Demonstra\c{c}\~ao Formal de um Algoritmo Alternativo da Multiplica\c{c}\~ao em Base 10

TL;DR

This paper formalizes and proves the correctness of a novel, student-invented multiplication method in base-10 that simplifies mental calculation by restructuring digit interactions into partial sums.

Contribution

It introduces a new, formally verified multiplication algorithm discovered by a 10-year-old, expanding the understanding of student-invented arithmetic methods.

Findings

Provides a full mathematical proof of the method's correctness.

Compares the new method with classical multiplication algorithms.

Highlights implications for cognitive processes in arithmetic learning.

Abstract

This article presents and formalizes an elementary multiplication method discovered independently by a 10-year-old student, Anthony Lima Dias. The method reorganizes digit interactions in base-10 multiplication into a structured sequence of partial sums, reducing cognitive load and allowing reliable mental or semi-written computation. We provide a full mathematical proof of correctness, a comparison with the classical algorithm, formal notation, and a detailed contextual account of the discovery. The method expands the known catalog of student-invented algorithms and raises questions about cognitive pathways in arithmetic learning. Keywords: multiplication methods, mathematics education, mental calculation, student-invented algorithms, alternative algorithms, arithmetic strategies. -- -- Este artigo apresenta e formaliza um metodo elementar de multiplicacao descoberto de forma independente por um estudante de 10 anos, Anthony Lima Dias. O metodo reorganiza as interacoes entre algarismos na multiplicacao em base 10 em uma sequencia estruturada de somas parciais, reduzindo a carga cognitiva e permitindo um calculo mental ou semi-escrito mais confiavel. Fornecemos uma demonstracao matematica completa de corretude, uma comparacao com o algoritmo tradicional, notacoes formais e um relato contextual detalhado da descoberta. O metodo amplia o catalogo conhecido de algoritmos inventados por estudantes e levanta questoes sobre caminhos cognitivos na aprendizagem aritmetica. Palavras-chave: metodos de multiplicacao, educacao matematica, calculo mental, algoritmos inventados por alunos, algoritmos alternativos, estrategias aritmeticas.