本研究探討臺灣與美國中學數學職前教師數學語言相關教學思維，以及兩個國家職前教師在數學語言相關教學能力上的表現。
研究樣本為兩個國家在數學師資培育跨國研究（Teacher Education and Development Study in Mathematics, TEDS-M）樣本的子集（sub-sample），由臺灣、美國分別在其全體樣本中隨機抽出，共有161名臺灣中學數學職前教師、172位美國中學數學職前教師參與研究。
本研究發現，兩國職前教師思維中能連結到之文字敘述數學語言的特徵，都是較為一般性、整體性的描述，例如，抽象、冗長等，並不能做更深入、考量語句組成的分析。然而，分析他們實際提供給學生語句時，卻可發現他們認為學生易理解的語句應具有較程序性，例如，以運算動作取代大量名詞化、提供可操作之具體物件，較低數學專門用語的使用量，較口語化，訊息進展速度較緩慢等等特徵。本研究發現在數學語言相關教學能力表現上，臺灣職前教師在「執行」及「推理與判斷」方面較美國職前教師優異，而兩個國家在「執行」方面的表現都優於「推理與判斷」方面的表現。上述教學思維與教學能力的現象都反映出職前教師思維中所連結的概念，乃屬於Schön（1983）提出無聲的（tacit）、實踐的知識（practical knowledge）。
在數學語言相關教學能力表現上，本研究也發現，兩個國家的職前教師在思考影響學生理解數學語言的因素時，都缺乏能從數學語言角度切入分析的能力，尤以美國更為嚴重。臺灣職前教師表現並非皆優於美國，在選用能培養學生數學語言能力的教學活動上表現即較美國差，且有相當高比例職前教師僅聚焦於數學概念而非數學語言的培養。
此外，職前教師在描述其想法時，用詞侷限，不能明確、精準使用數學教育中使用的專門詞彙，從Skemp（1987）的角度，職前教師數學教育中的概念與承載它的語言連結，職前教師便能自由控制自己思想、與他人溝通，也能促進新概念的形成，職前教師關於數學教育中詞彙的使用乃反映其在師資培育學程中的培養情況（Blömeke et al., 2008），故而此現象值得師培界考量。

第一章 緒論 1
第一節 研究動機 1
第二節 研究目的暨研究問題 4
第三節 名詞界定 5
第四節 研究限制 7
第二章 文獻探討 9
第一節 語言 9
第二節 數學語言 32
第三節 數學教學思維與知能 51
第三章 研究方法 60
第一節 研究架構 60
第二節 研究工具 65
第三節 研究樣本 67
第四節 資料處理 68
第肆章 研究結果 72
第一節 職前教師數學語言相關教學思維 72
一、職前教師對文字敘述表徵與學生知能在學習上的機制之思維 72
二、職前教師對學生知能、教學活動、文字敘述數學語句在教學中的機制之思維 103
三、職前教師對學生知能在文字敘述數學語句之組成與特徵的機制之思維 131
第二節 職前教師之數學語言相關教學能力 165
一、函數表徵之教學情境 166
二、平方根算則之教學情境 186
三、數學語言相關數學教學能力總論 216
第五章 結論與建議 220
第一節 結論 220
第二節 建議 228
參考文獻 230

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