Unary One-dimensional Inequality Learning Advanced Research

The 14 th Five-Year Plan proposes to build a high-quality education system through deepening reform and comprehensively promote quality education to satisfy the requirement of talents from all sectors of society in the new century.Combined with the new curriculum reform,in order to correctly deal with the problem of the connection of knowledge with a certain mathematical concept as the core,educators should train students to look at learning from the most basic and original mathematical knowledge and from the perspective of connection and development.Students should pay attention to the overall construction of concepts and learn how to explore advanced knowledge according to the existing foundation,and master the ability of lifelong learning.Progression learning advocates that students’ thinking,understanding and practice of core concepts should change from simple to complex,from low level to high level,from quantitative change to qualitative change,and constantly deepen and enrich,so that they can master the basic knowledge and skills of the system and look at learning from the perspective of linkage and development.In addition,learning progression also attaches importance to the overall construction of core concepts and the cultivation of students’ ability to explore higher-order knowledge based on existing foundations.At this stage,most studies on progression learning focus on which stage students are in and how to construct each stage according to the learning content,but few construct progression learning and design effective teaching design from the improvement of students’ perception,understanding,demonstration and application ability.Studying the textbook of the second volume of The Seventh Grade Mathematics which is compiled by People’s Education Press for compulsory education,and the New Mathematics’ Curriculum Standards for Primary and Junior Middle School which is edited in 2021,we learn that it divides the teaching of the unary inequality into three dimensions: The origin of knowledge(perceive,express unary inequality),problem solving(simple solution,including parentheses,including the denominator unary inequality),value(expand the unary inequality from each dimension),and redesign the advanced learning of the core knowledge combined with6 case analysis.At last,used SPSS and Winsteps software to analyze the validity of the corresponding tests.Conclusions: Based on the triangle evaluation model of learning progression,Berkeley evaluation model and structure-centered design method,the advanced teaching of "Unitary inequality" is developed.Through teaching practice,it is concluded that: 1.The progression learning can improve students’ ability to solve higher and more complex problems by cultivating their transfer ability;2.From the simple concept construction of learning progress,it can help students understand the concept from simple to continuous refinement,so as to use the basis to analyze higher-order problems;3.Reverse construction can solve the problem of students’ fault knowledge effectively and make logical thinking more coherent;4.Although learning progression can improve the learning ability of students with medium or above ability level,it has little effect on students with low ability.