Author: |
李金雀 Chin-Chueh Li |
---|---|
Thesis Title: |
問題基模與基模圖示表徵解題課程對國小三年級學童數學解題表現之影響 The Effects of Teaching Schematic Drawing on Mathematical Problem-Solving Performance of Third Grade Students |
Advisor: |
陳李綢
Chen, Li-Chou |
Degree: |
碩士 Master |
Department: |
教育心理與輔導學系 Department of Educational Psychology and Counseling |
Thesis Publication Year: | 2006 |
Academic Year: | 94 |
Language: | 中文 |
Number of pages: | 190 |
Keywords (in Chinese): | 問題基模 、基模圖示 、表徵 |
Keywords (in English): | problem schema, schematic drawing, representation |
Thesis Type: | Academic thesis/ dissertation |
Reference times: | Clicks: 270 Downloads: 22 |
Share: |
School Collection Retrieve National Library Collection Retrieve Error Report |
本研究主要目的在設計一套問題基模圖示表徵解題課程,探討該課程對國小三年級學生在改變與比較題型之加減應用題解題表現的立即及追蹤效果,以及分析學生形成問題基模和自行產生問題基模表徵圖示的情形。以國小三年級六十名學生為研究對象,實驗組、控制組學生各三十名,實驗組接受實驗課程處理,控制組則無。本研究以「加減應用題成就測驗」為量化資料的評量工具,於課程結束二週後再進行追蹤後測,將所得資料以前測成績為共變數,使用獨立樣本單因子共變數分析統計方法進行資料處理,並分析「問題基模分類作業」、「問題基模圖示表徵作業單」、「問題基模圖示表徵學習心得問卷」及「教師省思札記」為輔佐資料,以瞭解本研究課程方案介入的效果。研究結果主要發現如下:
一、問題基模與基模圖示表徵解題課程對加減應用題解題表現具有提升效果
(一)實驗課程對加減應用題解題表現具有立即提升效果
(二)實驗課程對加減應用題解題表現具有追蹤提升效果
二、實驗組學生能形成加減應用題問題基模並據以分類加減應用問題
三、實驗組學童在加減應用題上能自行產生適當的問題基模圖示表徵
四、實驗組學童對問題基模圖示表徵具有正向的意見看法
最後,根據本研究結果加以討論,對未來數學解題教育及未來研究提出具體建議,以做為後續數學教育及未來研究的參考。
The purpose of this study is to design a schematic drawing training program for 3th grade students and to investigate its immediate and tracking effects on students’ problem-solving performance on “changed and compared” word problems. Also, it focuses on the situation of student’s generating problem schema and representation. 60 students from an elementary school were as subjects, 30 students for experimental group and control group. Students in the experimental group went through schematic drawing training program, while those in the control group didn’t. The quantitative instrument utilized to examine the effcts of the training is“Addition and Subtraction Word Problem Achievement Test”, which was administered at the end of the training and 2 weeks later for tracking. The collected data were analyzed with one-way ANCOVA. The other data including “problem schema sorting tasks”, “schematic drawing tasks”, “learning questionnaire of schematic drawing”, and “teacher’s reflective journals” were also analyzed to examine the effects of the training. The findings were presented as follows: 1.Schematic drawing training program could improve the performance of problem-solving for addition and subtraction word problems.for example, (1) The experimental program could immediately improve the performance of problem-solving for addition and subtraction word problems. (2) The experimental program could maintain the improvement in problem-solving for addition and subtraction word problems.2.Experimental group could generate problem schema of addition and subtraction word problems and classify the problems according to the schema.3.Experimental group could generate suitable schematic drawing of addition and subtraction word problems.4.Experimental group have positive opinions on schematic drawing.
Finally, based on the experimental results, we propose suggestions for education of mathematical problem-solving and future research.
