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Balanced incomplete block designs for teaching combinatorics: Construction and applications
The Teaching of Mathematics, XXVIII (2025) no. 1, p. 42

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This article presents balanced incomplete block designs as an effective pedagogical tool for teaching combinatorics. Through their construction, analysis, and practical application, the article proposes an interdisciplinary approach that enables abstract content to be addressed in a contextualized and meaningful way. Specifically, it explores algebraic and matrix structures that model situations with structural regularity, fostering the development of logical and abstract thinking in the classroom. Additionally, key statistical concepts, such as experimental design and analysis, are introduced to provide an applied perspective on decision-making and data interpretation. These tools are presented through real-world examples that help students develop reasoning, modeling, and critical analysis skills, while also reinforcing the understanding of mathematics as a powerful tool for solving relevant and structured combinatorial problems.
DOI : 10.57016/TM-NOQK3870
Classification : 97K20, K25
Keywords: BIBD, balanced incomplete block design, combinatorial design, teaching combinatorics, Steiner triple system, resolvable design, Kramer-Mesner, Hadamard matrix, experimental design. 
Daniel Martín-Cudero. Balanced incomplete block designs for teaching combinatorics: Construction and applications. The Teaching of Mathematics, XXVIII (2025) no. 1, p. 42 . doi: 10.57016/TM-NOQK3870
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