解釋數學：透過科技支援創作與討論以增強小學生的數學溝通能力

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楊馥祤(Fu-Yu Yang) 查詢紙本館藏

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網路學習科技研究所

論文名稱

解釋數學：透過科技支援創作與討論以增強小學生的數學溝通能力
(Explaining Mathematics: Technology Enhanced Elementary Students′ Mathematical Communication Abilities through Creation and Discussion)

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摘要(中)

數學溝通是學習數學的重要方法和能力。本研究以兩個年級為研究對
象，檢驗學生如何使用平板電腦培養數學溝通能力。研究一維持一學期，
使用等組前後測實驗設計，組間情境變項為RPTMC 和傳統變項，而組內則
採前、後測時間變項。在RPTMC 實驗組中，鼓勵學生產生數學創作，包含
數學表徵、解法和解法解釋，作為自己的教材，將之和同學作交互同儕教
學以增加數學溝通的機會。採用數學小老師的系統支持學生的數學創作和
同儕交互教學活動。有51 位二年級學生參與此實驗，研究評估他們數學溝
通能力進步程度。控制組學生接受一對一自我數學學習和教師引導教學，
而實驗組則在同環境中以相同設備投入電腦支援的同儕交互教學。使用數
學溝通能力測驗和線上數學創作評估兩組學生的學習成效，結果指出實驗
組在測驗中表現明顯高於控制組。此外，本研究也分析學生的數學創作以
評量他們的形成性發展。結果顯示學生的數學創作變得更清楚且有效率。
換句話說，他們的數學表徵和解釋在學習活動後變得更為精確。
研究二也鼓勵學生產出數學創作，包括表徵、解釋、解釋型寫作、總
結性寫作和擬題作為溝通媒材。此研究設計一個新的數學解說員系統支持
學生的創作和討論活動。91 位學生參與其中並以數學溝通測驗、線上數學
創作和動機問卷評估其數學溝通能力，結果揭露創作和討論溝通活動可以
促進學生的數學溝通能力，且低成就學生展現明顯的進步，除了數學表徵
的表現以外。不同成就的學生在數學創作上，由於文字題特徵和難度，使
他們在面積單元的解釋型寫作和時間單元的解題展現明顯的差異。然而，
學生的總結性寫作表現未如預期，只有少數學生找到文字題的關鍵特徵。
此外，學生的動機問卷結果顯示他們對概念討論和擬題較有興趣。然而，學生的擬題和系統提供的問題相似，只有稍微改變。值得注意的是，他們的解釋型寫作、解題和對創作討論溝通活動的動機能夠預測數學溝通活動的表現。研究最後也討論了對教學設計、數學老師和數學教育研究者的影響。

摘要(英)

