From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations

Area of Science:

• Mathematics Education
• Algebraic Pedagogy

Background:

• Traditional algebra teaching emphasizes syntactic rules over functional understanding.
• Modern trends advocate for a functional approach and inter-register conversions in algebra instruction.
• A gap exists between modern recommendations and current classroom practices in algebra.

Purpose of the Study:

• To propose and evaluate interactive activities for teaching algebra with a functional approach.
• To investigate how these activities enhance students' problem-solving strategies and understanding of algebraic formulas.
• To identify common challenges students encounter when learning algebra through a functional lens.

Main Methods:

• Development of interactive, functional algebra activities for eighth-grade students.
• Implementation of activities in a classroom setting with approximately 300 students.
• Analysis of both qualitative and quantitative data to assess learning outcomes and challenges.

Main Results:

• Students demonstrated the ability to develop multiple problem-solving approaches.
• Enhanced comprehension of algebraic formulas was observed.
• Key difficulties faced by students in learning algebra were identified.

Conclusions:

• Interactive, functional algebra activities can effectively support conceptual understanding in secondary education.
• A geometric context provides a valuable framework for teaching algebraic formulas.
• The findings offer practical insights for educators seeking to modernize algebra instruction.