一、中文部分
古明峰(民86)。加減法應用題語文知識對問題難度之影響暨動態評量在應用問題之學習與遷移歷程上研究。國立台灣師範大學教育心理與輔導研究所博士論文,未出版。
吳昭容(民79)。圖示對國小學童解數學應用問題之影響。國立台灣大
學心理研究所獨立研究,未出版。
李長燦(民83)。比較不同方法對數學解題認知及後設認知能力之測量。
國立台北師範學院初等教育研究所碩士論文。
邱上真、詹士宜、王惠川、吳建志(民84)。解題歷程導向教學對國小四年級數學科低成就學生解題表現之成效研究。特殊教育與復健學報,4,75-108。
林美惠(民86)。題目表徵型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,未出版碩士論文。
林淑玲(民87)。國小數學學習障礙學生對比較類加減應用題解題表徵之研究。碩士論文,國立臺灣師範大學特殊教育研究所。
林香(民91)。國小數學資優生的解題策略探究-以圖畫表徵策略為例。碩士論文,國立台北師範學院數理教育研究所。
林秀燕(民93)。以圖示策略融入低年級教學對改變類及比較類加減法文字題學習成效之研究。碩士論文,屏東師範學院數理教育研究所。
洪義德(民90)。不同表徵面積題目對國小六年級學生解題表現之探討。碩士論文,國立台北師範學院數理教育研究所。
涂金堂(民83)。國小學生後設認知、數學焦慮與數學解題表現之相關研究。碩士論文,國立高雄師範大學教育研究所。
馬祖平、蔣治邦(民92)。國小學童理解問題方式的發展:加減比較問題。教育與心理研究,26,頁305-330。
翁嘉英(民77)。國小兒童解數學應用問題的認知歷程。國立台灣大學心理研究所碩士論文,未出版。
徐文鈺(民81)。圖示策略訓練課程對國小五年級學生的數學應用題解題能力與錯誤類型之影響。碩士論文,國立臺灣師範大學教育心理與輔導研究所。
張春興(民78)。張氏心理學辭典。台北:東華書局。
張淑怡(民84)。加減問題之解題活動類型: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,未出版碩士論文。
張馨尹(民90)。國小輕度智障學生加減應用題解題歷程之研究。碩士論文,國立嘉義大學國民教育研究所。
張熙明(民92)。國小五年級學童分數表徵教學之研究。碩士論文,國立嘉義大學國民教育研究所。
許家驊(民82)。國小二年級學生改變型數學文字題錯誤偵測表現之研究。國立台南師範學院初等教育研究所碩士論文。
陳李綢(民74)。表徵方式與教學策略對國小學生認知發展之成效研究。碩士論文,國立臺灣師範大學輔導研究所。
陳雯貞(民93)。圖示表徵型式對國小四、五、六年級學生解題表現之影響以面積、周長單元為例。碩士論文,國立台北師範學院數學教育研究所。
教育部(民92)。國民中小學九年一貫課程綱要數學學習領域。台北:教育部。
黃美華(民93)。國小二年級學生學習加減文字題解題歷程之網路電腦輔助教學的研究。碩士論文,國立臺南大學教育經營與管理研究所。
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,未出版。
游自達(民84)。數學學習與理解之內涵—從心理學觀點分析。國立台中師範學院初等教育研究所初等教育研究集刊,3,31-45。
楊淑芬(民89)。國小資源班學生使用圖示策略解決比較類加減應用題之成效研究。碩士論文,國立台北師範學院特殊教育學系碩士班。
劉秋木(民85)。國小數學科教學研究。台北市: 五南。
劉貞宜(民89)。數學資優生的解題歷程分析- 以建中三位不同能力的數
學資優生為例。國立台灣師範大學特殊教育研究所碩士論文。
蔣治邦(民83)。由表徵的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)(60-76)。台北縣:台灣省國民學校教師研習會。
鄭人豪(民93)。電腦化圖示策略對國小輕度智能障礙學生比較類加減法應用問題學習成效之研究。碩士論文,國立新竹教育大學特殊教育學系碩士班。
鄧少林、蔣治邦(民82)。三、五年級學生對比較應用問題的分類。國教學報,6,97-113。
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
研究所碩士論文,未出版。
二、英文部分
Bruner, J. S. (1966). Toward a theory of instruction. NY: Mcgraw-Hill.
Desoete, A., Roeyers, H. & Buysse, A. (2001). Metacognition and
Mathematical Problem Solving in Grade 3. Journal of Learning
Disabilities, 34(5), 435-449.
Carpenter , T. P. (1985). Learning to add and subtract: Anexercise in problem solving . In E. A. Silver(Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, NJ: Lawrence Erlbaum Associates.
Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist to
representational view of mind in mathematics education. Journal for Research in Mathematical Education, 123(1),2-33.
Dufour-Janvier,B.,Bednarz,N.,&Belanger,M. (1987).Pedagogical
Considerations concerning the problem of representations. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp.109-122). Hillsdale , NJ : Lawrence Erlbaum Associates.
Fuson, K. C.,& Willis, G. B.(1989).Second Graders' Use of Schematic
Drawings in Solving Addition and Subtraction Word Problems. Journal of Educational Psychology, 81(4) , 514-520.
Ginsburg, H.P., & Yamamoto, T.(1986). Understanding, motivation, and
teaching : Comment on Lampert's “Knowing, Doing, and Teaching Multiplication.” Cognition and Instruction, 3,357-370.
