建構SOTO分類法並探討其評價高中數學教學之蘊涵

Constructing a Structure of Observed Teaching Outcomes Taxonomy to Evaluate the Teaching Knowledge Quality of High School Mathematics Teachers

本研究目的在於建立可觀察教學成果結構（The Structure of Observed Teaching Outcome, SOTO）分類法，以此分類法評價高中數學教師的數學教學知識，探討其所展現的SOTO認知層次及其發展的主要特徵。本研究採用質為主、量為輔的個案研究法，並參照自Learning Mathematics for Teaching（LMT）計畫所發展的教學數學品質指標（Mathematical Quality of Instruction, MQI）之教學觀察系統，整合出四位高中數學教師數學教學知識的課室觀察系統，針對108課綱普高數學第一冊多項式之四個教學單元，分析與評價四位個案教師的數學教學知識在SOTO分類法的認知層次，及其發展途徑之樣貌。研究結果有：（1）四位個案教師之數學教學知識，展現出SOTO分類法之單一（U）、多重（M）、關聯（R）、等價（E）以及結晶（C）等五種不同的認知層次與知識類別；他們的數學教學知識之認知發展的主要特徵為，出現個數不一之U-M-R迴圈或路徑之教學通路。（2）四位個案教師數學教學知識的SOTO認知層次與知識面向之差異性，在教學實作中呈現不同樣貌的教學認知發展漸進圖，進而導致產生不同風格的數學教學知識。同時，也發現四位個案教師數學教學知識在SOTO分類法的認知層次愈高，其所展現的教學知識品質也愈好。從教學評價的蘊涵來看，其意義揭示透過SOTO分類法之質性評價，可以讓高中數學教師的數學教學知識變得更加可見與可覺察。

The structure of observed learning outcomes (SOLO) taxonomy is a model that assesses student progress toward understanding a subject. In this study, we adopted SOLO for teachers and created a structure of observed teaching outcomes (SOTO) taxonomy. We used SOTO to evaluate the mathematics teaching knowledge (MTK) of four high school mathematics teachers. We executed this through a qualityoriented and quantity-supplemented case study method by implementing the mathematical quality of instruction teaching observation system proposed by the Learning Mathematics for Teaching (LMT) project in the classrooms of four high school mathematics teachers. The four teachers were observed in their teaching of four units on polynomials from the first volume of general high school mathematics of the 12-year Taiwan National Basic Education Mathematics Curriculum. The four teachers in the case study demonstrated five different cognition levels of MTK: unistructural, multistructural, relational, equivalence, and crystalline. Several U–M–R loops appeared in the cognitive development paths of the four case teachers' MTK. The differing SOTO cognition levels and knowledge dimensions of the four case teachers reveal different progressions of MTK mastery, which in turn lead to different styles of MTK. The higher the four teachers' SOTO cognition levels, the better their teaching knowledge quality. The SOTO taxonomy can be used to qualitatively evaluate the MTK of high school mathematicsteachers.