万双网讯 2024年4月19日，VBS四年级数学组在小剧场开展了《桥的几何结构》PBL项目式学习展示活动。从项目启动、确定方案、分工合作、成果展示到反思总结，在四年级数学老师的指导下，全体学生积极参与，乐在其中，在解决一个个具有挑战性任务的同时，感受着数学学科的无限魅力与乐趣。

On April 19, 2024, the Math group of Grade 4 at VBS conducted a PBL demonstration of "Geometric Structures of Bridges" in the Theater. Under the guidance of the 4th grade math teachers, from project initiation, determining the plan, division of tasks, presentation of results to reflection and summary, all students actively participated and enjoyed themselves, and felt the infinite charm and fun of the subject of mathematics while solving one challenging task after another.

一 、项目启动 

Project initiation

项目探究前，学生观看了广州沥心沙大桥被船只撞击事故的相关视频，引发了学生的思考：为什么桥梁会被撞断？造成了什么样的后果？怎样才能避免此类事故的发生？通过观察各种各样的桥的图片，学生发现桥的结构中有三角形、长方形、梯形等大家所熟悉的平面图形。随后确定了本次项目式学习的核心问题：怎样才能搭建最稳固的桥？从核心问题出发，学生分组讨论，确定了以下子问题：建桥时需要用到哪些我们熟悉的几何图形？什么样的图形结构最稳固？怎样用这些图形造出最稳固的桥？从以上问题出发，学生开启了《桥的几何结构》PBL项目式学习活动。

Before doing the project, students had watched a video related to the accident of Lixinsha Bridge in Guangzhou being hit by a boat, which triggered students' thinking. Why was the bridge broken? What were the consequences? How can such accidents be avoided? Through observing various pictures of bridges, students discovered that the structure of bridges includes familiar shapes such as triangles, rectangles, and trapezoids. Subsequently, the core question of this PBL was how to build the most stable bridge. From the core question, the students worked in groups to identify the following sub-questions. For example, what familiar geometry do we need to use to build a bridge? What kind of graphic structure is the most stable? How do you make the most stable bridge out of these shapes? Starting from the above questions, the students started the PBL activity "Geometry of Bridges".

二、确定方案

Identify the scenario 

经过项目启动，学生对国内各大桥的设计原理进行了了解，发现目前国内最常见的桥结构是斜拉索桥，比如上海的南浦大桥、江苏的苏通大桥、港珠澳大桥等，都采用了斜拉索桥结构。通过探究，学生发现三角形具有稳定性。斜拉索桥索塔的两侧是对称的斜拉索，为等腰三角形，通过斜拉索将索塔主梁连接在一起。

After the project was initiated, students learned about the design principles of various bridges in China and found that the most common bridge structure in China is the cable-stayed bridge, such as the Nanpu Bridge in Shanghai, the Sutong Bridge in Jiangsu, the Hong Kong-Zhuhai-Macao Bridge, etc. All of which use cable-stayed bridge structures. Through exploration, students discovered triangles are the most stable structures. The two sides of the cable-stayed bridge pylons are symmetrical, which are isosceles triangles, and the main girders of the cable-stayed cables are connected together.

在对桥梁的结构有所了解后，学生利用清明假期开始在纸上进行设计，每位同学都设计了一份图纸。经过商议，每个小组选择确定了其中一位同学的图纸作为桥梁模型的制作方案。

After learning about the structure of the bridge, students took advantage of the Qingming Holiday to start designing on paper, and each student designed a drawing. After deliberation, each group chose one of the students' proposals.

三、分工合作 

Group tasks distribution

设计桥梁前，同学们自行分成小组，选出一名组长，每个小组向老师汇报最终确定的方案，并向老师申请了原材料：木棍和白胶等。制作时，每个组的成员分工合作：有人负责搭桥面、有人搭桥墩，还有人负责拍照，记录搭桥的过程。

Before designing the bridge, the students divided into groups and elected a group leader, and each group reported the final plan to the teacher, and applied to the teacher for raw materials, such as wooden sticks and white glue. During the production, the members of each group worked together. Some were responsible for building the bridge deck. Some were building the pier, and some were responsible for taking pictures and recording the process of building the bridge.

