數學建模評量規準之研究

數學建模問題是一種具有真實或逼真的情境問題，不同的解題者可能會有不同的考量和方法完成這樣複雜的任務。因此，數學建模問題也是一種能啟發學生主動學習的開放性任務。此外，在考量給予適當的評量規準有助於促進學生的數學學習之下，本研究想藉由實作評量與概化理論來探討評量數學建模表現的評量規準。首先，參考文獻上提出的建模歷程共同元素，再透過數學建模專家與國中數學教師的意見調整元素及其內涵，希望此規準能夠涵蓋數學建模中各種想法的共同元素，以完整地評量各種想法的長處與不足。形成數學建模表現評量規準後，基於概化理論檢驗此評量規準的變異來源並計算不同評分人數的概化係數和可靠性係數。最後，以準實驗研究檢驗其對學生數學建模表現的影響。結果顯示，在引模、探模和展模問題中，評分者在各個面向給分的一致性還不錯，而且如果有兩位評分者時，概化係數和可靠度係數皆能達至.86的水準。另外，在學生尚未參與建構本評量規準的情況下，提供實驗組評量規準的學生數學建模表現仍顯著優於未提供本評量規準的對照組學生。

關鍵字

概化理論；實作評量；數學建模

並列摘要

Mathematical modeling problems are problems with real or realistic situations. Different problem solvers may use diverse methods to solve the same modeling problems, and thus we assumed that modeling problems are the type of tasks that can elicit students' active learning. Moreover, taking into account that providing appropriate assessment is helpful to facilitate students' learning of mathematics, this study aimed at constructing a rubric for assessing mathematical modeling performance based on generalizability theory and performance assessment. In order to construct a complete rubric which could be used to assess the strength and weakness of varied ideas for solving modeling problems, we firstly referred to the elements of modeling process in literature. Next, we modified the elements and their content according to a mathematics modeling expert and mathematics teachers’ opinions. After formulating the rubric, its generalizability and dependability was evaluated by the generalizability theory, and a quasi-experimental study was implemented to assess its effect on students' performance in mathematical modeling. The results show that the agreement among the raters was good and both the generalizability coefficient and the dependability index with two raters were above .86 for each rating facet of each modeling task. Moreover, students who were provided this rubric performed better on the modeling task than students who were not provided this rubric.