2026 / April

國中學生數學學業投入與數學復原力交叉延宕模式之縱貫研究
A Longitudinal Study on the Autoregressive Cross-lagged Model of Mathematics Academic Engagement and Mathematical Resilience among Junior High School Students

研究論文 Article

林園修, 李靜儀, 龔心怡
Yuan-Hsiu Lin, Ching-Yi Lee, Hsin-Yi Kung

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本研究旨在以縱貫研究設計來探究國中學生的數學學業投入與數學復原力的交叉延宕模式，以七年級至九年級每間隔一學年的三個波次共1,069位國中學生為研究樣本，整合生態系統理論為架構，藉由結構方程模式進行分析，獲致結果如下：1.整體模式的適配度指標顯示模式可被接受，數學學業投入與數學復原力的交叉延宕模式獲得支持。2.國中學生之數學學業投入對數學復原力具預測力，但不具縱貫效果；第一波數學學業投入可以顯著預測第二波數學復原力，第二波數學學業投入至第三波數學復原力卻未能達到顯著預測；3.國中學生之數學復原力對數學學業投入具預測力，且具縱貫效果；第一波數學復原力可以顯著預測第二波數學學業投入，第二波數學復原力也可以顯著預測第三波數學學業投入。本研究希望透過數學領域中的復原力機制，提供學生在面對數學學習壓力時能積極面對挫折與挑戰，最後根據研究結果提出建議，進而為教育介入策略提供實證基礎及後續研究之參考。

This study proposed a cross-lagged model of mathematical academic engagement and resilience among junior high school students using a longitudinal design. Data from 1,069 students were collected in three waves every school year from the seventh to ninth grades. The study used structural equation modeling within an ecological systems theory framework, and the results are as follows. (a) The proposed autoregressive cross-lagged model indicates a reasonable goodness-of-fit. (b) Students’ mathematical academic engagement can predict their mathematical resilience but not longitudinally, while mathematical resilience in the second wave can be significantly predicted by the first wave of mathematical academic engagement and mathematical resilience in the third wave cannot be significantly predicted by the second wave of mathematical academic engagement. (c) Students’ mathematical resilience can predict their mathematical academic engagement with a longitudinal effect. Mathematical academic engagement in the second wave can be significantly predicted by the first wave of mathematical resilience and mathematical academic engagement in the third wave can be significantly predicted by the second wave of mathematical resilience. By examining the mechanism of resilience within the domain of mathematics, this study sought to empower students to actively overcome the frustration and challenges associated with learning pressure. These findings can be used to propose practical recommendations and offer an empirical foundation for intervention strategies and future research.

數學學業投入, 數學復原力, 交叉延宕模式, 縱貫研究
mathematics academic engagement, mathematical resilience, autoregressive cross-lagged modeling, longitudinal study

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