数学问题提出是发展数学学科核心素养和培养实践创新能力的重要方式。现有研究结果表明，学生有能力提出数学问题，但对于具体情境下学生是如何提出数学问题的，即数学问题提出的具体过程并不清楚。此外，基于数学问题提出的过程，探讨数学问题提出的水平，即判断学生在数学问题提出表现的差异，哪些方面表现较好，哪些方面存在问题等，相关研究也较为匮乏。为此，开展数学问题提出过程和数学问题提出水平的研究，对于更好揭示数学问题提出的内在机制具有重要意义。数学问题提出的过程能够提供从哪些关键要素入手考虑课程设置、教学设计、学生引导；数学问题提出水平则为判断在具体要素上学生的学习应该达到什么程度，已经达到什么程度，还应该做哪些调整和改进提供依据。二者相辅相成，有利于数学问题提出的课程设置，教师教学和学生学习。

论文的研究问题是揭示数学问题提出的过程，并在此基础上探究数学问题提出的水平。首先，本研究基于半结构化问题情境，借助62个出声思维探究初中生数学问题提出的过程，包括数学问题提出的过程模型及个性化差异；其次，探究初中生数学问题提出的水平，包括构建数学问题提出水平分析框架、编制与之匹配的测试题、通过测试题调查初中生数学问题提出的水平现状三部分。其中，初中生数学问题提出的水平分析框架是通过学生的具体表现以及专家论证进行建构，该水平分析框架也是对数学问题提出过程的进一步阐释和补充；测试题的编制是基于水平分析框架，运用文献分析法，结合学生访谈、出声思维测试，经过多轮专家论证修改并完善，最后实施测试检验测试题质量；最终选取我国1039名学生，运用编制的测试题调查初中生在不同年级、不同问题情境类型上数学问题提出的水平现状。研究的主要结论如下：

（1）初中生数学问题提出过程的结论是：

第一，初中生的数学问题提出过程具有一般性模型，主要包括：理解情境、建立关联、形成问题、评估调节和拓展问题五个阶段。其中，发现数量或图形之间的关系，从而建立数学关联是数学问题提出过程的关键活动之一；能对发现的数量或图形关系进行数学表达是另外一个关键活动；反思提出的数学问题，对数学问题进行评估、修改是第三个关键活动；能进一步使用策略拓展提出新问题是数学问题提出的第四个关键活动，这些关键活动突出反映数学问题提出的学科特点。

第二，初中生数学问题提出过程的五个阶段的走向呈现复杂性的特点，表现为阶段之间走向的非线性、多样性和不确定性。

第三，数学问题提出的过程非常复杂。尽管数学问题提出具有一般性的过程模型，但因个体的思维差异而存在明显的个性化差异，这种差异主要表现为提出数学问题时的思维不同。

（2）初中生数学问题提出水平的结论是：

第一，以过程视角构建的数学问题提出水平分析框架，从维度和水平两个方面进行揭示，每个方面有二级分类，并有具体的学习表现描述。其中维度分为建立数学关联、表达数学问题、反思数学问题和使用策略拓展，每个维度下有水平一、水平二和水平三三个水平层次。

第二，通过编制的测试题，调查初中生的数学问题提出水平的现状，结果表明：首先，初中生数学问题提出的水平较低，主要表现为能发现简单的数学关系并清晰地表述为数学问题，且能够拓展提出新的数学问题，但很难用数学符号表达数学问题，同时，较难有依据地对数学问题进行评价、反思和改进。其次，随着年级的升高，建立数学关联的水平从低水平段逐渐过渡到高水平段；表达数学问题从低水平段和高水平段持平的情况变为以高水平段为主；各个年级在反思数学问题维度上都处于低水平段，但高水平段的比例逐渐增加；使用策略拓展维度在各年级都处于低水平段，高水平段的比例从七、八年级的持平状态到九年级变为上升状态。最后，从情境维度来看，生活情境中数学问题提出的水平低于数学情境和科学情境，不同类型情境中，随着年级的升高各维度上的水平变化有所差异。

总之，本研究探究了初中生数学问题提出的过程和水平，可以为教师问题提出的教学提供支架，帮助教师从哪些关键要素入手设计教学、引导学生学会提出数学问题；同时，了解学生的差异，帮助教师因材施教，有效发展进阶教学，培养学生的数学核心素养和实践创新能力。

Mathematical problem posing serves as an important method to develop core mathematical competencies and foster innovative practical abilities. Existing research results demonstrate that students possess the ability to pose mathematical problems. However, the specific process through which students pose mathematical problems in particular contexts, that is, the concrete process of mathematical problem posing, remains unclear. Furthermore, there is a lack of exploration into the levels of mathematical problem posing, which involves assessing the variations in students' performance in posing mathematical problems, identifying areas of proficiency, and highlighting areas of concern. Consequently, there is a need to conduct research on both the process of mathematical problem posing and the levels of mathematical problem posing. This holds significant significance for a better understanding of the underlying mechanisms of mathematical problem posing. The process of mathematical problem posing can provide insight into which key elements to consider when planning curriculum, designing instruction, and guiding students. The levels of mathematical problem posing, on the other hand, serve as a basis for assessing what level of learning students should achieve in specific elements, what they have already achieved, and what adjustments and improvements should be made. These two aspects complement each other and are advantageous for curriculum development, teacher instruction, and student learning in the context of mathematical problem posing.

