本研究主旨在建構一個「結合問題導向學習與翻轉教學的差異化教學模式」，以提 供國小教師在進行數學差異化教學時參考，進而提升數學差異化教學的實施成效。為 達此研究目的，本研究採文獻分析法（documentary analysis)，發現翻轉教學有助於差 異化教學的實施，而問題導向學習又有助於翻轉教學模式具體化，因此，本研究乃結 合問題導向學習與翻轉教學，而建構出1吉合問題導向學習與翻轉教學的差異化教學 模式」。此教學模式如下：一、課前：1.教師於線上提出待解決的真實性問題（以基礎 級程度設計PBL問題）；2.學生透過線上教材自學（線上自學教材分成三種不同程度的 版本）。二、課中：1.小組成員討論與剖析真實性問題（採取異質分組的合作學習方法）； 2.小組成員蒐集及分享相關資訊（採STAD合作學習法的加分制度）；3.小組成員產生 可能的解決方案；4.小組成員提出問題的報告；5.教師統整與補充相關學習内容（教師 運用「一題多解策略」，並針對適中級與進階級學生講解線上教材中之「補充資料」的 部分，且鼓勵全班學生聽講與參與）；6.作業鍊習與討論（教師針對三個不同程度的學 生給予符合其程度的學習單）。三、課後：1.課後延伸學習與交流（教師針對不同程度 的三組學生建議不同難度的課後延伸學習内容）；2.小組成員學習評估與省思（依不同 教學目標分成三個版本）。

The purpose of this study is to construct a differentiated instruction model of problem-based learning combined with flipped instruction to provide teachers in elementary school a reference when they are doing the differentiated instruction of mathematics and to improve the effectiveness of teaching. Through documentary analysis, it shows that the flipped instruction helps the implementation of differentiated instruction; problem-based learning helps the flipped instruction model objectify. Therefore, this research is based on problem-based learning and flipped instruction, and construct a differentiated instruction model of problem-based learning combined with flipped instruction. The model of teaching as follows: A. Before the class: (a) Teachers bring out the realistic questions on-line. (The PBL questions are based on basic level.); (b) Students do self-study online. (The on-line self-study teaching material are divided in to three editions by different levels.); B. During the class: (a) Group members discuss and analyses the realistic question. (The groups work in method of heterogeneous grouping); (b) Group members gather and share the relevant information. (Adopting the bonus-point system of Students Teams-Achievement Divisions); (c) Team members come up with possible solutions; (d) Group members submit a report of the questions; (e) Teachers integrate and supply the related learning content. (Teachers use the strategy of solving one question with multiple solutions, also explain the supplementary information of the on-line material to students from average and advance level. In addition, teachers encourage all students not only listen but also participate in class.); (f) Assignment and group discussion. (Teachers give different worksheet to students regarding to different levels.); C. After the class: (a) Do further studies and share ideas after class. (Teachers give different further studies to students from three diverse levels.); (b) Study assessment and reflection of the group members. (Divided in to three editions by different teaching objects.)