Banca de DEFESA: ALBERTO DE SOUSA E SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : ALBERTO DE SOUSA E SILVA
DATE: 29/08/2024
TIME: 14:00
LOCAL: UFRN
TITLE:

Mathematical Induction in Proving Combinatorial Formulas: From Textbooks to the Classroom

KEY WORDS:

High School; Mathematical Induction; Combinatorics; Following teaching.

PAGES: 74
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

Mathematical induction is an extremely important and useful proof technique in establishing
results in various areas of mathematics, such as number theory, combinatorics, geometry, and
others, However, currently, this technique is not widely taught or explored in the context of
high school education. Given this, the central objective of this work is to propose the use of
mathematical induction at this level of education, specifically in the study of combinatorial
analysis (Newton's binomial theorem and Pascal's triangle). Additionally, we seek to promote
reflection on the approach to this topic in high school textbooks. To achieve this objective, we
initially selected four collections of high school textbooks and conducted a critical analysis of
how these books address the mentioned concepts. We deliberately chose collections from
different decades to highlight the change in approach over a thirty-year period. We concluded
the work by presenting a didactic sequence that allows teachers to use mathematical induction
in the classroom to prove combinatorial formulas (Newton's binomial theorem and Pascal's
triangle theorems), aiming to facilitate the understanding of the mentioned combinatorial
content. The approach adopted in our didactic sequence contrasts with the approaches
traditionally found in high school textbooks.

COMMITTEE MEMBERS:
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Interna - 1552847 - DEBORA BORGES FERREIRA
Externa à Instituição - ENAI TAVEIRA DA CUNHA - UFERSA