Study On The Influence Of Students’ Mathematical Thinking Way Of Teachers Intervention Activities In Origami

The "compulsory education curriculum standard(2011 Edition)" clearly put forward "help students initially formgeometric intuition and operation ability, and developtheir image thinking and abstract thinking ", "Develop students’ abstract thinking and reasoning ability", emphasizing the influence on students’ thinking.In addition, it is also mentioned that "students learning should be a lively, active and personalized process. Except accepting learning, hands-on practice, autonomous exploration and cooperative communication are also important ways to learn mathematics". We can see that The Standard pays attention to earning mathematics in Hands-on activities and associating mathematics in action thinking.This study finds great differences among the students’ origami operation in two years’ origami primary and secondary school teaching practice. Combined with interviews, we find origami can be a medium indirectly reflect the students’ mathematical thinking. 2015.3 to 2015.6, the researchers take videos of eight origamicourses of certain Class in Grade six(40 minutes per lesson) and collect origami works of students. According to the data collected,we analyzestudents’ action, language(including the instant interview of teachers and some students) and origami works, and combined with action features expressed by seven axioms of the Origami,based on basic graphics folding, plane assembling and three-dimensional assembling three aspects to initially establish the behavior standards reflectingthe students’ mathematical thinking way. The origami is an operational activities, large-scale classesis not good for teachers’ intervention to particular students. Therefore, it is necessary to study the case. The researchers repeat the same study on another three sixth graders, a total of 24 videos. In which the teachers intervene the students’ actions from three aspects including intervention time, intervention methods and presentation and intervention behavior.Through video analysis, work analysis method and thinking aloud method, we modify and supplement the behavior standards. And we judge students’ changes in mathematical thinking before and after the intervention. We found the following conclusions:(1) There are three kinds of mathematical way of thinking reflected in origami activity:action thinking, action thinking lead by image thinking, action thinking lead by image thinking and abstract thinking.(2) In the initial stages of origami activity,the sixth graders rely on intuitive perception of origami in their hands, unaware of geometric elements and their relevance. They get the crease or finish the assembling by imitating teachers’ actions or action thinking lead by contrasting sample image.(3) Through the teachers’ intervention, students are able to realize the geometric elementsand their relevance in origami works. They can also associate to mathematics,observe the geometric properties and turn to image thinking. And then, finish the origami works.(4) Through the teachers’ intervention, students can turn to image thinking based on the geometric properties in the origamiwork. They can also associate to mathematical proposition, reason out the location of the crease or assembling regulars and turn to abstract thinking. And then, finish the origami works.(5) Intervention methods including the hints of geometric elements, the application of origami axioms, the understanding of crease expansion and the memory of special graphics in, help students to take the initiative to use image thinking leading to action thinking.(6) A good understanding ofcrease expansion and the relevance of geometric elementshelp to take the initiative to use action thinking lead by abstract thinking and image thinking.(7) The cognitive interventionof "Require explanation" and "problem driving"(auxiliaryproblems, deep problems) in intervention behavior, and helping students to interpret the relationship between steps, will help the action thinking rise to image thinking or abstract thinking.(8) Among the intervention methods and presentation, visual intervention is more suitable than auditory intervention for sixth gradersin origami operation.