INSTRUCTIONAL APPROACH AND PROOFS OF PYTHAGORA’S THEOREM FOR PROBLEM-SOLVING

This chapter explores effective instructional approaches and various proofs of Pythagoras' theorem to enhance problem-solving skills in mathematics education. Pythagoras' theorem, a fundamental principle in geometry, serves as a critical tool in both mathematical and real-world applications. An applied research approach was employed, emphasizing the integration of multiple proof techniques including geometric, algebraic, and visual proofs within instructional strategies to cater to different learning styles. The chapter engages students in discovering and validating the theorem through hands-on activities and critical reasoning, guiding them to develop a deeper understanding and promote analytical thinking. It also discusses how these approaches foster problem-solving proficiency by enabling learners to apply the theorem flexibly across a variety of mathematical contexts. Ultimately, the combination of diverse proofs and instructional methods supports a robust learning experience, empowering students to approach complex problems with confidence and creativity. It also considers the impact of the theorem on mathematics and science. It concludes that Pythagoras' theorem can be applied to solving everyday problems in schools, at home, in industries, and in construction. Therefore, teachers should adopt practical instructional approaches (e.g., geometric, algebraic, trigonometric, and proof by similar triangles) when teaching for problem-solving purposes. The chapter recommends that teachers emphasize the application of Pythagoras' theorem during instruction to help students solve problems both inside and outside the classroom. Additionally, the government and stakeholders are encouraged to organize seminars, workshops, and symposiums on the practical instructional methods of Pythagoras' theorem to enhance problem-solving skills in mathematics and science.