Construction Of The Learning Progression Model Of Proportional Reasoning For Primary School Students

The concept of “learning progression” refers to the development process of students' understanding of some core concepts in a long time span.In recent years,China has also started to pay attention to the application of "learning progression" in education area,but the study of learning progression in the mathematics teaching is still in its infancy.Proportional reasoning is a very important concept in the elementary school mathematics.In order to build a learning progression model of proportional reasoning for primary school students,the following four research questions are proposed:(1)What are the hypothetical learning progression model and test questions for proportional reasoning?(2)How to revise and verify the hypothetical learning progression model of proportional reasoning?(3)What is the learning progression model of proportional reasoning after optimization?(4)What is the distribution of primary school students in the learning progression model of proportional reasoning?In this study,630 elementary school students were selected as the research objects to build a learning progression model of proportional reasoning for primary school students,and the distribution of primary school students in this model was analyzed based on the research results.The research is mainly divided into the following four steps:First,based on existing research,literature analysis and questionnaire are used to select progress variables.The hypothetical progress levels are composed according to the progress variables to perform the hypothetical learning progression model.Prediction questionnaire is used to simplify the progress variables,optimizing the hypothetical learning progression model of proportional reasoning for primary school students.Second,develop test papers by compiling test questions based on the hypothetical learning progression model and its corresponding progress levels.Then,research data are obtained by summarizing individual interview and questionnaires.SPSS and Winsteps software are used to perform the difference test and the Rasch model calculation,which can help revise and verify the hypothetical learning progression model of proportional reasoning.Finally,according to the results of the study,the distribution of primary school students' learning progression model in proportional reasoning is obtained.Analysis of the distribution includes the following three aspects:(1)Study the specific learning performance and distribution of primary school students in the learning progression model of proportional reasoning.(2)Analyze the distribution of the progress levels of students in different grades in the learning progression model of proportional reasoning.(3)The progress level of the progress variables is obtained according to the score rate and the Rasch model.The following conclusions are obtained through research:(1)A set of test papers is developed to measure the proportional reasoning ability for pupils.(2)A learning progression model of proportional reasoning for primary school students is constructed,which contains seven progress levels.(3)Analyze the distribution of primary school students in the learning progression model of proportional reasoning.Primary school students' ability of proportional reasoning is gradually progressing from a low level to a high level as students' grades go up.According to the analysis,juniors are mainly at level 4 and the seniors are mainly at level 7.Through research,the following suggestions are provided for the preparation of curriculum standards and teaching materials,instructional design and subsequent study of learning progression:(1)Improve the content of the proportional reasoning and adjust the order in the curriculum standards and textbooks.(2)In the teaching design,the progress levels of the proportional reasoning should be matched.Cultivation of the ability of proportional reasoning should be focused on.(3)In subsequent researches,add more progress variables to supplement the progression model,develop diversified evaluation questions and evaluation standards,and use longitudinal tracking research method.