探究歷史導向微積分課程與發展學生數學觀點之關係__臺灣人文及社會科學引文索引資料庫

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題名：	探究歷史導向微積分課程與發展學生數學觀點之關係
書刊名：	科學教育學刊
作者：	劉柏宏
作者(外文)：	Liu, Po-hung
出版日期：	2007
卷期：	15:6
頁次：	頁703-723
主題關鍵詞：	微積分；數學史；數學觀點；數學本質；Calculus；History of mathematics；View on mathematics；Nature of mathematics
原始連結：	連回原系統網址
相關次數：	被引用次數:期刊(3) 博士論文(2) 專書(0) 專書論文(0) 排除自我引用:3 共同引用:13 點閱:171

本探究之主要目的在探討以歷史進展為導向的微積分課程，對於培養學生的數學觀點有何種關聯。本研究採取單一群體前後測研究法，研究工具包括開放式問卷、數學自傳、歷史導向的微積分課程、隨堂報告、與半結構式一對一訪談。研究結果顯示，大部份受測者在學前表示數學思考是一種牽涉到數字計算與套用公式的求解過程，但到學期末絕大部份的學生對於數學思考都有另一番論述，並且對數學家解題情境的想像投射到對於數學思考的認知上。在數學知識的認知方面，大部份學生對於數學知識始終抱持著強烈的工具化觀點。不過，學生於學期末的論述增加了兩方面的覺察：(1) 數學知識承先啟後的概念；(2) 數學家所扮演的角色。本研究最後不僅分析歷史導向課程與發展學生數學觀點之間的關係，也探討了學生對數學本質的瞭解在數學學習中的重要性。

以文找文

To explore the relationship, between a historical calculus course and students' views on mathematics, the one-group pretest-posttest design was adopted in which an open-ended que-stionnaire, students' mathematics biographies, a history oriented teaching material of calculus, students' self-reports, and the follow-up semi-structured interviews were served as the tools. The results indicated that most of the students considered mathematics thinking as the processes involved calculation and formula at the very beginning, nonetheless expressing different viewpoints after finishing the course. They attempted to connect the context of mathematicians' problem solving with the characteristics of mathematics thinking. On mathematics knowledge, students strongly held a consistent instrumentalist view on mathematics, before and after the course. However, at the end of the course, they were more likely to recognize mathematics as the continuity and in-heritance knowledge and the role of mathematicians on its development. Furthermore, this study also emphasizes the importance of students' understanding of the nature of mathematics.

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期刊論文
1.	洪萬生(20000900)。「無異解」中的三案初探--一個HPM的觀點。科學教育學刊，8(3)，215-224。延伸查詢
2.	Schoenfeld, A. H.(1989)。Explorations of students' mathematical beliefs and behavior。Journal for Research in Mathematics Education，20(4)，338-355。
3.	Ruthven, Kenneth、Coe, Robert(1994)。A Structural Analysis of Students' Epistemic Views。Educational Studies in Mathematics，27(1)，101-109。
4.	許良榮、李田英(19950400)。科學史在科學教學的角色與功能。科學教育，179，15-27。延伸查詢
5.	廖麗貞、林寶英、洪振方(20000600)。將達爾文演化論發展史融入大學生命科學通識課程之研究。科學教育學刊，8(2)，179-198。延伸查詢
6.	蕭碧茹、洪振方(2000)。以歷史認知分析法探究科學史及其在科學教育上的意涵。科學教育（臺灣師大），235，2-14。延伸查詢
7.	Liu, P.-H.、Niess, L. M.(2006)。An Exploratory Study of College Students' Views of Mathematical Thinking in a Historical Approach Calculus Course。Mathematical Thinking and Learning，8(4)，373-406。
8.	Liu, P.-H.(2003)。Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?。Mathematics Teacher，96(6)，416-421。
9.	Furinghetti, F.(1997)。History of Mathematics, Mathematics Education, School Practice: Case Studies in Linking Different Domains。For the Learning of Mathematics，17(1)，55-61。
10.	Sierpinska, A.(1987)。Humanities Students and Epistemological Obstacles Related to Limits。Educational Studies in Mathematics，18，371-397。
11.	Siu, M. K.(1993)。Proof and Pedagogy in Ancient China: Examples from Liu Hui's Commentary on Jiu Zhang Suan Shu。Educational Studies in Mathematics，24，345-357。
12.	Kloosterman, P.、Stage, F. K.(1991)。Relationships between Ability, Belief and Achievement in Remedial College Mathematics Classrooms。Research and Teaching in Developmental Education，8(1)，27-36。
13.	Katz, V. J.(1997)。Some Ideas on the Use of History in the Teaching of Mathematics。For the Learning of Mathematics，17(1)，62-63。
14.	Rodd, M.(1993)。Students' Views on the Nature of Mathematics。Mathematics Teaching，143，8-10。
15.	Sriraman, B.(2004)。The Characteristics of Mathematical Creativity。The Mathematics Educator，14(1)，19-34。
16.	Ernest, P.(1998)。The History of Mathematics in the Classroom。Mathematics in School，27(4)，25-32。
17.	Carlson, M. P.(1999)。The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success。Educational Studies in Mathematics，40，237-258。
18.	Swetz, F. J.(1995)。To Know and to Teach: Mathematical Pedagogy from a Historical Context。Educational Studies in Mathematics，29，73-88。

