Equivalent Structures on Sets

LAUR Repository

Show simple item record

dc.contributor.author Hamdan, May
dc.date.accessioned 2016-04-25T11:08:31Z
dc.date.available 2016-04-25T11:08:31Z
dc.date.copyright 2006
dc.date.issued 2016-04-25
dc.identifier.issn 0013-1954 en_US
dc.identifier.uri http://hdl.handle.net/10725/3646
dc.description.abstract This study reports on how students can be led to make meaningful connections between such structures on a set as a partition, the set of equivalence classes determined by an equivalence relation and the fiber structure of a function on that set (i.e., the set of preimages of all sets {b} for b in the range of the function). In this paper, I first present an initial genetic decomposition, in the sense of APOS theory, for the concepts of equivalence relation and function in the context of the structures that they determine on a set. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my observations of students’ learning processes. Based on this analysis, I then suggest instructional procedures that motivate the mental activities described in the genetic decomposition. I finally present empirical data from informal interviews with students at different stages of learning. My goal was to guide students to become aware of the close conceptual correspondence and connections among the aforementioned structures. One theorem that captures such connections is the following: a relation R on a set A is an equivalence relation if and only if there exists a function f defined on A such that elements related via R (and only those) have the same image under f.
dc.language.iso en en_US
dc.title Equivalent Structures on Sets en_US
dc.type Article en_US
dc.description.version Published en_US
dc.title.subtitle Equivalence Classes, Partitions and Fiber Structures of Functions en_US
dc.author.school SAS en_US
dc.author.idnumber 199829020 en_US
dc.author.woa N/A en_US
dc.author.department Computer Science and Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal Educational Studies in Mathematics en_US
dc.journal.volume 62 en_US
dc.journal.issue 2 en_US
dc.article.pages 127-147 en_US
dc.keywords APOS theory en_US
dc.keywords Equivalence classes en_US
dc.keywords Equivalence relations en_US
dc.keywords Functions en_US
dc.keywords Genetic decomposition en_US
dc.keywords Set structures en_US
dc.keywords Partitions en_US
dc.identifier.doi https://doi.org/10.1007/s10649-006-5798-9 en_US
dc.identifier.ctation Hamdan, M.. (2006). Equivalent Structures on Sets: Equivalence Classes, Partitions and Fiber Structures of Functions. Educational Studies in Mathematics, 62(2), 127–147. en_US
dc.author.email mhamdan@lau.edu.lb
dc.identifier.url http://link.springer.com/article/10.1007/s10649-006-5798-9

Files in this item

Files Size Format View

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record

Search LAUR

Advanced Search


My Account