Scripting Approaches in Mathematics Education by Rina Zazkis & Patricio Herbst

Author:Rina Zazkis & Patricio Herbst
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Research on Student Thinking in Abstract Algebra

Research on student thinking in abstract algebra has seen a flurry of activity over the past two decades, and is now an impressive body of research in its own right, reporting on students’ understanding of such foundational concepts as group (Dubinsky, Dautermann, Leron & Zazkis, 1994), isomorphism (Larsen, 2009; Leron, Hazzan, & Zazkis, 1995), and quotient group (Asiala, Dubinsky, Mathews, Morics & Oktac, 1997; Larsen, 2013). Another avenue of research has focused on related ideas like proof (Weber, 2001) and abstraction (Hazzan, 1999; Simpson & Stehlíková, 2006). The research presented in this chapter adds to this growing body of literature by addressing two deficiencies. First, the aforementioned studies employed only task-based clinical interviews or teaching experiments to obtain their results. This study introduces scripting as an effective means of gaining insight into student thinking in conjunction with these conventional methodologies. Second, with only one exception (Simpson & Stehlíková, 2006), the studies focus exclusively on students’ understanding of concepts and related ideas in group theory, and thus little is known about how students understand concepts that are specific to rings and fields. This is a notable deficiency in the literature because the foundational structures of ring theory are abstractions of the familiar algebraic structures from school algebra (including ℤ, ℝ, ℚ, and ℤ[x]) and are thus thought to be important not only for the general population of mathematics majors (as a means of formalizing their prior knowledge) but especially for the population of pre-service secondary mathematics teachers (as a means of enhancing their potential for effective algebra instruction). This chapter, in turn, examines students’ understanding of the ZPP, a concept that is important in both school algebra and abstract algebra .

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