Students’ algebraic approach and the geometric visualization of irrational numbers

Authors : Shiva Mafakheri

Pages : 3-8

View : 85 | Download : 56

Publication Date : 2025-06-01

Article Type : Research Paper

Abstract :Students typically learn about irrational numbers in math class, particularly in topics such as algebra and geometry. They may encounter irrational numbers when solving equations involving square roots or other non-perfect square roots. In algebraic expressions, students may need to simplify square roots or manipulate irrational numbers to solve for variables. In geometry, irrational numbers may also be used in connection with measurements and calculations involving square roots of areas or lengths of geometric shapes. For example, students would need to work with irrational numbers to find the diagonal of a square given the side length. The research project partially presented in this paper aims to investigate learning geometric and algebraic visualization have been studied. As discussion students in the research showed what they learn about irrational numbers and weakness in learning and inability to perform was evident with a focus on improving classroom discourse to adapt to the conceptual development of most students in 9th and 10th grade. An empirical investigation of the enacted learning environment revealed its potential to enhance classroom discourse and students\\\' conceptual and geometric development by introducing an explicit distinction between empirical and theoretical aspects of measurement concepts. The findings include the identification of conditions and limitations that need to be addressed in the design and instructional practices of integrated mathematics interventions in general and for the next steps of the current project.
Keywords : İrrasyonel sayılar, Cebirsel yaklaşım, Geometrik görselleştirme, Matematik Eğitimi.

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