四、最终成果 

The final outcome

通过四节课的努力，各种各样的桥终于搭好了，一起欣赏一下学生的作品。

After four classes of hard work, various bridges were finally built, and we could enjoy the students' works together.

五、评价

 Evaluation

及时评价能帮助学生认识自己、改进自己。本次评价从两个层面进行：评价的内容分为知识类和操作实践类，评价的主体分为生生评价和师生评价。

①生生评价：学生分小组完成评价表。

②师生评价：教师点评总结整个项目式学习的过程和成果，强调团队合作、创新思维和实践能力的重要性。

Timely evaluation can help students understand themselves and improve themselves. The evaluation was carried out from two levels. The content of the evaluation was divided into knowledge and operation. In addition, the main body of the evaluation was divided into student evaluation and teacher-student evaluation.

(1) Student evaluation. Students complete the evaluation form in small groups.

(2) Teacher and student evaluation. Teachers commented and summarized the process and results of PBL, emphasizing the importance of teamwork, innovative thinking and practical ability.

六、成果展示

 The results of the display

展示分为两个阶段，第一阶段在班级内进行展示，由同学们、老师给出评价和反馈。第二阶段根据班级同学的评价和反馈进行改进后，在年级组进行展示。

The presentation was divided into two stages. The first stage was to be presented in the class, and students and teachers would give evaluation and feedback. In the second stage, improvements would be made based on the evaluation and feedback of the classmates, and they would be presented in the grade group.

七、反思总结 

Reflection and summary

4V班张艺饶同学：我们一开始材料没有及时准备好，大家比较茫然，不知从何下手，所以我们应先分配好小组各成员的职责，并根据需要完成的时间制定时间进度表；在进度受阻时，应多请教同学或老师。

Zhang Yirao, Class 4V: At the beginning, the materials were not prepared in time, and everyone was at a loss and didn't know where to start. Therefore, we should first assign the responsibilities of each member of the group and make a time schedule according to the time. If progress is blocked, we should consult our classmates or teachers.

4O班管礼娴同学：在制作的过程中，我们发现三角形的结构最稳定。但不是所有三根小棒都能搭成三角形，只有满足任意两边之和大于第三边或任意两边之差小于第三边的三根小棒才能搭成三角形。

Guan Lixian, Class 4O: In the process of making, we found that the structure of the triangle is the most stable. However, not all three sticks form a triangle. Only when the sum of any two sides is greater than the third side, or the difference between any two sides is less than the third side, can three sticks be assembled into a triangle.

4V班叶牧荑同学：通过这次项目式学习，我们在自主探究中知道了三角形具有稳定性，有着稳固、坚定、耐压的特点。在我们日常生活中有广泛的应用，比如自行车的车架、三角形房层架、三角吊臂、电线杆的固定等都有运用。在未来的生活中，我们也应该学会灵活运用所学知识解决问题；制作过程中遇到问题能及时调整与完善；组员与组员之间沟通紧密，提出不同的意见，这样合作才更高效。

Ye Muti, Class 4V：Through this project-based learning, we discovered that triangles are stable, characterized by their firmness, steadfastness, and pressure resistance in our self-exploration. This property is widely applied in our daily lives, such as in the frames of bicycles, triangular roof trusses, boom arms, and the stabilization of utility poles. In our future lives, we should also learn to flexibly apply the knowledge we've acquired to solve problems, be able to adjust and improve promptly when encountering issues during the creation process, and maintain close communication between team members, offering diverse opinions. Only through such collaboration can we work more efficiently.

4O班骆嘉仪同学：原来数学课可以这么好玩，数学离我们每个人的生活这么近。要想高质量完成本次PBL项目式学习，真正造好一座桥，不但要有好的设计想法，还要依靠团队协作。

Luo Jiayi, Class 4O: It turns out that math class can be this much fun, with mathematics being so closely intertwined with each of our lives. To complete this PBL (Project-Based Learning) task with high quality and truly construct a well-made bridge, not only do we need good design ideas but also depend on teamwork.

