Research Of How Students Solve Inequalities And Handicap In Grade 10 And 11

There are two basic relations of quantity in the real world: the relation of inequality and the relation of equality. Inequality is the mathematical modeling of the relation of inequality. It is an important part in mathematics study. The solving of inequalities has close relations with functions, equations, sequences, trigonometry, linear programming, solid geometry and analytic geometry. On the one hand, though the solving of inequalities is not an important part in the senior high school mathematics, it is of great importance in the teaching of mathematics due to its basal and instrumental functions; on the other hand, teachers often pay much attention on how to solve inequalities and the common methods of solving inequalities rather than how students solve inequalities, what difficulties they might have and the correlation to the students' gender and the grade. This article is based on a study of how students solve inequalities in grade 10 and 11.Three main conclusions are drawn in the article through the investigations and interviews on how the students solve linear, quadratic, rational and radical inequalities: 1, students mainly use three ways of solving algebraic inequalities, solving by algebraic manipulations, sketching graphs, using the number line. While most of the students use algebraic manipulations, some adopted the method of using the number line, and still some few solve by sketching the graphs. In solving quadratic and rational inequalities, students achieve high rate of correctness by using graphics. In solving quadratic inequalities, higher rate of correctness is achieved by using algebraic manipulations than by using the number line. In solving rational inequalities, using the number line yields a higher correctness rate than using algebraic manipulations. 2, Students have difficulties in the following five aspects in solving inequalities: (1) excluded values, (2) the choice of logic connectives, (3) judging signs of the factors of products/quotients, (4) the transformation between radical inequalities and rational inequalities (5), analogy of inequalities to equations. The study reveals that the percentage of difficulties met in excluded values is the highest, less higher is the difficulties met in analogy of inequalities to equations and difficulties met in the choices of logical connectives. 3. The conclusions drawn from comparing the students' gender and grades are: (1) boy and girl students have their own advantages in solving algebraic inequalities, there are no obvious differences in the methods chosen, the correctness of the methods and the kinds of difficulties met according to the statistics. (2) Students in grade 10 obviously do well than those ingrade 11 in solving algebraic inequalities, and meanwhile, they adopted more balanced methods according to the statistics. And in Grade 10, the percentage ofstudents who met with various difficulties is also lower than that of the Grade 11.In the end of the article, the author here makes some suggestions on how to solve the inequalities in teaching students.