會議論文
1.	Horng, W.-S.(2004)。Teacher's Professional Development in Terms of HPM。0。
2.	Cifarelli, V.、Goodson-Espy, T.(2001)。The Role of Mathematical Beliefs in the Problem Solving Actions of College Algebra Students。0。

學位論文
1.	Liu, , Po-Hung(2002)。The Relationship of a Problem-based Calculus Course on Students' Views of Mathematical Thinking，Corvallis, OR。

圖書
1.	Torp, L.、Sage, S.(1998)。Problems as Possibilities。Alexandria, VA：Association for Supervision and Curriculum Development。
2.	Meredith, D. G.、Walter, R. B.、Joyce, P. B.(1996)。Educational Research。New York, NY：Longman Publishers。
3.	Hadamard, J.(1945)。The psychology of Invention in the Mathematical Field。Princeton, N.J.：Princeton University Press。
4.	American Association for the Advancement of Science(1990)。Project 2061: Science for all Americans。New York, NY：Oxford University Press。
5.	Hersh, Reuben(1997)。What is Mathematics, Really?。New York：Oxford University Press。
6.	Lakatos, Imre(1976)。Proofs and Refutations: The Logic of Mathematical Discovery。Cambridge。
7.	Boud, D.、Feletti, G.(1991)。The Challenge of Problem-Based Learning。New York：St. Martin's Press。
8.	National Council of Teachers of Mathematics(2000)。Principles and standards for school mathematics。Reston, Virginia：National Council of Teachers of Mathematics。
9.	National Council of Teachers of Mathematics(1989)。Curriculum and evaluation standards for school mathematics。Reston, VA：National Council of Teachers of Mathematics。
10.	Kline, M.(1980)。Mathematics: The Loss of Certainty。Mathematics: The Loss of Certainty。New York, NY。
11.	(1993)。Humanistic Mathematics。Humanistic Mathematics。Washington, DC。
12.	(2002)。Beliefs: A Hidden Variable in Mathematics Education?。Beliefs: A Hidden Variable in Mathematics Education?。Dordrecht, Netherlands。
13.	Schoenfeld, A. H.(1985)。A Framework for the Analysis of Mathematical Behavior。Mathematical Problem Solving。New York, NY。
14.	Ervynck, G.(1991)。Mathematical Creativity。Advanced Mathematical Thinking。Dordrecht, Netherlands。
15.	Schoenfeld, A. H.(1994)。Reflections on Doing and Teaching Mathematics。Mathematical Thinking and Problem Solving。Hillsdale, NJ。
16.	Siu, M.(1995)。Euler and Heuristic Reasoning。Learn from the Masters。Washington, DC。
17.	Avital, S.(1995)。History of Mathematics can Help Improve Instruction and Learning。Learn from the Masters。Washington, DC。
18.	Siu, M.(1995)。Mathematical Thinking and History of Mathematics。Learn from the Masters。Washington, DC。
19.	Barbin, E.(1996)。The Role of Problems in the History and Teaching of Mathematics。Vita Mathematica。Washington, DC。
20.	Horng, W.-S.(2000)。Euclid versus Liu Hui: A Pedagogical Reflection。Using History of Mathematics in Teaching Mathematics。Washington, DC。
21.	Presmeg, M.(2002)。Beliefs about the Nature of Mathematics in the Bridging of Everyday and School Mathematical Practice。Beliefs: A Hidden Variable in Mathematics Education?。Dordrecht, Netherlands。

圖書論文
1.	Schoenfeld, A. H.(1992)。Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics。Handbook for research on mathematics teaching and learning。New York：MacMillan。

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