数学建模能力是社会发展和人才储备所需的重要素养之一，其评估与提升备受世界各国数学教育改革关注。随着复杂认知评价需求的日渐严苛，原有针对数学建模能力的测评框架、测验形式、评估颗粒及证据角度，已不能满足其强调现实情境、循环迭代和精细测评的评估需求。尽管信息技术的优势在高阶认知能力测评领域得以探究和应用，但基于计算机技术的数学建模能力测评研究仍十分匮乏。尤其是针对整个建模过程对外显和内隐认知证据进行获取及分析的相关研究，已经成为该领域评价及提升的突破要点。由此，开展数学建模能力计算机交互式测评及其提升证据的深入探究具有重要理论价值和实践意义。

本研究依据证据中心设计(Evidence-Centered Design, ECD)为理论指导，探索了一套利用计算机交互式测评形式，基于同一现实情境且覆盖整个建模流程的混合视角，通过模拟实际建模反馈指导对初中生样本数学建模表现的评估模式。通过分析不同亚群体在关键建模阶段中的过程性表现，深入探究交互反馈模式下多次重复作答表现趋势特点，为数学建模及相似高阶认知能力评价与提升提供可行的理论和实践参照依据。具体五个子研究及结果如下：

研究一构建了融合过程性指标和交互式测评属性的初中生数学建模能力计算机交互式测评的指标框架。首先，梳理数学建模及过程数据(Process data)相关文献初拟指标框架；其次，邀请相关领域专家针对框架指标评审打分，并对专家评审的积极性、权威性、集中性和离散性进行验证；最后，经过两轮专家评审及研讨修整后，确定初中生数学建模能力交互式测评框架。共包括5个一级维度及10个二级维度：理解与简化（理解任务情境/有效简化问题）、数学化建模（获取变量及信息/构建数学模型）、验证与解释（验证模型/解释模型）、反馈与重建（模型修正/重建并验证）、反思与归纳（反思建模逻辑/归纳建模规律）。效度验证结果显示框架对建模能力核心要素和周期特点具有较好的合理性和代表性，具备较强指导价值和可操作性。

研究二研发了从混合视角出发，涵盖整个建模过程且对应具体建模周期的数学建模计算机交互式测评任务及系统工具。基于ECD理论的概念评估框架(Conceptual Assessment Framework, CAF)，从学生模型、任务模型、证据模型、组合模型、呈现模型和发布系统模型六个环节统筹研发数学建模计算机交互式测评工具。首先，确定任务模型：基于学生模型（测评框架）研发数学建模任务并验证；其次，确定证据模型：设定评分标准和测量模型并验证；第三，确定组合模型：制定测评证据来源及细则；第四，确定呈现模型：设置契合交互式测评属性的任务和题目呈现、反馈及监测形式；最后，设定系统发布模型：从任务、用户、技术等角度确保系统工具在交互性、准确性、实时性、丰富性、安全性等方面提供全方位保障。结果显示，基于ECD理论研发的数学建模计算机交互式测评工具契合研究目的、反映学生建模认知状态、符合标准化大规模施测时严谨、稳定且流畅的测评需求，具备在相应及拓展领域中的可迁移及参考价值。

研究三验证了数学建模能力计算机交互式测评工具质量。包括：(1)内容效度：基于作答结果及过程行为策略梳理测评指标，采用专家评审及研讨法加以验证；(2)结构效度：基于297名初中生构成的预试样本数据，采用探索性和验证性因素分析，经过四轮筛选验证指标结构；(3)效标关联效度：利用语文及数学期末成绩作为效标加以验证；(4)一致性信度：针对整体及子维度得分验证Alpha一致性系数。结果表明测评工具符合测量学标准，具有较好的信效度，具备初中生群体测评的科学性及适用性。

