Translated Titles

Affective Issues of Pre-service Teachers in Research on Mathematical Problem Solving




陳正賢(Zen-Same Chen);邱守榕(Sou-Yung Chiu);林來居(Lai-Jiu Lin)

Key Words


Volume or Term/Year and Month of Publication

2期(1991 / 03 / 01)

Page #

1 - 58

Content Language


Chinese Abstract

本研究旨在探討職前教師數學解題行為中的情意因數。研究中一面觀察配對受試者之解題過程,一面加以錄音、錄影,做成原案彼,再以無止盡三分法做原案分析。 本文從十組主修數學或物理的受試者中,選出解題行為差異最大,堪稱對立的兩組,各歸為專家與生手,深入分析其在解題時表露的情意因數,發現夾纏相伴出現的認知與非認知的因數。從所觀察到的現象,可做出下列的推論: 1.數學知識與解題的背景知識,影響解題的成敗。然而更重要的是在許多的情況下,生手縱然知道了作圖有關的解題策略,卻依舊是「知而不行」、「依然故我J ,未能在適當的時機將策略用於解題。 2.生手在解題的時候,由於缺乏控制力,置相關的知識於一邊,故大量的使用直觀與嘗試錯誤法。專家解題時,使用基模性的知識,對問題的類型先予定位,接著才做分析與評估的工作。 3.有信心的解題者,解題的意願較高,具有堅持的態度。信必不足的解題人,則處處表現出依賴性,甚至求助於測試者。即使已具有必需的知識,每進一步就猶疑一次,不飲放手使用這些知識。 4.自我觀念較強的解題者,不易受他人的影響,相對地也比較不顧同儕的看法與意見。自我觀念較弱的解題者,會有依賴的傾向。 5.解題者動機的高低,直接影響解題的意願;解題者的信念也影響其解題的態度。 6.意識使得解題者注意到控制力,無意識則使得解題者無法覺察到自己的能力,不斷地嘗試錯誤而無法突破解題過程中的障礙。 從事師資教育實務的人員,對於上述的現象應加以瞭解和關心,並籌劃調查「將為人師者」要具備那些相關的數學知識。

English Abstract

This paper addresses the affective issues arising from cognitive analysis of mathematical problem solving behavior among pre-service mathematics teachers. Qualitative mtheodology, highlightened by Schoefeld’s research is replicated and modified by researcher’s intervention in the problem situation. Ten pairs of college or graduate students are recruited to solve three construction probems in Euclidean geometry. Problem solving sessions, using thinking aloud techniques, are audiorecorded and vedeotaped to facilitate the collection of verbal data, compilation of protocols and protocol analysis. Two extreme cases, post classified as experts and naives respectively, are investigated more closely with time-line representations and infinite triangulations. It is found that, though there are differences between chinese subjects and Schoenfeld’s counterparts due to differences in school mathematics curriculum, similar inferences can be drawn upon the data obtained as a whole: 1. To have domain knowledge or not is influential in the success of problem-solving. Howrever, naives are unable to make appropriate use of known facts and reglect the hints provided by the researcher. 2. Due to lack of control, naives depend largely on intuition and try-and-error strategy. Experts make use of schematic knowledge to allocate the problem before analyzing and exploring it. 3. Confident solvers have higher motivation and are more persistent. Less confident solvers wait for help, even solicit help from the researcher, show uncertain of their own knowledge, and proceed with hesitation. 4. Solvers with strong self-concept reject other’s suggestion and attend little to the peers. Solvers with weak self-concept tend to depend on others. 5. Mathematical beliefs influence the attitude towards problem-solving. 6. Consciousness of mathematical ability helps the solver to attend to his/her own control. Unconscious solvers attend only to empiricist’ a trial. It is suggested that teacher education practioners pay attention to the above phenomena and plan for more investigations about mathematical needs of prospective teachers.

Topic Category 社會科學 > 教育學