本研究結合質性取向的個案研究與錄影分析的量化數據，形成一個嵌入式設計的混合研究(embedded design of mixed-methods research)，用以探究兩位資深高中數學教師(林師與吳師)專門內容知識(specialized content knowledge)可能的內涵與特質以及它與內容與教學的知識(knowledge of content and teaching，簡稱 KCT)、內容與學生的知識(knowledge of content and student ，簡稱 KCS)間的關係。在為期一年的研究中，作者進入兩位個案教師的教學現場，透過課堂教學觀察與訪談，探索兩位個案教師和學生之間的互動與SCK呈現的情形。在錄影分析系統的部分，則是引用Learning Mathematics to Teaching (2006)所發展的Mathematical Quality of Instruction (MQI)登錄系統。個人首先修改系統的編碼，以符合兩位個案教師實際的數學教學特質，接著，進行教學影片分析，最後，商請另一位獨立登錄者協助信度的檢測。依據蒐集準則的質性與量化資料，並借助Ball, Thames與Phelps (2008)的MKT架構，本文描述兩位資深高中數學教師SCK可能樣貌以及它與KCT、KCS間的關係。
本研究結果顯示，兩位個案教師除了具有MKT原始定義的SCK特性外，也顯現其他SCK的內涵與特質，例如含有近似於HCK的特徵。其次，某些事件中教學的「不確定性(uncertainties)」會喚起林師即興的(improvisational)SCK，它的顯現與林師具有的數學知識相關，也反應了這些教學事件「不確定性」的程度。此外，兩位個案教師的SCK也會影響其教學的安排與教學的評價(亦即KCT)，是影響他們教學決策的原因之一，而KCS也會影響兩位個案教師SCK呈現的方式與時機。
最後，根據研究結果，本文指出即興SCK與「不確定性」的關係，可以作為未來進一步探究高中數學教學中的「不確定性」。希望，本研究的結果可以用來幫助在職高中數學教師，進一步了解自己在教學中所需數學知識的內涵與影響的因素，以發展高中數學教師的SCK。

This study combines qualitative case study data with quantitative video analysis as an embedded design of mixed-methods research to explore two experienced senior high school mathematics teachers’ specialized content knowledge (SCK). Using systematic classroom observations and the follow-up interviews, this research explores the explicit and implicit aspects of the SCK that the two teacher cases reveal. For encoding the videos, I used Mathematical Quality of Instruction (MQI) developed by Learning Mathematics to Teaching (2006). First, I modified the MQI coding system to adapt to the classroom teaching of two cases. Second, I analyzed the video tapes by using the adapted codes. Last, the coding results were mostly supported from another independent coder to establish acceptable inter-coder reliability. The study results properly describe two teacher cases’ SCK as well as its relationship with their KCT and KCS.
The results also show that the two teachers not only have the characteristics of SCK of the original definition in MKT study, but also show other SCK types, for example it also embodied some characteristics similar to HCK. Moreover, "uncertainties” in teaching will evoke some improvisational aspects of SCK. In addition, the two teachers’ SCK clearly affected the arrangement of their teaching and evaluation of teaching (i.e. KCT). KCS also affected the manner and timing of their SCK.
As a whole, the research results of the present study clearly point out the inherent relationship between the "uncertainties" of classroom teaching and the improvisational aspects of SCK. It is assumed that the results of this study might be used to help in-service high school mathematics teachers to understand more about the required mathematical knowledge in teaching and to develop their own SCK.

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