随着信息时代的深入发展，人们对数学教育的期待不再满足于单纯的数学知识掌握，培养能应用数学解决实际问题、具备创新思维、批判性思维等高阶思维的人成为教育的重中之重，在此背景下，数学建模和批判性思维逐渐成为数学教育的中心话题之一，其中，数学建模素养更是在我国高中阶段的课程标准中被明确列为核心素养之一。然而，由于教育环境或缺乏理论支持等原因，我国数学建模教育在高中的实施情况和学生的批判性思维现状并不乐观。从理论上深入剖析批判性思维的内涵与数学建模的过程，可以发现批判性思维是数学建模过程中必不可少的部分，批判性思维倾向亦是如此，因此分析两者之间的影响路径可以为培养学生的批判性思维和数学建模能力提供有力的依据。从已有研究来看，部分研究已证实数学问题提出能力与批判性思维倾向、数学建模素养之间的关系，但尚未有对批判性思维倾向和数学建模能力及三者之间的复杂关系展开的研究。

为了填补这一研究空白，进而为培养学生的数学建模能力和批判性思维提供理论支持，本研究通过对高一年级学生数学建模能力的评估和其与数学批判性思维倾向、问题提出能力之间关系的探索，了解高一学生批判性思维倾向的现状以及批判性思维倾向对数学建模能力的影响路径。基于上述研究目的，提出研究问题：1）高中生数学批判性思维倾向现状如何？2）高中生数学批判性思维倾向与数学建模能力有何关联？3）数学批判性思维倾向对数学建模能力的影响是否通过问题提出能力介导？

为解决上述研究问题，本研究采用质性与量化研究方法相结合的混合研究方法展开研究，首先，利用访谈法和出声思维法遴选数学建模和问题提出的测试工具，而后利用问卷调查法和纸笔测验法考察学生的批判性思维倾向、数学建模能力以及问题提出能力，并利用文本分析法对学生的作答进行评分与编码，最后，运用统计分析方法验证三者之间的关系，得到以下结论：

针对研究问题一，大部分高中生批判性思维倾向处于中高水平及以上，具体来看，学生的开放性表现最好，大部分学生对不同的观点均保持宽容的态度；但在自信心和系统性这两方面仍存在发展空间。

针对研究问题二，高中生数学批判性思维倾向和数学建模能力之间存在显著中度正相关，但部分子维度和子能力之间不存在显著相关。

针对研究问题三，数学问题提出能力在数学批判性思维倾向与数学建模能力之间起部分中介作用，表明批判性思维倾向对高中生数学建模能力有着直接和间接的影响作用。

基于研究结论，为教育者培养学生批判性思维倾向和数学建模能力提出如下建议：1）问题驱动教学，激发学生求知欲；2）鼓励质疑，促进反思，创设批判包容型数学课堂；3）依托数学建模教育，传授批判技能，提升批判倾向；4）充分利用数学建模的问题提出环节。

With the in-depth development of the information age, people's expectations of mathematics education are no longer satisfied with the simple mastery of mathematical knowledge, and the cultivation of people who can apply mathematics to solve practical problems and have higher-order thinking such as creative thinking and critical thinking has become the top priority of education. In this context, mathematical modeling and critical thinking have gradually become one of the central topics of mathematics education, of which mathematical modeling competence has been explicitly listed as one of the core competences in the curriculum standard of China's high school stage. However, due to the educational environment or lack of theoretical support, the implementation of mathematical modeling education in high schools in China and the current situation of students' critical thinking are not optimistic. Theoretically, critical thinking is an essential part of the process of mathematical modeling, and so is critical thinking disposition (CTD). Therefore, the analysis of the influence path between the two can provide a strong basis for the cultivation of critical thinking and mathematical modeling ability. From the existing studies, some of them have confirmed the relationship between mathematical problem posing ability and CTD and mathematical modeling literacy, but there has not yet been any research on CTD and mathematical modeling competence and the complex relationship between the three.

In order to fill this research gap and thus provide theoretical support for the cultivation of mathematical modeling competence and critical thinking, the present study was conducted to understand the current situation of the CTD of senior students and the path of the influence of the CTD on mathematical modeling ability through the assessment of senior students' mathematical modeling ability and the exploration of the relationship between it and the mathematical CTD and the ability to formulate problems. Based on the above research objectives, three research questions are proposed as follows: 1) What’s the current status of high school students' mathematical CTD? 2) Is high school students' mathematical CTD related to mathematical modeling ability? and 3) Is the influence of mathematical CTD on mathematical modeling ability mediated through problem posing ability?

In order to address the above research questions, this study adopts a mixed research method combining qualitative and quantitative research methods to carry out the research. Firstly, the method of interview and thinking aloud are used to select the test items for mathematical modeling and problem posing. Then, the questionnaire and paper-and-pencil test methods are used to examine the students' CTD, mathematical modeling ability and problem posing ability. And the text analysis method is used to score and code the students' responses. Finally, statistical analysis was used to verify the relationship between the three and the following conclusions were obtained:

In response to research question one, most high school students' CTD is at a medium-high level and above, specifically, students' openness performs the best, and most of them maintain an open attitude towards different viewpoints; however, there is still room for development in the aspects of self-confidence and systematicity.

In response to research question two, there is a significant moderate correlation between high school students' mathematical CTD and mathematical modeling ability. But there is no significant correlation between some of the sub-dimensions or sub-competencies.

In response to research question three, mathematical problem posing ability partially mediates the relationship between mathematical CTD and mathematical modeling ability, suggesting that CTD has a direct and indirect influence on high school students' mathematical modeling ability.

Based on the findings of the study, the following recommendations are made for educators to develop students' CTD and mathematical modeling skills: 1) problem-based teaching to stimulate students' inquisitiveness; 2) encouraging questioning, promoting reflection, and creating a critically inclusive mathematics classroom; 3) relying on mathematical modeling education to teach critical skills and enhance CTD; and 4) taking full advantage of the problem-posing segment of mathematical modeling.