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio(Eds.), The roles of representation in school mathematics(pp.1-23). Reston, VA:NCTM.
Greeno ,J.G .(1987). Instructional representations based on research
about understanding . In A.H. Schoenfeld (Ed.) , Cognitive Science and Mathematics Education .Hillsdale .
Jitendra, A. K., & Hoff, K. (1996) .The effects of schema-based
instruction on the mathematical word-problem-solving performance of students with learning disabilities. Journal of Learning Disabilities, 29(4), 422-431.
Jitendra, A. K., Griffin, C. C., & McGoey, K.(1998).Effects of
mathematical word problem solving by students at risk or with mild disabilities. Journal of Educational Research, 91(6), 345-355.
Jitendra, A. K., DiPipi, C. M.,& Perron-Jones, N.(2002). An exploratory study of schema-based word-problem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding.Journal of Special Education,36(1), 23-38.
Jitendra, A. K.(2002).Teaching Students Math Problem-Solving Through
Graphic Representations. Teaching Exceptional Children.34(4),34-38.
Kaput, J. J. (1987a). Representation systems and mathematics. In C.
Janvier (Ed.). Problems of representation in the teaching and learning of mathematics (pp.19-26). Hillsdale, NJ:Erlbaum.
Kaput, J. J. (1987b). Toward a theory of symbol use in mathematics. In C.Janvier(Ed.). Problems of representation in the teaching and learning of mathematics (pp.159-196). Hillsdale, NJ:Erlbaum.
Kilpatrick, J. (1985). A retrospective account of the past 25 years of research on teaching mathematical problem solving. Paper presented at E. A. Silver, (ed.),Teaching and Learning mathematical problem solving: multiple research perspectives.
Krulik, S.K., & Rudnick,J.A.(1989).Problem solving: A handbook for senior high school teachers. Boston, MA: Allyn & Bacon
Kintsch,W., & Greeno,J.G.(1985). Understanding and solving word
arithmetic problems. Psychological Review, 92,109-129.
Lewis, A.B.(1989). Training students to represent arithmetic word
Problems.Journal of Educational Psychology, 81,521-531.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations
among representation in mathematics learning and problem solving. In C. Janvier(Ed.).Problems of representation in the teaching and learning of mathematics(pp.33-40). Hillsdale, NJ:Erlbaum.
Mayer, R. E. (1985). Implications of cognitive psychology for instruction in mathematical problem solving. In E. A. Silver (Ed), Teaching and learning mathematical problem solving: Multiple research perspectives,123-138. Hillsdale, NJ: Lawrence, Erlbaum.
Mayer, R. E.(1987).Educational psychology:A cognitive approach.
Boston:Little, Brown, and Company.
Mayer, R. E. (1992). Think, problem solving, cognition. New York: W. H. Freeman and Company.
Morales, R.V., Shute, V.J., &Pellegrino, J.W.(1985).Developmental
differences in understanding and solving simple mathematics word problems. Cognition and Instruction, 2, 59-89.
National Council of Teachers of Mathematics (NCTM) (1980). An Agenda for Action: Recommendations for School Mathematics of the 1980s, Reston, Virginia: NCTM.
National Council of Teachers of Mathematics(1989). Curriculum and
Evaluation Standards for School Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics(2000). The principles and
standards for school mathematics. Reston, VA:NCTM.
Peterson, P.L., Carpenter, T., & Fennema, E.(1989). Teachers' knowledge of students' knowledge in mathematics problem solving: Correlational and case analyses. Journal of Educational Psychology,81,558-569.
Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
Polya, G. (1957). How to solve it(2ed.). Princeton, NJ: Princeton University Press.
Riley, M. S., Greeno, J. G., & Heller, J. I.(1983). Development of
children’s probleming- solving ability in arithmetic. In H. P. Ginsburg(Ed.). The development of mathematical thinking(pp.153-196). New York: Academic Press.
Rumelhart, D. E., & Norman, D. A. (1988). Representation in memory. In R. C. Atkinson, R. J. Herrnstein, G. Lindzey, & R. D. Luce (eds.), Stevens´ handbook of experimental psychology: Vol. 2. Learning and cognition ( 2nd ed., 511- 587). New York: Wiley.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando,FL:
Academic Press.
Willis, G. B.,& Fuson, K. C.(1988).Teaching Children to Use Schematic
Drawings to Solve Addition and Subtraction Word Problems . Journal of Educational Psychology, 80(2) ,192-201.
Xin, Y. P.,Jitendra, A. K.,& Deatline-Buchman, A.(2005). Effects of
mathematical word problem-solving instruction on middle school students with learning problems. Journal of Special Education, 39(3), 181-192.