Universal Journal of Educational Research 8(2): 477-489, 2020 http://www.hrpub.org DOI: 10.13189/ujer.2020.080219 Enhancing Creative and Critical Thinking Skills of Students in Mathematics Classrooms: An Experimental Study of Teaching the Inequality in High Schools Duong Huu Tong 1,* , Nguyen Phu Loc 1 , Bui Phuong Uyen 1 , Thach Hong Son 2 1 School of Education, Can Tho University, Vietnam 2 Can Tho University, Vietnam Received November 12, 2019; Revised December 18, 2019; Accepted December 27, 2019 Copyright©2020 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract Teaching mathematics in high schools not only provides knowledge to solve problems or apply them into practice but also trains the students' ability to think mathematically. Therefore, in order to promote the students' mathematical thinking skills, teachers need to involve students in learning activities, help them train and develop their thinking. The purpose of this study was to enhance creative and critical thinking skills for 10th-grade students through teaching inequality topics. The experimental class had 41 students and was taught with activities of proving an inequality to enhance critical and creative thinking skills; while the control class consisted of 35 students and they approached conventionally. The qualitative method was used to evaluate students' creative and critical thinking skills for two types of exercises, namely, proving an inequality and finding the maximum value of a function. The findings showed that students in the experimental class showed a better ability to prove inequalities than students in the control class, and they also presented more solutions for a problem proving the inequality. Keywords Creative and Critical Thinking, Inequality, Proving an Inequality, Mathematics Education 1. Introduction Thinking is one of the categories of philosophy that reflects the attributes of the spirit, helping people to understand an object or phenomenon through improvement properly, change from feelings, from material activities, thereby behave positively. In particular, thinking from an educational perspective is the improvement of the brain to solve new problems, or to form a new knowledge based on the relationship as well as the improvement of the old, the known ones, thereby forming a new way of thinking that is more optimal with the old. Moreover, thinking can be understood as an activity of the cognitive process when facing a problem or solving a problem; there is an impact from the senses or the familiar ones stored in the brain. In favourable conditions and circumstances, thinking can be promoted effectively, so the problem is better solved. Thinking in general and thinking in particular in teaching mathematics always have objects, which are needs objects [12]. The needs may be the need to discover new knowledge such as new concepts, new laws, new relationships, through conflict resolution, overcoming a cognitive obstacle, overcoming mistakes. Thus, to stimulate students' thinking, it is necessary to build situations containing obstacles, contradictions, related issues and formulate thinking for students to reveal problems in order to discover new knowledge, perceiving the new by the existing knowledge. As we know, each subject has its unique characteristics. If the social sciences are about the memory, the feelings, the personal feelings of the writer, then the natural sciences require inquiry, thought, flexibility in problem-solving. Especially, mathematics is a primary subject which is the foundation of natural sciences and is one of the critical subjects in educational systems. Mathematics is put into the education system in countries at all levels from kindergarten to university because mathematics helps learners to practice the ability to think logically, become independent of thinking, be able to self-study and address problems. Mathematics is a relationship between specific problems expressed by one calculation or many calculations, so developing the capacity of mathematical thinking for students is a vital factor. Mathematical competence is an expression of an individual's mathematical ability through acquiring