学生的课堂学习是数学教育重要的研究领域。为实现学生合作问题解决等“21世纪技能”在数学学科中的整合发展，促进实践创新人才培养，基于数学问题解决的合作学习以其独特的教学价值受到学界重视。其中，合作“知识建构”强调学生在团队合作中交流观点，讨论协商，解决问题，为团队创造有价值的公共知识，从而促进学生相互学习，提高学习绩效，成为反映学生新型学习方式下学习质量的重要视角，从而为学情分析与教学改进提供支持。然而，国内外少有研究聚焦初中数学课堂从合作“知识建构”视角剖析学生基于数学问题解决的合作学习质量。基于此，该研究以优化学生在新型学习方式下的学习过程，提高合作数学问题解决效率与学习质量为目的，在基于数学问题解决高低绩效组的比较中考察初中生合作“知识建构”，主要针对以下四项研究问题进行了探索：1.初中生合作“知识建构”总体上是怎样的？2.初中生合作“知识建构”路径是怎样的？3.初中生合作“知识建构”层次是怎样的？4.初中生合作“知识建构”组内交互是怎样的？

采用基于设计的方法开展实验性调查。考虑到不同学校的学情差异，该研究以代表B市T学区平均教学水平的3所初中学校7年级学生作为样本总体，分别选取每所学校的一个教学班，由该班级数学教师以4人为单位（“组间同质、组内异质”分组原则）组织学生开展基于数学问题解决的合作学习活动。以“小明的公寓”数学问题解决为例，在开发初中生合作数学问题解决成果质量评价工具，对3个班级29组学生数学问题解决成果质量进行评价的基础上，遴选出公认的高低绩效组各6组24名学生作为研究对象。综合运用文献研究法、内容分析法、社会网络分析法、录像视频观察法等研究方法，参考国内外具有较高认同度的合作“知识建构”交互过程模型开发相应研究工具。利用视频录像、对话录音的方法记录学生过程性学习数据并将其转录为文字稿，最终形成12个小组合作“知识建构”文本数据共计3244条交互对话，9万余文字转录稿，利用质性分析软件ATLAS.ti 8、社会网络分析软件UCINET 6、数据可视化软件Tableau 2019以及数据分析软件SPSS 22.0等进行反复编码和分析，所得主要研究结论如下：

1.初中生合作“知识建构”总体分析的主要结论：第一，初中生均能以数学问题解决为核心开展合作“知识建构”，高低绩效组学生知识建构相关讨论占比80%以上；第二，初中生基于数学问题解决的合作学习均存在一定比例无关讨论；第三，初中生的无关讨论存在相同类型，如为完成数学问题解决形式化要求所产生的讨论等。然而，高低绩效组存在一些差异：第一，高绩效组学生基于数学问题解决的合作学习信息交互量略低于低绩效组；第二，高绩效组合作“知识建构”相关讨论比重高于低绩效组且无关讨论低于低绩效组。

2.初中生合作“知识建构”路径分析的主要结论：第一，初中生合作“知识建构”需要经历信息分享与理解、分歧发现与明确，内容协商与共建，内容验证与调整，共识达成与应用，成果反思与评价六个阶段；第二，初中生合作“知识建构”中的观点演进路径存在多种样态，包括观点整合、观点裂变、观点异变等；第三，初中生合作“知识建构”中的“共享型观点”数量占比最高，其次为“讨论型观点”，最后为“升华型观点”。然而，高低绩效组存在一些差异：第一，高绩效组学生观点数量低于低绩效组，但高绩效组学生“升华型观点”占比远高于低绩效组；第二，高绩效组学生在观点演进过程中表现出较好的螺旋上升形态，而低绩效组学生观点演进形态相对混乱。

3.初中生合作“知识建构”层次分析的主要结论：第一，初中生基于数学问题解决的合作“知识建构”整体上达到了深层次的知识建构水平，存在“成果反思与评价”阶段交互讨论，但占比偏低；第二，初中生均以中层次和浅层次知识建构交流讨论为主，中层次的知识建构与浅层次的知识建构占比均达到35%以上。然而，高低绩效组存在一些差异：第一，高绩效组学生深层次知识建构，如“共识达成与应用”和“成果反思与评价”阶段占比高于低绩效组；第二，高绩效组学生“信息分享与理解”、“内容验证与调整”阶段比重高于低绩效组；第三，高绩效组学生“观点分歧与明确”和“内容协商与共建”阶段比重低于低绩效组。

4.初中生合作“知识建构”组内交互分析的主要结论：第一，初中生合作“知识建构”整体参与度较好，均能通过积极的发言和交流进行数学问题解决，从而促进了交互群体产生，使得信息在不同个体间生成和流动；第二，初中生合作“知识建构”交互群体存在多样态交互模式，主要包括2人交互子群、3人交互子群等类型；第三，初中生合作“知识建构”组内交互过程中存在个别学生极少参与，表现为极少与小组成员交互的现象。

基于以上研究结论，根据已有文献对可能原因进行追寻的基础上，分别为初中数学课程教材建设、初中生基于数学问题解决的合作学习及其学习质量监测、开展信息技术支持下初中生基于数学问题解决的合作学习提供一些启示。

