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. 1-15Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; Zeitschriftenaufsatz
ISSN	1504-9922; 2065-1430
Schlagwörter	Kindheitsforschung; Lehrer; Lehrerausbildung; Unterricht; Fachdidaktik; Mathematikunterricht; Reale Zahl; Europa; Rumänien
Abstract	In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing toa deeply set automatism rooted in their primary and secondary education, teacher trainees thinkthat such characteristics of addition are so trivial that they do not need to be proved. It does notcause a difficulty in applying mathematical knowledge in everyday situations but primary teachersmust have a deeper insight. That is why it is reasonable to show these characteristic features toprimary teacher trainees in a different algebraic structure. An example for that could be the algebraof vectors. In this paper the algebraic structure of exploded numbers containing the set of realnumbers 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, wetry to extend addition for exploded numbers as well. The question of the method of extensionand the examination of the characteristics of the extended addition arises. While seeking for theanswer, surprising facts emerge, such as the phenomenon that each real number will have oneand only one addition incompetent pair among exploded numbers. In this paper we introducethe 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 realnumbers. Moreover, we investigate some properties (for example commutativity, associativity) ofquasi-extended addition. Finally, we find some similarity between the countable infinity and theexploded of 1. The quasi-extension of addition is useful for students to observe different kinds ofalgebraic properties, too. (Orig.).
Erfasst von	Externer Selbsteintrag
Update	2009/3