國小中年級數學科解題歷程導向之評量

Assessing 4th Graders' Performance on Tests of Arithmetical Verbal Problems: Componential Approach

本研究的主要目的在於發展一以解題歷程導向的國小中年級數學科評量工具。此工具共分為兩部份，第一部份為形成性測驗，第二部份為總結性測驗。兩份測驗內容均涵蓋數學解題歷程的五個成份：閱讀與理解問題、探究問題、選擇策略、執行解題、驗算（回顧與驗證解答）。施測對象為台南市勝利國小四年級107人與台南市安慶園小四年級102人。研究結果為：（1）在形成性測驗方面難度偏容易，在總結性測驗方面則難易適中；除少數試題之外，兩份測驗試題皆具有鑑別力。（2）兩份測驗皆具有內容效度。（3）本測驗與智力測驗、標準化數學科能力發展測驗以及數學科學業成績皆有高度或中度相關。（4）兩份測驗之試題皆可抽離一共同因素「一般文字解題能力」。（5）總結性測驗之重測信度為.78。本研究結果可提供教師未來設計較細步以及較有系統之解題歷程導向的評量工具，並据以發展教學活動設計與教學策略之用。

A Psychometric instrument that assesses five problem solving components of arithmetical verbal problems was developed and tried out. This instrurment included formative and summative test forms. Both forms of test consisted of five types of test items which are problem understanding, problem exploring, strategies selecting, plan executing, and answer reviewing and verifying. The subjects of formative tests were 107 4th graders from Sheng-Li primary school and the Subjects of summative test were 102 4th graders from An-Ching primary school. The results showed that(a) 104 out of 202 test items of formative tests were very easy (item difficulty indices were above .80) but the item discrimination indices were adquate.(b) both item difficulty indices and item discrimination indices of summative test were adequate.(c) both forms of tests had content validity based on experts' judgement.(d) the relationships between the test scores of this study and the group intelligent test scores, standardized mathematical achievement test scores, mathematical grades were ranged from high to moderate correlates.(e) five problem solving components from both forms of tests were extracted one common factor-general prooblem solving abilities.(f) the test-retest reliability of summative test was .78. Implications of the results suggested that detailed and systematic assessing student's arithmetical problem solving abilities instead of componential approach is feasible.