Inequalities

When sums and dierences with a variable component are compared with a fixed number, simple inequalities suitable for solving in the set N of natural numbers are obtained. Solving of these inequalities bases upon the properties of such expressions to increase or decrease, depending on the change of values of their compo- nents. To establish the meaning of an inequality, children have to be stimulated to see it as a representation of a whole set of numerical relations, some of which are true and some false. Then, the search for those values of the variable component for which these relations are true is the procedure of solving an inequality. Thinking of prerequisite knowledge and skills for this procedure, some exercises have to be planed that will help children assimilate the meaning of some operative terms: expression, value of an expression, to take value, etc., as well as to instruct them in using first set-theoretical notations properly. Not counting general observations, the en...

2015

The study tries to analyze the students’ difficulties and explore the errors done by the students when finding solution sets for inequalities. For these purpose a test was given to college of natural and computational science students who have taken calculus I or applied mathematics I course in Dilla University, Ethiopia. The results showed that the students are not successful in solving inequalities. The mostly observed mistake was to multiply both sides of inequality by expression that includes variable without paying attention to the sign of this expression. Moreover, significant number of procedural and technical errors is made by the students.

Jurnal Elemen

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 o...

We remark on the teaching of linear inequalities in the pedagogic situations of schooling, reflecting on the treatment of the topic in a popular grade 10 textbook, in an example of classroom teaching of inequalities to Grade 10 students, and in an example of a grade 10 student’s work on inequalities in a mid-year examination. What we find is that schooling uses a trio of implicitly-defined operations for working on the inequality symbols in expressions. Those operations are auxiliary to the operations described in the field axioms for the reals. We speculate that the production of such operations is a pedagogic effect of a general recontextualising strategy of school mathematics; namely, the replacement of the study of propositions with lists of computational rules.

2015

This study investigated the strategies that pre-service teachers used and the errors they made while solving linear inequalities in one variable. Fifty one pre-service teachers enrolled in an introductory mathematics course participated in this study. Data were collected from a test that consisted of four linear inequalities in one variable. Participants were asked to solve these linear inequalities and show their work. Participants’ errors while solving each linear inequality were recorded. The results of the study indicated that many pre-service teachers made few errors when solving linear inequalities. These include errors in representing the solution as interval or on the number line, multiplying/dividing by a negative number and arithmetic errors.

Readings in Qualitative Reasoning About Physical Systems, 1990

The Mathematics Teacher, 2014

The trichotomy property and order relation symbols show the Cartesian plane divided into three regions, as students connect tabular and graphical representations of functions.

The inequalities elaborated in this study are about real and complex numbers. That is an intuitive idea and acquaintance with the properties and used as a background of the study. The more stressing of Analytic Inequalities because of the sophistication, but unsuitable for nearly all undergraduate mathematics education students. Namely, the students are unaccustomed in analyzing the exploitation of inequalities. On terms with inequalities, especially geometric, the students find the concepts as a basis to the inequalities but, less elaborated. In fact, the majority of calculus students are capable of the subject based on the previous learning in the use of inequalities. This mathematics education research is bringing out an elaboration of problems on elementary inequalities dealing with algebra and geometry. The students solve the problems with pencil and paper at hand for amplifying arguments and supplying details and computation. The problems of the students not always ordered in degree of difficulty. Although the students better in coping the concepts of continuity, derivative, and integral, many of them are rather hard. In this case, researchers facilitated them for knowing more easily way to solve the problem. The result is an elaboration monogprah that consisted of inequalities in the development of mathematical theory and a glimpse of the analysis. The problems are in following the fundamental rules of algebra and in constructing geometric figures. In proving a problem, the students also need a hypothesis that developed from numerous definitons and postulates or axioms. So, the exercises are available and arranged orderly. Working with the inequalities also required the ability for describing, illustrating and visualizing the problems, especially in a plane.