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| Title: | 論乘法啟蒙教學中的詞序問題：語言學的觀點
On the Controversy over Word Orders in the Initial Teaching of Multiplication: A Linguistic Perspective |
| Authors: | 郭惠婷
Kuo, Hui-Ting |
| Contributors: | 何萬順
Her, One-Soon
郭惠婷
Kuo, Hui-Ting |
| Keywords: | 乘法教學
乘數
被乘數
位數詞
分類詞
詞序
倍數
Multiplication teaching
Multiplier
Multiplicand
Numeral base
Numeral classifier
Word order
Multiples |
| Date: | 2024 |
| Issue Date: | 2024-02-01 13:01:06 (UTC+8) |
| Abstract: | 本研究從語言學的觀點探究在乘法啟蒙教學中，乘數(multiplier)與被乘數(multiplicand)之間的詞序問題，主張在臺灣應優先採用乘數在前的主動句式。在認知概念層面，乘數與被乘數的意義分別是單位數(number of units)與單位量(number in a unit)，兩者為非線性(non-linear)的關係。然而在口語與文字的表述中，必然有線性的要求，乘法因此存在有「乘法交換律 (Commutative Law of Multiplication)」:被乘數與乘數位置互換，其結果仍然不變。在大多數人類語言的數詞系統中，以乘法構成的複合數詞(complex numeral)因此也存在兩種詞序:位數詞(numeral base)在後(base-final)，例如中文「三百」和英文 three hundred ，均為「3×100」;位數詞在前(base- initial)，如非洲尼日-剛果語系中的伊比比歐語的 ikie ita 以及南島語系中的基里維納語的 lakatu-tolu 卻都是「100×3」。而採用位數詞在後的詞序，也就是「乘數-被乘數」的語言在數量上較多一些。
有趣的是，乘法的兩種詞序卻在國小的數學啟蒙教育中成為爭議，各國作法不一。以「三隻兔子有幾隻腳?」為例，臺灣採行的算式是「4×3=12」，讀為「四『乘以』三等於十二」，因此是「被乘數×乘數」的被動句式。而美國卻以「3×4=12」為主，讀為 Three times four equals twelve(三「乘」四等於十 二)，是乘數在前的主動句式。本研究亦將檢視美中日韓等國的作法，也討論台灣支持被動句的理由。本研究將從語言學的角度出發，依序從詞序差異、主動句與被動句、係數詞與位數詞的詞序關係、數詞與分類詞/量詞的詞序關係等四個面向進行討論。主張在乘法啟蒙教學上，台灣應該優先採取乘數在前的主動句表達法。
在詞序差異上，本研究認為如果乘法算式的語言和學童本身的語言詞序是相同的，將會大幅降低兒童學習乘法的難度。在主動句與被動句的討論中，本研究認為華語乃賓格語言，乘法算式以主動句表達，將會比被動句更容易讓兒童理解。從位數詞與量詞詞序的觀點來看，六七歲的小學兒童已習得了「乘數─被乘數」的主動句表達法，乘法教學理應順勢而為。本研究認為其他國家亦可考慮本文的觀點，檢視學童的母語在乘法啟蒙教學上所能產生的正面影響。
This thesis explores the word order issue between the multiplier and the multiplicand in the teaching of initial multiplication from a linguistic perspective. We suggest that the multiplier-multiplicand word order is better than the multiplicand-multiplier word order in Taiwan. In fact, the multiplier and the multiplicand represent the number of units and the number in a unit, respectively, and they constitute a non-linear relationship between them. However, in oral and written expressions, linearization is necessary, leading to the presence of the "commutative property of multiplication": changing the order of the multiplier and multiplicand does not change the product. In most numeral systems, complex numerals formed by multiplication also exhibit two word orders: the base-final order, such as san bai ‘three hundred’ in Mandarin Chinese and three hundred in English, both representing "3×100" the base-initial order, such as ikie ita ‘hundred three’ in Ibibio (Niger-Congo) and lakatu-tolu ‘hundred three’ in Kilivila (Oceanic), both representing "100×3." And, the quantity of the base-final languages is greater than that of the base-initial languages.
In fact, the two word orders in multiplication have become a controversy in the teaching of initial multiplication. Taking the question "How many legs do three rabbits have?" as an example, Taiwan adopts the equation "4×3=12," read as "four
multiplied by three equals twelve," using the multiplicand-multiplier word order, which represents a passive expression. In contrast, the United States predominantly uses "3×4=12," read as "three times four equals twelve," choosing the multiplier-multiplicand word order, which signifies an active expression.
