本研究之目的在探討：⑴國小教師對分數知識、學生分數認知的知識、分
數教學知識的了解。⑵探討國小教師分數教學相關知識的了解。研究目的
一的三種知識，分別以國小數學新課程的數學觀，數學學習的了解層次理
論，及診斷教學理論為內涵，發展研究工具。本研究抽取國立台北師範學
院國小教師暑期學士班，各系二年級各一班，共136 人進行筆測，並從中
選取33人，進行一對一的半結構性面談。研究結果：1.將國小教師對分數
知識、學生分數認知的知識、分數教學知識的了解，分別分成優、中、差
三種程度。對這三類知識有較佳了解者分別占33%、10% ∼20% 、13%
∼30% 。 2.從教師的觀點，利用主成份分析，得到分數教學之相關知識
有五類：分數知識、分數相關教材的知識、因應學生想法調整教學設計的
能力、分數了解層次的知識、及學生解題策略的知識。3.根據群聚分析，
將上述五類知識分成：數學及其教材教法的知識、學生數學學習的知識。
這二個範疇知識都佳者占7.4%，只有數學及其教材教法知識佳者占16.9%
，只有學生數學學習知識佳者占26.5% ，另外，有將近一半的教師，這二
個範疇知識都欠佳。再利用綜合評判，將每位教師對二個範疇知識的了解
程度數值化，發現國小教師分數教學相關知識的了解呈現分流發展的現象
。根據研究結果，提出在台灣的特定脈絡中，國小教師數學教學相關知識
發展的模式。此模式可應用於職前及在職的師資培育，有效發展國小教師
的數學教學相關知識。

This study aims to 1.investigate elementary school teachers''''
knowledge of fractions,knowledge of students'''' cognitions in
fractions and pedagogical knowledge; and 2.assess elementary
school teachers'''' understanding of these three components of
knowledge in fractions teaching. A sample of 136 elementary
school teachers took the pencil and paper test in this study.
Among these 136 subjects,33 were selected for interview in one
-to-one semi-structure way.The findings were as follows. 1.The
percentages of teachers'''' excellence understandings of those
three kinds knowledge were 33%、10%∼20%、13%∼30%
respectively. 2.Using the Principal Component Analysis,the
above mentioned knowledge can be decompounded into five
components:the knowledge of fractions, the knowledge of
fractions teaching materials,the ability to adjust
instructional design responsive to students'''' thinking patterns
,the knowledge of the hierarchy of students'''' understanding
fractions,as well as the knowledge of students'''' problem-solving
strategies.3.Using the Cluster Analysis,the above mentioned
five components can be categorized into two areas:the knowledge
of mathematics 、materials and methods ,as well as the
knowledge of students'''' mathematics learning. 7.4% of the
teachers excelled in both areas ;16.9% of the teachers excelled
in the knowledge of mathematics、materials and methods ; 26.5%
excelled in the knowledge of students'''' mathematics learning;
while approximately half of the teachers performed
unsatisfactorily in both areas.Taiwan in-service elementary
school teachers'''' understanding the knowledge in fraction
teachings is in a two-streams way. A model of the development
of elementary school teachers'''' mathematics teaching knowledge
within the context of Taiwan society is proposed according to
the results of this study.