研究四分析了不同数学建模能力亚群在关键建模阶段过程性动作行为表现及特点。首先，基于719名初中八年级学生的测试数据提取作答结果及过程性指标，获取数学建模能力；其次，采用K-means聚类方法对不同数学建模表现群体进行分类，并基于类群锚定关键建模环节；再次，采用社会网络分析(SNA)对关键建模环节中的过程性作答行为动作进行分析，自下而上地分析建模表现特点。结果如下：(1)聚类结果显示个体在现实与数学世界双向阶段中存在困难，类别为：进入数学世界困难、返回现实世界困难、均衡少困难三大类群；(2)SNA结果显示不同类群之间的动作网络形态存在差异，高能力群体的动作行为更为高效简洁。动作行为表现不存在显著性别差异，基于建模交互反馈模式，不同水平群体在交互反馈模式下的建模表现呈提升趋势且存在差异。

研究五深入分析了计算机交互测评模式下学生数学建模中多次反馈作答表现的变化趋势。首先，对两关键环节内的多次反馈作答效果进行潜增长模型分析，结果显示：(1)进入数学世界困难、返回现实世界困难群体在关键建模环节的重复测量中与其他群组存在初始水平和增长速度的显著差异；(2)在理解简化及反馈重建环节的增长速度随时间分别呈线性和非线性（二次）关系变化；(3)建模表现增长趋势不存在显著的性别差异。其次，对两关键环节间（理解简化、反馈重建）的多次作答表现相互影响进行交叉滞后模型分析，结果显示：(1)首次建模结果的反馈在多次反馈中效果最佳；(2)中后段多次建模协助与沟通对建模效果产生显著积极影响；(3)中后段多次反馈与协助的建模效果会在两环节之间具有显著的双向积极影响。

本研究表明：基于计算机技术的交互式测评是从混合视角下进行数学建模能力精细化评估的有效形式，交互反馈的测评理念为数学建模能力评估和培养提供理论和实践层面的参照途径。研究创新体现在：在理论层面，将蕴含隐性认知过程的过程性指标融合到数学建模能力测评框架及评分标准的构建之中，是精细化测评模式构建的新探索；在工具层面，将计算机交互测评形式引入到数学建模全过程的能力评估中，为混合视角下的数学建模能力评估带来新突破；在方法层面，利用作答反馈的重复测量嵌套结构将多水平追踪模型运用数学建模周期内及周期间表现剖析中，并从自下而上和自上而下的双向角度探索数学建模作答反应内外测评证据，是技术方法的新运用；在实践层面，人机交互反馈式的数学建模测评为以评促学的实施践行提供了新途径。

Mathematical modeling proficiency is crucial for societal progress and individual development, making its cultivation central to global mathematics education reforms. However, traditional assessment methods struggle to address the nuanced needs of this proficiency, which emphasizes real-world application and iterative problem-solving. This creates challenges in fostering its effective development. Despite advancements in new-generation assessments for higher-order cognitive abilities, research in mathematical modeling remains scarce. Leveraging information technology for dynamic, interactive assessments and analyzing cognitive evidence during modeling represents a critical breakthrough. Therefore, research aimed at enhancing mathematical modeling proficiency through computer-based interactive assessments and evidence-based strategies holds significant theoretical and practical value.

Guided by Evidence-Centered Design (ECD), this study employed computer-based interactive assessments to evaluate middle school students' mathematical modeling performance. The assessment focused on a unified real-world scenario, encompassing the entire modeling process. By analyzing the performance of different subgroups at critical stages of modeling and exploring trends in multiple-answer iterations under interactive feedback, the research aimed to provide valuable insights for assessing and enhancing mathematical modeling as well as similar higher-order cognitive abilities. Detailed findings from the five sub-studies are presented below:

Study 1 developed an indicator framework for a computer-based interactive assessment of middle school students' mathematical modeling abilities, integrating process indicators and interactive assessment attributes. Initially, a literature review was conducted to draft the indicator framework. Domain experts then reviewed and rated the indicators, confirming the validity of their assessments. After two rounds of expert review and discussion, the final framework was established. It includes five primary dimensions and ten sub-dimensions: Understanding and Simplification, Mathematical Modeling, Verification and Explanation, Feedback and Reconstruction, and Reflection and Induction. Results from validity verification indicated that the indicators had strong guidance value and operability, reflecting good rationality and representativeness regarding the core elements and cyclical characteristics of modeling ability.

