Research On The Teaching Of Mathematical Concepts Based On The Implementation Of Logical Reasoning Literacy

Logical reasoning is an important way to obtain mathematical conclusions and construct a mathematical system.Therefore,logical reasoning literacy has always been the focus of educational research.However,most of these studies are based on proposition teaching and problem solving teaching,and ignore the implementation of logical reasoning literacy in concept teaching.Therefore,in order to perfect the study of logical reasoning literacy in teaching,the theme of this paper is established as: the teaching research of mathematical concepts based on the implementation of logical reasoning literacy.First of all,based on the 2017 version of General High School Mathematics Curriculum Standard,combined with existing theoretical research,this article proposes that logical reasoning literacy consists of three parts: logical reasoning knowledge,logical reasoning application and logical reasoning ability.Logical reasoning knowledge is the tool for logical reasoning literacy,logical reasoning application is the most direct reflection of logical reasoning literacy,and logical reasoning ability is the core of logical reasoning literacy.Secondly,because the goal and focus of logical reasoning literacy training are different in each stage of concept teaching,the specific manifestations of logical reasoning literacy in concept teaching are studied in stages:(1)In the concept acquisition stage,the manifestation of mastering the logical reasoning methods is: using different logical reasoning methods explore the formation of concepts;the manifestation of mastering the logical principles followed by the definition,and forming the expression ability is: forming an accurate and concise definition.(2)In the concept deepening stage,the manifestation of forming the judgment ability is: judging the type of concepts;the manifestation of forming the analysis ability is: constructing a conceptual system;the manifestation of forming the argument ability is: establishing an equivalence relationship between multiple representations of concepts;the manifestation of forming the reasoning ability is: deriving relevant properties from the concept.(3)In the concept application stage,the manifestation of logical reasoning application in the process of discovering problems is: discerning concepts;the manifestation of logical reasoning application in the process of solving problems is: decomposing mathematical concepts into sequential programs to solve problems;the manifestation of forming innovative ability in the process of logical reasoning application is: flexible application of concept.The above manifestations,on the one hand,illustrate that concept teaching is an important way to implement logical reasoning literacy.On the other hand,it determines the direction for implementing the specific components of logical reasoning literacy in concept teaching.Aiming at the manifestation of logical reasoning literacy in concept teaching,this article proposes corresponding teaching strategies to promote the development of different components of logical reasoning literacy:(1)creating effective mathematical situations to master the logical reasoning methods;(2)guiding students to experience the recreation of mathematical concepts to form accurate and concise definitions;(3)attaching importance to the multiple representations of mathematical concepts to improve logical reasoning ability;(4)organizing variant training to promote concept recognition;(5)applying meta-cognitive strategies to form a structured thinking habit;(6)set up the open problem situations to comprehensively improve logical reasoning literacy.Finally,based on the teaching strategy research of this article,three cases of conceptual teaching are designed,which illustrate the implementation methods of logical reasoning literacy in the new teaching classes and review classes.These three cases reflect the teaching strategies constructed in this article,and promote the development of logical reasoning literacy in concept teaching.