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arXiv · 2512.03105

Demonstração Formal de um Algoritmo Alternativo da Multiplicação em Base 10

Albert Lucas Lima Dias·Anthony Lima Dias·Ib Couto·Mabia Lima Chaves dos Santos·Marcus Vinícius da Conceição Morro
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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.

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Albert Lucas Lima Dias, Anthony Lima Dias, Ib Couto, Mabia Lima Chaves dos Santos, Marcus Vinícius da Conceição Morro. 2025-12-02. Demonstração Formal de um Algoritmo Alternativo da Multiplicação em Base 10. https://arxiv.org/abs/2512.03105

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