Summer School Online Edition Lecture Notes

Introduction

• Welcome to the online summer school.
• Typically, 20 participants attend in person in Utrecht, Netherlands.
• This year: 479 participants from 36 countries.
• Session timings: two days from 2 PM to 5 PM.
• Emphasis on interactivity through live chat.

Practical Information

• Website contains all necessary information on:
  • Program details
  • Research pitches
  • Workshop preparations
• Certificates will be issued to active participants.
• Changes noted regarding the broadcasting channel for talks.

Upcoming Sessions

• Introduction by Professor Paul Drijvers.
• Parallel sessions at 3 PM:
  • Session on upper secondary mathematics (by host).
  • Session on numeracy from primary to secondary level (by Case Hochland).
• End of the day: discussions on comments and reflections.

Lecture by Professor Paul Drijvers

Realistic Mathematics Education (RME)

• Overview of RME and its key concepts.
• Historical context:
  • Developed by Hans Freudenthal and Adri Treffers.
  • Still relevant today.
• RME focuses on the connection between real-life situations and mathematics learning.

Key Concepts in RME

1. Mathematization

   • Human activity: Making mathematics from real situations.
   • Horizontal Mathematization: Translating between realistic contexts and mathematical models.
   • Vertical Mathematization: Building within the world of mathematics.

2. Didactical Phenomenology

   • Focuses on what students experience as real.
   • Identifying suitable contexts that invite mathematical development.
   • Emphasizes the importance of meaningful problem situations.

3. Models

   • Use of educational models to support understanding.
   • Different levels of engagement with mathematics (immersion, referential, general, and formal).

4. Guided Reinvention

   • Balancing student discovery with necessary guidance.
   • Importance of listening to students to tailor the learning process.

Task Discussion

• Evaluated three tasks from Dutch textbooks:
  1. Lawn Extension Task: Critique on realism and common sense of task.
  2. Ice Cube Melting Task: Issues with context and realism.
  3. Parabola Task: Potential for meaningful engagement if framed appropriately.

Summary of Key Points

• RME is about meaningful learning experiences rather than just real-life contexts.
• The role of teachers is crucial in guiding students through mathematical concepts.
• Emphasis on designing tasks that allow for natural sense-making and engagement.

Conclusion

• Importance of critical evaluation of tasks and contexts in mathematics education.
• Encouragement for participants to engage actively and reflect on their experiences.
• Thank you for attending the session.