教育部公佈的能力指標中，只以紙筆測驗無法完整呈現學習成就，必須以多元評量來評估學生的數學表現。教師在評估學生能力過程中，部分能力指標偏向質性，因此以傳統的評分和計算方式明顯呈現不妥。本文以模糊理論為基礎，在多元評量的條件下，建構綜合學生數學學習的綜合成績。首先將所有的能力指標列成階層（hierarchical）關係，其中部分能力可從紙筆測驗得到明確成績的，仍以紙筆測驗為主，部分成績由平時教師的觀察和上課的表現，給予一個可能區間範圍的成績，然後分別求出這些成績在模糊等第中的隸屬度（membership degree）或相似度（similarity measure），稱為客觀性的證據（objective evidence）h值。另一方面，由任課教師在同一能力指標下的各細項能力，給予重要性評估，分別算出相對權重g值。接著將成績的表現h值和權重g值，以模糊積分（fuzzy integral）綜合成上一層的成績表現h值。如此一層一層地，由底層綜合至總成績表現。
以此建構的綜合成就的模式比傳統的方式，得到更多的訊息。在個別能力的表現，提供教師在教導個別學生的參考，不論優秀的還是待加強，都會被保留下來，不會被其他分數稀釋掉。另一方面，個別在全體中的表現中，可清楚的分別出能力等第，不會為區區0.1分的差距而細分名次，甚至分佈在不同等第。因此比傳統的方式更合理，從教育的觀點來看更符合教育理念。

In the ability index published by the Department of Education, the written test itself cannot completely reflect achievement in learning.　Multiple evaluation methods must be applied in evaluating students’achievement in mathematics.　During the process where teachers evaluate students’ ability, some ability indices focus on quality.　Therefore, it is inappropriate to represent the ability achievement by traditional grading and calculation methods.　This article employs Fuzzy Theory as the basis, under multiple test conditions, for the calculation of a collective grade that combines all the students’achievement in mathematics.　First, all ability indices are arranged in hierarchical relationship.　Where it is possible to obtain accurate grades for some of the abilities from a written test, the focus will remain on the written test.　Some abilities are given grades within a possible range by factoring in teachers’ observations and the students’ performance in the class.　The membership degree or similarity measure under the fuzzy grade is calculated for these grades and is called the objective evidence h value.　On the other hand, the student’s teacher evaluates the importance of each sub-ability under the same major ability and calculates its relative weight g value.　The Fuzzy interval is then applied by combining the h value, that reflects the grade, and the g value, that reflects the weight, and presents them in the h value, an upper level of grade performance.　By doing this, level-by-level, combining is done from the bottom level until the total grade appears.
The model of combined achievement constructed with this method reveals more information than the traditional method.　The performance of individual ability provides teachers with references in teaching individual students.　Students’ performance, regardless of whether it is excellent or to needs to be reinforced, will be preserved and will not be diluted by other grades.　On the other hand, individual performance in the group will be differentiated clearly with ability ranking.　The standing, or even ranking, will not be differentiated because of a minor difference of 0.1.　As a result, this is a more reasonable method than the traditional method and conforms more to education theories and concepts from the perspective of education.

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