Reducing abstraction level when learning computability theory concepts

Abstract

The paper illustrates how theories from mathematics education can be applied for explaining student conception of computing science ideas. It does this by demonstrating how the theme of reducing abstraction [5] can be used for analyzing students' mental processes when the students are in the process of solving problems in Computability Theory. The topic of Computability Theory in presented here as an example for demonstrating how research in Computing Science education can use learning theories, "borrowed" from mathematics education research, for explaining learning processes.

The anatomy of a mathematical proof: Implications for analyses with Toulmin’s scheme

“…One might ask why it is acceptable to omit the step involving division of a polynomial as implicit but important to have commutativity of multiplication explicit. One interpretation is that, as Hazzan (1999) notes, commutativity is an issue that may only become explicitly a focus of attention when encountering abstract algebra for the first time, so it is important that students can demonstrate that they know when it does and does not apply, while division by a (non-zero) polynomial is more peripheral to the study of group theory.…”

A handbook of mathematical discourse

“…This is discussed in [Hazzan, 1999]. Example 6 One metaphor for the real line is that it is a set of points (as in Example 3.)…”

A Sample Webquest Applicable in Teaching Topological Concepts

“…Mathematical concepts in abstract algebra are related to topological concepts and various studies have been carried about abstract algebra (e.g., Clark et al, 1999;Hazzan, 1999). Clark et al (1999) examined students' attitudes toward abstract algebra course.…”

“…Results showed that although abstract algebra was a difficult course, students desired group activities and computer-aid learning environment. Abstract algebra concepts are mostly difficult to understand, reducing abstraction-a way of understanding abstract topics-helps students to understand algebra concepts simply (Hazzan, 1999). Hazzan (1999) investigated undergraduate students' reducing abstraction level while learning abstract algebra concepts.…”