| With the development of society and education,the Compulsory Education Mathematics Curriculum Standards,which is published in 2011,regards the model thinking as one of the ten core qualities of primary mathematics for the first time.At the same time,as one of the basic ideas of mathematics,model thinking plays an important role in both the development of students’ mathematical thinking,and the cultivation of mathematical ability.Based on the steps of cultivating model thinking,“problem situation,model establishment,solution verification” in Compulsory Education Mathematics Curriculum Standard(2011),with the classification of primary school mathematical models proposed by Ningzhong Shi—the Total Model,the Tree Planting Model,the Engineering Model and the Distance Model being the research dimensions,this project studies the current situation of mathematical thinking cultivation in upper primary class,taking 4-to-6-grade 20 mathematics teachers and 300 students from an urban elementary school a rural one in S District of Chongqing as research objectives.From the perspective of model thinking cultivation and thinking development of upper grades in elementary schools,the thesis,which is directed by Constructive Learning Theory,Scaffolding Teaching Theory,and Mathematical Model Theory,analyzes the current situation of model thinking cultivation from teaching content,teaching goals,teaching design,teaching implementation,to teaching effects.Taking the three steps—problem situation,model building,and solution verification—as the horizontal axis,and the five models—Total Model,Tree Planting Model,Engineering Model,Route Model,and Equation Model—as the vertical axis,the author observes the infusion of model thinking in 20 lessons in the 2 primary schools,and analyzes those 20 teaching designs from teaching objectives,teaching process,teaching difficulties,to some other dimensions.Centering on the four dimensions,cognitive identity,training status,training problems and training strategies,after-class interviews for the 20 teachers are hold to learn the current situation of the cultivation of pupils’ mathematical model thinking.Lastly,the five modals,Total Model,Tree Planting Model,Engineering Model,Route Model and Equation Model,are used as dimensions to test the effect of model thinking training on 300 students.The survey finds that,during the process of cultivating students’ mathematical model thoughts,the scaffold based on the latest developing areas of students and the problem situations set are closely related to the real life of students,and can correctly guide students to seek solution and verification.Meanwhile,the following problems also exist: firstly,teachers are not sure about the infiltration of model thoughts,thus the combination with the content of teaching materials is not enough;next,teachers do not fully grasp the training goals of model thoughts,causing the unbalance in teaching design;moreover,the teaching methods for model thoughts are not effective enough,therefore,students can not apply them well;last but not least,it is difficult for students to extract effective information,which leads to difficulties in model construction.The main reasons for these problems are teachers’ lack of core competence to implement model teaching effectively,students’ scarce problem presentation ability,and schools’ weak cultural atmosphere of mathematical model thinking.Based on the above problems,following strategies are raised to improve teaching: first,teachers should improve their mathematics cultural literacy,deeply understand the teaching goals of model thinking,study the curriculum standards carefully,clarify the connotation and goals of the model,delve into high-quality modeling class examples,and communicate the teaching modes and methods of model thinking with each other;secondly,teachers should improve the teaching ability of model thinking,and enrich the teaching processes of model thinking,from refining mathematical problems in problem situations,perceiving the model initially,making good use of teaching strategies in the processes of model building,building the model accurately,to emphasizing the diversity of problems and flexibly understanding the model during the process of solving and verifying;thirdly,students should be trained to extract mathematical information effectively and develop problem representation ability;lastly,the school should create a strong mathematical cultural atmosphere,construct a mathematical model learning community,carry out teaching training and discussion of model thinking,establish the platform for teaching research cooperation,and regularly conduct extracurricular activities for mathematical modeling to increase students’ interest in it. |
