![Sample our Education journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5932/TOC-Subject-Sample-2021-Education.jpg"})
Abstract
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors.
Notes
1 For more information on guided reinvention, see Gravemeijer [Citation4]. For more information about similar instructional sequences in abstract algebra, see Larsen [Citation5] (for group theory) and Cook [Citation1] (for ring theory).
2 If the instructor plans to compare zero-divisors across domains (or, indeed, formally name the term “zero-divisor”), the students must eventually come to terms with 3 × 4 = 0. Such explorations are not included in this task sequence. The point of the above comment, then, is that the identification of the modulus with zero need not be done immediately.
Additional information
Notes on contributors
John Paul Cook
Dr John Paul Cook is an Assistant Professor of Mathematics at the University of Science and Arts of Oklahoma in Chickasha, OK. His areas of research include developing inquiry-based methods of instruction in advanced mathematics courses, particularly abstract algebra. He lives in Norman, Oklahoma with his wife and two children.