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研究生:李貞慧
研究生(外文):Chen-hui Lee
論文名稱:低年級學童使用數的分解紀錄對解決加減問題效性之研究
論文名稱(外文):The research of the efficiency of how junior(second grade)students solving the addition and subtraction problem by adopting the numeric separate record
指導教授:葉啟村葉啟村引用關係
學位類別:碩士
校院名稱:國立臺南大學
系所名稱:數學教育學系
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
畢業學年度:90
語文別:中文
論文頁數:121
中文關鍵詞:數的分解紀錄加減問題
外文關鍵詞:numeric separate recordaddition and subtraction problem
相關次數:
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本研究係為了協助學生形成加減互逆概念的過程能夠更有效的學習,以獲得較正確的加減互逆概念,因而運用此概念進行數學解題活動,本研究依此目的作為實驗教學設計的準繩。
在實驗教學設計中,藉由「數的分解紀錄」(a=b+c)引入,協助學生了解加減問題背後的「部份-全體」基模,引導學生形成加減互逆概念。
因此,本研究有以下兩項研究方向:
一、研究者擬設計將「數的分解紀錄」引入實際教學課程中,欲探討此一課程是否有助於學生形成加減互逆概念。
二、研究者欲探討進行實驗教學後,不同數學成就表現的學生在加減互逆概念運用的情形為何。
本研究針對台南市安平國小二年級的學生,選擇二個班在八次的成績考查平均相當,且班級教師願意協助的班級進行研究,其中一班作為實驗班進行「數的分解紀錄」引入教學,另一班則作為對照班依課程內容進行教學,在教學前先進行前測,教學後隨即進行後測,並在一個月後進行延後測;還挑選高分組、中分組、低分組學生進行訪談。
在教學實驗處理後,將所得的成績,以前測為共變量的因素下,以單因子共變數分析加以考驗,其結論如下:
一、在後測表現上,實驗班與對照班在成績表現上並未達顯著差異,亦即「數的分解紀錄」引入對學生學習加減互逆概念上並未有明顯的影響。
二、在延後測表現上,實驗班與對照班在成績表現上達顯著差異,亦即「數的分解紀錄」引入對學生學習加減互逆概念的保留概念上有顯著影響。
三、實驗班高分組學生已可以掌握加減問題的「部份-全體」基模,並運用此基模進行解題;對照班高分組、實驗班中分組、對照班中分組學生則能在形成階段;實驗班低分組與對照班低分組的學生解數學加減文字題易從題目的關鍵字作答,對加減互逆概念的形成沒有幫助。
根據上述教學實驗之研究結果,提出下列建議:
一、教師可在教學中試著引入「數的分解紀錄」,引導學生思考,協助學生形成概念。
二、教科書編輯委員們亦可試著將此教案(如:附錄七)引入課程中,或把此課程放置教學指引中提供教師教學參考用。
This research is based on the concept wants to help students learn the concept of correlated with addition and subtraction more efficiently, acquire the concept of correlated with addition and subtraction more correct, and adopt the concept to proceed the activity of solving mathematics questions. The objective of this research is to be the guide of the experimental course.
In the design of the experimental course, it will assist students to understand the part-whole schema behind the addition and subtraction problem by adopting the numeric separate record(a=b+c). Therefore, there are two researching directions in this research. First, researcher plans to adopt the numeric separate record in the experimental course and to research whether this course helps students form the concept of correlated with addition and subtraction. Second, researcher would like to research how students with different mathematics performance will apply the concept of correlated with addition and subtraction after taking the experimental course.
The experimenters of this research are the second grade students of An-Ping elementary school in Tainan. This research picks two classes that have the commensurate grade in eight times of examinations and the preceptors of the classes are willing to help this research to perform this experiment. One of the two classes is the experimental team to adopt the numeric separate record into the courses, and the other is the contrastive team and takes the original courses. Students will take the pre-test before taking the courses, take the post-test after taking the courses immediately and take the follow-up test after one month. Students will be divided into high-grade, medium-grade, low-grade groups and interviewed respectively.
After the experiment, the grades will be proofed by one-way analysis of covariance with using the pre-test for factor of the covariate. Below are the conclusions :
First, in the performance of the post-test, the grade of the test is no specific difference between experimental class and the contrastive class. It means there is no conspicuous influence on students to understand the concept of correlated with addition and subtraction after adopting the numeric separate record. Second, in the performance of follow-up test, there is a conspicuous difference between the experimental class and the contrastive class. It means there is conspicuous influence on students to understand the concept of correlated with addition and subtraction after adopting the numeric separate record. Third, the students in the high-grade group of the experimental class has captured the idea of the part-whole schema in the addition and subtraction problem; Students of the high-grade group in the contrastive class and the students of the medium-grade group in the experimental class are in the forming stage; Students of the low-grade group in the experimental class and the students of the low-grade group in the contrastive class are used to solve the question according to the key words in the question instead using the concept of correlated with addition and subtraction.
Based on the result of the teaching experiment, here are some suggestions. First, teachers can try to adopt the “numeric separate record” into the courses to guide the students to think and help students form the concept. Second, schoolbook committees can try to innovate the teaching plan (appendix 7) into the course or put this course into the teaching direction for teachers to use.
第一章 緒論
第一節 研究動機 1
第二節 研究目的 3
第三節 待答問題 3
第四節 研究限制 3
第五節 名詞釋義 4
第二章 文獻探討
第一節 加減文字題的回顧 5
第二節 加減文字題解題策略之探討 7
第三節 加減互逆概念之介紹 9
第四節 表徵與數學課程的關係 12
第五節 一、二、三年級加減教材內容介紹 15
第六節 實施延後測的案例 19
第三章 研究設計與實施
第一節 研究對象 21
第二節 研究工具 21
第三節 研究步驟 21
第四節 實施程序 22
第五節 資料處理與統計方法 23
第四章 研究結果與討論
第一節 統計分析結果 25
第二節 訪談結果的分析 28
第五章 結論與建議
第一節 研究結論 54
第二節 建議 55
參考書目 56
附錄 59
一、中文部份
古明峰(民87)。加減法應用題語意知識對問題難度之影響暨動態評量在應用問題之學習及遷移歷程之研究。新竹師院學報。11,391-420頁。
古明峰(民88)。加減法文字題語意結構、問題難度與解題關係之探討。新竹師院學報。12,1-25頁。
李舜隆(民87)。加減問題解題活動類型-一個國小四年級兒童的個案研究。國立嘉義師範學院國民教育研究所碩士論文。

