On Teaching of Generalized Catalan Numbers with the Maple's Help

Autor/in	Alves, Francisco Regis Vieira
Titel	On Teaching of Generalized Catalan Numbers with the Maple's Help
Quelle	In: Acta Didactica Napocensia, 11 (2018) 1, S.25-40 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2065-1430
Schlagwörter	Mathematics Instruction; Textbooks; History; Mathematical Concepts; Generalization; Epistemology; Computer Software; Educational Technology; Technology Uses in Education; Foreign Countries; Numbers; Matrices; Teaching Methods; Knowledge Level; Calculus; Teacher Education; Mathematics Teachers; Brazil + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Textbook; Text book; Schulbuch; Lehrbuch; Geschichte; Geschichtsdarstellung; Erkenntnistheorie; Unterrichtsmedien; Technology enhanced learning; Technology aided learning; Technologieunterstütztes Lernen; Ausland; Zahlenraum; Matrizenrechnung; Teaching method; Lehrmethode; Unterrichtsmethode; Wissensbasis; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Lehrerausbildung; Lehrerbildung; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Brasilien
Abstract	In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts, moreover, mathematical objects more close to the Brazilian school reality. Thus, the present work discusses the notion of Catalan numbers, including its generalization process and epistemological aspects, with the adoption of some assumptions of Didactic Engineering. The work also presents a series of matrices and combinatorial properties that can be explored with the CAS Maple with the scope to attract a larger number of students to a teaching that shows the historical, mathematical and evolutionary epistemological aspects of the generalized Catalan numbers. In this way, it is observed that the teacher must present an extensive knowledge about the notion of "numbers" and not only of the fundamentals of Differential and Integral Calculus. (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