| As one of the six core competencies of mathematics,mathematical modeling has been widely adopted to a variety of fields of the society,fostering students' mathematical modeling competencies,as well as improving their abilities of observation,abstract summary,problem exploration,imagination,logical thinking,calculation,operation,practice and creativity,etc.Starting with definitions of some core concepts,the article states the evaluation theory,influencing factors,and fostering theory of senior high school students' mathematical modeling competencies;then it introduces the current situation of mathematical modeling teaching competitions among several senior high schools home and abroad;thereafter through conducting surveys on a number of senior high school students of their mathematical modeling recognition levels,it reaches the conclusion that,though appealed,those senior high school students lack both self-teaching ability and related necessary mathematical modeling knowledge.The author has performed a series of experiments: selectively interviewing parts of senior high school teachers to comprehend how mathematical modeling or application in mathematical teaching and practicing were carried out in class,school and society;meanwhile testing how well parts of senior high school Grade 1 students applied their mathematical modeling competencies,followed by a two-month-anda half control experiment to finally determine that after being trained in different ways of mathematical modeling,the participants have gained apparent development on average,therefore concluding that two major factors influence senior high school students' mathematical modeling core competencies: the inner interest of students and the outer guidance from teachers.In the Chapter of Fostering Strategy,the major current problems are summarized as the deviation of teachers' cognition towards mathematical modeling,the current educational evaluation system which fails to support teachers' related experiments,lack of knowledge and relevant resources,and the College Entrance Examination,“the baton”,which directs both teachers and students away from study on mathematical modeling;then it comes up with fostering strategies: during the preparation period,teachers should equip students well as to select appropriate mathematical modeling problems,understand why it is of great significance,meet the basic requirements,and experience the macro and the micro process searching for and confirming a subject;during the presumption and modeling period,teachers should focus on students' development on non-intelligence factors,the educational value of mathematical modeling,students' sense of success and teamwork through experience,as well as the first step that students are “forced” to make in a way of maximizing their advantages and minimizing their disadvantages,shaping their characteristics,and finding their talents;during the problem-solving period,teachers should assist students to select mathematical modeling problems of acceptable complex and depth;during the analysis/test and application period,teachers should perfect the evaluation system so as to encourage students to innovate;during the routine class period,teachers should take some effective measures to arouse students' interest and motivation on learning mathematics,establish creative problem situations,involve students into such situations full of suspense,challenges,and inspirations attracting students to attempt bravely and deduct carefully,meanwhile teachers are to concretely develop students' interest in mathematical modeling,pick out appropriate materials allowing arguments for students of individual background,and give way for students' simultaneous performances.Herein a diversity of exercises are required combining simple problems to preserve students' confidence and challengeable ones for students' joys to fight,besides,the problems should also be arguable for prompt ideas and flexible in digging out the beauty of mathematics. |
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