The content of this paper is to uncover the process of mathematical problem posing and, based on this foundation, explore the levels of mathematical problem posing. Firstly, the study employs 62 verbal thinking sessions within a semi-structured problem context to investigate the process of mathematical problem posing among middle school students. This includes a process model of mathematical problem posing as well as the exploration of individual differences. Secondly, the study delves into the levels of mathematical problem posing among middle school students. This involves constructing an analysis framework for problem posing levels, developing corresponding test items, and conducting a survey of the current problem posing levels of middle school students through the administration of the test items. In the construction of the analysis framework for problem posing levels, specific student performances are analyzed, and expert validation is employed. This framework serves as both a further interpretation and supplementation of the mathematical problem posing process. The development of test items is guided by the analysis framework, utilizing literature analysis, student interviews, and verbal thinking tests. These test items undergo multiple rounds of expert validation and refinement before being administered in tests to assess their quality. Finally, a sample of 1,039 students in China is selected to investigate the current problem posing levels across different grade levels and various problem context types using the developed test items. The primary conclusions of the study are as follows:

(1) The conclusion of the process of middle school students' mathematical problem posing is as follows:

Firstly, the mathematical problem posing process of middle school students follows a general model, mainly consisting of five stages: Orientation, Connection, Generation, Reflection, and Extension. Among these stages, identifying relationships between quantities or figures to establish mathematical connections is one of the key activities of the process. Another key activity involves expressing mathematical problems by applying mathematical expressions to the identified relationships. Reflecting on posed mathematical problems, evaluating and modifying them, constitutes the third key activity. The fourth key activity involves the capability to further employ strategies to extend and propose new problems. These key activities prominently reflect the disciplinary characteristics of mathematical problem posing.

Secondly, the transitions between the five main stages in the process of mathematical problem posing by middle school students exhibit characteristics of complexity. These characteristics manifest as non-linearity, diversity, and uncertainty in the progression between stages.

Thirdly, the process of mathematical problem posing is inherently complex. Although there exists a general process model for mathematical problem posing, pronounced individual differences arise due to variations in thinking patterns. These differences are primarily observed in the thought processes employed when posing mathematical problems.

(2) The conclusions regarding the levels of mathematical problem posing among middle school students are as follows:

Firstly, the analysis framework for the levels of mathematical problem posing, constructed from a process perspective, reveals perspectives of dimensions and levels. Each perspective includes secondary classifications with specific descriptions of learning performances. The dimensions encompass Establishing Mathematical Connections, Expressing Mathematical Problems, Reflecting on Mathematical Problems, and Using Strategies to Expand. Under each dimension, there are three levels: Level One, Level Two, and Level Three.

Secondly, the investigation of current middle school students' mathematical problem posing levels through the developed test items yields the following results: Firstly, the problem posing proficiency of middle school students is generally low. They can identify simple mathematical relationships and articulate them as clear mathematical problems. They can also expand upon and propose new mathematical problems, although they struggle with expressing mathematical problems using mathematical symbols. Additionally, they face challenges in evaluating, reflecting upon, and improving mathematical problems based on reasoning. Secondly, as grade level increases, proficiency in Establishing Mathematical Connections transitions from lower to higher levels. Proficiency in Expressing Mathematical Problems, which was initially balanced between lower and higher levels, becomes predominantly higher-level. Reflecting on Mathematical Problems generally remains at lower levels across all grades, but the proportion of students achieving higher-level proficiency gradually increases. Using Strategies to Expand element remains at lower levels across all grades, with the proportion of students at higher levels increasing from seventh and eighth grades to ninth grade. Finally, when considering different contextual dimensions, the problem posing proficiency in everyday life contexts is lower than that in mathematical and scientific contexts. The changes in proficiency levels of different dimensions vary across different types of contexts as grade level increases.

In conclusion, this study investigated the process and level of mathematical problem posing among middle school students. It can provide a framework for teachers' instruction in problem posing, aiding them in designing teaching methods and guiding students to learn how to propose mathematical problems. Furthermore, by understanding the differences among students, teachers can tailor their instruction to individual needs, effectively advancing teaching methods, and fostering students' core mathematical competencies and innovative abilities.