Research About Space Vector's Impact On Students' Ability Of Space Imagination

In the new round of mathematics curriculum reform, there are large changes from concepts and content of high school's mathematics, in which the introduction of"vector"receives particular concerns. Vector is considered as one of the important mathematical concepts in modern mathematics, it has both geometry concept and algebra concept, is the bridge communicating algebra, geometry and trigonometry, as well as it has been widely used in physics, engineering and structurology of space material. However, in the teaching of three-dimensional geometry, some teachers are still skeptical about the introduction of the vector. Some believes that"the introduction of space vector will not conducive to cultivate student's ability of space imagination",The introduction of"space vector"is inconsistent with the cultivations of"computational capability, the ability of space imagination and logical thinking ability"that the new mathematics curriculum reform stresses . The teachers holding this view often display inadequate attention to the teaching of the vector,thus student's understanding about the vector is too one-sided and superficial, and it will not fully elaborate vector's use in mathematics learning.At the beginning of the research, the author had read a lot of the research documentation about the space vector, investigated the relationship of space vector and the ability of space imagination, and initially determined the research direction , experimental methods, this research's thought and what should been done. Before the experiment, the author had designed and scheduled《the questionnaire of"vector"learning profile and content effect of middle school student》,《Volume I test of space ability》and《Volume II test of space ability》. In the course of the experiment, author first choosed two parallel classes which are equivalence in the study mark and lever of space ability, and divided them into two classes: control class and experimental class. We applied the conventional teaching design(no introduction of space vector)for the control class, applied the teaching design which introduce the space vector for the experimental class, and carried out a complete teaching of three-dimensional geometric content. Before the experiment, according to the pre-test result and the suggestions of instructors, we respectively selected students of three levels: outstanding student, middle student and backward student in the two classes, and did track research of their learning, abstracted the three stage's marks of beginning,mid-term and last term and did the comparative analysis to find difference. At the end of the experiment, the author had done a post-test about the study result and the ability of space imagination in two classes and analyzed its data. Meanwhile, he interviewed with individual student. Through the final experiment's result, he got that the introduction of the vector space would impact the ability of space imagination of middle school student. The data in the experiment was statistically analyzed by the software SPSS13.We could receive the scientific conclusions.This article is written to study the effect on the ability of space imagination and their study result after introducing"space vector"in the content of solid geometry , to analyze and discuss the relationships of students'learning interest in"space vector", their self-confidence and the cultivation of the ability of space imagination. There are two points of this research's significance as below: (1) The result of the research can proof the space vector's effect on the cultivation of the ability of space imagination, it can provide references for the teaching of"space vector"and correct some wrong understanding about it. (2) After the formal generation of the new mathematics course, research conclusion will help student make the rational judgment and choice. In the process of the research, the author analyzed the development of vector, the conditions of vector's teaching in middle school at home and abroad, and the profile of vector studying in China, collected and analyzed data to work out the result by using experimentation. The result shows that:"space vector"has some effect on improving the ability of space imagination。For one thing, the effect contributes to the fact that"space vector"helps students develop their ability of space imagination, but the effect is not great for the whole ability. For another, effect of this kind has something to do with students'previous knowledge level and their mathematical capacity. The effect differs according to their different level. For outstanding students,"space vector"help them develop the mathematical interest, strengthen self-confidence and improve their study grade and the ability of space imagination. For the middle students, the effect is not so great on these aspects of interest, self-confidence, grade and space imagination. While for those backward students, the introduction of"space vector"doesn't do any good to these aspects, instead, it will only hinder the improvement of them.