today. He was 84 years old.
Dr. Piaget was hospitalized 10 days ago at Geneva Cantonal Hospital. He is survived by three children. The cause of death was not disclosed.
The question to which Jean Piaget addressed himself was deceptively obvious and simple: How does a child learn? His answer, often phrased in obtuse language, was in brief that a child learns by discrete stages related to age and that he is a significant agent in the process.
His stress on the interaction of biological functions and the structure of the environment, elaborated in more than 60 years of research, was, in the opinion of many psychologists and education specialists, as liberating and as revolutionary as Sigmund Freud's earlier insights into the stage development of human emotional life. Many hailed him as one of the century's most creative scientific thinkers.
And indeed Dr. Piaget's theories exercised a profound effect on thinking about children in Europe and America. They have basically altered man's perceptions of the mechanism and functioning of his intelligence. Educators seized upon his work.
In contrast to the traditional views of how we acquire knowledge--that heredity plays a dominant role or that environmental factors are controlling--Dr. Piaget proposed that each child, starting from birth, constructs and reconstructs his very own model of reality, of the world about him, in a regular sequence. He does this through a multitude of direct experiences with persons and objects, in the course of which cognitive growth takes place not merely by amassing new facts. The child's transformation of these experiences into conceptions is constantly revised through his own self- discoveries, which tend to eliminate errors in previous conceptions.
A simple example of this phenomenon was cited recently by Dr. David Elkind of Tufts University, a Piaget specialist. He wrote:
"The child of 3 or 4 already has an elementary concept of quantity: confronted with two identical glasses of orangeade filled to the same level, he would say that both had the 'same to drink.' But if the orangeade from one glass were poured into a tall, narrow beaker while he looked on, the child would say, Piaget found, that the tall glass had 'more to drink' than the shorter one.
"Not until about 6 or 7 do most children understand that changing the shape of a quantity does not change the amount. The young child has a concept of quantity, but it is clearly a different concept from the one held by older children and adults: he thinks the amount of liquid can be gauged by its level without taking its width into account. Older children and adults, however, assess liquid quantities by taking both height and width into consideration.
Mental Growth by Integration
"This is mental growth by integration, wherein a new, higher-level idea (amount is determined by height and width) is formed by the integration of two lower-level ideas (amount is determined by height or width). It suggests that mental growth is an expanding upward spiral in which the same problems are attacked at successive levels but are resolved more completely and more successfully at each higher level."
In addition, Dr. Piaget explained that mental growth takes place by integration of diverse concepts and replacement or primitive notions of nature by more mature ideas with age. Thus, very young children tend to believe that the sun and the moon follow them around, a notion that is replaced in later years.
Four Stages of Growth
Four major stages of mental growth were delineated by Dr. Piaget, based on the cognitive tasks accomplished in each.
In the sensory-motor period--the initial two years of life--the child is chiefly concerned with the mastery of objects, blocks, large toys, rocks, household objects and the like. From 2 to 6, his main concern is with symbols such as those in language, fantasy, dreams and play. For about the next five or six years, or until age 12, the child learns to master numbers, relations and classes and how to reason about them. Finally, in the three years to age 15, he is occupied with the mastering of purely logical thought, and he can think about his own thinking and that of others. The continuum, in Dr. Piaget's presentation, is quite complex, yet each stage has its telltale characteristics.
A number of hardy theories were challenged by Dr. Piaget's work: that a child is a little adult; that ideas are inborn; that learning takes place by environmental conditioning or reinforcement; that the young child is capable of absorbing facts as they are understood by adults; and that he copies the world about him. In place of these notions, Dr. Piaget sought to substitute what he called genetic epistemology.
In this concept, the timetable that appears to underlie the development of intellectual skills indicates that the capacity for logical thought is coded, along with sex, eye color and the shape of the nose, in the genes. Rational tendencies, however, do not mature simply because they are innate; rather, they grow with use.
The application of this theory in education stresses the importance of what is called the "discovery method" of teaching, in which a child gets an opportunity to apply his developing abilities and test their limitations. The teacher is a guide, not a force-feeder of ready-made truths.
"The goal of education is not to increase the amount of knowledge but to create the possibilities for a child to invent and discover, to create men who are capable of doing new things," Dr. Piaget explained.
Dr. Piaget's early discoveries with children gained him worldwide acclaim in the 20 and 30's, but after that his works were considered too remote from the dominant trends in American behavioral science. Then in the late 50's and early 60's he was rediscovered. In the last few years most of his basic works have been translated and several explications for the general reader have been published. The most accessible of Dr. Piaget's own works are "Six Psychological Studies" and "The Psychology of the Child;" books about him include "Understanding Piaget," "The Essential Piaget" and "An Outline of Piaget's Developmental Psychology for Students and Teachers."
Along with an enthusiasm for Dr. Piaget in some American academic and educational circles there has been criticism. Traditionalists objected to the radical way he conceived of the child's task of acquiring knowledge. And many sympathetic with Dr. Piaget's overall interpretation feel alternative interpretations can be put forth for many of the phenomena he uncovered. Other critics also argued that his theory offered little help in clarifying the motivations and accomplishments of individual children. Many critics, however, agreed with Robert Coles of Harvard that Dr. Piaget had focused psychologists' attention on "man the developing thinker rather than on man the universal neurotic."
Tall, portly and rumpled-looking in his bulky suits, Dr. Piaget resembled a magnified Einstein, an impression that was accented by his bushy white hair. Out of doors he covered part of this unruly mane with a navy blue beret. To many who met him, according to Professor Elkind, Dr. Piaget gave off "an aura of intellectual presence not unlike the aura of a dramatic presence emanated by a great actor." Smoking a meerschaum and chatting with friends--and especially with children--he seemed benign and gracious, but members of his staff in Geneva knew that he could also be aloof and remote.
Followed a Strict Schedule
For years he followed a strict schedule. Up at 4 A.M., he wrote at least four publishable pages in a small, even hand. Later, he taught classes or attended meetings. After lunch he walked and pondered whatever problem faced him. "I always like to think on a problem before reading about it," he said. And in the evening he read.
In the summer he departed to an Alpine retreat to talk, meditate and write. Apart from articles and lectures, his output totaled more than 50 books and monographs. Several of them, including "The Child's Conception of Space" and "The Growth of Logical Thinking From Childhood to Adolescence," were written with Barbel Inhelder, his longtime associate at the Institute of Educational Science in Geneva.
Dr. Piaget's road to child psychology started with a youthful interest in zoology. The son of specialist on the Middle Ages, he was born Aug. 9, 1896, in Neuchatel, Switzerland. Something of a prodigy, he published articles on mollusks in scientific journals by the age of 15. At 22 he was granted a doctoral degree with a thesis on mollusk distribution in the Valais Alps. He became interested also in psychology, attending lectures by Carl Jung. From these and his own speculations, he recalled, he became "haunted by the idea of discovering a sort of embryology of intelligence." This was the basis for his later idea that life could be understood best in terms of "structures of the whole."
In 1920 he went to Paris to work with Theodore Simon, a co-developer with Alfred Binet of an intelligence test for children. Scrutinizing responses to the test questions, Dr. Piaget believed he saw a pattern in the wrong answers, a pattern that related to a child's age group. This finding led him to investigate the children's world, including the crib activities of his own three youngsters.
Inside the Child's Mind
Possessed of a remarkable empathy with children, he spent long hours on his hands and knees shooting marbles with them, exploring their notions of space, ethics, numbers and the like. From these observations came his first book, "The Language and Thought of The Child," which traced the development of child's speech from egocentric to socialized forms.
His researches in psychology spanning over a half-century built up an impressive body of insights. His basic approach was to get inside of the child's mind and see the world through its eyes. "I engage my subjects in conversation," Dr. Piaget recounted, "patterned after psychiatric questioning, with the aim of discovering something about the reasoning underlying their right but especially their wrong answers."
Among other things, he found that "children not only reasoned differently from adults, but also that they had quite different world views, literally different philosophies." For example, he noted that in a child's view "objects like stones and clouds are imbued with motives, intentions and feelings." The mind is thus not a passive mirror but an active artist as it develops increasingly sophisticated versions of reality.
The unfolding of Dr. Piaget's explanations occurred over a lifetime, so there were refinements as new evidence was sifted; but these did not alter his basic theories.
The elaboration of these was institutionalized in the International Center for Genetic Epistemology that he established in Geneva in 1955 with funds from the Rockefeller Foundation.
In his mature years Dr. Piaget was widely acclaimed. There were honorary degrees from dozens of universities, including Oxford and Harvard, and impressive guest appearances at scholarly meetings. He remained, however, a remote public figure--more the distant philosopher than the polemicist.


