二次函數為國中階段重要的數學概念之一，許多研究卻指出學生在學習二次函數單元容易面臨概念理解與表徵轉換的困難。現今十二年國教課綱中所規範二次函數的學習內容，聚焦在二次函數的意義與圖形特性，減少了情境問題的比例，但二次函數卻又與生活息息相關。
教師在課堂中常以講述取向結合動態數學軟體的操作，來呈現二次函數式與圖形的變化，較少看到一套完整且有系統的教學活動設計，幫助學生釐清國中二次函數單元的相關概念。因此，本研究期望以自行開發的二次函數建模教材，發展國中生對二次函數單元的理解，並且提升學生的情意態度。
本研究採個案研究法，旨在探討六名國二資優生在二次函數建模活動中的學習歷程，以及認知、情意的改變。透過學習單、前後測、課堂錄影與訪談記錄等多種資料，以Blum & Leiß（2006）的數學建模循環架構與Pirie & Kieren（1994）的數學理解成長模型分析學習歷程，並探討教師介入類型對學習歷程的影響，再以認知和情意前後測分析認知與情意的改變。
研究結果顯示二次函數建模活動中，循序漸進式的問題設計有助於學生自行發展二次函數相關概念的理解。從學生的學習歷程中，發現數學化階段為數學建模歷程中最具挑戰性的環節。此外，學生經過二次函數建模活動後，增進對二次函數的概念定義、圖形與極值的理解，並提升二次函數情境問題的解題思考能力。在情意方面，除了自信心提升之外，亦增進學生對課堂的投入程度。

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