國中生在數學代數概念學習之評量研究--以二元一次方程式為例

An Evaluative Research Study on Learning the Mathematics Concept of Algebra by High School Students--Using the Quadratic Equation as an Example

本研究屬於探索性的研究分析，旨在嘗試發展一套能夠敏銳偵察學生學習的評量方法。其研究特色即是透過客觀的學業成就評量，以知識結構的表徵為基礎，利用路徑蒐尋網路分析（Pathfinder network analysis）方法，試圖提出並驗證一套新的評量技術，此乃為認知診斷測驗的重要先驅。本研究所使用的工具有：第一次月考考卷、教師之自編成就測驗。樣本為普通班學生33名，依上學期的數學成績，將之分成三組，分別為高、中、低成就，每組各為11人。研究程序以量化分析為主，將一系列學生客觀的學業成就評量結果，利用Schvaneveldt（1994）所發展的電腦程式（KNOT）進行知識結構分析，本研究歸納提出下列的結論：一、低成就學生的概念結構圖與教師的概念結構圖差甚大；中學習成就學生次之；高成就學生在代數概念上的理解情形近似於教師，尤其數學學習成就較佳的學生，其學習的表現與教師相同。二、低成就學生的概念結構圖大多相，且高成就學生的概念結構圖有明顯的差異存在。三、以學生在校的實際評量成績為依變項，三種相似性指數值為自變項，分別對其進行迴歸分析，由結果可得知PFC指數（或C值）的預測效果最佳。

This research is a kind of explorative research， aimed to develop the evaluative approach in order to accurately track the student learning process. It is unique in that the objective homework achieved assessment is based on the schema of knowledge construction， using Pathfinder network analysis t justify a new set of evaluative techniques. This study will serve as a significant pioneer of cognitive diagnostic test.The tools of this research include：the first-month exam paper and teacher-edited achievement tests. The samples of this research are 33 students in a normal classroom setting which is divided into three groups of 11 (high， medium， and low) based on the students’ previous semester’s grades. A series of assessment results of students were analyzed by Schvaneveldt’s KNOT computer program， which uses quantitative analysis as its primary method. Based on these findings， several conclusions were made as follows：1.There is an outstanding difference between the concept-constructed map of under-achieving students and the concepts-constructed figure of the teacher. The concept-constructed map of medium-achieving students was more similar to the teacher’s. Over-achieving students produced a map that was most similar to the teacher’s， especially the students with the highest levels of achievement， whose performance proved to be the same as the teachers.2.There is a striking similarity among the concept construction maps produced by the under-achieving students. When comparing the group’s results as a whole to those of the over-achieving students， an obvious difference exists.When the independent variable is the student’s actual academic result， and the three similar indexes are the dependent variables， after regression analysis， it can be said that the PFC Index (or C value) is the best tool for prediction.