On the Quasi-Extended Addition for Exploded Real Numbers

Autor/in	Szalay, István
Titel	On the Quasi-Extended Addition for Exploded Real Numbers
Quelle	In: Acta Didactica Napocensia, 1 (2008) 2, S.1-15 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2065-1430
Schlagwörter	Numbers; Teacher Education Curriculum; Teacher Education Programs; Mathematics Education; Mathematics Instruction; Mathematical Applications; Problem Solving; Number Concepts; Arithmetic; Algebra; Science Education; Preservice Teacher Education; Elementary School Mathematics + Suchen Sie Ihr Suchwort? Zahlenraum; Mathematische Bildung; Mathematics lessons; Mathematikunterricht; Angewandte Mathematik; Innermathematische Anwendung; Problemlösen; Number concept; Zahlbegriff; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Naturwissenschaftliche Bildung; Lehramtsstudiengang; Lehrerausbildung; Elementare Mathematik; Schulmathematik
Abstract	In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need to be proved. It does not cause a difficulty in applying mathematical knowledge in everyday situations but primary teachers must have a deeper insight. That is why it is reasonable to show these characteristic features to primary teacher trainees in a different algebraic structure. An example for that could be the algebra of vectors. In this paper the algebraic structure of exploded numbers containing the set of real numbers as a subset is selected as an example. With the help of super-operations (super-addition, super-multiplication, super-subtraction and super-division) introduced for exploded numbers, we try to extend addition for exploded numbers as well. The question of the method of extension and the examination of the characteristics of the extended addition arises. While seeking for the answer, surprising facts emerge, such as the phenomenon that each real number will have one and only one addition incompetent pair among exploded numbers. In this paper we introduce the quasi-extended addition for exploded real numbers which is essentially different from super-addition. On the other hand, the quasi-extended addition is the (traditional) addition for real numbers. Moreover, we investigate some properties (for example commutativity, associativity) of quasi-extended addition. Finally, we find some similarity between the countable infinity and the exploded of 1. The quasi-extension of addition is useful for students to observe different kinds of algebraic properties, too. (As Provided).
Anmerkungen	Babes-Bolyai University. Kogainiceanu 1, Cluj-Napoca, 400084 Romania. e-mail: submit_adn@yahoo.com; Web site: http://adn.teaching.ro
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01