Abstract algebra

Abstract algebra, at this stage in a student’s education the rapid development of reasoning skills is important and we have taken it as a major objective of the course. Abstract algebra is a particularly good vehicle for teaching reasoning because the proofs are less complicated than, say, advanced calculus, and the notation is not particularly complex. It is also useful that students have not seen this topic before and it is difficult for them to lift proofs from textbooks, so they must rely on their own reasoning and ideas. Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields.
From searches made on the internet, studies on misconceptions about abstract algebra learning among students are not much to be done. From observation, it was found that the study only focused on linear algebra as it was a subject often found at the school level. Among the studies that can be featured are from Julie L. Booth and Kenneth R. Koedinger entitled Key Misconceptions in Algebraic Problem Solving. This study illustrates the misconception of the major problems faced by students in solving algebraic equations correctly and learning to correct mistakes in the problem. The student sample has a problem in the same symbol or negative number in the equation derived from the pretest. After the students learn the techniques correctly, they can improve their understanding and correct the mistakes they have made. This study focuses only on linear algebra and does not involve abstract algebra. But what can be drawn from this research findings, students need to master the concepts in algebra before they can master and solve questions in algebra. Similarly, in the group theory that is one of the abstract algebraic branches, students need to understand the theories or the laws contained therein before they can translate into learning outcomes. These theories require effective techniques and learning sessions to reinforce the students’ understanding of the results. Among the steps teachers can take, is to build a topic-related module and provide adequate training according to student’s learning cognitive level. In addition, teachers can also use technology in learning which has been proven in improving student understanding. Abstract algebra requires students to visualize the theory in mind before they can understand it deeper. The use of technology can help a teacher overcome this problem. There are lots of software that can help teachers in learning sessions in the classroom. After they master the concept well, it will provide a high motivation for students to achieve the next level of abstract algebra learning (L. Booth ; R. Koedinger, 2008).
Among the problems faced by the students is, they are difficult to understand the theorem given. The difficulty in describing the things found in the theorem causes their motivation to solve the question is low. In Group topics, there are four properties that need to be understood best with each properties being abstractly imaginative. If a student has a high level of imagination, this may be overcome. The second thing that students face is the symbols that are widely used in explaining theory. Each symbol has a variety of meanings and values. This will give rise to problems remembering each letter being represented. There are many theories that need to be remembered. Students need to understand the evidence in the theorem (A. Gallian, 2005). This poses a bit of a problem to the student because proving a theorem requires good imagination. This level of understanding can be assisted with easy examples but with adequate training. The preparation of this module will help students and teachers understand the topics contained in abstract algebra.