古斯塔夫·多雷
法國版畫家和插畫家
——————————
 ♑️ 保羅·古斯塔夫·路易·克里斯托夫·多雷(1832 年 1 月 6 日 - 1883 年 1 月 23 日)是法國版畫家、插畫家、畫家、漫畫家、諷刺畫家和雕塑家。他最出名的作品是大量的古典文學木版畫,尤其是武加大聖經和但丁的《神曲》。這些作品取得了巨大的國際成功,他也因版畫創作而聞名,儘管他通常只是一名設計師;在他職業生涯的巔峰時期,大約有 40 名刻版工匠被雇用來將他的圖畫刻到木製印版上,通常還會在圖像上簽名。
代表作品:繪畫、蝕刻版畫、插圖
運動:浪漫主義、象徵主義
出生日期:1832 年 1 月 6 日,法國史特拉斯堡
逝世日期:1883 年 1 月 23 日(51 歲),法國巴黎
時期:浪漫主義、象徵主義、浪漫主義藝術
代表作品:繪畫、蝕刻版畫、插圖
父母:尚‧菲利普‧多雷、亞歷山大‧多雷
納達爾 (Nadar) 於 1856 年至

Gustave Doré
French printmaker and illustrator
——————————
♑️ Paul Gustave Louis Christophe Doré (6 January 1832 – 23 January 1883) was a French printmaker, illustrator, painter, comics artist, caricaturist, and sculptor. He is best known for his prolific output of wood-engravings illustrating classic literature, especially those for the Vulgate Bible and Dante's Divine Comedy. These achieved great international success, and he became renowned for printmaking, although his role was normally as the designer only; at the height of his career some 40 block-cutters were employed to cut his drawings onto the wooden printing blocks, usually also signing the image.
Known for: Painting, etching, illustrations
Movement: Romanticism, Symbolism
Born: 6 January 1832, Strasbourg, France
Died: 23 January 1883 (age 51 years), Paris, France
Periods: Romanticism, Symbolism, Romantic art
Known for: Painting, etching, illustrations
Parents: Jean-Philippe Doré, Alexandrine Doré
Photograph by Nadar, between 1856 and 1858.
可能是 1 人的圖像


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