Effective Teaching of Abstract Algebra :: Mathematics Education Papers

Effective Teaching of Abstract AlgebraAbstract Algebra is one of the great bodies of knowledge that the mathematically educated person should know at to the lowest degree at the introductory level. Indeed, a degree in mathematics everlastingly contains a course covering these concepts. Unfortunately, abstract algebra is also seen as an exceedingly difficult body of knowledge to learn since it is so abstract. Leron and Dubinsky, in their makeup An Abstract Algebra Story, penned the following two statements, summarizing comments that are often perceive from both teacher and assimilator alike.1.The teaching of abstract algebra is a disaster, and this dust true(a) almost independently of the quality of the lectures. (Leron and Dubinsky agree with this statement.)2.Theres little the scrupulous math professor great deal do about it. The stuff is exactly too hard for most students. Students are not well-prepared and they are nonvoluntary to make the effort to learn this very di fficult material. (Leron and Dubinsky disagree with this statement.)(Leron and Dubinsky, p. 227) thence the question is raised if there is something the conscientious math professor tooshie do about the seemingly disastrous results in the learning of algebra, what is it that we can do? As a teacher of undergraduate mathematics, I requisite 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 literature that I reviewed. In this paper, they summarize theirexperimental, constructivist approach to teaching abstract algebra. Among the classroom activities are data processor 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 calculating machine activities use the I SETL scheduleming language. As an example of its use, students write a program implementing the group axioms. They then can enter what they consider to be a group, and the estimator will give as output a true or false response. They can use the same process to baffle 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 be possessed of 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 sure enough seems patterned after Dubinskys theoretical foundation for student learning lay out in his work Reflective Abstraction In in advance(p) Mathematical Thinking.