本研究設計、實作並初探一套結合多模態互動畫布與AI數學同伴的系統，探討其應用於國小高年級數學幾何應用題解題歷程之可行性。有鑑於傳統純文字對話系統在輔助幾何空間問題上的限制，系統嘗試透過互動畫布作為學生外顯思考軌跡的工具，並轉化為AI引導之情境脈絡。系統採多代理人架構，由「數學思考狀態分析師」推估學生解題時的自我調節學習階段，再由「數學AI小幫手」動態切換引導角色並融入提問引導與同理回應，在不直接提供解答的前提下，探索提供適性認知與情意支持的可能性。 本研究為小樣本初探研究，有效樣本共9名五年級國小生。歷程分析顯示，人機協作以「圖文並行」模式為主，學生多採用簡短文字搭配畫布軌跡與AI同伴互動；受任務難度與可用時間等因素影響，學生的互動策略呈現多元樣態。量化結果顯示，數學焦慮呈下降趨勢，自我效能則有小幅波動，但前後測差異均未達統計顯著。訪談指出，AI較少責備且可反覆提問的特質，為部分學生提供較具容錯性的求助經驗，或可作為理解焦慮分數下降的參考線索。然而，本研究系統限制包括自動判定解題階段的準確性尚未經充分驗證，以及制式且重複的正向回應可能降低互動自然度。研究初步呈現手寫畫布與AI同伴應用於數學學習輔導的實作可能性，未來可持續改善不規則筆跡判讀、建立判讀回報與教師介入機制，並進行較大規模與長期的實證。;This pilot study designs， implements， and explores an AI mathematics companion integrated with a multimodal interactive canvas for upper-grade elementary geometric word problem solving. To address the limitations of text-only interaction in spatial tasks， the canvas captures students’ problem-solving traces and provides contextual information for AI guidance. Using a multi-agent architecture， the system estimates self-regulated learning (SRL) phases and dynamically switches AI roles， providing guided questioning and empathetic responses without directly revealing answers. Nine fifth-grade students participated in the study. Process analysis showed that human-AI collaboration mainly involved a combined text-and-canvas mode， with students using brief text alongside canvas markings. Interaction strategies varied with task difficulty and available time. Quantitative results showed a downward trend in mathematics anxiety and slight fluctuations in self-efficacy， but neither pre–post difference was statistically significant. Interviews suggested that the AI’s non-scolding responses and availability for repeated questioning provided some students with a more tolerant help-seeking experience and offered contextual clues for interpreting the decrease in anxiety. Limitations included unverified SRL-stage detection accuracy and reduced interaction naturalness caused by repetitive， formulaic praise. The findings present the preliminary classroom applicability of canvas-based AI companions. Future research should improve irregular-handwriting recognition， establish feedback and teacher-intervention mechanisms， and conduct larger-scale， longitudinal studies.
