A Research On The Knowledge Connectedness In Solid Geometry Problem Solving

The solid geometry is the important content of high school mathematics,it is on the basics of studying plane geometry knowledge, further studying the relations, the nature, the drawing techniques, the computation and the application among the geometric figure spot, the line, the surface .It is one of the difficult content in mathematics teaching and studying. The reason mainly lies in that student often felt at a loss when face concrete question in the solid geometry study , the teacher how to change the teaching method also have many questions.The solid geometry's research is also gradually increasing, but what the former researcher and teacher pay more attention is the factors: spatial imagination ability, observation ability, the logical thinking ability. They pay less attention to the connectedness among the axiom, the theorem, the formula, the definition. Because the solid geometry involves a lot of axiom, theorem, definition and formula, we should consider the connectedness of the theorem, the formula etc, when we consider the influencing factor in which the question is solved successfully.This research mainly wants to examine the factors that influence solid geometry problem solving. We mainly pay great attention to examine the solid geometry knowledge connectedness'influence to the solid geometry question solution. This research carry on the contrast test between two groups students(the high-achieving students and the low-achieving students) using the method of establish examination paper from two dimension , the geometry content and the geometry knowledge connectedness, then carries on the statistical analysis to understand two group of students'differences in two dimension. The result shows that two groups of students do not have obvious difference in remembering and reminding geometry content, but they have obvious difference in the geometry knowledge organization quality or in geometry knowledge connectedness.Judging knowledge connectedness' method, we had the further understanding about cognitive structure's research condition and the research results through reading literature massively, on the basics of analyzing and using for reference the former studies, have made the improvement to its research technique and have established the suitable topic to examine student's geometry knowledge connectedness.This research's central content is to examine the relationship between the quality of the organization of the students'knowledge's and the solid geometry problem-solving performance. We report findings: The high-achieving students and low-achieving students have obvious difference in content indicators and connectedness indicators when they undertake the geometry duty. The high-achieving students'performance on the indicators of knowledge connectedness shows that, compared with the low-achieving students, they can retrieve more knowledge spontaneously and could activate more links among knowledge. Connectedness indicators are more influential than content indicators in differentiating the groups on the basis of their success in problem solving. The result shows simultaneously that the high-achieving students'knowledge organization condition is opposite compared with low-achieving students. And it shows the connectedness of geometry knowledge and the quality of the organization of geometry knowledge is the important influential factor attributing to solid geometry problem-solving performance.This research provides effective ways for high school teachers to gain information about the organizational quality of students'knowledge. And through gaining the information of the organizational quality of students'knowledge, we can improve teaching method and the strategy, and promote the formation of the students'good cognitive structure. Meanwhile it provide theory basis for the transformation of the teaching appraisal way and studying appraisal way. In solid geometry teaching, strengthening the teaching of knowledge connectedness including the axiom, the theorem, the definition, the formula and the graph, has important meaning to problem-solving ,and should be valued by researcher and educator .