Different countries may choose either order for different reasons. Therefore, this thesis will examine the choices made by countries such as Japan, South Korea, China, and the United States while discussing the reasons for Taiwan's choice of the passive expression. This thesis will also explore four aspects from a linguistic perspective: differences between a natural language and the language of mathematics, active and passive constructions, the base word order, the classifier word order. We then argue that the active expression should be preferred in the teaching of initial multiplication in Taiwan.
Here are the viewpoints proposed in this thesis: First, we propose that if the language of mathematics is consistent with the natural language of children, it will significantly reduce the difficulty of children learning multiplication. Second, we believe that Mandarin Chinese as an accusative language, active sentences will be easier for children to comprehend than passive sentences. Finally, in terms of the base and classifier word order, six to seven-year-old Mandarin-speaking children have already acquired the multiplier-multiplicand word order. Therefore, we suggest that other countries may also consider the viewpoints presented in this paper, examining the impact of children's native language on the teaching of initial multiplication. |
| Reference: | 一、中文文獻
何萬順、林昆翰(2015)。分類詞與量詞的區分──以台灣華語為例。漢語學報，4，56-68。
李國偉(2014 年 2 月 5 日)。穿了衣服的數字。《科學人》雜誌。 https://www.scitw.cc/posts/6973
李珮妘(2022 年 1 月 13 日)。小二數學「6×9=54」竟是錯的?老師揭正解。中時新聞網。https://www.chinatimes.com/realtimenews/20220113005817-260405?chdtv
阿哈羅尼 (Aharoni, R.) 、李國偉(2018)。小學算術教什麼,怎麼教 : 家長須知, 也是教師指南 (第 1 版)。遠見天下文化。
南一書局(2022a)。國民小學國語首冊課本。南一書局。
南一書局(2022b)。國民小學國語 1 上課本。南一書局。
南一書局(2022c)。國民小學國語 1 下課本。南一書局。
南一書局(2022d)。國民小學國語 2 上課本。南一書局。
南一書局(2022e)。國民小學數學 1 上課本。南一書局。
南一書局(2022f)。國民小學數學 1 下課本。南一書局。
南一書局(2022g)。國民小學數學 2 上課本。南一書局。
南一書局(2022h)。國民小學生活 1 上課本。南一書局。
南一書局(2022i)。國民小學生活 1 下課本。南一書局。
南一書局(2022j)。國民小學生活 2 上課本。南一書局。
南一書局(2022k)。國民小學健康與體育 1 上課本。南一書局。
南一書局(2022l)。國民小學健康與體育 1 下課本。南一書局。
南一書局(2022m)。國民小學健康與體育 2 上課本。南一書局。
南一書局(2022n)。國民小學數學 2 上教師手冊。南一書局。
徐熙娣(作詞、作曲)(2022)。〈九九乘法表〉[徐熙娣主唱]，《elephant DEE 的 demo Oops!》。亞神音樂。
陳淑琳(2002)。國小二年級學童乘法文字題解題歷程之研究-以屏東市一所國小為例。〔碩士論文。國立屏東師範學院〕臺灣博碩士論文知識加值系統。 https://hdl.handle.net/11296/hmjcvv。
陳羿如、何萬順(2020)。華語分類詞的界定與教學上的分級。華文世界， 126，19-34。https://www.airitilibrary.com/Article/Detail?DocID=10170855- 202012-202101150016-202101150016-19-34
教育部(2018)。十二年國民基本教育國民中小學暨普通型高級中等學校數學領 域課程綱要。作者。
教育部(2022)。十二年國民基本教育課程綱要總綱。作者。
康軒文教事業(2022)。國民小學數學 2 上教師手冊。康軒文教事業。
黃敏晃(2013)。從乘法交換律談起。科學研習，52(2)，20-27。
張顯達、張鑑如、柯華葳、蔡素娟(2011)。台灣兒童語言語料庫之建置。行政院國家科學委員會專題研究成果報告(編號:NSC96-2420-H-002- 030)，未出版。
甯自強(1994)。新課程對乘法啟蒙教材的處理。載於教育部台灣省國民學校研 習會(主編)，國民小學數學科新課程概說(低年級)(頁 77-85)。教育部台灣省國民學校研習會。
甯自強(2005)。彈性的掌握數的雙重角色-單位量與單位數:以乘法對加法的分配性為例。 國教輔導雙月刊, 45(1), 19–26。
楊明憬(2009)。台灣與美國國小二到三年級數學乘法教材之研究。〔碩士論文。國立嘉義大學〕臺灣博碩士論文知識加值系統。 https://hdl.handle.net/11296/u6xak2。
楊德清、施怡真(2010)。臺灣與美國國小九九乘法教材內容之比較研究。教育研究月刊，190，52-68。
楊正凡(2017)。臺灣與中國國小數學教科書二年級乘法教材之分析比較。〔碩士論文。臺北市立大學〕臺灣博碩士論文知識加值系統。 https://hdl.handle.net/11296/58y6y5。
臺大科學教育發展中心 case(2019 年 10 月 23 日)。小學算術教什麼，怎麼教#李國偉【CASE 說書人】[影片]。YouTube。https://youtu.be/cZxi- eHMwzw?si=fHkkozV aDsZZj8GQ
