Some Researches On The Teaching And Examination Of Selected Lectures On Inequality

In the General High School Mathematics Curricular Standards (Experimental)(Hereinafter referred to as Curriculum Standards), the contents of inequality are divided into two sections. The first section is included into the Chapter3Inequality of Compulsory Modular Math5, while the second section is incorporated into Special Topic5-Selected Lectures on Inequality in Elective Series4.Inequality is mainly based on the basic knowledge of inequality and focuses on the concept and nature of inequality, and the essential thought and methodology concerning dealing with inequality problems.Selected Lectures on Inequality emphasizes the actual background of inequality, geometrical significance, and practical applications, places much importance on the learning of mathematical methodology, and uses inequality as a mathematical tool to portray the unequal relationships in the real world and as a mathematical model to describe optimized questions. This significantly increases students’understanding of the mathematical nature of these inequalities and enhances their reasoning skills, logical thinking skills, and problem analyzing and solving skills. Therefore, it’s necessary to study the contents of Selected Lectures on Inequality.On the basis of the understanding above, the compulsory section of Inequality and the elective section Selected Lectures on Inequality are of equal significance and value of learning. In other words, sufficient attachment of importance to the learning of Selected Lectures on Inequality is necessary as well as essential.In light of the teaching and tests of Selected Lectures on Inequality, the present study is primarily focused on the following areas:1. Four problems related to the teaching and tests of Selected Lectures on Inequality are presented and solutions are proposed grounded on the interviews of the teachers from the school, the author’s teaching practice and a review of the tests of Selected Lectures on Inequality.2. Corresponding teaching recommendations and teaching designs befitting the characteristics of the students at the school are presented based upon an in-depth understanding and analysis of the teaching contents, objectives and difficult points of Selected Lectures on Inequality, in view of a combination of Curriculum Standards and the College Entrance Examination Syllabus.3. The notion of "including selected tests into compulsory tests" is put forward on the basis of the questionnaires for high school mathematics teachers in Fujian Province and the College Entrance Examinations in recent years. The necessity and feasibility of this notion is analyzed and its foundation is identified:to reflect its nature as a tool while conducting case studies.Lastly, a few questions requiring further in-depth research are presented.