吳昭容(民89)。實驗班與對照組延後評量之結果分析。國民小學數學科新課程概說(高年級)。台北縣:台灣省國民學校教師研習會。
林宜臻(民89)。促成思考過程之形成性評量在學校本位數學學習領域課程設計之應用。九年一貫課程的教與學。台北縣:台灣省國民學校教師研習會。
林美惠(民86)。題目表徵形式與國小二年級學生加減法解題之相關研究。國立嘉義師範學院國民教育研究所碩士論文。

翁嘉英(民77)。國小兒童解數學應用問題的認知歷程。國立台灣大學心理學研究碩士論文。

張淑怡(民84)。加減問題解題活動類型-一個國小低年級兒童的個案研究。國立高雄師範大學數學教育研究所碩士論文。

教育部(民82)。國民小學課程標準。台北市:台捷。
陳立倫(民89)。兒童解答數學文字題的認知歷程。國立中正大學心理學研究所碩士論文。

葉雪梅(民79)。國小兒童對比較類應用問題的解題行為。國立政治大學教育研究所碩士論文。

黃淑華等人(民86)。教學指引。台北市:康軒文化。
甯自強(民81a)。正整數的啟蒙(三)∼計算活動的引入∼。教師之友,34(4),55-58。
甯自強(民81b)。經濟計數的活動∼高階單位『十』的首度引入∼。教師之友,33(5),47-51。
甯自強(民82)。兩步驟的問題。教師之友,34(2),45-49。
蔣治邦(民89)。由表徵觀點探討新教材數與計算活動的設計。國民小學數學科新課程概說(低年級)。台北縣:台灣省國民學校教師研習會。
劉秋木(民89)。國小數學科教學研究。台中市:五南圖書出版有限公司。
謝毅興(民80)。國小兒童解數學應用問題的策略。國立台灣大學心理學研究碩士論文。

二、英文部份
Bruner,J.S.(1966).Toward a theory of instruction. Cambridge,MA:Harvard University.
Carpenter,T.P.,& Moser,J.M.(1982).The development of addition and subtraction problem-solving skills.In T.P.Carpenter ,J.M. Moser,&T.A.Romgerb(Eds), Addition and subtraction:A cognitive perspective.(pp 9-24).Hillsdale,NJ:LEA.
Carpenter,T.P.(1985).Learning to add and subtract :An exercise in problem solving.In E.A.Silver(E.d),Teaching and learning problem solving:Multiple research perspective. (pp.17-40). Hillsdale,NJ:LEA.
Lesh,R.(1979).Mathematical learning disabilities:Considerations for identification,diagnosis,and remediation.In R.Lesh,D.Mierkiewicz,& M.G.Kantowski(Eds.). Applied mathematical problem solving. Columbus,OH:ERIC/SMEAC.
Lesh,R.(1981). Applied mathematical problem solving. Education Studies in Mathematics,12,235-264.
Lewis, A.B.,& Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79, 363-371.
Mayer, R. E.(1987). Educational Psychology : A Cognitive Approach , Boston : Little, Brown and Company.
Nesher,P.(1976).Three determinants of difficulty in verbal arithmetic problem. Education Studies in Mathematics,7,369-388.
Nesher,P.(1982).Levels of description in the analysis of addition and subtraction word problem.In T.P.Carpenter,J.M.Moser,&T.A.Romberg(Eds.),Addition and subtraction:A cognitive perspective.(pp.25-38). Hillsdale,NJ:LEA
Riley,M.S.,Greeno,J.G., & Heller,J.I.(1983).Development of children’s problem solving ability in arithmetic. In H.P.Ginberg(Ed.).The development of mathematical thinking.(pp.153-196). Orlando,FL:Academic.
Rosenthal,D.J.A.,& Resnick,L.B.(1974).Children’s solution processes in arithmetic word problem. Journal of Educational Psychology. 66.817-825.
Steffe,L.P. (1988).Children’s construction of number sequences and multiplying schemes. In J.Heibert & M.Behr(Eds.),Number concepts and operations in the middle grades. (pp 119-140).Hillsdale, NJ:LEA.
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