臺大科學教育發展中心 case(2019 年 10 月 30 日)。小學算術教什麼，怎麼教#翁秉仁【CASE 說書人】[影片]。YouTube。 https://youtu.be/YwQTR4yuE5k?si=gzHZn0WzYOxBJv9T
翰林出版事業(2020)。國民小學數學 2 上課本。翰林出版事業。
翰林出版事業(2021)。國民小學數學 2 下課本。翰林出版事業。
賴宛君(2011)。準確界定漢語中分類詞。〔碩士論文。國立政治大學〕臺灣博碩士論文知識加值系統。 https://hdl.handle.net/11296/m764rf。
二、英文文獻
Aikhenvald, A. Y. (2000). Classifiers: A Typology of Noun Categorization Devices. Oxford: Oxford University Press.
Beilin, H. (1975). Studies in the cognitive basis of language development. Academic Press.
Comrie, B. (2013). Numeral Bases (v2020.3). In M. S. Dryer & M. Haspelmath (Eds.), The World Atlas of Language Structures Online. Zenodo. https://doi.org/10.5281/zenodo.7385533.
Chomsky, N. (2016). Minimal Computation and the Architecture of Language. Chinese Semiotic Studies, 12(1), 13-24. https://doi.org/10.1515/css-2016-0003
Chen, Yupin and Her, One-Soon. (in press). Parallel development of numerals and numeral classifiers in children's acquisition of Mandarin Chinese. Journal of Chinese Linguistics.
Dixon, R. M. W. (1994). Ergativity. Cambridge University Press.
Foster, C. (2022). Getting multiplication the right way round (Version 1). Loughborough. University. https://hdl.handle.net/2134/19299752.v1
Freudenthal, H. (2005). Didactical Phenomenology of Mathematical Structures. Springer Netherlands.
Greenberg, J. H. (1990). Numeral classifiers and substantival number: Problems in the genesis of a linguistic type. In K. Denning & S. Kemmer (Eds.), On language: Selected writings of Joseph H. Greenberg (pp. 166–193). Stanford: Stanford University Press. (Original work published 1972).
Her, O.-S. (2012). Distinguishing classifiers and measure words: A mathematical perspective and implications. Lingua, 122 (14), 1668–1691.
Her, O.-S. (2017). Deriving classifier word order typology, or Greenberg’s Universal 20A and Universal 20. Linguistics 55(2), 265-303.
Her, One-Soon, Yung-Ping Liang, Hsu Hung-Hsin, and Marc Allassonnière-Tang. (2022, December 10-12). Is It 'three hundred' or 'hundred three'? An Exploration of the Worldwide Distribution of Numeral Base Orders in Human Languages and Its Implications. 13th International Conference of Digital Archives and Digital Humanities, Taichung, Taiwan.
Isoda, M., & Olfos, R. (2021). Teaching Multiplication with Lesson Study: Japanese and Ibero-American Theories for International Mathematics Education. Springer Nature.
Sum, E., & Kwon, O. N. (2018). An Analysis of Linguistic Features of the Multiplication. Tables and the Language of Multiplication. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), 2839-2856. https://doi.org/10.29333/ejmste/90760
Shibatani, M. (Ed.). (1988). Passive and voice. John Benjamins Publishing.
Watanabe, T. (2003). Teaching multiplication: An analysis of elementary school mathematics teachers’manuals from Japan and the United States. The Elementary School Journal, 104(2), 111-125. https://doi.org/10.1086/499745 |
| Description: | 碩士
國立政治大學
語言學研究所
109555008 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109555008 |
| Data Type: | thesis |
| Appears in Collections: | [語言學研究所] 學位論文
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