Mathematical communication is an important approach and ability when learning mathematics. This study examined how to foster students’ mathematical communication abilities by using tablet PCs. Two studies using students from different grades were conducted. In Study 1 , a pretest-posttest 2 x 2 factorial design with two levels of between-subject conditions (“RPTMC” and “traditional”), and two levels of within-subject time variables ("pre" and "post") were used.
In the experimental group, RPTMC, the students were encouraged to generate math creations, including mathematical representations, solutions, and solution explanations, as their instructional materials. They then reciprocally tutored classmates to increase opportunities for mathematical communication throughout the semester. A Math Teacher System (MTS) was designed for supporting students’ math creations and reciprocal peer-tutoring activities.
An experiment involved 51 second-graders to evaluate their improvement in mathematical communication abilities. While the control group received one-to-one self-learning of mathematical materials and teacher-led instruction, the experimental group was engaged in computer-supported reciprocal peer tutoring (RPTMC), in the same environment with the same materials. Both groups were evaluated using a mathematical communication assessment.
The results indicated that the experimental group outperformed the control group in the post-assessment. Additionally, students’ math creations were analyzed to assess their formative development. The results showed that students’ math creations became clearer and more efficient. In other words, their mathematical representational abilities and writing became more accurate after the learning activity.
In Study 2, students were also encouraged to generate math creations, including mathematical representations, solutions, explanatory writing, summarizing writing, and problem posing as their communication materials. A new mathematical communication system, Math Narrator System, was designed for supporting students’ math creations and discussion activities.
Ninety-one students were involved in this study. Mathematical communication abilitieswere measured with a mathematical communication assessment, online math creation, and questionnaires according to students’ achievement performance. The results revealed that the CD communication activity enhanced students’ mathematical communication abilities, and the low achievers showed significant progress in all abilities except for mathematical representation.
Regarding the math creations, students only showed significant differences in their writing in the area unit and solution in the time unit. This might have been due to the features and difficulty of the word problems. However, students’ summarizing writing did not meet the expectations, and few students identified the critical features of word problems. Further, the questionnaire showed that students′ motivation in mathematics communication were more spurred by the concept discussion and problem posing. Additionally, students’ problem posing exhibited similar problems as those found in the system provided with slight changes. Their mathematical explanatory writing, solutions, and motivation for the CD communication activity were found to be predictive of mathematical communication abilities. The conclusions of this study, along with related pedagogical implications for instructional designers, math teachers, and math educational researchers, are also discussed.

關鍵字(中)

★ 數學溝通能力
★ 同儕解釋
★ 數學寫作
★ 數學表徵
★ 解題

關鍵字(英)

★ Mathematical Communication Ability
★ Peer Explanation
★ Mathematical Writing
★ Mathematical Representation
★ Problem-Solving

論文目次

摘要 i
ABSTRACT iii
Acknowledgements v
Table of Content vi
List of Figures ix
List of Tables xi
Chapter 1 Introduction 1
1-1 Background and Motivation 1
1-2 Research Purposes and Questions 7
1-3 Definitions 9
1-4 Study Limitations 10
1-4-1 Time 10
1-4-2 Subjects 10
1-4-3 Content 10
1-4-4 Tools 10
Chapter 2 Literature Review 12
2-1 Mathematical Communication 12
2-2 Problem Solving 18
2-3 Mathematical Representation 20
2-4 Problem Posing 21
2-5 Mathematical Writing 24
2-6 Self Explanation and Peer Explanation 26
Chapter 3 System Design and Activity Flow 29
3-1 Study 1 29
3-1-1 System Design: Math Teacher System (MTS) 29
3-1-2 Activity Flow: RPTMC activity 35
3-2 Study 2 38
3-2-1 System Design: Math Narrator System (MNS) 38
3-2-2 Activity Flow: CD communication activity 52
Chapter 4 Methods 60
4-1 Study 1 60
4-1-1 Participants 60
4-1-2 Study Procedure 61
4-1-3 Evaluative Methods 62
4-2 Study 2 66
4-2-1 Participants 66
4-2-2 Study Procedure 67
4-2-3 Evaluative Methods 68
Chapter 5 Results 78
5-1 Study 1 78
5-1-1 Mathematical Communication Assessment 78
5-1-2 Math Creation 80
5-1-3 Findings and Influences 82
5-2 Study 2 87
5-2-1 Mathematical Communication Assessment 87
5-2-2 Math Creation 98
5-2-3 Questionnaire 117
5-2-4 Factors Facilitating Mathematical Communication Ability 120
Chapter 6 Discussion and Contribution 123
6-1 Empirical contribution 123
6-2 Theoretical contribution 127
6-3 Practical contribution 128
Chapter 7 Conclusion and Future Directions 130
Reference 132
Appendix 142
Test Instructions of Mathematical Communication Assessment 142
Pre-Test: Mathematical Communication Assessment 143
Evaluative Criteria of Pre-Test 150
Post-Test: Mathematical Communication Assessment 156
Evaluative Criteria of Post-Test 163
Questionnaire of the CD communication activity 169

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指導教授

陳德懷

審核日期

2016-8-31

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