本研究旨在設計數學解題問答系統，讓學生對詳解中有問題的地方更直覺做記號方便提問，降低學生提問時的困難，並評估系統在操作上的易用性。

本研究參與者為台南市某公立國中八年級學生一班30人。學習活動需五節課的時間，分五天利用早自修完成。以八年級下學期數學第三章3-2「三角形的全等性質」為學習內容，整理國中該單元中的證明題形成題庫，並依照難易程度不同分為五類題庫，作為本次學習活動的教材內容。除探討系統滿意度外，亦蒐集前後測成績，探討透過本系統進行課外練習的學習活動是否能增加熟練度，是否能提升學習成就。學習活動結束後，讓學生填寫系統滿意度與幾何證明學習態度問卷。

研究結果顯示多數學生表示本系統容易操作。學生遇到難以表達的困難點，使用圖片模式提問的比例會上升。透過錄音模式提問則是喜好度最低的一種方式。整體來說，本數學解題問答系統操作上易用性高，學生對於利用問答系統進行幾何學習活動持正向的態度，並能提升幾何學習成效。

The purpose of this research was to design a questioning system for mathematical problem solving to allow students to explain their problem more intuitive and easy to do a question mark, reducing the difficulty of students asking questions, and to assess the system on the operating ease of use.

Participants are 30 eight grade students. Research instruments included a question pool database, a geometry learning attitude questionnaire, and an achievement test.

On the basis of data collected at this stage, following results were found. When the participating students encounter difficulties point difficult to express, use an image mode questioning proportion will rise. Through questioning the recording mode is the lowest degree of preference way. The research results indicate that the majority of participating students said our questioning system is easy to operate and hold a positive attitude toward the geometric learning activities. The achievement test showed that learning activities through the questioning system can enhance the effectiveness of learning geometry.

中文部份
沈紀伶(2010)。依據 van Hiele 幾何思考理論探究臺灣中部地 區國三學生幾何概念發展之研究(未出版之碩士論文)。國立台中教育大學，臺中市。

李姿慰(2004)。改善國小五年級學生自然課發問之行動研究(未出版之碩士論文)。國立台中教育大學，臺中市。

呂鳳琳(2010)。幾何證明不同文本呈現方式對學生認知負荷與閱讀理解影響之研究(未出版之碩士論文)。國立臺灣師範大學，臺北市。

吳德邦、吳順治(1989)。解題導向的數學教學策略。台北市：五南。

林緯謦(2014)。如何有效應用行動裝置於課堂即時發問的探討(未出版之碩士論文)。私立中原大學，桃園市。

秦麗花(2007)。數學閱讀指導的理論與實務。台北市：洪葉。

張祐瑄(2010)。閱讀理解能力與數學能力對小學六年級低成就學生在數學文字題解題表現之影響(未出版之碩士論文)。國立臺灣師範大學，臺北市。

張筱珊(2009)。國小提問系統的設計與評估(未出版之碩士論文)。國立臺灣師範大學，臺北市。

張敬楷(2007)。中學生平行槪念認知結構之研究(未出版之碩士論文)。國立臺灣師範大學，臺北市。

游文通(2012)。國小數學資優生解幾何題策略之探究：以小學數學奧林匹亞競賽獲獎選手為例(未出版之碩士論文)。國立臺北教育大學，臺北市。

喩平(2002)。論數學解題教學的現代理論基礎。數學傳播，26(4)，64-65。

楊凱琳、林福來、王繹婷(2008)。幾何證明的文本特徵與提問類型對學生閱讀理解表現的影響。當代教育研究季刊，16(2)，77-100。

劉錫麒(1993)。數學思考教學研究。台北市：師大書苑。

英文部份
Aliakbari, M., & Mashhadialvar, J. (2006). Does it matter who makes comprehension questions? A comparison between the levels of comprehension obtained from authorgenerated questions and student-generated questions. In Proceedings of the 11th Conference of Pan-Pacific Association of Applied Linguistics (PAAL 2006), Chuncheon, Korea (pp. 1-7). Seoul, Korea: PAAL.

Chen, N. S., Wei, C. W., Wu, K. T., & Uden, L. (2009). Effects of high level prompts and peer assessment on online learners' reflection levels. Computers & Education, 52(2), 283-291.

Chin, C., & Kayalvizhi, G. (2002). Posing Problems for Open Investigations: what questions do pupils ask? Research in Science & Technological Education, 20(2),
269-287.

Healy, L., & Hoyles, C. (1998). Technical Report on the Nationwide Survey: Justifying and proving in school mathematics. London: Institute of Education,
University of London.

Hanna, G., & Jahnke, H. N. (1996). Proof and proving. In A. Bishop, K. Clements, C.Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 877-908). Dordrecht, Netherlands: Kluwer.

Janssen, T. (2002). Instruction in self-questioning as a literary reading strategy: An exploration of empirical research. L1 Educational Studies in Language and
Literature, 2(2), 95-120.

King, A. (1991). Improving lecture comprehension: Effects of a metacognitive strategy. Applied Cognitive Psychology, 5(4), 331-346.

King, A. (1992). Facilitating elaborative learning through guided student-generated questioning. Educational Psychologist, 27(1), 111-126.

King, A. (1993). Effects of guided cooperative questioning on children’s knowledge construction. Journal of Experimental Education, 61(2), 127-148.

Lester, K. F. (1980). Research on mathematical problem solving. In R. J. Shumway (Ed.), Research in mathematics education. The National Council of Teachers of Mathematics.

Lester, K. F. (1983). Trends and Issues in Mathematical Problem Solving Research. In R. Lesh & M. Landau, (Eds.), Acquisition of mathematical concepts and processes (pp.229-261). Orlando, FL: Academic Press.

Lester, K. F. (1985). Methodological Consideration in Research on Mathematical Problem-Solving Instruction. In E. A. Silver (Ed.).Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale. New Jersey: Lawence Erlbaum Associates.

Ng’ambi D and Hardman J (2004). Towards a knowledge-sharing scaffolding environment based on learners’ questions. British Journal of Educational Technology. 35(2), 187-196

Niss, M. (2002). Mathematical competencies and the learning of mathematics: The Danish KOM project. Retrieved December 1, 2010, from http://www7.na-
tionalacademies.org/mseb/mathematical_com_petencies_and_the_learning_of_mathematics.pdf.

Rosenshine, B., Meister, C., & Chapman, S. (1996). Teaching students to generate questions: A review of the intervention studies. Review of Educational Research,
66(2), 181-221.

Salden , R., Aleven, V.,Schwonke, R.,Renkl, A. (2010). The expertise reversal effect and worked examples in tutored problem solving. Instructional Science, 38(3), 289-307.

Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

Schoenfeld, A. H. (1992).Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.). Handbook of Research on Mathematicx Teaching and Learning. Macmillan
Publishing Company, Maxmell Macmillan Canada.

Stylianou,D.A.（2010）. An examination of middle school students’ representation practices mathematical problem solving through the lens of expert work：Towards an organizing scheme. Educational Studies in Mathematics, 76,265-280.

Wellman, H. M. (1985). The origins of metacognition. In Forrest-Pressley, D. L., Mackinnon, G. E. &Waller, T. G. (Eds.), Metacognition, cognition, and human performance. N. Y.: Academic Press.

Yang, K. L., & Lin, F. L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59-76.

Yu, F.Y., Liu, Y.H., & Chan, T.W. (2005). A web-based learning system for question-posing and peer assessment. Innovations in Education and teaching International, 42(4), 337-348.