| 摘要: | 真實情境數學應用題（AMWPs）作為重要的教學資源，不僅能評估學生對多元數學概念的掌握程度，更能培養數學推理與解題能力。然而，建構真實情境數學應用題（AMWP）實屬艱鉅任務，因其需兼顧數學正確性、情境相關性與教育價值三者平衡。要生成既可解又具意義的真實情境數學應用題，需謹慎整合真實世界情境、精確數值數據、適當認知需求，並與學習目標相契合。此外，確保題型與難度層級的多樣性更為生成過程增添複雜性。在此背景下，自動生成數學應用題能有效應對這些挑戰，實現高效產出多元、情境相關且數學運算正確的題目。
現有自動化數學問題生成研究主要採用三種核心技術：模板式生成、問題改寫及神經網路驅動的文本生成。其中模板式方法常涉及勞力密集的流程，因其需人工設計模板，且部分情況下依賴特定語言工具或資源，導致跨情境的擴展性與適應性受限。問題改寫法透過改寫或修改現有題目，卻受限於語義漂移問題——措辭變動可能無意間改變數學含義或解法。此法亦因高度依賴既有題庫而缺乏創新性，且可能引發情境錯配或歧義。此外，基於神經網路的問題生成雖具更高靈活性，卻衍生其他挑戰：例如產生事實矛盾、生成不可解題型，以及缺乏教學控制力以符合課程標準或目標技能。神經模型可能產生文化偏見或無關情境，且其輸出品質因訓練數據依賴性而差異懸殊。
相較於現有數學應用題生成研究，我們提出一種嶄新方法，運用生成式人工智慧自動生成具備情境化、個人化與社會化特性的數學應用題。情境化策略旨在將數學概念置於真實世界、實際情境或個人相關情境中，使數學應用題更具意義，這些情境能反映學習者的日常經驗與環境。情境化AMWP將數學連結至日常體驗、實務情境或相關事件，使其對學習者更具相關性、真實性與吸引力。個人化機制則藉由調整難度以匹配個別學習者能力，提升AMWP的有效性。藉由依學生技能水平量身打造問題，確保每位學習者獲得適當挑戰，從而促進參與度、激發動機並達成最佳學習成效。最後，社會化機制則進一步融入社交互動提示與團體導向任務，將AMWP從個人練習工具轉化為協作學習工具，支持共同解題並發展合作、協商、觀點分享等社會認知能力。
我們的主要貢獻包括：
1) 透過系統性文獻回顧（SLR）對數學應用題自動生成研究進行全面綜述。本綜述整合了當前數學應用題生成的進展，涵蓋尖端技術與評估方法，為研究者與教育工作者提供完整參考，為未來研究在選擇生成方法與評估方式時提供指引。此外，本研究提出整合情境化、個人化與社會化原則的數學應用題生成與評估綜合框架。該框架不僅能引導自動生成數學精確且符合情境的應用題，更提供結構化評估標準，用以衡量應用題品質、教學契合度，以及在個別學習與協作學習情境中的成效。
2) 提出並實施自動化AMWP生成系統。該系統運用生成式人工智慧，提出一種創新的三難度等級AMWP生成方法，並將其整合至自動化系統中。透過自動化指標、人工評鑑與啟發式評估等多重技術，驗證生成之應用題與系統品質，證實生成式人工智慧結合真實情境資訊於AMWP 生成技術之可行性。
3) 透過在真實教育環境中的實施與驗證，對 AQG 系統的有效性進行實證分析。我們在真實學習情境中，透過準實驗研究評估該系統的成效。結果顯示該系統能促進數學問題解決能力，並提升學生的數學學習表現，證實其在課堂環境中的實用價值。
4) 提出名為SocioMathLLM的社會化多模態大型語言模型框架。該框架整合創新提示工程策略，融合多模態真實情境資訊（文字與圖像）、多元群體背景資料及社會化準則（如群體規模、任務性質、社會目標、互動頻率、交流數量與社會依存性等），以生成旨在培養群體社會化能力的真實情境數學應用題。SocioMathLLM 特別強調其在協作式數學學習中的應用潛力，可培養群體協作、合作、協商及想法分享等社會化能力。;Mathematical Word Problems (MWPs) serve as an important instructional resource that not only assesses students’ proficiency in diverse mathematical concepts but also supports mathematical reasoning and problem-solving skills. Generating authentic MWP (AMWPs) is a challenging task due to the need to balance mathematical correctness, contextual relevance, and educational value. Generating AMWPs that are both solvable and meaningful requires careful integration of real-world scenarios, accurate numerical data, appropriate cognitive demand, and alignment with learning objectives. Additionally, ensuring diversity in problem types and difficulty levels adds further complexity to the generation process. Here, the automatic generation of MWPs can help address these challenges by efficiently producing diverse, contextually relevant, and mathematically accurate problems.
