| With the advent of the era of national innovation,in order to meet the needs of the development of Socialism with Chinese Characteristics in the new era,training builders and successors with high mathematical literacy,innovative consciousness and modeling practice ability has become the goal of mathematics education in senior high schools in China.As the core accomplishment of general high school mathematics curriculum,cultivating students’ mathematical modeling ability has become the theme of a new round of mathematics curriculum.A number of studies have found that senior high school students have insufficient understanding of mathematical models and the nature of mathematical modeling,and their mathematical modeling ability needs to be improved.It is the basis of cultivating students’ ability of mathematical modeling to clarify the influencing factors of mathematical modeling ability.Therefore,the research discusses the internal influencing factors of mathematical modeling ability and the cultivation of students’ modeling ability.These resluts have theoretical and practical significance for the developing students’ mathematics core literacy.This study focuses on the internal influencing factors of mathematical modeling ability and the cultivation strategy of mathematical modeling ability.There include three problems:The first problem is to analyze the internal influencing factors of mathematical modeling.The second problem is to analyze the relationship between the influencing factors and the mathematical modeling level on the basis of investigating the current situation of the mathematical modeling level of senior high school students.The third problem is to put forward the teaching strategy to cultivate the mathematical modeling ability of senior high school students.In view of the first problem,Grounded Theory was used to find the internal influencing factor model of mathematical modeling,and the reliability of the model was tested by the knowledge graph.The specific steps are as follows.In the first step,those quotations of 19 college and high school students in the modeling were transcribed into the interview texts by oral reporting method,and the three-level coding was carried out.A total of 1308 data fragments were found,the researchers coded it into 19 categories,including anxiety,mathematical modeling efficacy,attitude toward mathematics,confidence,interest,tenacity,background knowledge,knowledge of mathematical modeling,mathematical knowledge,innovation ability,migration ability,reasoning ability,monitoring,testing,reflection,planning,cognition,strategy and task.The second step,according to the definition of categories,the relationship between categories was established,and the 19 categories were combined into9 main categories,namely,emotion,attitude,interest,will,cognitive structure,basic ability,metacognitive monitoring,metacognitive experience,and metacognitive knowledge.The third step is to systematically analyze the 9 main categories and extract three core categories with centrality and explanatory power,namely,non-intellectual factor,cognitive factor and metacognitive factor.In short,the internal influencing factors of mathematical modeling were obtained.The fourth step,with the knowledge graph,the research focus of scholars in the study of influencing factors of mathematical modeling is explored.On this basis,the co-word matrix is constructed,and the common factors are obtained by factor analysis,which are basic ability,core ability,Non-intelligence Factor,knowledge expanding and model knowledge.Thus,the reliability of the conclusions obtained from qualitative analysis is verified.Therefore,this study constructs the theoretical framework of the internal influencing factors of mathematical modeling.In view of the second problem,the current situation of mathematical modeling level and the influencing factors obtained above of senior high school students was investigated,and the relationship between them was studied.Through the questionnaire and test questions for the senior high school students,the relevant data of the current situation of the mathematical modeling level and the influencing factors of mathematical modeling are collected,and these data are quantitatively analyzed.The first step is descriptive statistics.It is found that students have good performance in modeling,but there are some problems in solving problems and model verification.The second step is correlation analysis.Spearman correlation analysis was used to explore the correlation between the influencing factors and the level of mathematical modeling.It is found that there was a significant correlation between students’ life common sense,creativity level,mathematical metacognition level,scientific reasoning ability,non-intellectual characteristics of mathematics learning,students’ academic performance and the level of mathematical modeling.The third step is decision tree model.The random forest model was used to explore the effects of various influencing factors on the level of mathematical modeling.The prediction success rate of random forest model was 67%,and the cognitive factors of students were the most important among many influencing factors.The fourth step,analysis of variance.Through analysis of variance and mean comparison,it is found that students with high level of mathematical modeling have higher scores than those with low level of mathematical modeling except self-efficacy.Based on the above analysis,this study found that the internal influencing factors of students’ mathematical modeling were significantly correlated with their mathematical modeling ability.The cognitive factor is the most important factor in mathematical modeling.The scores of students with high level mathematical modeling were better than those of low level students in many influencing factors.In view of the third problem,according to the results of descriptive statistical analysis,Spearman analysis,random forest model and variance analysis,the teaching strategies are proposed from four aspects: cognition,metacognition,non-intelligence factors and evaluation. |
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