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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

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