A Study On Exploring The Students' Problem Posing And Problem Solving Of Average Algorithm

With the progress of science and technology and the development of the era of big data,the thought and method of statistics have become the essential basic knowledge of citizens' production and life.In the stage of compulsory education,it has become a hot topic to emphasize the development of students' data analysis,to strengthen statistical education and to carry out statistical teaching reasonably.Average,as an important statistical concept in primary school,requires students not only to use the average algorithm to deal with complex problems flexibly,but also to understand the meaning and role of the average,which plays a very basic and important role in the subsequent statistical learning of students.Problem solving has always been the core content and important goal of curriculum reform in various countries.Recently,as a teaching method and learning method,problem solving has attracted more and more attention in the world.The research on the relationship between students' problem presentation and problem solving performance and the relationship between them is helpful to understand the thinking process of students' learning and understanding,to help teachers make targeted teaching improvements,to promote the optimization of classroom teaching,and to promote the development of students' cognitive and non-cognitive abilities.Therefore,this study focuses on three research questions :(1)what is the general performance of elementary school students' problem raising and problem solving on the "average" of mathematical knowledge?(2)is there any difference in the "average" problem presentation and problem solving among primary school students in different regions?(3)what is the internal relation between the problem presentation performance and problem solving performance of pupils on the "average" of mathematical knowledge?Aiming at the research problem,this research mainly adopts the literature analysis method,the investigation method,the content analysis method,the statistical analysis method and so on.Through the analysis of the literature concept of average elementary school type(arithmetic conceptual understanding of conceptual understanding and statistics),as well as problems and problem solving after the connotation of value,selection of high reliability in past authoritative research 4 average test topics as a measurement tool,develop the "problems" and "problem solving" 2 sets of test paper.Subsequently,the measurement tool was tested,and after the final test paper was determined,301 students from 8 urban and rural primary schools in 4 districts and counties in chongqing and sichuan were investigated and data were collected.According to the theoretical research and students' actual performance,the author codes and analyzes the rationality,expansibility and content nature of the questions raised by students,as well as the accuracy of problem solving,problem-solving strategies and the perspective of representational mode.In view of the three research questions in this study,the following conclusions are drawn:According to a study by the study found that the student's overall performance on problem put forward:(1)in terms of problems the rationality of the proposed,students situation in task 1,2,4 items(hat problem,score problem cub problem)per capita under the rationality of two or more questions,but on the topic "problem" jack 3 per capita is only 1.25 rationality question,in addition,the ascension,as the difficulty to request the number of students put forward the rationality problem in falling;(2)in terms of the extensibility of questions raised by students,the vast majority of the rationality questions raised by students are non-extensibility questions(over 76%),among which "score question" and "cub question" account for over 95%.(3)in terms of problem put forward the content of the nature,the students put forward problems in each question at a number of different types and their distribution,put forward the issue of the average student more than the average students,this problem is but the claims of "more difficult"(P3)issues,put forward the issue of average students accounted for more than,and students in the same concept on the types of tasks,the nature of the questions.The overall performance of students in problem solving is as follows :(1)in terms of the accuracy of problem solving,students' mastery of conceptual understanding of average arithmetic(3.81)is obviously superior to their level of conceptual understanding of average statistics(2.09);(2)in the problem solving strategies,students in the title ofarithmetic average conceptual understanding(1,2)the chosen problem solving strategy similar to the 3 questions students prefer to use "divide matching" and "trial-and-error" according to the total problem-solving strategies,number 4 only about half of all students to use the correct judgment "average" strategy;(3)in terms of representation model,while the students in different types of selection of characterization model is different in the title,but the students are in the title of the concept of average is more adept at using arithmetic representation,for example,nearly 99% of the students in the arithmetic representation in 1,2,and more than half of the students in question 3 and 4(both conceptual understanding of the topic for the average statistics)on also chose the representation mode(55.4%,72.0%).In view of the research question 2,through the study found that students' performance on problem is put forward for different regions:(1)in terms of problems the rationality of the proposed,the rationality of the urban students question number(M= 8.32)than rural students(M = 7.96)is a bit more,but there was no statistically significant difference,and in the number 4 on the rationality of the proposed problem for students in different regions has significant difference(t = 2.549,p < 0.01);(2)in terms of the extensibility of the question raised,most of the questions raised by urban students and rural students are non-extensibility problems,showing similar performance;(3)in terms of the content and nature of questions raised,in general,although both urban and rural students are more inclined to raise "sum" type of questions,the distribution of content and nature of questions raised by students on different test questions is different,and there are statistically significant differences.The performance of students in different regions on problem solving is as follows :(1)in terms of the accuracy of problem solving,compared with the performance on conceptual understanding of average statistics,the performance of urban and rural students on conceptual understanding of average arithmetic is better,but on the whole,the performance of urban students is obviously better than that of rural students.(2)in terms of problem-solving strategies,the strategy choices of urban and rural students on questions 1 and 2 are similar,but there is a significant difference in the correct problem-solving strategies on questions 3 and 4(c2=13.174,p<0.01;Z =2.31,p<0.05),and in the third question,urban students are more able to choose the correct strategy;(3)in terms of the representational pattern,both urban and rural students have similar representational choices on questions 1,2 and 4,and are good at using arithmetic representation,but there are significant differences in the representational patternchoices on question 3.According to the research question 3,it is found that :(1)comparing the students with the top 10% of the total score and the students with the bottom 10% of the total score,the rationality of the question put forward is significantly correlated with the accuracy of the problem solving in a statistical sense,that is,the students with high accuracy of the problem solving can also put forward more reasonable questions;(2)students who can put forward statistical conceptual understanding problems(that is,students with higher thinking level)are different from other students in the selection of problem-solving strategies and representational modes,and they are more able to choose the correct problem-solving strategies.Through this study for students in math and problem solving performance on "average" problems of investigation and study,using the same mathematical structure and context,details about the whole situation of students about the average concept understanding,thinking,and to explore the problem of student performance and problem solving performance of inner link,pertinence of teachers teaching and improving teaching methods,improve classroom teaching quality has certain help.According to the results of this study,three Suggestions are put forward :(1)to improve students' understanding of the concept of statistical significance of averages,and to conduct statistical teaching in combination with the real situation;(2)using teaching methods to improve classroom teaching and improve the quality of classroom teaching;(3)continue to strengthen the quality of rural education to ensure rural education resources,so as to improve rural teaching.