在学校数学学习中，发现和提出数学问题是学生数学经验和能力的重要部分。然而，关于数学问题提出能力内在机制的研究并不成熟，对学生数学问题提出能力的发展也知之甚少。本研究聚焦初中生数学问题提出能力的年级差异，探讨初中三个年级段学生在数学问题提出的流畅性、灵活性、深刻性方面的差异。研究希望促进数学问题提出能力相关的理论研究进展，为教学实践提供一定的参考。 研究将“数学问题提出能力”界定为：学生经过多方面、多角度的数学思维，从表面上看来没有关系的一些现象中找到并提炼出数量或空间方面的某些联系或者矛盾，并进一步用数学语言、数学符号以“问题”的形式表述出来的能力。 研究确定三个二级指标——流畅性，灵活性，深刻性量化初中学生数学问题提出能力的年级差异。其中，“流畅性”意味着学生能够以数学语言或数学符号清晰不矛盾地将数学问题表述出来，并且思维具有发散性，能产生大量想法；“灵活性”意味着学生能够多方面多角度地数学思维；“深刻性”意味着学生能够透过表象看本质——提炼出数量关系或空间结构。 研究样本选取北京市东城区某所中考成绩中等的初中学校，从初一、初二、初三年级分别随机抽取两个班级，共计229名初中生进行测试。测试题为两个代数领域的半结构化数学情境，使用指导语“根据以上情境，请你尽可能多地提出数学问题，尽可能从多个角度提出数学问题，尽可能提出难的数学问题”，引导学生按照二级指标答题。研究结果表明： 1.大部分的学生能够基于2-3个左右的角度提出4个左右的问题，但是所提的问题大部分比较容易。 2.随着年级的增长，学生基于的问题角度的个数以及提出的问题个数没有显著性的差异。 3.随着年级的增长，学生是否基于一般规律去进行提问存在显著性差异。 4.对于较为常见的提问类型年级差异不大，但不同年级学生提出问题的类型会有所差异。 研究的进一步展望是： 1.相对于关注数学问题提出能力的流畅性和灵活性品质，深刻性是更可能体现初中生数学问题提出能力在年级差异方面的品质。 2.可进一步通过教学实验了解不同年级学生的数学问题提出能力的差异。

Discovering and proposing mathematical problems is an important part of students ' mathematical experience and ability during their school mathematics learning. However, the research on the internal mechanism of the mathematics problem posing is not mature, and little is known about the development of students ' ability to pose mathematical problems. This study focuses on the grade difference of junior high school students ' ability to propose mathematics problems. It is hoped that this will promote the theoretical research on the ability of mathematics problem posing, provide useful reference for the development and design of relevant courses with students ' mathematics problem posing, and provide corresponding empirical basis for the teaching practice of teachers in junior high school. Regarding the ability of mathematical problem posing as the performance of students ' innovation, this study defines "the ability of mathematical problem posing" as: through many aspects and multi-angles, students can find and refine some of the links or contradictions in quantity or space from some phenomena which is not obvious, and further use mathematical language or mathematical symbols to pose mathematical problem. Based on the above definition and the combing of the existing literature, this study defines mathematical problem posing in terms of -fluency, flexibility, profundity. "fluency" means that students can express mathematical problems clearly and without contradiction in mathematical language or mathematical symbols, and the thinking is divergent and can produce a large number of ideas. "Flexibility" means that students can think mathematically in many ways; "profundity" means that students are able to see the essence through appearances, extracting quantitative relationships or spatial structures. Taking the Dongcheng district of Beijing as an example, a junior high school with medium score in the district was selected as the sample of this study, and researcher randomly sampled two classes at each grade. There was 229 junior middle school students for testing in total. This test sets up two semi-structured situations about algebra. The instruction is " Please try to come up with as many questions as you can, from as many angles as you can, and try to produce as difficult questions as you can.’’, which is intended to capture the potential ability related to mathematics problem finding. The study shows that: 1. Most students are able to ask about 4 questions based on about 2-3 angles, but most of the questions are easy. 2. There is no significant difference in the number of angles and of the number of the problems which are posed by students between different grades. 3. There is significant difference in the difficulty of students ' questions between different grades. 4. There is little difference in the common question type between different grades, but there are differences in some types of questions asked by students of different grades. The following prospects are presented for future research: 1.Instead of the fluency and flexibility of this ability, it is more worth to pay attention to profundity of the ability of mathematical problems posing, which is more likely to reflect the quality of junior high school students ' ability to raise mathematical problems in grade differences. 2.The differences in the ability to pose mathematical problems among students of different grades can be further explored through instructional experiments.