4D班罗文灿同学：这次活动，不仅让我对几何知识有了更深入的理解，更在动手实践中体会到了学习的乐趣和团队合作的重要性。在制作桥的过程中，我深刻感受到了三角形具有稳定性，这使得桥的基础结构牢固可靠，我们将这些知识运用到桥的每一个部分，不断调整、完善，最终完成了一座稳固的桥。活动结束后，我收获颇丰。我意识到，学习不仅仅是学书本上的知识，更是将所学知识运用到实际中的过程。这次活动还锻炼了我的动手能力和团队合作能力，让我更加明白了团结合作的重要性。

Luo Wencan, Class 4D: This activity not only gave me a deeper understanding of geometric knowledge but also allowed me to experience the joy of learning and the importance of teamwork through hands-on practice. During the process of making the bridge, I deeply felt the stability of triangles, which ensured that the foundation of the bridge was solid and reliable. We applied this knowledge to every part of the bridge, continuously adjusting and improving until we completed a sturdy structure. After the activity concluded, my gains were substantial. I realized that learning is not just about the knowledge in books; it is also about applying that knowledge in practice. The activity also honed my practical skills and ability to collaborate within a team, underscoring the significance of unity and cooperation.

4C班潘彦廷同学：通过这次活动，我深刻认识到了团队合作的重要性。在制作桥的过程中，我们互相学习、互相帮助，共同克服了一个又一个难题。这种团结协作的精神不仅让我感受到了集体的温暖，也让我明白了在团队中发挥自己的优势、尊重他人的意见是多么重要。同时，这次活动也让我认识到了自己的不足。比如，我在动手能力和创新思维方面还有待提高。在今后的学习和生活中，我将更加注重这些方面的锻炼和提升。

Pan Yanting, Class 4C: Through this activity, I have come to a profound realization of the importance of teamwork. In the process of building the bridge, we learned from each other, helped each other, and overcame numerous challenges together. This spirit of unity and collaboration not only made me feel the warmth of the collective but also made me realize how important it is to play to my strengths within a team and respect the opinions of others. At the same time, this activity has also made me aware of my own shortcomings. For instance, I need to improve my practical skills and innovative thinking. In my future studies and life, I will pay more attention to training and enhancing these areas.

4X班王泓霖同学：这次活动不仅考验了我们的知识储备，更锻炼了我们的实践能力和毅力。在制作桥的过程中，我深深体会到了知识与实践的紧密结合。我们运用三角形的稳定性来设计桥的基础结构，确保桥的坚固。在这个过程中，我们学会了如何分析问题、解决问题，也学会了如何与他人合作、共同克服困难。

Wang Honglin, Class 4X: This activity not only tested our knowledge reserves, but also exercised our practical ability and perseverance. In the process of making bridges, I deeply realized the close integration of knowledge and practice. We used the stability of the triangle to design the basic structure of the bridge and ensure that the bridge is strong. In this process, we learned how to analyze and solve problems, and also know how to cooperate with others to overcome difficulties together.

4E班李廷谦同学和李屹睿同学：在桥梁的构建过程中，我们不仅仅是在建桥，更是收获了丰富的知识。我们始终保持着明确的分工，相互帮助，共同促进，相信在不久的将来，我们能够打造出一座既安全又美观的桥梁。

Li Tingqian and Li Yirui, Class 4E: In the process of building the bridge, we were not only building the bridge, but also gaining a wealth of knowledge. We always maintained a clear division of tasks, helped each other, and promoted together, and believe that in the near future, we can build a bridge that is both safe and beautiful.

