3D Printing Supports The Design Research Of Elementary School Students' Mathematical Space Concept Formation

Throughout the years of mathematics teaching documents about the spatial sense,we can find that the spatial sense has been very important in Chinese mathematics curriculum."Compulsory Education Mathematics Curriculum Standards(2011Edition)" puts forward the spatial sense as one of the ten core words of mathematics,and emphasizes the importance of the spatial sense again.However,in the current teaching practice,the cultivation of students’ spatial sense has some practical difficulties,such as paying more attention to observation than experience,paying more attention to conclusion than reasoning,paying more attention to score than ability.As an auxiliary tool for teaching,3D printing has entered the classroom and played a positive role in innovating teaching forms.The educational characteristics of3 D printing "learning by doing" and the technical characteristics of 3D modeling visual representation,dynamic presentation and all-round perspective transformation make it able to provide a boost to the cultivation of students’ spatial sense.This study aimed to use 3D printing to support the formation of primary school students’ mathematical spatial sense.Based on the existing teaching practice mode of3 D printing,the research constructed the characteristic process of 3D printing activities by summarizing its core activities.Then the main ideas of mathematical spatial sense were analyzed to tease out the cognitive process of spatial sense and the formation path of mathematical spatial sense of primary school students.The characteristic process of 3D printing activity,the formation path of mathematical spatial sense and the cognitive process of spatial sense of primary school students were integrated,and a three-layer "millstone" model pointing to mathematical spatial sense was constructed.Then,the teaching content of spatial sense of primary school mathematics was analyzed,and specific 3D printing learning activities were designed with "graphics and geometry" knowledge as the content carrier,including three theme activities named "personalized key chain","variable building block tower" and "my creative world".This study selected students in Class One,Grade Four from a primary school in Nanjing as the research object.Using design-based research methods,three theme activities were implemented in sequence under the guidance of the activity model.During the activity,the effect of the activity was implemented through four methods: classroom observation,learning task list records,class learning results questionnaire analysis,and 3D modeling work evaluation.Then,reflected on the deficiencies,modified and perfected the model,and proposed strategies for improving activities.Through the implementation of a series of 3D printing activities,the level of students’ spatial sense had been significantly improved,which was mainly reflected in the following two points: First,the four aspects of students’ spatial sense had been improved.The students’ overall performance was outstanding in the transformation and view of two-dimensional and three-dimensional graphics,direction and position,and movement and change of graphics.In terms of language description of graphics and geometric intuitive problem solving,students’ spatial sense was only outstanding at level 1.Second,students’ spatial sense developed to a higher level.In terms of the transformation and view of two-dimensional and three-dimensional graphics,direction and position,most students’ spatial sense can reach level 3.In terms of movement and change of graphics,most students’ spatial sense can reach level 2.In terms of language description of graphics and geometric intuitive problem solving,most students’ spatial sense can only reach level 1.It can be seen that students’ ability to perform complex analysis and comprehensive reasoning had improved,and their spatial sense had developed well in terms of the transformation and view of two-dimensional and three-dimensional graphics,direction and position,movement and change of graphics,but the language description of graphics and geometric intuitive problem solving was limited.