本行動研究旨在增進教學者（亦即研究者本人）關於高職數學教學之專業知能，本研究的參與對象是研究者本人，以及研究者任教班的32名高職二年級學生。此次行動研究將進行基於APOS Theory的ACE teaching cycle為一個教學循環，共進行兩個循環，歷時6週共18節課。
研究者在每一個教學循環結束後，皆進行資料整理與省思，並以此作為下一階段教學策略調整與優化的依據。歷經兩次教學循環後，教師逐漸觀察到學生的學習歷程從「學會」邁向「想學」，進而促使教學者重新思考自身的教學信念與專業知能。教師的教學信念也從最初的老師「教完」，轉向重視是否真正「教會」學生，最終發展為「啟學」的理念，致力於激發學生主動探索與反思的學習態度。最後，研究者基於教學歷程與省思，提出運用APOS理論之ACE教學循環與科技輔助學習於數學教學的具體建議，以作為未來課堂教學設計與實踐的參考。
本行動研究的結論為教學者在ACE教學循環中得到的教學實務經驗，除了形成一套數學教學活動準備與進行流程，也提供教師在規劃數學教學活動時的注意事項，另外藉由此次的行動研究，研究者除了發現行動研究對教師專業發展的正面意義，也建議教師可以將APOS理論中的ACE教學循環應用於其他學科課程中進行。

This action research aimed to enhance the professional knowledge of the teacher-researcher in vocational high school mathematics instruction. The study involved the teacher-researcher and 32 second-year students from the researcher’s class and was conducted over two instructional cycles, spanning six weeks and 18 class sessions, using the ACE Teaching Cycle grounded in APOS Theory. After each cycle, the researcher collected and analyzed data, reflected on the instructional process, and used these insights to adjust teaching strategies. Throughout the two cycles, the teacher observed a shift in students’ learning attitudes—from acquiring knowledge to a desire to learn—which prompted a re-evaluation of teaching beliefs and professional growth. The teacher’s perspective evolved from focusing on being able to teach well, to ensuring students truly understand, and ultimately to inspiring students to actively explore and reflect. Based on the instructional process and reflections, the researcher offers practical suggestions for applying APOS Theory, the ACE Teaching Cycle, and Technology-Enhanced Learning in mathematics instruction to inform future lesson design and teaching practice.. The study concludes that engaging in the ACE Teaching Cycle provides not only a structured approach to planning and implementing mathematics instruction but also valuable insights for professional development. Furthermore, the researcher suggests that the ACE Teaching Cycle may be beneficially applied to other subject areas.

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