發展高中教師教數學所需的知識之問卷：探索性研究 developing an instrument for capturing high school teachers’ mathematics knowledge for teaching: an exploratory study

本研究旨在描述如何發展高中教師「教數學所需的知識」（MKT）問卷。研究結果以一個具代表性的問題為例。呈現這個代表性問題如何發展與不斷精緻，最後報導本問卷的前導測驗結果。本研究發現三個有效的創造問卷的策略：一、使用具有「關鍵」教學知識的數學問題（教導這個數學問題，需要一個基礎、重要且不能忽略的核心知識）。二、使用學生非例行性解法。三、使用教師在實際教學上的錯誤。本研究希望提供相關領域研究者，如何設計MKT問卷的參考依據。 This paper addresses an effort to design and test a set of items for assessing the mathematics knowledge for teaching. The paper begins by describing how a representative item was developed based on three experienced high school teachers’ analyzing classroom instruction. Subsequently, item refinement by two experts is documented. Finally, the initial results of a pilot-test of a focus group of 11 high school mathematics teachers are reported. This study revealed three useful methods for creating items for assessment: (1) using mathematics problems containing certain key mathematical ideas; (2) using nonstandard approaches of students that are unfamiliar to the teachers; and (3) using the errors of teachers.