On Teaching Geometry: a practical guide to building thinking, not just routines.
This book examines how to introduce geometry in a way that develops clear reasoning, precise definitions, and strong logical thinking. It argues that teaching should start with axioms and definitions, then show how every demonstration follows a careful, syllogistic path. The author also explores the teacher’s role in fostering independent thought and resistant reasoning, rather than simply guiding the class through traditional demonstrations.
The text discusses a careful balance between using established truths and encouraging original work. It explains how to help students see why each step in a proof is justified, and why precise language matters. By focusing on the mental processes behind geometry, it aims to train students to make reasoned conclusions with confidence.
- Clear guidance on laying a solid logical foundation through axioms, definitions, and proofs
- Strategies to cultivate independent thinking and careful self‑checking in students
- Practical demonstrations of aligning classroom work with rigorous reasoning
- Advice on balancing textbook structure with active student discovery
Ideal for teachers who want geometry to develop mental poise, honesty of expression, and disciplined problem‑solving in their students.