Effective Teaching of Abstract Algebra :: Mathematics Education Papers

Effective Teaching of epitomeedness AlgebraAbstract Algebra is one of the important bodies of screwledge that the mathematicsematically educated person should know at least at the introductory level. Indeed, a degree in mathematics always contains a course covering these concepts. Unfortunately, regard algebra is overly seen as an extremely concentrated body of knowledge to learn since it is so abstract. Leron and Dubinsky, in their paper An Abstract Algebra Story, penned the following two statements, summarizing comments that are often heard from both teacher and educatee alike.1.The teaching of abstract algebra is a disaster, and this remains true almost independently of the quality of the lectures. (Leron and Dubinsky play off with this statement.)2.T presents little the conscientious math professor can do near it. The stuff is simply too hard for most students. Students are non well-prepared and they are un get outing to make the effort to learn this very difficult mat erial. (Leron and Dubinsky disagree with this statement.)(Leron and Dubinsky, p. 227)Thus the question is raised if there is something the conscientious math professor can do about the seemingly disastrous results in the learning of algebra, what is it that we can do? As a teacher of undergrad mathematics, I want and need to know what these effective methods of teaching abstract algebra are.Leron and Dubinskys paper referred to above and papers resulting from their research contain the bulk of lit that I reviewed. In this paper, they summarize theirexperimental, constructivist approach to teaching abstract algebra. Among the schoolroom activities are computer activities, work in teams, individual work, class discussion, and sometimes a mini-lecture summarizing the results of student work (which by this time is familiar to them), providing definitions, theorems, and proofs in their abstract forms.The computer activities use the ISETL programming language. As an example of its use, students economise a program implementing the group axioms. They indeed can enter what they dig to be a group, and the computer will give as turnout a true or false response. They can use the alike(p) process to determine whether their proposed group is closed, has an identity, etc. They choose their answer and then let the computer respond. In this way, students construct the group process, with the view that they will also turn in a parallel construction occurring in their minds. Students have an experience on which to base their learning of group theory.The method proposed here by Leron and Dubinsky certainly seems patterned after Dubinskys theoretical foundation for student learning laid out in his work Reflective abstract In Advanced Mathematical Thinking.