本研究欲了解如何藉由試題評量學生的數學素養，經由文獻探討後可知數學知識與認知數學能力為數學素養的重要成分。因此本研究以103年到109年國中教育會考數學科試題為研究對象，並從數學知識向度與認知向度兩個面向逐年分析並探討後，對應至108新課綱學習重點之「學習內容」與「學習表現」，藉以了解其發展趨勢。本研究利用內容分析法比較結果如下：
一、歷年各種知識發展趨勢，「幾何」歷年所占比例落在43%到54%之間、「代
數」大部分比例落在21%到30%之間、「數與量」大部分比例落在13%到21%之間以及「機率與統計」比例幾乎為7%。歷年認知數學發展趨勢，「概念性理解」所占比例趨勢大部分落在13%到18%之間、「程序性執行」大部分比例落在24%到30%之間、「解題思考」大部分比例落在55%到60%之間。對應108課綱中「學習內容」中的「空間與形狀」每年至少有5到7題、「坐標幾何」每年至少有2題；「學習表現」中的「認識、理解與熟練」大部分趨勢落在37%到48%、「解題」大部分落在55%到60%、「具體情境」近五年之試題數量上升且情境脈絡主要以個人經驗為主要方向以及「操作活動」每年至少有1到2題，其中操作工具以尺規作圖為主。
二、歷年知識向度中認知向度發展趨勢，根據分析結果對應108課綱之「學習內容」中「數與量」與「幾何」中近五年在「解題」每年至少有13到17題，比例約43%到56%。其中「方程式與不等式」近五年每年在「具體情境」居多且每年至少有2到4題、「機率與統計」歷年在「報讀」至少有1到2題。「代數」以「具體情境」和「幾何」以「抽象情境」固定出現之題型。
三、歷年認知向度中知識向度發展趨勢，根據分析結果對應108課綱之「學習表現」中的「認識、理解與熟練」在「幾何」和「機率與統計」每年至少有3到5題，數學程序的「熟練」中評量「學習內容」在「數與量」和「代數」每年至少有5到9題，比例約16%到30%，其中以「數的四則運算」和「方程式與不等式」、「代數的四則運算」、「數學符號」為主。「解題」以「空間與形狀」每年至少有6到10題，比例約20%到33%。
最後，根據研究結果提出建議未來協助九年級複習的教師，在教材內容比例的安排、教材內容中題型的設計以及教學時間的比例，可針對「學習內容」與「學習表現」比例做調整。
關鍵字：數學試題分析、數學知識、數學能力

This study aims to understand how to assess students' mathematical literacy with test questions. After examining the literature, we find that mathematical knowledge and math-
ematical cognitive ability are important components of mathematical literacy. Hence, in this study, the mathematics test questions of the CAP (Comprehensive Assessment Program for Junior High School Students) from 2014 to 2020 were used as the subjects. The study also analyzed and explored the two dimensions - the knowledge dimension and the cognitive dimension of mathematics year by year. Then, we referred to the "Learning Content" and "Learning Performance" among the learning goals of the Curriculum Guidelines of 12-Year Basic Education, known as 108 (2019) Curriculum Guidelines (108 CG), to understand their developmental trends. The results of this study were compared using the content analysis method as follows.
1. The trend in the development of various types of knowledge over the years shows that
the proportion of "Geometry" falls between 43% and 54%, the majority of "Algebra" falls between 21% and 30%, the majority of "Numbers and Quantities" falls between 13% and 21%, and the proportion of "Probability and Statistics" is almost 7%. The development trend in cognitive mathematics over the years indicates that the majority of "Conceptual Understanding" falls between 13% and 18%, the majority of "Procedural Knowledge"
falls between 24% and 30%, and the majority of "Problem Solving" falls between 55% and 60%. For "Learning Content" in 108 CG, there are at least five to seven questions
per year for "Space and Shape" and at least two questions per year for "Coordinate Geometry"; for "Learning Performance", most of the questions for "Knowledge, Understanding, and Proficiency" tend to fall between 37% and 48%, most of the questions for "Problem Solving" fall between 55% and 60%, the number of questions
for "Concrete Context" increases in the past five years and the contextual background
is mainly oriented to personal experience, and there are at least one to two questions
per year for "Manipulative Activities", in which the tools for manipulation are mainly ruler-and-compass constructions.
2. The development trend of the cognitive dimension under the knowledge dimension over the years: According to the analysis results referred to the "Number and Quantity" and "Geometry" under 108 CG’s "Learning Content", there are at least 13 to 17 questions appearing in "Problem Solving" in the past five years, with the proportion of about 43%
to 56%. Among them, "Equations and Inequalities" has mostly appeared in "Concrete Context" for the past five years with at least two to four questions per year, and "Probability and Statistics" has at least one to two questions in "Reported Reading" for each year. "Algebra" appears regularly in "Concrete Situations" and "Geometry" in "Abstract Situations.”
3. The development trend of the knowledge dimension under the cognitive dimension over the years: According to the analysis results compared with the "Knowledge, Understanding and Proficiency" under 108 CG, at least 3 to 5 questions appears in "Geometry" and "Probability and Statistics" each year. The "Proficiency" in Procedural Knowledge rated to "Learning Content" in "Number and Quantity" and "Algebra" has at least 5 to 9 questions per year, about 16% to 30%, which include "Four Arithmetic of Numbers", and "Equations and Inequalities", "Four Basic Arithmetic of Algebra", "Mathematical Symbols". There are at least 6 to 10 questions per year in the "Problem Solving" and "Space and Shape", with about 20% to 33%.
Finally, based on the results of the study, we propose suggestions for future teachers
to assist ninth graders in reviewing. In terms of the arrangement of teaching materials, the design of question types and the proportion of teaching time, the proportion of "Learning Content" and "Learning Performance" can be adjusted accordingly.
Key word：Analysis of Mathematical Test, Mathematical Knowledge, Mathematical Competencies

第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與研究問題 4
第三節 名詞釋義 4
第四節 研究限制 5
第二章 文獻探討 6
第一節 國中教育會考數學科試題 6
第二節 數學素養中的數學知識與能力 7
第三節 數學知識向度 12
第四節 認知向度之數學能力 18
第五節 數學試題分析相關研究 31
第三章 研究方法與設計 37
第一節 分析架構 37
第二節 研究流程 40
第三節 研究對象 41
第四節 資料分析處理 41
第五節、信效度分析 61
第四章 研究結果與討論 64
第一節 國中教育會考數學科試題綜合分析 64
第二節 知識向度與認知向度年度分析比較 75
第三節 歷年知識向度與認知向度異同比較 91
第五章 結論與建議 104
第一節 結論 104
第二節 建議 107
參考文獻 108

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