4F杨妍浠和张然同学：我们深刻体会到了团队合作的重要性，学会了在分歧面前寻求共识，共同为项目的成功而努力。其次，我们在实践中掌握了三角形的特征，并将其运用到桥梁加固中，这不仅加深了我们对几何知识的理解，也提高了我们的动手实践能力。

Yang Yanxi and Zhang Ran, Class 4F: We deeply realized the importance of teamwork, learned to seek consensus in the face of differences, and worked together for the success of the project. Secondly, we have mastered the characteristics of triangles in practice and applied them to bridge reinforcement, which not only deepens our understanding of geometric knowledge, but also improves our hands-on practical ability.

4I班段姝妤同学:为了建造最酷最稳定的桥，我们小组上网搜索了很多关于桥的相关信息，发现原来建造桥真不是一件容易的事。后来动手造桥时也遇到了很多困难，找不到合适的材料、反复修改设计图纸等等，好多次都想放弃，但是最后我们小组调整心态，一起努力，我们的“波克布林大桥”终于成功啦，成为了最特别的桥。

Duan Shuyu, Class 4I: In order to build the coolest and most stable bridge, our group searched a lot of relevant information about the bridge on the Internet, and found that it was not easy to build a bridge. Later, when we started to build the bridge, we encountered many difficulties. For example, we couldn't find suitable materials or repeatedly revised the design drawings. We were to give up many times, but in the end, our group adjusted our mentality and worked together, and our "Pokebrin Bridge" finally succeeded and became the most special bridge.

4G班陈也非同学:这是我们小组的四号桥，之前的三个桥因为考虑不全面，有的因为结构问题，有的因为材料问题都失败了。我们汲取经验和教训，先绘制图纸，接着讨论分析，再具体分工，最后我们的桥终于搭好了，虽然可能还有些问题，但是我们组觉得它是最棒的桥。

Chen Yefei, Class 4G: This is our group's Bridge No. 4. The previous three bridges failed due to incomplete considerations - some were structurally unsound, others had material issues. We learned from these experiences and lessons by the first drawing blueprints, then discussing and analyzing, followed by delegating specific tasks. Finally, we successfully constructed our bridge. Although there may still be some issues, we believe it is the best bridge.

4Y班钟蔚源同学:通过这次搭桥活动，我开始对数学感兴趣啦，原来数学不仅仅是计算、做题目，还可以这么有趣。搭桥的时候，我们把图形知识学以致用，利用三边关系构建三角形，提高桥的稳定性。我以后还要学习更多的数学知识。

Zhong Weiyuan, Class 4Y: This bridging activity has sparked my interest in mathematics. I now realize that math is not just about calculations and problem-solving. It can be truly fascinating. During the construction of the bridge, we applied our knowledge of geometry to use triangular relationships for enhancing the stability of the bridge. I am motivated to learn more mathematical concepts in the future.

VBS建校便将PBL列入课程表，经过不断探索实践，再将PBL项目学习方式不断融入学科教学，鼓励学生运用PBL的学习方式开展学习活动，让学生体验最真实且严谨的学习过程。学生在真实情境中，在强烈兴趣的驱动下，自主探索，分工合作，充分激发了创新能力和学习兴趣。项目开展过程中，指导老师及时给予学生引导，调动学生潜力和创造力。学生在PBL项目式学习中，完成具有挑战性的任务，将学科知识应用于生活，收获了丰厚的具有生活价值的成果，点燃了学习的内驱力，能更好地站在未来中央。

VBS incorporated PBL (Project-Based Learning) into its curriculum since its establishment. Through continuous exploration and practice, VBS has progressively integrated PBL methodologies into subject teaching, encouraging students to learn by PBL approaches, allowing them to experience the most authentic and rigorous learning processes. In real-world scenarios, driven by strong interest, students independently explore and collaborate, which greatly stimulates their innovative abilities and learning interests. Throughout the project, instructors provide timely guidance to students, stimulate student’s potential and creativity. In PBL, students tackle challenging tasks and apply subject knowledge to life, reaping substantial results that are valuable in real life, igniting intrinsic motivation for learning and better positioning themselves for the future.

撰稿/谢冬梅

翻译/唐华琳 周金凤

版式/徐娜

编辑/燕子