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

Francisco Regis Vieira Alves

doi:10.24193/adn.11.1.3

Abstract

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

Highlights

In Brazil we record historical and epistemological knowledge as especially important for mathematics teachers
In this work we will discuss some elementary properties on Catalan numbers
Catalan was the mathematician who made known a subject of study that still preserves the interest of the current research on the subject and that contributed to the generalization of the numbers of Catalan, including the FussCatalan numbers (Andrews, 1971) and Catalan's bivariate numbers (Bernhart, 1999; Buescu, 2010; Koshy & Salmassi, 2006; Gessell 1992; Gessel & Xin, 2004)

Summary

Introduction

In Brazil we record historical and epistemological knowledge as especially important for mathematics teachers. In teaching in the context of the History of Mathematics, the research methodology named Didactic Engineering can contribute in the sense of describing a way to a new approach of certain historical contents that, in general, are not available in the History books of ordinary mathematics. We have exposed the use of GeoGebra and CAS Maple softwares with the aim of exploring certain mathematical properties neglected by the History of Mathematics books (Alves, 2017). The following section we will describe some elements of a didactic engineering and, aiming at the formation of Mathematics teachers for the teaching in a historical context

Some elements of didactic engineering

Some historical aspects about the generalized numbers of Catalan

2: Given the integers we define

Cm n L

Conclusion