Extending the Conception of Horizon Content Knowledge: Fundamental Mathematical Knowledge and Its Sample Assessment Item

擴展教師眼界數學知識－基礎數學知識與一個評量範例

10.6173/CJSE.2015.2301.01

林勇吉(Yung-Chi Lin)；金鈐(Chien Chin)

評量 ； 基礎數學知識 ； 眼界數學知識 ； 教數學所需的知識 ； 教師知識 ； Assessment, Fundamental Mathematical Knowledge (FMK) ； Horizon Content Knowledge (HCK) ； Mathematics Knowledge for Teaching (MKT) ； Teacher Knowledge

科學教育學刊

23卷1期（2015 / 03 / 01）

1 - 22

英文

「眼界數學知識」（horizon content knowledge）意謂教師對目前所教授的數學內容，有更廣闊與深層的瞭解。本研究旨在提出「基礎數學知識」（fundamental mathematical knowledge），藉以精緻「眼界數學知識」之架構；並呈現一個評量教師基礎數學知識之範例問題。基礎數學知識定義為：對所教授之數學內容或數學問題，具有深層、透徹且融會貫通的理解。當教師具有基礎數學知識時，能夠察覺（awareness）教學主題中，核心且最基本的數學知識（洞察問題背後的一致性）。掌握這個核心且基本的數學知識，可幫助學生融會貫通整個數學問題，有助於學生解決更高難度的相關數學問題，並幫助未來更高階數學的學習。基礎數學知識是從基礎的角度來看待高階數學（elementary on advanced）。此外，發展基礎數學知識的評量，不但可幫助教師提升基礎數學知識，並能透過實徵的研究資料，健全基礎數學知識的定義。

The purpose of this article is to extend the concept of Horizon Content Knowledge and provide a sample assessment item. Fundamental mathematical knowledge (FMK) is defined as an awareness of the core or in-depth mathematics behind solving a problem. Teachers with fundamental mathematical knowledge can provide students with a more broad and comprehensive approach to solving mathematical problems that extends beyond the rote procedures used to solve a particular problem. We propose that this type of knowledge should be included in the model of Horizon Content Knowledge. Developing items that assess teachers' Horizon Content Knowledge is worthwhile because this process provides a practical way to illuminate and refine the structure and content of Horizon Content Knowledge.

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