| According to the Compulsory Education Mathematics Curriculum Standards(2011),students should be able to think in a mathematical way,strengthen the ability to find and raise questions,and analyze and solve problems.Some studies have found that students' behavioral performance in solving problems is in line with the students' own cognitive level.Therefore,improving students' cognitive level also improves their ability to solve problems.This study defines the level of geometric cognition according to the SOLO Classification Theory,selects three junior middle school students at the high middle and low level respectively from a key middle school in Chongqing as case study objects,and designs a “three-fold origami activity model”.Based on the students performed a total of 16 origami activities for two-month,through classroom observation,video analysis and sound thinking methods,the study collects,records,organizes,and analyzes the student's performance in origami activities and their corresponding knowledge status,and finally construct problem behavior diagrams of students in origami activities.According to the SOLO Classification Theory,the geometrical cognitive level corresponding to each knowledge state in the problem behavior diagram is analyzed.Each student's question map of origami activity is compared and analyzed on a vertical basis,and the development of the student's geometrical cognitive level in origami activities has been found out.The following conclusions are obtained:(1)Through a series of origami activities,the level of geometric cognition of students with learning difficulties has been raised from “Pre-structure”to “Uni-structural”.When these students with learning difficulties solve geometric problems arising from origami activities,they often fail to understand the problems in the early stages of origami activities,but can only repeat the problems.At the end of the paper-folding activity,it is possible for them to find out one relevant characteristics by observing the folding operation and the crease pattern alone.(2)Through a series of origami activities,the level of geometric cognition of secondary students was raised from “Uni-structure” to “Multi-structure”.When average students solve geometric problems in origami activities at the beginning period,only one relevant feature of the problem can be found by most of them in most of the time.However,at the end of origami activity,several related features to solve the problem by observing folding operation and crease graph can be found by them.But in most cases they cannot relate the correlation features which are found.(3)Through a series of origami activities,the level of geometric cognition of gifted students is raised from “Uni-structure” to “Relation level”.In solving the geometric problems in origami activities,the gifted students can find a relevant characteristic by observing the creases in the early stage of origami activities.At the end of origami activity,however,in most cases,it is possible to independently discover several relevant features needed to solve the problem through folding operations and the observation of the crease graph,and to integrate them into a whole so that the problem can be solved.(4)Through a series of origami activities,gifted students and average students can sometimes sum up general principles or conclusions by solving geometric problems.That is to say,both gifted and average students can sometimes reach the level of extended abstraction in the process of solving geometric problems.(5)Origami activities and the teacher's guiding language have the greatest influence on the geometric cognition of gifted students and the least on the geometric cognitive level of students with learning difficulties.(6)The selection of origami activities and the selection of teachers' guidance methods will affect the students' geometric cognitive level in the origami activity. |
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