1.2 Desarrollo del protocolo de investigación
Research Protocols in Mathematics Education
Introduction to the Research Topic
- Giovanni Ordóñez introduces himself as a doctoral student in Educational Sciences, presenting Activity 1.2 focused on research protocols.
- He highlights the historical challenge of overcoming procedural mechanization in rural mathematics education to achieve deep algebraic reasoning.
Proposed Solution
- The research proposes a disruptive solution: integrating learning trajectories with artificial intelligence (AI), functioning not merely as a calculator but as a Socratic tutor that encourages critical thinking.
Central Research Question
- The central question investigates how the use of an AI-mediated platform, guided by Socratic tutoring, influences students' algebraic reasoning development.
Theoretical Framework
- Ordóñez emphasizes that theoretical frameworks are essential for coherence between initial facts and research outcomes, citing William Daros on science as a human construction.
Key Theories Discussed
- Learning Trajectories (LT)
- LT serves as a map detailing student progress in algebra, defining clear goals and allowing observation of changes in mathematical thinking patterns.
- Zone of Proximal Development (ZPD)
- Drawing from Vygotsky, he explains that learning occurs within ZPD; thus, teachers cannot be the sole mediators in classrooms with many students.
- Intelligent Tutoring Systems (ITS)
- ITS employs language models to understand student confusion and guides them towards constructing their own formal truths rather than providing direct answers.
Synthesis of Theoretical Insights
- In summary:
- Learning trajectories indicate "what" to learn,
- ZPD explains "how" through mediation,
- ITS provides "with what" support for genuine algebraic reasoning capable of generalization and justification.
Conclusions and Implications
- Observations reveal bright students lacking private tutors or costly platforms; the gap is not due to intelligence but rather inadequate learning mediation.
- This research aims to demonstrate that well-designed AI can serve as an equitable tool rather than one of exclusion.