在本研究中，探究不同函數關係式（標準變因）與不同變數（熟悉變因）對高中生數學表現的影響。透過事件相關電位（Event-Related Potential, ERP）技術，了解臺灣高中生在函數圖形與函數關係式表徵之間轉換的大腦皮質活動。本研究對34名來自新竹與苗栗地區10年級和11年級高中生進行抽樣調查，並以一般資優因子作為學生分類憑據，進一步探討這兩個因子對高中生數學函數轉換能力的影響。數據分析將透過兩種方式進行分析：第一種為行為測量，分析一般資優因子在函數圖形與函數關係式表徵之間轉換問題時的答題正確率和答對所需的反應時間；第二種為腦電生理訊號測量，主要透過ERP成分和腦波平均振幅分析一般資優因子對於大腦不同區域反應的差異。
研究結果分為兩部分介紹：(1) 在行為測量方面，一般資優因子、標準因子和熟悉因子在答題正確率和答對反應時間無顯著差異。然而，資優組學生整體表現在答題正確率上優於非資優組，反應時間則較長。(2) 在腦電生理訊號方面，在記憶圖形並轉換成函數關係式的S1階段和確認答案的S2階段，單獨探討資優組和非資優組學生，在不同腦區的P100和P300成分均受到標準與熟悉因子的影響而有顯著差異。

In this study, the impact of different functional expressions (standard variable) and different variables (familiar variable) on high school students' mathematical performance is explored. By utilizing Event-Related Potential (ERP) technology, the aim is to understand the cortical activities of Taiwanese high school students during the transformation between function graphs and function expressions. This study conducted a sample survey of 34 high school students in the 10th and 11th grades from the Hsinchu and Miaoli regions, using general giftedness factors as a basis for student classification. The effects of these two factors on high school students' abilities to transform mathematical functions were further investigated. Data analysis will be conducted in two ways: the first method involves behavioral measurements, analyzing the accuracy rate and response time required to answer questions related to the transformation between function graphs and function expressions based on general giftedness factors. The second method involves electrophysiological signal measurements, primarily through ERP components and average EEG amplitude to analyze the differences in responses from different brain regions affected by general giftedness factors.
The research results are introduced in two parts: (1) In terms of behavioral measurements, there is no significant difference in the accuracy rate and response time between general giftedness factors, standard factors, and familiar factors. However, the overall performance of gifted students in accuracy rates is superior to that of non-gifted students, with longer response times. (2) In terms of electrophysiological signals, during the S1 stage of memorizing graphs and transforming them into function expressions and the S2 stage of confirming answers, the P100 and P300 components in different brain regions of gifted and non-gifted students are significantly affected by standard and familiar factors.

張玟溢（2020）。臺灣、美國、新加坡國中函數主題教材之比較研究。國立嘉義大學數理教育研究所碩士論文，嘉義市。 取自https://hdl.handle.net/11296/ufkmbj
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