本研究透過問卷調查和因子分析法，從修讀台灣師大數學系一班教材教法課的46位學生中篩選出八名具代表性的個案，以個案研究法持續追蹤此八位個案學生教師的數學教學認知與情意(簡稱知情)面向間的互動情形，並探討影響知情優勢轉變的原因。研究的過程分成「知情競爭」、「知情實驗」和「知情沉澱」三個階段,配合問卷調查、個案晤談和教室觀察,蒐集個案的各類實徵資料，據此分析與詮釋個案的知情內涵與轉變情形。

研究的結果顯示，個案教學認知的發展可以強化情意的展現，而教學情意的實踐亦能使其體會認知面向的重要性，因此，認知和情意實為數學教學概念的一體兩面、無法分割。個案學生教師在三個研究階段中的知情狀態大致上都持續地擺盪，時而認知主導、時而情意優先、有時則兩者處於平衡的狀態。另外，這種教學知情優勢的轉變與師資培育者的介入、個案缺乏強而有力的PCK來展現教學信念和價值以及個案對情意因子認知的不足有關。本研究的結果應有助於數學師資培育者進一步掌握學生數學教師階段性的教學認知與情意面間的競爭和擺盪原因，據此也可設計相關的培育活動或課程，以促使學生教師進一步察覺與體會情意教學的重要性，而且同時促進此兩個面向的專業認知發展。

Through questionnaire survey and statistical factor analysis, eight cases were selected from a group of 46 students who participated in a class of mathematical teaching methods. Case study method was used to track the eight student cases for understanding their cognitive and affective interaction in mathematics teaching and tried to find out the influences and the change of cognition-affection. This research consists of three phases including the competitive, the experimental and precipitative stages of cognition-affection with questionnaire investigation, interview,and classroom observation. The author analyzed and interpreted the connotation and the chang of the cognition-affection interaction for the these cases.
The results showed that the cognitive development of teaching can strengthen the represention of affective aspect of teaching , and practice of affective teaching can also let the students realize the importance of cognition. Hence it seems that cognition and affection are a unity of the two sides of students’ pedagagical concepts. During three research stages, the situation of cognition and affection for the cases was continuously swinging, sometimes the cognitive leads, sometimes the affective overrides, and sometimes the two are balance. In addition, the change of the advantage for cognition and affection was related to the teacher educators’ intervention, the absence of powerful PCK for the student teachers to represent their belief and value of teaching and the absence of the cognition for those affection factors of teaching mathematics. The results of the study might be useful for mathematics teacher educators to understanded the reasons why cognition and affection of student teachers competition and swings in every stages. In view of the above, they could design relative educational activity or curriculum in order to educate students teachers to realize the importance of affective aspect of teaching mathematics further, and promote the professional cognitive development of the two aspects at the same time.

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