一、该案例设计的出发点我们所提出的多重表征模型是指:存在着和学习过程相关的三个世界(现实世界、知觉世界和认知世界),每个世界都存在相同的一个三维坐标体系(由认知轴、抽象轴和空间轴构成),每个坐标体系中对应地存在三种表征类型(宏观表征、微观表征和符号表征)。现实世界对象的呈现状态和方式等诸多因素都将会影响到知觉对象。在知觉世界中所形成的知觉对象是一种外在表征。面对相同的信息或者情境结构,所知觉到的外部表征信息越多,则任务就越容易解决。由此我们也可认为,从现实世界中获得的有效信息越丰富、越翔实,则越有利于认知世界中表征的形成和发展。因此,对于问题解决教学而言,问题要来源于现实世界。不同学生有不同的认知风格、思维水平和学习需要,教学要以学生的需要为本。因此,对于不同认知水平的问题解决者而言需要从现实世界中选择不同的表征类型进行教学。例如,对于中小学生应倾向于使用现实世界中的宏观表征出发进行教学,以使其能够建立较为形象和深 First, the starting point of the case design Our proposed multi-representation model means that there exist three worlds (real world, perceptual world and cognitive world) related to the learning process, and each world has the same three-dimensional coordinate system (Composed of cognitive axis, abstract axis and spatial axis). Correspondingly, there are three types of characterization (macroscopic characterization, microscopic characterization and symbol characterization) in each coordinate system. Many factors, such as the state and manner in which real-world objects are presented, affect the perceived object. Perceptual objects formed in the perceptual world are an outward manifestation. In the face of the same information or contextual structure, the more externally perceived information is perceived, the easier it will be for the task to be solved. From this we can also think that the richer and more informative the effective information obtained from the real world, the more conducive to the formation and development of the representation in the cognitive world. Therefore, for problem-solving teaching, the problem comes from the real world. Different students have different cognitive styles, thinking levels and learning needs, teaching should be based on the needs of students. Therefore, for different cognitive level problem solvers need to choose from the real world different types of character for teaching. For example, primary and secondary school students should be inclined to use the macroscopic representations in the real world to teach in order to be able to establish a more image and depth