Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/73283


Title: 國中學生在絕對值相關問題之概念錯誤研究
An investigation into junior high school students’ conceptual errors on absolute value
Authors: 郭盈瑜
Kuo, Ying Yu
Contributors: 譚克平
Tam, Hak Ping
郭盈瑜
Kuo, Ying Yu
Keywords: 絕對值
錯誤概念
調查法
無結構性訪問
absolute value
conceptual error
survey research
unstructured interview
Date: 2013
Issue Date: 2015-02-03 10:24:05 (UTC+8)
Abstract: 本研究的目的主要為探討學生在解決絕對值相關題目時所遇到的困難,進而瞭解學生在解此類問題時出現錯誤之原因,希望研究的結果能夠提供教師作為補救教學或改進教學策略的依據,增進教學成效,並作為未來教學及研究的參考。

  本研究採調查法,並輔之以訪談蒐集資料。第一階段為問卷調查,經由對絕對值相關概念作文獻探討,以及與多位數學教師討論之後,研究者以自編之絕對值相關概念試題本進行施測,藉此瞭解學生在各向度的答題情況,並且作為選擇訪談對象的依據。第二階段為無結構開放式訪談,主要訪談學生作答時之想法與解題策略,所有訪談皆全程錄音,並轉錄成文字檔後進行內容分析,進一步瞭解學生在概念上錯誤的內涵,以及探討解題困難產生的原因。

  研究結果發現,學生在絕對值相關概念之錯誤可歸納出五大原因:過度簡化絕對值定義之口訣、無法進行絕對值概念中「幾何概念」與「算術概念」之間的轉化、不瞭解絕對值概念中各同義詞之間的關係、以偏概全絕對值之定義以及文字符號概念之理解困難。文後尚有提供絕對值相關教學改善的建議。
This study aims to explore the kinds of difficulties encountered by junior high school students in solving problems related to absolute value as well as analyzing and identifying the probable causes of such difficulties. It is hoped that the results from this attempt can provide teachers with useful information regarding how to improve their instructional practices and plan remedial instruction, thereby enhancing their teaching effectiveness.

The main methodology for this study is survey design supplemented with clinical interviews that allowed for in-depth information collection regarding problem solving strategies and difficulties from selected respondents. During the first stage, a literature review was conducted on research studies that focused on absolute values. This was followed by discussions with several junior high school mathematics teachers relating to learning difficulties they observed. Subsequently, a paper and pencil test instrument on absolute values with three main dimensions was compiled by the author to test the learning status of the participating students. Their performances would form the basis for selecting them to participate in the second stage of the study, namely, the interview phase. All clinical interviews were unstructured and they were recorded and transcribed into verbal records. Analyses were then performed to identify the presence of conceptual misunderstandings and explored the causes of such difficulties.

It was found that students’ conceptual errors on absolute values can be classified into five different types, namely, oversimplifying the definition of absolute value into mnemonic phrases, inability to perform inscriptional transformation between geometric properties and arithmetical concepts of absolute values, incomprehension of the relationships among the synonyms related to the concept of absolute value, over-generalizing the definition of absolute values and difficulties in understanding the connotation behind letter symbols. Several suggestions regarding instructional practices as well as future direction of research based on the present findings were provided at the end of this study.
Reference: 一、 英文文獻
Ahuja, M. (1976). An approach to absolute value problems. The Mathematics Teachers, 69(7), 594-596.
Brumfiel, C. (1980). Teaching the absolute value function. The Mathematics Teachers, 73(1), 24-30.
Dreyfus, T. (1985). A graphical approach to solving inequality. School Science and Mathematics, 85(8), 561-662.
Almog, N., & Ilany, B.-S. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Education Studies in Mathematics, 81, 347-364.
Ozmantar, M., & Roper, T. (2004). Mathematical abstraction through scaffolding. In M. J. Høines, & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education, 3, 481–488.
Parish, C. R. (1992). Inequalities, absolute value, and logical connectives. The Mathematics Teacher, 85(9), 756-757.
Sink, S. C. (1979). |Understanding absolute value|<0. The Mathematics Teachers, 72, 191-195.
Shuell, T. (1990). Phases of meaningful learning. Review of Educational Research, 60, 531-547.
Siegel, A. W. (1981). The externalization of cognitive maps by children and adults: A search of ways to ask better questions. In L. S. Liben, A. H. Patterson & N. Newcomb (Eds.), Spatial representation and behavior across the lifespan (pp.167-194). New York, NY: Academic Press.
Taira, K. T. (1987). Error reduction strategies for whole number operations in grade four. Unpublished doctoral dissertation of the Brigham Young University, Provo, Utah.

二、 中文文獻
王克先(1996)。學習心理學。臺北市:桂冠圖書公司。
左台益(2013)。國民中學數學第一冊。臺南市:南一書局企業股份有限公司。
李美君(2007)。高職學生線型函數相關特徵概念錯誤類型之分析研究。未出版之碩士論文,國立政治大學應用數學研究所,臺北市。
李靜瑤(1994)。高雄市國二學生數學解題歷程之分析研究。未出版之碩士論文,國立高雄師範大學數學研究所,高雄市。
周何總主編(1987)。國語活用辭典。臺北市:五南圖書出版股份有限公司。
金玉麒(1987)。國中生絕對值與不等式概念的錯誤分析及補救教學。(NSC75-0111-S017-005)。臺北市:行政院國家科學委員會。
洪碧芳(2003)。青少年的絕對值與不等式開念發展研(NSC91-2522-S-240-002)。    
臺北市:行政院國家科學委員會。
張立群(2003)。台南地區國一學生整數的加減法單元錯誤類型之分析研究。未出版之碩士論文,國立高雄師範大學數學系,高雄市。
張春興(1996)。教育心理學。臺北市:東華書局。
張景媛(1994)。數學文字題錯誤概念分析及學生建構數學概念之研究。國立台灣師範大學教育心理與福導學系教育心理學報,27,175-200。
陳昭地(1986)。國民中學數學科教科書第一冊。國立編譯館。
陳瑾儀(2012)。國一學生一元一次不等式錯誤類型分析之研究。未出版之碩士論
 文,國立政治大學應用數學研究所,臺北市。
楊秀菁(2012)。高中生絕對值概念學習之錯誤類型分析研究-以彰化地區某高中為例。未出版之碩士論文,國立中興大學應用數學研究所, 臺中市。
楊瑞智(1990)。四則運算的錯誤類型及教學上的應用。國教月刊,36(9-10)。
趙文敏(1985)。數學史第一卷。臺北市,協進圖書公司。
劉雲章(2003)。數學溯源-數學名詞的故事。新竹市,凡異出版社。
黃武雄(1979)。中國數學史簡說。數學傳播第三卷第三期。2013年12月28日,
取自http://episte.math.ntu.edu.tw/articles/mm/mm_03_3_06/index.html。
蘇慧娟(1998)。高雄地區國二學生方根概念及運算錯誤類型之分析研究。未出版
  之碩士論文,國立高雄師範大學數學研究所,高雄市。
Description: 碩士
國立政治大學
應用數學系數學教學碩士在職專班
98972014
102
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0098972014
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

Files in This Item:

File SizeFormat
201401.pdf1470KbAdobe PDF100View/Open


All items in 學術集成 are protected by copyright, with all rights reserved.


社群 sharing