本文以臺灣資賦優異高中生與一般生為對象，探究其在函數圖形與方程式表徵轉換解題行為和腦波表現。以瑞文式空間智力測驗篩選出33位資賦優異生及38位一般生，檢測兩組學生的行為表現和腦波反應。就解題行為分析顯示資優生答題正確性顯著高於一般生；兩組學生在答題的反應時間則無顯著差異。就腦波分析顯示，所有學生在函數圖形與方程式轉換階段(S2)的腦區反應顯著高於函數圖形閱讀階段(S1)，顯示函數圖形和方程式表徵轉換需要較高的認知資源。另從P300分析顯示，函數圖形和方程式表徵轉換會造成側腦化現象。就兩組學生比較，其在閱讀函數圖形階段，事件相關電位(event-related potential)成分均無顯著差異，顯示兩組學生在函數圖形閱讀階段腦區反應並無顯著差別。但在函數圖形與方程式表徵轉換階段，資賦優異學生在P100、P300及N400的腦波振幅均顯著大於一般生；而一般生在P200的腦波振幅則是顯著高於資賦優異學生。顯示資賦優異學生在兩種表徵轉換時，會花費較高腦資源在視知覺、認知工作執行以及錯誤偵測監控上。而一般生則是花費較高腦資源在注意力選擇認知活動上。此研究結果與腦科學提出的神經效能假說及其他相關文獻討論將一併呈現。

The study aims to examine the problem-solving behaviors and brainwave performance of gifted high school students and non-gifted students in Taiwan when transforming between function graphs and equations. Thirty-three gifted students and thirty-eight non-gifted students were selected using the Raven’s Progressive Matrices Intelligence Test, and their behavioral performance and brainwave responses were examined. Behavioral analysis revealed that the gifted students had significantly higher accuracy in problem-solving compared to the non-gifted students, with no significant differences observed in response times between the two groups. Regarding brainwave analysis, all students showed significantly higher brain responses during the stage of transforming between function graphs and equations (S2) compared to the stage of reading function graphs (S1), indicating that transforming between the two types of representations requires higher cognitive resources. Furthermore, P300 analysis demonstrated a lateralization effect during the transformation from function graphs and equations. When comparing the two groups of students, there were no significant differences in ERP components during the reading of function graph stage. However, during the transformation stage, brainwave amplitudes in gifted students (P100, P300, and N400) were significantly higher than those in non-gifted students. This indicated that gifted students expend higher neural resources on visual perception, cognitive task execution, and error detection monitoring during these two types of representation transformation. Conversely, non-gifted students allocate higher neural resources to attentional selection cognitive activities. The findings of this study, along with discussions related to the neural efficiency hypothesis proposed in neuroscience and other relevant literature, will be presented comprehensively.

事件相關電位; 函數方程式; 函數圖形; 表徵轉換; 資賦優異學生

Event-Related Potentials; Function Equation; Function Graph; Representation Transformation; Gifted Students