Senior high school students’ understanding of mathematical inequality

Mathematics inequality is an essential concept that students should fully understand since it is required in mathematical modeling and linear programming. However, students tend to perceive the solution of the inequalities problem without considering what the solution of inequality means. This study aims to describe students’ mistakes variations in solving mathematical inequality. It is necessary since solving inequality is a necessity for students to solve everyday problems modeled in mathematics. Thirty-eight female and male students of 12th-grade who have studied inequalities are involved in this study. They are given three inequality problems which are designed to find out students’ mistakes related to the change of inequality sign, determine the solution, and involve absolute value. All student work documents were analyzed for errors and misconceptions that emerged and then categorized based on the type of error, namely errors in applying inequality rules, errors in algebraic operations, or errors in determining the solution set, then described. The result shows that there were some errors and misconceptions that students made caused by still bringing the concept of equality when solving the inequalities problem. It made them did not aware of the inequality sign. Students are still less thorough in operating algebra and do not understand the number line concept in solving inequalities. The other factor was giving “fast strategy” to the students without considering the students’ understanding.

Generalizations of Hardy's Integral Inequality

SynopsisExtensions of the integral version of Hardy's Inequality were given by Kadlec and Kufner (1967) and by Copson (1976). This paper provides several levels of further generalization of their results, obtained mostly by specializing four main inequalities. Most of the inequalities have the form ∥Kf∥ ≤ C ∥f∥, where K is an integral transform and ∥.∥ is a generalized Lp-norm; some have the inequality sign reversed. Best possible constants C are obtained in several cases, under mild extra hypotheses.