本研究旨在探討實施創思力導向的數學臆測教學於國小資優生之中可能出現的問題及解決方案。本研究的目的有兩個：其一，了解教師如何調整學習任務，發揮學習任務的潛力，增強國小資優生的數學創造力。其二，探討教師如何運用教學策略，以提升國小資優生的數學創造力。本研究採用行動研究法，以研究者授課的四年級和六年級的資優資源班為研究對象，運用抽離課程，為期三至四個月。教學單元則參考自《國小資優數學課程調整教學設計》分別進行周長與面積的變化關係、數方、解碼多邊形、體積與表面積的變化關係、因倍數大老二、蛋糕切切看等單元的任務設計。相關研究資料包括：教材和教案、教學時錄製的影片和對話、學生的學習單、成長小組的課後討論、與諍友的對話以及研究過程中的研究日誌。
研究結果發現，創思力導向的數學臆測任務設計在開放性設計原則，主要展現在造例階段與提出猜想階段；差異化與挑戰性原則，則主要展現在造例、證實階段；高認知需求原則，則主要展現在提出猜想階段；在延伸任務與一般化原則，則主要展現在造例、提出猜想、一般化猜想階段。比較兩個年級的任務皆能明顯的激發精緻性內涵，而六年級的任務相較於四年級的任務更能夠提升變通性與原創性的表現。至於創思力導向的數學臆測教學內涵，提升流暢性內涵主要展現在造例與提出猜想階段，兩個年級共同增進的內涵是產生個人多元造例，而四年級增進的內涵是從數據延伸增加猜想，六年級則是產生不同組內組間造例以及大膽提猜想；提升變通性內涵主要展現在提出猜想、效化與證實猜想階段，兩個年級共同增進的內涵是分辨猜想類別，而四年級增進的內涵是分類後再精煉猜想，六年級則是使用不同的閱讀造例方式、連結新舊經驗以及比較自己和他人想法；提升原創性內涵主要展現在造例與提出猜想階段，兩個年級共同增進比較與整合想法、從多類型產生原創猜想以及運用一般創思力的思考技巧。而不同處在於四年級的臆測教學歷程中，提升的原創性內涵是先比較與整合想法，再從多類型產生原創想法，最後是運用一般創思力的思考技巧等內涵。六年級則是先從多類型產生原創猜想，進而運用一般創思力的思考技巧，最後是比較與整合想法等內涵；提升精緻性內涵主要展現在提出猜想、效化與一般化猜想階段，在四年級的臆測教學歷程中，提升的精緻性內涵是精煉想法與修飾語句。六年級則是先調整前提、修飾語句，進而進行修飾想法等內涵。兩個年級共同增進的是精煉想法、修飾語句的內涵，除了次序性的差異，六年級則增加了調整前提的內涵。最後，本研究為創造性導向數學臆測教學教師和未來的研究方向提供建議。

This study aims to discuss the problems and solutions that may occur when implementing creativity-directed mathematical conjecturing teaching. The purpose of this study is two-fold. First, to understand how teachers modify learning tasks to promote their potential to enhance primary gifted students’ mathematical creativity. Second, to investigate how teachers utilize teaching strategies to enhance primary gifted students’ mathematical creativity. This study adopts action research method, focusing on fourth grade and sixth grade pull-out classes taught by the researcher for three to four months. Relative research materials include teaching materials and teaching plans, recorded videos and conversations while teaching, students’ worksheets, post-class discussion of teachers’ professional development groups, dialogues with critical friends, and research diary of the instruction-observer while the research is conducted. These records capture the difficulties encountered during this study and will be the basis to provide future strategies for solving them.

This research implicates several principles to design creativity-directed mathematical conjecturing task and teaching connotation. First, the principle of openness is mainly demonstrated in the stage of constructing cases and formulating conjectures. Second, the principle of increasing differentiation and challenge is mainly showcased in the stage of formulating conjectures and validation. Third, the principle of raising high cognitive demand is mainly performed in the stage of formulating conjectures. Fourth, the principle of extendindg task and generalization is mainly displayed in the stages of constructing cases, formulating conjectures, and generalizing conjectures. The tasks of both grades can obviously stimulate the connotation of elaboration. On the other hand, the tasks of the sixth grade can improve the connotation of flexibility and originality.

As for creativity-oriented conjecturing teaching connotation, the improvement of fluency is mainly seen in the stage of constructing cases and formulating conjectures. The common improvement of connotation in both grades is the generation of individual multiple cases. However, the connotation of the fourth grade is to extend and increase ideas from the data, while that of the sixth grade is to generate cases between groups and within different groups and boldly raise conjectures.

The improvement of flexibility connotation is mainly demonstrated in the stages of formulating conjectures, validation, and justification. Both grades developed the connotation of distinguishing the conjecture category. While the fourth grade develop the connotation of classifying and then refining the conjecture, the sixth grade develop the connotation of using different ways to read cases, connecting new and old experiences, and comparing their own ideas with others’.

The improvement of originality connotation is mainly demonstrated in the stages of constructing cases and formulating conjectures. Both grades developed the thinking skills of comparing and integrating ideas, generating original conjectures from multiple genres, and applying general creative thinking. The difference is that in the teaching process of the fourth grade, the original connotation of improvement is to first compare and integrate ideas, then generate original ideas from multiple types, and finally use general creative thinking skills and other connotations. In the sixth grade, original conjectures are generated from multiple types, and then general creative thinking skills are used, and finally, connotations such as comparison and integration of ideas are made.

The improvement of elaboration connotation can mainly be seen in the stages of formulating conjectures, validation, and generalization. In the process of teaching the fourth grade, the connotation of elaboration is to refine ideas and modify sentences; however, when teaching the sixth grade, the premise is first adjusted, the sentence is modified, and then the connotation (such as the ideas) is modified. Both grades improved the connotation of refining ideas and modifying sentences. Besides the difference in order, the sixth grade also increase the connotation of adjusting the premise. Finally, this research provides suggestions to the creativity-directed mathematical conjecturing teaching instructors and future research directions.

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