On' Calculation Thinking Differences Between Upper Grades Yi Rural Primary Students

Calculation is an important aspect of math learning for primary school students, and the accuracy of calculation even makes great differences in students'math learning. Yi rural primary school students face more difficulties than urban counterparts in calculation. Till now, most research about calculation lie in the stage of simp presentation of calculation methods or skills. However, whilst not many research go deep into students'psychological level of use of calculation representation system, there are even fewerresearch on Yi rural primary students.Combined with Information Processing Theory, Situated Cognition and Learning Theory, this study looked into the calculation thinking differences among upper grade students of Yi rural primary school in making use of calculation representation system, and analyzed relative culture, concept and habits that may cause these differences. Specifically speaking, the following two main problems were focused on:(1) What's the calculation thinking mode of uppergrade students of Yi rural primary school?(2) How could Yi culture, mathematical problem resolve methods and learning habits affect calculation representation?This study went as following steps:(1) Sort out relative documents, and bring forward the categories, levels and codes of calculation representation.(2) Design questionnaires according to our research content, and choose suitable schools and students as subjects, then interview subjects based on the result of the survey.(3) Code the questionnaires. Analyze the collected data with quantitative methods and qualitative methods separately, processing these data with the help of SPSS. Analyze the information got in interview.As a result, this study found following features of calculation thinking mode of higher grade students of Yi rural primary school.(1) Basically, in higher grade students of Yi rural primary school, those who have humble performance tend to make use of physical and verbal calculation representations, while those who have good performance tend to make use of propositional calculation representations, such as relationship, formula, and even chart.(2)The frequently used calculation representations in higher grade students of Yi rural primary school are:verbal representation, concept representation and relationship representation. For the same question, nearly75%of students can use one calculation method, nearly15%of students can use two calculation methods, and approximately10%of students cannot find a way to work it out. They tend to make use of oral language and symbolic calculation representations only in reading mathe problem.Specifically shows in the following aspects:①For the arithmetic of integer, decimal and fraction, Yi primary students prefer to use rule. For example, there're rules of calculation sequence, formulas, and vertical. The difference between differently performed students is whether they can understand these three calculation representations properly.②When formulating, higher grade Yi rural primary students frequently use representation translation between language and calculation relationship, for instance, they may translate such terms and relationships as plus, minus, quotient... into corresponding operators.③Higher grade Yi rural primary students usually use more language representation than graphic representation when working on geometric calculation problems.④Higher grade Yi rural primary students tend to use language and when working on real-life situation calculation problems. Nearly80%of students apply relationship and symbolic representation to real-life situation, and5-grade students do better than6-grade students in this way.⑤When formulating to resolve application problems with complex relationships, higher grade Yi rural primary students frequently use language representation, visual representation and relationship representation, but their representations appear to be messy and lack of logic. There is no big difference within different grades.(3)The accuracy of answering shows significant positive correlation with the rationalness of calculation representation. That is to say, the answer accuracy of those who frequently use relation and graphic representation is higher than that of those who tend to use visual and language representation.(4) There is remarkable difference in mathematical computation thinking among three kinds of students---mathematics learning is excellent, good or difficult, and also among those in four types school.(5)The calculation representation of higher grade Yi rural primary students is affected by the language, national psychology, customs, religion, and family education of Yi-people. An explicit, reasonable conception and habit of math problem-solving can help Yi rural primary students get better calculation representation, and then get higher accuracy. Reverse is also true.All stated above, we put forward the following suggestions to enhance the calculating education of Yi rural primary schools:(ⅰ)Develop math course with Yi culture background under the guidance of the mathematics curriculum standards.(ⅱ)Promote math teaching in both Chinese and Yi-language.(ⅲ)To carry out calculation education based on the students' math study psychology.(ⅳ)Teachers should make efforts to improve Yi rural primary students'calculation representation, math problem-solving concept, learning habits when teaching calculation.①Show students the process of calculation representation, and concern about the mutual conversion between the different representations.②Come up with particular ways to resolve the problem of Chinese understanding and lacking of long-term attention and interesting of Yi rural primary students.(ⅴ)When learning calculation, Yi students should also try to enhance their own language ability, calculation representation, math problem-solving concept and learning habits.(ⅵ)Consider national culture, regional differences into math teacher training.