Study 2 developed computer-based interactive tasks and tools for mathematical modeling, covering the entire process and specific cycles from a mixed perspective. Guided by the Conceptual Assessment Framework (CAF) of ECD theory, the system was meticulously developed across six phases: student modeling, task modeling, evidence modeling, combination modeling, presentation modeling, and deployment system modeling. Results indicated that the interactive assessment system, developed based on ECD theory, aligned with research objectives, reflected students' cognitive states, and met the rigorous, stable, and smooth assessment requirements for standardized large-scale testing. It demonstrated potential transferability and reference value in related and expanded fields.

Study 3 aimed to validate the tool quality of the interactive assessment system for mathematical modeling. This involved assessing content validity through expert reviews and discussions based on response results and process behavior strategies. Structural validity was evaluated using exploratory and confirmatory factor analyses on preliminary data from 297 junior high school (JHS) students. Four rounds of screening were conducted to validate the indicator structure. Criterion-related validity was assessed using language and mathematics final exam scores as criteria for validation. Reliability was confirmed through the alpha consistency coefficient for both overall and dimensional scores. The results indicated that the assessment tool met measurement standards, demonstrating good reliability and validity, and exhibited scientific rigor and generalizability for middle school student assessments.

Study 4 analyzed process-oriented actions and characteristics during key modeling stages across different mathematical modeling proficiency clusters. It utilized test data from 719 eighth-grade middle school students to assess modeling proficiency. The study conducted K-means clustering analysis on response performances and social network analysis (SNA) on process behaviors. The results revealed several insights: (1) Individuals encountered difficulties transitioning between reality and the mathematical world, categorized as difficulty entering, difficulty returning, and balanced or fewer difficulties. (2) Stronger relationships were observed between key termination action nodes and correct or error-correcting action nodes. Furthermore, action performance showed no significant gender differences, yet distinct variations existed in action network morphology among different proficiency groups. Modeling performance across groups showed improvement trends, influenced by interactive feedback modes during modeling.

Study 5 analyzed improvement characteristics of multiple feedback responses in mathematical modeling under computer interactive modes. Firstly, it conducted latent growth modeling (LGM) analysis on feedback effects within two critical stages, revealing: (1) Significant differences in initial levels and growth rates between challenging groups and others during repeated measurements. (2) Linear and quadratic growth improvement rates in understanding and feedback stages over time. (3) No significant gender differences in modeling performance trends. Secondly, cross-lagged modeling analysis indicated: (1) Initial modeling feedback had the most impact among multiple instances. (2) Assistance and communication in later stages positively influenced modeling outcomes. (3) Bidirectional positive effects of multiple feedback and assistance were observed between stages.

This study demonstrates that computer-based interactive assessment is an effective method for the refined evaluation of mathematical modeling abilities from a mixed perspective. The concept of interactive feedback provides both theoretical and practical references for the assessment and development of these abilities. Key innovations include integrating process indicators, encompassing implicit cognitive processes, into the framework and scoring criteria of mathematical modeling assessments, representing a new exploration in refined assessment models. Introducing computer-based interactive assessments into the entire mathematical modeling process signifies a breakthrough in evaluating mathematical modeling abilities. Methodologically, the study employs repeated measurement nested structures and multi-level tracking models to analyze performance within and between mathematical modeling cycles, exploring assessment evidence from both bottom-up and top-down perspectives. Practically, the human-computer interactive feedback approach offers a novel pathway for the implementation of assessment-driven learning.