國小六年級學生「數學論證評量工具」之建構

The Construction of Measuring Six-Graders' Mathematical Argumentation

過去有關學生學習成效之評量，其評量內容著重在數學知識而忽視高層次思考層面。本研究旨在建構一個適用於國小學生數學論證之評量工具，建構包含發展與驗證試題的品質。此評量工具透過預試和正式施測兩階段發展完成，兩階段的研究樣本都採用立意抽樣，預試和正式施測階段各從三縣市抽取六年級學生各為456與599人。從理論觀點建構數學論證評量架構的四個向度：「提出猜想」、「效化猜想」、「一般化」及「證明」，以提升評量工具的內容效度和建構效度，並利用統計分析，以項目分析、驗證性因素分析與信度分析，考驗「數學論證評量工具」的信效度。分析結果得到該份試題的難度介於0.30至0.74之間，鑑別度介於0.25至0.69之間，15題的總量表信度係數為.61，效度為專家效度；四個向度「提出猜想」、「效化猜想」、「一般化」及「證明」對數學論證的預測係數分別為.91、.84、.96、.83，顯示本研究中四個一階的預測因素能有效預測二階的數學論證之構念效度。本研究研發的數學論證工具之特色是不僅能對數學論證的四個向度以操作型定義，而且能將高層次思考的數學論證之評量試題以選擇題形式命題，並以論證品質的不同等級為誘答項設計的考量。本研究可提供教師及研究者一個值得信賴的評量工具。

In past, the assessment of student learning focused on mathematical knowledge instead of the high-order thinking. The study was to construct a measure of assessing six-graders' mathematical argumentation through pilot study and main study. The construction of the measure included two aspects: developing and testing. A total of 456 students and 599 students were purposely sampled from three counties for pilot study and main study, respectively. The validity and reliability of the measure to be constructed were based on both theoretical consideration and statistical analysis. From the theoretical consideration, the framework of the measure consisted of two dimensions: mathematical argumentation and mathematical content. Argumentation included four constructs: formulation, validation, generalization, and justification. From statistical analysis perspective, item analysis, reliability analysis, and confirmatory factor analysis were used to test the validity of the measure. The difficulty of the items ranged from 0.30 to 0.74 and the coefficiency of discrimination ranged from 0.25 to 0.69. The reliability coefficient of the total measure of 15 items was .61. We used the validity of expert. The coefficients of predicting the four factors of the mathematical argumentation including formulation, validation, generalization, and justification were .91, .84, .96, .83 respectively. The result indicates that the four first-order predictors had good prediction on the validity of the second-order argumentation. The measure developed in this study with multiple choice of the items to assess students' high-order thinking and mathematical argumentation with operational definition were the two features of the study. This study was able to provide a reliable instrument for teachers or researchers to measure students' argumentation.