The Role of Mathematical Folk Puzzles in Developing mathematical Thinking and Problem-Solving Skills

TL;DR

This paper reviews various mathematical folk puzzles and introduces a new problem, demonstrating their effectiveness in enhancing mathematical thinking and problem-solving skills through practical classroom applications.

Contribution

It introduces the 'Minimal Dissection Path Problem for Polyominoes' and discusses modern digital adaptations of folk puzzles for educational purposes.

Findings

Proven minimal cuts for dissecting polyominoes as N-1

Enhanced student engagement through digital puzzle modifications

Practical classroom applications for core mathematical concepts

Abstract

This paper covers a variety of mathematical folk puzzles, including geometric (Tangrams, dissection puzzles), logic, algebraic, probability (Monty Hall Problem, Birthday Paradox), and combinatorial challenges (Eight Queens Puzzle, Tower of Hanoi). It also explores modern modifications, such as digital and gamified approaches, to improve student involvement and comprehension. Furthermore, a novel concept, the "Minimal Dissection Path Problem for Polyominoes," is introduced and proven, demonstrating that the minimum number of straight-line cuts required to dissect a polyomino of N squares into its constituent units is $\mathrm{N}-1$. This problem, along with other puzzles, offers practical classroom applications that reinforce core mathematical concepts like area, spatial reasoning, and optimization, making learning both enjoyable and effective.