本研究以 OECD 公布之 PISA 2022 資料為基礎，探討臺灣與德國 15 歲學生主動數學學習行為與數學素養之關聯，並檢驗數學自我效能在兩者之間所扮演之中介角色。分析資料包含臺灣 5,857 名與德國 6,116 名 15 歲在學學生。主要變項包括主動數學學習行為、正式與應用數學自我效能、數學推理與 21 世紀數學自我效能及數學素養；並於總效果與中介效果模型中納入性別與家庭經濟社會文化地位（ESCS）作為控制變項。研究方法上，描述統計採加權估計；推論分析則依 PISA 設計相容原則，結合學生最終權重、Fay-BRR 複本權重及數學素養可能值，進行差異分析、相關分析、迴歸分析與中介效果檢定，並另以不納入家庭經濟社會文化地位之替代規格進行敏感度分析。
研究結果顯示，德國學生之主動數學學習行為高於臺灣學生，臺灣學生之數學素養則顯著高於德國學生；在數學自我效能方面，地區差異主要出現在正式與應用數學自我效能，且德國學生高於臺灣學生。相關分析結果指出，臺灣與德國學生之主動數學學習行為、數學自我效能與數學素養皆呈顯著正相關。總效果分析結果顯示，在控制性別與家庭經濟社會文化地位後，主動數學學習行為對兩國學生之數學素養皆具有顯著正向總效果，且臺灣樣本之效果強度顯著高於德國樣本。中介效果分析進一步顯示，無論以正式與應用數學自我效能或數學推理與 21 世紀數學自我效能作為中介變項，兩國樣本之中介效果皆達顯著，且臺灣樣本之中介效果均顯著高於德國樣本。敏感度分析結果與主分析方向一致，顯示本研究主要發現具有一定穩定性。整體而言，主動數學學習行為不僅與數學素養具有正向關聯，亦可透過數學自我效能間接連結至數學素養，且此一關聯路徑在臺灣與德國樣本中呈現不同強度。據此，本研究建議數學教學除重視知識與技能培養外，亦應系統性培養學生之主動數學學習行為，並支持其數學自我效能之發展。

This study investigated the association between proactive mathematics study behaviour and mathematical literacy among 15-year-olds in Taiwan and Germany, with mathematics self-efficacy examined as a mediator. The study used PISA 2022 data on proactive mathematics study behaviour (MATHPERS), self-efficacy in formal and applied mathematics (MATHEFF), self-efficacy in mathematical reasoning and 21st-century mathematics (MATHEF21), and mathematical literacy. The analytic data included 5,857 students in Taiwan and 6,116 students in Germany. Descriptive statistics were estimated using student final weights, whereas inferential analyses incorporated student final weights, Fay-BRR replicate weights, and plausible values for mathematical literacy. Gender and economic, social, and cultural status (ESCS) were included as control variables in the total-effect and mediation models, and sensitivity analyses without ESCS were conducted for these models.
German students reported higher proactive mathematics study behaviour, while Taiwanese students performed significantly better in mathematical literacy. Cross-national differences in mathematics self-efficacy were found only for MATHEFF, with German students reporting higher MATHEFF than Taiwanese students, whereas MATHEF21 did not show a significant difference. In both countries, proactive mathematics study behaviour, mathematics self-efficacy, and mathematical literacy were significantly and positively related. Proactive mathematics study behaviour had a significant positive total effect on mathematical literacy in both countries, and the total effect was significantly stronger in Taiwan than in Germany. Significant indirect effects were also found through both MATHEFF and MATHEF21, with stronger indirect effects in Taiwan. The results suggest that proactive mathematics study behaviour is positively associated with mathematical literacy and may be indirectly linked to mathematical literacy through mathematics self-efficacy.

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