Existing studies on automatic MWP generation have primarily employed three main techniques: template-based generation, question rewriting, and neural network–based text generation. Among these, template-based methods often involve labor-intensive and time-consuming processes, as they require manually crafted templates and, in some cases, rely on language-specific tools or resources that limit scalability and adaptability across contexts. Question rewriting, which involves paraphrasing or modifying existing problems, is limited by semantic drift, where changes in wording may unintentionally alter the mathematical meaning or solution. This approach also produces limited novelty, as it depends heavily on pre-existing problems, and may introduce context mismatches or ambiguity. Furthermore, neural network–based problem generation offers greater flexibility but introduces other challenges, such as factual inconsistencies, unsolvable problems, and a lack of pedagogical control to align with curriculum standards or targeted skills. Additionally, neural models may produce culturally biased or irrelevant contexts, and their outputs can vary widely in quality due to dependence on training data.
In contrast to existing works on MWPs generation, we propose a different approach that leverages generative AI to automatically generate AMWPs with contextualization, personalization, and socialization. Contextualization enhances the meaningfulness of AMWPs by situating mathematical concepts within authentic, real-world, or personally relevant contexts that reflect learners’ everyday experiences and environments. Contextualized AMWPs link mathematics to everyday experiences, practical situations, or relatable events, to make them relevant, authentic, and engaging for learners. Personalization contributes to making AMWPs more effective by adjusting the difficulty level to match individual learners’ abilities. By tailoring problems to students’ skill levels, it ensures that each learner is appropriately challenged, promoting engagement, motivation, and optimal learning outcomes. Finally, the socialization mechanism transforms AMWPs from tools for individual practice into instruments for collaborative learning by incorporating social interaction prompts and group-oriented tasks, supporting collaborative problem-solving and the development of social-cognitive competencies such as collaboration, cooperation, negotiation, and idea-sharing.
Our main contributions include:
1) Presenting a comprehensive review of MWP automatic generation research by Systematic Literature Review (SLR). It synthesizes current advancements in MWP generation, including state-of-the-art techniques and evaluation methods. This offers a comprehensive reference for researchers and educators, guiding the selection of generation approaches and evaluation methods in future work. In addition, this study proposes a comprehensive framework for generating and evaluating MWPs, which integrates contextualization, personalization, and socialization principles. The framework not only guides the automatic generation of mathematically accurate and contextually relevant problems but also provides structured evaluation criteria to assess problem quality, pedagogical alignment, and effectiveness in both individual and collaborative learning settings.
2) Proposing and implementing an automated AMWP generation system. It presents a novel method for generating AMWPs with three difficulty levels using generative AI, which was implemented in an automated system. Multiple evaluation techniques, including automatic metrics, human evaluation, and heuristic evaluation, were applied to validate the quality of both the generated MWPs and the system, demonstrating the feasibility of combining generative AI with authentic contextual information in AMWP generation.
3) Presenting empirical validation of the AQG system’s effectiveness through implementation and validation in real educational settings. We evaluated the effectiveness of the proposed system through a quasi-experimental study in authentic learning contexts. The results demonstrated that the system facilitates mathematical problem-solving and improves students’ mathematics learning performance, confirming its practical utility in classroom environments.
4) Proposing a socialized multimodal LLM framework called SocioMathLLM. It integrates an innovative prompt engineering strategy to incorporate multimodal authentic contextual information (text and image), diverse group background information, and socialization criteria (e.g., group size, task nature, social goal, social frequency, interaction quantity, and social interdependency, etc.) to generate AMWPs aimed at fostering group socialization. SocioMathLLM highlights its potential for application in collaborative mathematics learning and fostering socialization competencies such as group collaboration, cooperation, negotiation, and ideas-sharing. |
