本文结合 SOLO分类理论与《普通高中数学课程标准（2017年版 2020年修订）》的数学素养测评框架, 编制测试题和背景因素问卷，研究学生的数学运算 SOLO认知水平表现, 及其与背景因素表现的关系, 给出数学运算素养的培养启示与提升建议. 在研究中，数学运算素养测试框架分为知识、认知、素养3个维度, 根据PISA的情景测试题改编成测试题, 共 24小题；背景因素问卷分为自我概念、自我效能、学习动机、学习策略 4个维度, 共 54个问题.

研究结果表明：（1）学生整体数学运算 SOLO 认知水平较高, 43.2%，28.4%的学生分别具有关联结构和抽象拓展结构水平, 性别差异显著, 男生略高于女生, 但差异不大；（2）学生知识维度的表现从高到低依次为：几何与代数、函数、概率与统计, 各成分与 SOLO 认知水平相关性强, 当这些成分表现较好时, 学生的 SOLO 认知水平就会提高；（3）学生素养维度的表现从高到低依次为：情景与问题、知识与技能、思维与表达, 思维与表达与 SOLO 认知水平相关性最强, 知识与技能次之, 情景与问题相关性不强, 当思维与表达及知识与技能表现较好时, 学生的 SOLO 认知水平会提高；（4）学生背景因素表现从高到低依次为：内部动机、外部动机、学习策略、自我效能感和自我概念, 且性别差异显著, 男生高于女生, 但差异不大；（5）学生背景因素与 SOLO 认知水平相关性强弱依次为：自我效能、学习策略、内部动机、自我概念和外部动机, 其中学习策略中的计划、复述、组织、精加工、监视策略与 SOLO 认知水平有较强的相关性, 这些因素提高时, 学生的数学运算 SOLO 认知维度水平能够提高.

根据研究结果给出学生数学运算提升建议如下：（1）在教学中设置开放型或研究性问题将处于关联结构水平的学生提升至抽象拓展结构水平, 对女生需更关注；（2）通过数学试验教学和设计研究性作业加强学生概率与统计内容的教学；（3）利用变式类型或探究多种解题方法的教学继续强化学生几何与代数与函数内容的教学；（4）利用引导学生交流、探讨的教学方式或在课下组织学生互助讲题来培养学生的思维与表达能力；（5）通过强调思维方法的方式来继续强化学生知识与技能能力的培养；（6）通过定期做知识自我核对的方式来增强学生的自我概念、自我效能感, 对女生需更关注；（7）有意识地培养学生进行学习策略的应用, 通过趣味、多元的授课方式增强学生的学习内部动机.

Combining the SOLO taxonomy and the mathematical literacy assessment framework in the General High School Mathematics Curriculum Standards (2017 Edition and 2020 Revision), this paper compiles test questions and background questionnaire to obtain students' cognitive performance of mathematical operation and background factor performance. Then, studying the relationship between them, and giving enlightenments and suggestions for the cultivation and improvement of mathematical operation literacy. In the research, the mathematical operation literacy test framework is divided into three dimensions: knowledge, cognitive and literacy, and the test questions which contain 24 questions of 5 themes are adapted according to the PISA scenario test questions. Background factor questionnaire of 54 questions were compiled from four dimensions: self-concept, self-efficacy, learning motivation and learning strategy.

Research indicates: (1) Students' overall mathematical operation SOLO cognition level is relatively high, 43.2% of students are relational level and 28.4% of students are extended abstract level. There is a significant gender difference in the students' overall mathematical operation SOLO cognitive level, with boys slightly higher than girls, but not much of a difference. (2) The performance of students' knowledge dimension from high to low is: geometry and algebra, function, probability and statistics, each component has a strong correlation with the SOLO cognitive level, when these components perform well, the student's SOLO cognitive dimension level will increase. (3) The performance in the student literacy dimension from high to low is: scenarios and problems, knowledge and skills, thinking and expression, thinking and expression are most strongly correlated with SOLO cognitive level, knowledge and skills are second, scenarios and problems are not strongly correlated, when thinking and expression and knowledge and skills perform well, students' SOLO cognitive level will improve. (4) The background factors of students were displayed from high to low: internal motivation, external motivation, learning strategies, self-efficacy and self-concept, and the gender difference was significant, with boys higher than girls, but the difference was not large. (5) The correlation between students' background factors and SOLO cognitive level was: self-efficacy, learning strategy, internal motivation, self-concept and external motivation, among which the planning, retelling, organization, refining, and monitoring strategies in learning strategies had a strong correlation with SOLO's cognitive level.

According to the research results, the suggestions for improving students' mathematical operations are as follows: (1) In the teaching process, students at the level of relational are upgraded to the level of abstract expansion by setting up open-ended or research-based questions, and more attention needs to be paid to girls. (2) Strengthen the teaching of probability and statistics content to students through the teaching of mathematics experiments and the design of research assignments. (3) The teaching of geometry and algebra and functions continues to strengthen by utilizing variant types or explores multiple problem-solving methods. (4) Use teaching methods that guide students to communicate and explore, or organize students to help each other after class to cultivate students' thinking and expression skills. (5) Continue to strengthen the development of students' knowledge and skills by emphasizing thinking methods. (6) Enhance students' self-concept and self-efficacy by doing regular knowledge self-checks, and pay more attention to girls. (7) Consciously cultivate the application of learning strategies and enhance students' internal motivation for learning through interesting and diversified teaching methods.