Engaging Young Students in Mathematics through Competitions — World Perspectives and Practices

The following sections are included:

• Foreword
• About the Authors
• Contents
• Introduction

In this part, we take a look at some of the lines connecting the dots between mathematics competitions and the world of research mathematics. Since higher level competitions simulate a research environment anyway (albeit usually with the artificial constraints of time limits and prohibition of teamwork), it is not surprising that there should be many such connections…

The following sections are included:

• Introduction
• Lifting-the-Exponent-Lemma
• An Olympiad Problem
• Elliptic Curves
• Problem Formulation
• Sketch of the Solution Using Olympiad Methods
• Bibliography

The following sections are included:

• Introduction
• Australian Examples
• Further development
• Further outcomes
• Statement of problem in mathematics challenge
• New and Rediscovered Methods of Proof
• Conclusion
• Bibliography

The following sections are included:

• Introduction
• Some Information About the Polish Mathematical Olympiad
• Some Problems for Which Some Knowledge of University Mathematics May Be Helpful
• Bibliography

The following sections are included:

• Introduction
• Train I: The 1-10-100 Problem
• The Classic I
• The Classic II
• The Classic III
• Bibliography for Train I
• Train II: A Taste for Duality: Erdős, Dilworth, Gallai, Milgram, and Mirsky
• In Memory of Paul Erdős (1913–1996)
• Bibliography for Train II
• Train III: My Favorite Open Problem of Mathematics, Chromatic Number of the Plane: New Breakthrough
• Chromatic Number of the Plane: The Problem
• Aubrey D.N.J. de Grey’s Breakthrough
• Marijn J. H. Heule
• Geoffrey Exoo and Dan Ismailescu
• The Road Ahead
• Bibliography for Train III

In this part, we shift our perspective to try to illuminate how some aspects of mathematics competitions can or do play a role in the classroom. It is clear that successful participants of competitions will generally find mathematics quite enjoyable, which is a feeling not shared by every student in a standard classroom. Since it can certainly be expected that students will be able to learn a subject must more readily if they enjoy dealing with its details, it would be great from a didactic standpoint if we could get more students to appreciate the fascinating side of mathematics, and the competition world seems to be one possible way to introduce students to this…

The following sections are included:

• Introduction
• Revisiting the Rainbow of Mathematics
• Common Vocabulary
• Common Content
• Applications
• Public data
• Economic usefulness
• Preparation for tertiary studies
• Intellectual enjoyment and general knowledge (“Allgemeinbildung”)
• Common Tools
• Common Goals
• The value of IMO topics in the standard classroom
• The usefulness of competition-style thinking to the learning process and the importance of proof
• Increasing teachers’ competencies by engaging with Olympiad-style problems
• How teachers profit by developing their own competition-style problems
• A Two-Way Street
• Where DoWe Go from Here?
• Bibliography
• Websites (in order of their appearance; current as of July 2018).

The following sections are included:

• Introduction
• Test-Wiseness at the Mathematical Kangaroo
• Theoretical View for Constructing Distractors
• Items from the Point of Viewof Construction
• Items from the Point of Viewof Solving
• Conclusion
• Bibliography

Having taken a look at some connections between mathematics competitions and research on the one hand and the classroom on the other, we now shift our focus to possible positive consequences of mathematics competitions on entire countries…

The following sections are included:

• Introduction
• The Case of Colombia
• 2005. Bogotá. XV Congreso Colombiano de Matemáticas
• 2007. Medellín. XVI Congreso Colombiano de Matemáticas
• 2009. Cali. XVII Congreso Colombiano de Matemáticas
• 2011. Bucaramanga. XVIII Congreso Colombiano de Matemáticas
• 2013. Barranquilla. XIX Congreso Colombiano de Matemáticas
• 2015. Manizales. XX Congreso Colombiano de Matemáticas
• 2017. Bogotá. XXI Congreso Colombiano de Matemáticas
• Bibliography

The following sections are included:

• Introduction
• Mathematical Olympiads in Venezuela
• Conclusions

The following sections are included:

• History
• Organization
• Participation in the CPLP MO
• Elaboration of Tests
• Bibliography

In this part, we present several interesting alternatives to the more typical types of mathematics competitions. While there seems to be quite a wide consensus concerning the details of the most common types of math competitions, namely the Olympiad-style full solution contests on the one hand and the popular multiple-choice puzzle oriented events on the other, there are many aspects of these specific types of competitions that frequently come in for criticism. These include such points as the exclusion of technology, strict time limits, and the prohibition of teamwork, along with the limitation to specific types of pure-math topics. Many interesting attempts are constantly being tried out to address these issues, and seven such projects are described in this part…

The following sections are included:

• Introduction: A Brief History of the MMC
• The Problems: A Brief Anthology

The following sections are included:

• Introduction
• Benefits of this Competition
• Preparations in Advance
• How to Enter the Competition?
• Competition Day
• The History of Náboj
• Some Náboj Problems
  • Combinatorics: Náboj 2017, problem 48
  • Number theory: Náboj 2015, problem 29
  • Algebra: Náboj 2017, problem 42
  • Geometry: Náboj 2018, problem 1
  • Geometry: Náboj 2018, problem 15
  • Geometry: Náboj 2017, problem 13
  • Geometry: Náboj 2018, problem 20
  • Geometry: Náboj 2017, problem 35
  • Geometry: Náboj 2014, problem 56
• Bibliography

The following sections are included:

• Introduction
• CompMath Competition
• Problem Sets
• The Problem
• Acknowledgement
• Bibliography

The following sections are included:

• Introduction
• Problem Series 1
• Problem Series 2
• Problem Series 3
• Concluding Remarks
• Acknowledgment
• Bibliography

The following sections are included:

• An Autobiographical Introduction
• What is a Julia RobinsonMathematics Festival?
• The Audience
• The Content
• A Comparison of JRMF and Competition Materials
• Conclusion
• Acknowledgments
• Appendix
• Broken Calculators

The following sections are included:

• Movement 1: Archeology in Service of Math
• Ancient Persian Seal Stamp Sialk 4000 BC
• Movement 2: Tiling and Coloring
• Movement 3: Maths for Meds
• Movement 4: Math of Politics
• Bibliography

The following sections are included:

• Introduction
• Computational Thinking
• The Playground
• Hackathon
• Computational Thinking Cloud
• Pilot
• Afterword
• Bibliography

The following section is included:

• Index