数学与问题解决表现是备受重视 的教育问题之一， 如何培养 与提高 数学 与问题解决表现是值得学校教育思考的问题 。 教学是一个互动的过程，学生、教师都参与其中，

学生的意愿态度和教师教学行为对数学与问题解决表现的提高起 着 重要作用，目前关于数学与问题解决表现的影响因素的研究在数据分析的过程中较少地关注到整体效益和相互

之间的关系。因此，分析教学行为、意愿态度、数学 与 问题解决 表现 的影响及机制非常必要。

   本研究综合 利用 宏观描述与微观分析，不仅对数据进行 客观描述， 也利用 学生问卷 、学生 访谈 研究 教学行为和意愿态度对数学与问题解决 表现的影响 ，深度挖掘原因，解释大样本数据结果。 研究 选取 PISA2012 中国上海中学生 2970 名与广东深圳某中学学生 98名作为研究对象，对学生的数学与问题解决表现的影响因素进行实证研究。首先，通过描述统计、差异分析、相关分析，了解中国上海学生和广东学生数学 与 问题解决 表现 的基本情况、在各变量上的表现。然后，利用结构方程模型分析在控制学生和学校背景后，学生的意愿态度与感知到的教学行为对数学与问题解决表现的影响，以及意愿态度的中介作用。最后，对小样本典型 8 名学生进行访谈，挖掘背后的原因，解释印证大样本结论。 本究得到 以下结论:(1)教学行为能有效提高学生的数学与问 题解决表现。学生感知到的教师支持行为和认知激发行为越多，其数学成绩与问题解决表现越好。由访谈结果可知，学生认为 老师的关心与帮助会让他们更有动力投入 数学学习 ，更积极且更有耐心参与问题解决 。(2)意愿态度是数学与问题解决表现的重要影响因素。学生意愿态度对数学与问题解决表现有积极影响 其中坚持性对数学成绩的影响以及开放性对问题解决能力的影响较强 。(3)意愿态度在教学行为对数学与问题解决表现的影响过程中起到了中介作用。学生表示教师的支持以及认知激发能够影响他们的意愿态度，让学生更有动力与信心，从而间接促进了学生的数 学成绩和问题解决能力的提升。

Problem-solving ability is the core ability that students should have in the 21st century. How to cultivate students' problem-solving ability has become the focus of school education. Student mathematics performance has always been one of the educational issues that have attracted much attention. Teaching is an interactive process in which students and teachers are involved. The willingness and attitude of students and teachers’ teaching behaviors play an important role in improving mathematics and problem-solving performance. Current research on factors affecting mathematics and problem-solving performance is in data analysis. In the process, less attention was paid to the overall benefit and the relationship between each other. Therefore, it is necessary to analyze the influence and mechanism of teaching behavior, willingness and attitude, mathematics achievement, and problem-solving ability.

This study uses the publicly available international large-scale database to objectively describe the macro level, through student questionnaires, and student interviews to deeply explore the impact of teaching behaviors and willingness attitudes on mathematics performance and problem-solving ability at the micro level, dig deep into the reasons, and explain the large sample data result .2970 middle school students from Shanghai, China and 98 students from a middle school in Shenzhen, Guangdong were selected as the research objects to conduct empirical research on the factors affecting students' mathematics and problem-solving performance. First, through descriptive statistics, difference analysis, and correlation analysis, to understand the basic situation of Chinese students in Shanghai and Guangdong in mathematics performance and problem-solving ability, performance on each variable. Then, the structural equation model is used to analyze the influence of students' willingness and perceived teaching behavior on mathematics and problem-solving performance after controlling the students and school background, and the mediating role of willingness and attitude. Finally, interviews were conducted with eight typical students from a small sample to explore the reasons behind, explain and confirm the conclusion of the large sample. This research has the following conclusions: (1) Teaching behavior can effectively improve students' performance in mathematics and problem solving. The more teachers' supportive behaviors and cognitively aroused behaviors perceived by students, the better their math scores and problem-solving performance. The students talked about in the interview that the teacher’s care and help will make them more motivated to engage in mathematics learning, and participate more actively and patiently in problem solving. (2) Willingness attitude is an important factor influencing mathematics and problem solving performance. Students' willingness and attitude have a positive impact on mathematics and problem-solving performance. Among them, persistence has a strong influence on mathematics performance and openness has a strong influence on problem-solving ability. The effect of persistence on mathematics performance is obviously stronger than that of openness on mathematics performance. (3) Willing attitudes play an intermediary role in the influence of teaching behavior on mathematics and problem-solving performance. Students said that the teacher's support and cognitive stimulation can affect their willingness and attitude, and make students more motivated and confident, which indirectly promotes the improvement of students' mathematics performance and problem-solving ability.