Competitions for Young Mathematicians

Part I. Goals of Mathematics Instruction

1. Goals of Mathematics Instruction: Seven Thoughts and Seven Illustrations of Means
Alexander Soifer

Part II. Geometry for Competitions

2. From a Mathematical Situation to a Problem
Francisco Bellot-Rosado

3. Techniques for Solving Problems of Plane Geometry
K. P. Shum

Part III. Combinatorics for Competitions

4. Arrangements and Transformations of Numbers on a Circle: An Essay Inspired by Problems of Mathematics Competitions
Kiril Bankov

5. Combinatorial Problems in the Mathematical Olympiad of Central America and the Caribbean
L. F. Cáceres-Duque, J. H. Nieto Said, R. J. Sánchez Lamoneda

Part IV. Role of Competitions in the Classroom

6. The Rainbow of Mathematics—Teaching the Complete Spectrum and the Role Mathematics Competitions Can Play
Robert Geretschläger

7. Competition Aims to Develop Flexibility in the Classroom
Ingrid Semanišinová, Matúš Harminc, Martina Jesenská

8. Discovering, Development, and Manifestation of Mathematical Talent
Iliana Tsvetkova

Part V. Original Competitions

9. International Mathematical Tournament of Towns
Nikolay Konstantinov, Sergey Dorichenko

10. Madhava Mathematics Competition—A Recent Initiative in India
V. M. Sholapurkar

Part VI. Thoughts About Competitions’ Present and Future

11. From the Lifetime Experience of a Seasoned Math Educator—Thoughts, Hopes, Views and Impressions
Romualdas Kašuba

12. Future Directions for Research in Mathematics Competitions
Peter James Taylor

Part VII. A Bridge Between Competitions and ‘Real’ Mathematics

13. Are Mathematics Competitions Changing the Mathematics that Is Being Done and the Way Mathematics Is Done?
María Falk Losada

14. Classic Conjectures Allow Young Mathematicians to Commence Research
Alexander Soifer

Avainsanat: Education, Mathematics Education