问题解决一直是数学教育改革的一个核心方面，我国在高中课标中提出数学教师应该通过解决问题来进行教学，要求学生在探索和解决数学问题时发展数学知识和技能，而不是简单地告诉或展示他们该做什么，并要求他们练习。数学教育研究界的普遍共识是，通过问题解决进行教学有助于促进学生的数学理解，教师应在巧妙的问题设置下，启迪学生思维，引导学生积极思考，培养学生问题解决能力。目前有许多一线教师都在努力通过解决问题来教学，在数学课堂上让学生参与深思熟虑的数学活动，这就意味着需要对数学教师如何实施问题解决课程进行更多的研究，以便更好地理解他们在这样做时面临的挑战。

因此，本研究主要有两个研究问题：在数学问题解决教学中，（1）教师会产生怎样的提问行为，让学生参与课堂互动交流的？（2）教师是如何通过提问启发学生思维，让学生投入数学问题解决过程的？通过以上问题可以更丰富地了解数学教师如何在数学课堂上实施问题解决活动。

本研究选取广东省珠海市 J 学校高一年级的教师A与教师B的问题解决教学课堂作为研究对象，首先对两名教师进行第一次访谈，以便了解两名教师对于问题解决教学的看法；再选取两个教学案例：《一元二次不等式的解法》、《对数函数的概念》进行录像，基于IRF框架（教师启动/发问（Initiation）——学生回答/反应（Response）——教师反馈/评价（Feedback））分析问题解决教学模式下的教师提问行为，重点关注教师提问、学生回答、教师跟进、等待时间的提问轮次，并在课后对两个班级的学生发放课堂参与度问卷，结合学生课堂行为表现观察量表，分析学生的参与情况。最后，结合录像和与第二次访谈分析教师是如何启发学生数学思维贡献数学思想的。

研究表明在问题解决教学中，教师与学生会进行进行一系列的互动，这些互动可能会持续几次交流，至少需要有两个IRF结构被链接在一起，并且涉及到一个以上的学生，这说明引用单一的IRF结构作为分析单位本身不足以掌握课堂话语的复杂性。主要特征为：（1）问题解决教学中的教师提问数量相对适中，每节课的提问数量约为55个，比平时教学的教师提问数量少了将近一倍；（2）问题解决教学中的教师提问类型比重较为均衡，在功能方面，新问题占整堂提问的一半，要求阐述和重新启动问题的数量各占四分之一。在认知需求方面，真实和不真实问题的出现的频率接近；（3）问题解决教学中的教师跟进以简单反馈或无反馈居多，教师更倾向于对学生进行简单的口头表扬，评价方式较为单一，甚至还会出现没有回应的现象；（4）课堂上，已实现问题较多（有学生回答或学生思考时间超过5s），接近90%，但也发现对于高认知水平的问题时，教师留给学生思考的时间较短，会产生学生不能作出回应导致问题未实现的现象；（5）问题解决教学对提高学生数学课堂参与度有积极可行的效果，其中对学生行为参与与社交参与方面表现出非常明显的积极作用；（6）问题解决教学有助于教师启发学生思维，以现实生活为背景的数学问题可以为教师提供提问的机会，让学生参与到认知需求更高的数学工作中。

基于以上结果给出了以下四条教学建议，具体包括：（1）借助情境问题启发学生思维；（2）以核心问题链培养学生高阶思维；（3）根据问题类型给予学生不同思考时间；（4）注重问题解决教学课堂中的教师评价。

Problem solving has always been a core aspect of mathematics education reform. In our high school curriculum standard, mathematics teachers should teach by solving problems, requiring students to develop mathematical knowledge and skills while exploring and solving mathematical problems, rather than simply telling or showing what they should do and requiring them to practice. The general consensus in the research circle of mathematics education is that teaching through problem solving is helpful to promote students' understanding of mathematics. Teachers should enlighten students' thinking, guide students to think positively and cultivate students' problem-solving ability under the clever problem setting. The fact that many front-line teachers are currently striving to teach through problem solving, engaging students in thoughtful math activities in math classrooms, means that more research is needed on how math teachers implement problem solving curricula in order to better understand the challenges they face in doing so.

Therefore, there are two main research questions in this study: in the teaching of mathematical problem solving, (1) what kind of questioning behaviors do teachers have to engage students in classroom interaction and communication? (2) How do teachers inspire students' thinking and engage them in the process of mathematical problem solving by asking questions? Through the above questions, we can better understand how math teachers implement problem solving activities in math class.

In this study, Teacher A and Teacher B of Grade One in J School, Zhuhai City, Guangdong Province were selected as the research object. Firstly, two teachers were interviewed for the first time, so as to understand their views on problem solving teaching. Then choose two teaching cases: Methods of Solving Unitary Quadratic Inequalities and Concept of Logarithmic Functions were recorded. Teachers' questioning behavior under problem solving teaching mode was analyzed based on the IRF framework (teacher Initiation/questioning) -- student Response -- teacher Feedback. Focus on the question rounds of teacher's question, student's answer, teacher's follow-up, and waiting time. After class, classroom participation questionnaire is distributed to students in two classes, and students' participation is analyzed by combining with the observation scale of students' classroom behavior. Finally, the video and the second interview are combined to analyze how teachers inspire students' mathematical thinking and contribute mathematical thoughts.

Research shows that in problem solving teaching, teachers and students carry out a series of interactions, which may last several times. At least two IRF structures need to be linked together, and more than one student is involved. This indicates that referencing a single IRF structure as a unit of analysis is not sufficient to grasp the complexity of classroom discourse. The main characteristics are as follows: (1) The number of questions asked by teachers in problem solving teaching is relatively moderate, about 55 questions per class, nearly double that of teachers in normal teaching; (2) The proportion of questions asked by teachers in problem-solving teaching is relatively balanced. In terms of function, new questions account for half of the whole class, and the number of questions requiring elaboration and restarting accounts for a quarter respectively. In terms of cognitive needs, the frequency of real and unreal problems is similar; (3) In the problem solving teaching, teachers mainly follow up with simple feedback or no feedback. Teachers are more inclined to give simple oral praise to students, and the evaluation method is relatively simple, and even there is no response. (4) In class, there are more realized questions (some students answer or students think for more than 5s), nearly 90%. However, it is also found that for questions with high cognitive level, teachers leave students less time to think, which may cause students to fail to respond and problems to be realized. (5) Problem solving teaching has a positive and feasible effect on improving students' participation in mathematics class, which has a very obvious positive effect on students' behavioral participation and social participation; (6) Problem solving teaching can help teachers inspire students' thinking. Math problems based on real life can provide teachers with opportunities to ask questions and let students participate in math work with higher cognitive needs.

Based on the above results, the following four teaching suggestions are given, including: (1) Using situational problems to inspire students' thinking; (2) Cultivate students' high-level thinking with core problem chain; (3) Give students different thinking time according to the types of questions; (4) Pay attention to the teacher evaluation in problem solving teaching classroom.