Research On Mathematical Modeling Process Under Different Task Situations And Cooperation Ways

Mathematical modeling is a bridge connecting the mathematical world and the real world,and it is the foundation and prerequisite for cultivating students' core literacy.academic attention.Through literature review,there are few studies to analyze the mathematical modeling process of students from the perspective of cognition,the task situation lacks "reality",and it is easy to ignore the mutual influence between peers.To this end,from the perspective of "metacognitive modeling",this study takes Blum's seven-stage modeling cycle as a theoretical framework,combined with the adjusted Maa? coding category table,through qualitative and quantitative combination of two Research,which collects and analyzes empirical data from 60 students to explore the mathematical modeling process students experience in different task contexts and collaborative styles.Study 1 used a three-factor mixed design,the between-group factors were mathematical modeling experience(yes/no)and gender(male/female),and the withingroup factor was task context(personal/social).Coding materials such as thinking aloud reports and task lists of 24 students in two mathematical modeling tasks,reconstructed48 personal modeling roadmaps,and analyzed the modeling roadmaps from the three dimensions of thinking,structure and sequence.Analyze,compare and categorize.The results show that:(1)The actual individual independent modeling process is consistent with Blum's seven-stage modeling cycle in idea,but there are differences in structure and sequence.(2)According to three dimensions,students' mathematical modeling thinking can be divided into three categories: novice,quasi-expert and expert.(3)Through chi-square test and multiple regression,mathematical modeling experience and task context have a significant impact on the type of mathematical modeling process,but gender has no significant impact.Study 2 adopted a single-factor mixed design,the between-group factor was the cooperation method(high-high,high-low,low-low),and the within-group factor was the mathematical modeling level(high,low).On the basis of Study 1,according to the mathematical modeling level,36 students were divided into focus groups of high-high,high-low,low-low,etc.,to explore the similarities and differences between group cooperative modeling and individual independent modeling and group cooperation The effect of patterns on the mathematical modeling process.The results show that:(1)Group cooperation and individual independent modeling are similar in thinking,structure and sequence.(2)The repeatability of individual independent modeling has the characteristic that the total number decreases or stays the same as the sequence of stages increases;the repeatability of group cooperative modeling increases with the sequence of stages and the total number increases relatively.In conclusion,this study deeply analyzes the cognitive characteristics and difficulties of students in the process of mathematical modeling,enriches the research on differences between individuals and groups in mathematical modeling,and helps to improve the teaching and training of mathematical modeling.