Research On Proportional Reasoning Ability Of Sixth Grade Students In Kashgar Area

The standard for mathematics of full-time compulsory education clearly propose that students' reasoning ability should be taken as the core qualityProportional reasoning is an important thinking process that uses algebraic methods to solve proportional problems.The knowledge of "ratio and proportion"runs through the entire compulsory education stage,and finally develop into a proportional and inverse proportional function.The process is extremely important,in which students form a proportional concept and do proportional reasoning.The Kashgar region is located in the southern part of Xinjiang.It is part of education poverty alleviation.The education foundation is weak and the students' mathematics academic performance is not good.Have the student mastered the relevant concepts of proportionality?And which level are the proportional reasoning ability of students in?The test questions of meta-analogical awareness and routine proportionality are formulated in accordance with the dimension division of proportional reasoning test questions from Modestina Modestou and Athanasios Gagatsis,and the questions make appropriate adjustments according to the implementation of the test volume.The type of problem includes contrast problem and missing value problem.This study investigated the grade six students' performance of proportional reasoning in Kashgar,including the level of proportional reasoning and strategies for solving proportional problems.Participants were selected from different gender,schools,and teaching model through stratified sampling and simple random sampling.The study explored the factors affecting the students' proportional reasoning ability from three perspectives by statistical software SPSS that is used to analyze the difference among the different groups'ability.The research mainly get the following conclusions,after data statistics and analysis:Firstly,in routine proportionality,there are significant differences between contrast problem and missing value problem both in the highest level and the lowest level.And in meta-analogical awareness,there are significant differences between contrast problem and missing value problem in the highest level.However,problem situations and task types have different degrees of influence on students' solution to proportional reasoning.Secondly,in the routine proportionality,none of the three factors discussed in this paper have a significant impact on the results of the questions;in the meta-analogical awareness of proportional reasoning,gender,school and teaching mode all have certain influence on the level of students' reasoning ability.Overall,boys are less complete than girls in proportional reasoning,but the number of boys reaching the multi-level structure level and above accounts for more girls.The ability of students from urban schools is stronger than the students from rural schools,which indicates that teaching resources have a certain influence on the development of students' proportional reasoning ability.The students whose learning language is Mandarin has stronger ability to reason proportions than the students whose learning language is Uighur.The students want to express his method by his language in Uighur,which is not found in the Mandarin paper.Explain that students are more willing to use their familiar language in trying to reason,which gives advice on the setting of teaching mode.Thirdly,the student's answer to the question mainly includes two major strategies:the collection strategy and the double compound strategy.There is no common factor method and the public multiple method in the two categories.The formula method and the multiple method are the most used.The students are more willing to use the internal ratio strategy of formula method than external ratio strategy.The common unit price ratio strategy is less than.It can be indicated that students do not fully understand the meaning of the four quantities in the conventional proportional reasoning,because the main type of error in students'conventional proportional reasoning is that they are accustomed to comparing absolute quantities and only consider them as numbers rather than quantities.The students have lower ability to express the concept of self-distribution and to reason in the meta-awareness problem of proportional reasoning.Finally,combined with the conclusions drawn from this study,this paper proposes local teachers to cultivate students' proportional reasoning ability in Kashgar.