Students’ classroom learning is an important research field of mathematics education. To realize the integration of “21^st century skills” in mathematics education, and enhance the instruction for practical and innovative talents, collaborative learning based on mathematical problem-solving has attracted much attention of the academics with its unique teaching value. During this learning activity, collaborative knowledge building emphasizes that students exchange views, discuss, negotiate, solve problems, and create valuable public knowledge for the team. Then, Students could share views, negotiate meanings among team members, improve their academic achievements, promote mutual learning. Thus, collaborative knowledge building becomes an important perspective reflecting the learning process and learning quality under the new learning style, which could support the analysis of learning and the improvement of teaching. However, few researches focus on mathematics classroom in junior high school and from the perspective of collaborative knowledge building to analyze students’ collaborative learning quality based on mathematical problem solving. Based on the analysis of above, the purpose of this research is to optimize the learning process of students in the new learning style and improve the efficiency and quality of collaborative mathematics problem-solving. In the comparison of high and low performance groups’ mathematical problem solving, this research investigates the collaborative knowledge building of junior high school students, and mainly answers the following four research questions: 1. What is the junior high school students’ general situation of collaborative knowledge building? 2. What is the junior high school students’ collaborative knowledge building trajectory? 3. What is the junior high school students’ collaborative knowledge building level? 4. What is the junior high school students’ interaction in a team when they build knowledge collaboratively?

Design based method was used to carry out the experimental investigation. Because different schools have different teaching quality, this research takes seven-grade students of three junior high schools representing the average teaching level of the T school district in B city as the sample population, selects one class in each school, and organizes the students to participate collaborative learning activities based on mathematical problem-solving in the unit of 4 students (Grouping principle is that there is a similar structure between groups and different structure within groups based on students’ mathematical competencies). Taking “Xiaoming’s apartment” as an example of a mathematical problem, and developing a quality evaluation tool for junior high school students’ mathematical problem-solving results, this research evaluates the quality of the results from 29 groups in three classes, and 48 students from 12 groups are selected as the research objects, which were recognized high and low performance groups. Using research methods of literature review, content analysis, social network analysis, video observation and so on, the research tools are developed by referring the interactive process model of collaborative knowledge building with high recognition in the academics in the world. The process learning data were recorded by video and dialogue recording and then transcribed into text manuscripts. Finally, a total of 3244 interactive dialogues and more than 90 000 words transcripts were formed from 12 groups. Using qualitative analysis software ATLAS.ti 8, social network analysis software UCINET 6, data visualization software Tableau 2019, and data analysis software SPSS 22.0 to code and analyse collected data repeatedly, the main research results are as follows:

1. The main conclusions of the junior high school students’ general situation of collaborative knowledge building: First, junior high school students can build public knowledge collaboratively for mathematical problem-solving, and high and low performance groups collaborative knowledge building related discussions are more than 80%; Second, there is a certain proportion of irrelevant discussion in collaborative learning based on mathematical problem solving; Third, there are the same types of irrelevant discussions among junior high school students, such as those for the formal requirements of solving mathematical problems. However, there are some differences between high and low performance groups. First, the amount of information interaction of high performance groups are slightly lower than low performance groups; Second, the proportion of discussion for knowledge building of high performance groups is higher than the low performance groups, and irrelevant discussion of high performance groups is lower than the low performance groups.

2. The main conclusions of the junior high school students’ collaborative knowledge building trajectory: First, junior high school students’ collaborative knowledge building needs to go through six stages: information sharing and understanding, divergence discovery and clarification, content negotiation and co-construction, content verification and adjustment, consensus reaching and application, and achievement reflection and evaluation; Second, there are multiple viewpoints evolution paths, including opinion integration, opinion fission, and opinion variation; Third, the number of “shared viewpoints” is the highest, followed by the “discussable viewpoints”, and finally the “sublimation viewpoints”. However, there are some differences between high and low performance groups. First, although the number of viewpoints of the high performance groups is lower than that of the low performance groups, the proportion of “sublimation viewpoints” of the high performance group is much higher than that of the low performance group; Second, the high performance groups show a good spiral in the process of viewpoints evolution, while the low performance groups are relatively chaotic.

3. The main conclusions of the junior high school students’ collaborative knowledge building level: First, the junior high school students’ collaborative knowledge building has reached a deep level at the stage of “achievement reflection and evaluation”, but the proportion is low. Second, junior high school students are mainly engaged in the communication and discussion at the middle level and shallow level, and both middle level and shallow level's proportion is more than 35%. However, there are some differences between high and low performance groups. First, the proportion of deep level knowledge building in high performance groups is higher than that in low performance groups, such as “consensus reaching and application” and “achievement reflection and evaluation”. Second, the proportion of “information sharing and understanding” and “content verification and adjustment” of high performance groups is higher than that of low performance groups; Third, the proportion of “divergence discovery and clarification” and “content negotiation and co-construction” of high performance groups is lower than that in low performance groups.

4. The main conclusions of the junior high school students’ interaction in a team when they build knowledge collaboratively: First, junior high school students’ participation in collaborative knowledge building is good, and students in a team can solve mathematical problems through active talk and communication. Thus, the process of collaborative knowledge building could promote the generation of interactive groups and enhance information flow among different individuals. Second, there are various interaction modes during collaborative knowledge building, which mainly includes two-person interaction subgroup and three-person interaction subgroup; Third, in the interaction process of collaborative knowledge building, some individual students seldom participate in this process, which shows that they seldom interact with group members.

Based on the research results above, and tracing the possible causes according to relevant literature, this research provides some suggestions for the construction of junior high school mathematics curriculum and teaching materials, classroom collaborative learning and its quality monitoring, and using information technology to support collaborative learning.