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How Great Problem Solvers Prepare to Change the World

Highlights from Expert Series

The following article shares highlights and insights from one of our Expert Series events, which are exclusive for Young Scholars and their parents.

Over nearly four decades, I’ve watched tens of thousands of great problem solvers prepare to change the world.  First, they were my competitors in math contests, then my friends, my college classmates, my coworkers, and over the last 20 years with Art of Problem Solving, my students.  In this presentation, I shared many of the common strategies these outstanding problem solvers used to develop the skills they need to make great contributions.

Here are the strategies I discussed:

  1. Listen – Great problem solvers ask great questions.  Some of your children will be reluctant to ask questions out of fear of admitting they don’t know something.  You can help them overcome that fear by modeling – ask questions yourself.  You might learn something, too!
  2. Read – Most (not all!) great problem solvers are voracious readers.  The number one thing most parents can do to help their young students (5-8 yrs) is probably simply feeding a reading habit.
  3. Write – At some point students need to learn how to communicate with the written word.  They’ll learn best if they’re in a situation where an editor hands their writing back to them covered in red ink with the expectation that they’ll keep rewriting until it’s good enough.
  4. Code – People who can talk to the machines have more and more options in the world, as do the people who can understand the people who talk to the machines.  So, even if experience with programming doesn’t mean “job as a programmer”, it can still unlock opportunities.
  5. Play – Solving really hard problems often requires a long period of experimentation and playing with ideas, of doing something just for sake of doing it, rather always working towards a specific goal.  Playing comes naturally to students, but we lose that facility as we age and demands on our time squeeze out our strongest intrinsic interests.  Try to keep space in your children’s day to keep a sense of playfulness alive.
  6. Exercise – Our mind and our emotions are connected to our physical well-being.  Establishing a habit of fitness will help students develop and maintain mental and emotional fitness for hard times.
  7. Explore – It gets harder and harder to explore new possible areas of interest after college.  Expose students to a wide range of opportunities before college to help them find a few activities that really resonate with them.
  8. Excel – And once they find one or two of those activities, help them create the time and space they need to master those activities.  Through developing expertise in one or two areas, they’ll learn the strategies they’ll need to quickly excel in new areas as needed in the future.
  9. Aspire – In the last decade or so, I’ve seen more and more of my students choose to pursue really hard, meaningful problems.  I hope your children choose to join them!

Additional Math and Coding Resources

Websites with more information about Art of Problem Solving programs:

  • artofproblemsolving.com – Our flagship website with an online school for very advanced middle and high school math/science students, our textbooks (physical and digital), a massive community of middle and high school problem-solvers, and some free problem-solving resources.
  • aopsacademy.org – Our learning centers in 12 locations around the US.
  • virtual.aopscademy.org – An online version of our learning centers, with classes starting in elementary school for math and language arts.
  • beastacademy.com – Our elementary school math curriculum, with both books and an online learning system.
  • beammath.org – A philanthropic effort I founded separate from Art of Problem Solving to offer advanced math opportunities to high-potential math students from underserved communities.

During the Q&A, some parents asked about math summer programs.  You can find an extensive list of summer programs with links to their websites as well as links to AoPS community members’ descriptions of the camp at artofproblemsolving.com/wiki/index.php/Mathematics_summer_program.

There were some questions about coding resources.  Here are some of my favorites combined with some that our engineering team highlighted:

  • Lightbot and Scratch for young kids.
  • Some of our engineers mentioned Game Maker as being an important activator of their desire to create with code.
  • Three that I’ve used myself in the last few years are Advent of Code, Codewars, and Project Euler. These are not great places to start for someone new to coding, but they are good sources of interesting problems.  Project Euler is most appropriate for the very mathy programmer.  (Perhaps that’s why it was probably the most immersive for me.)
  • Students interested in coding competitions should know about the USACO training site and guide.
  • Nand to Tetris might be interesting for somewhat older students who really want to learn how computers work.

Authored by: Richard Rusczyk

Bio: Richard Rusczyk founded Art of Problem Solving in 2003 to teach avid math students in an innovative, interactive way. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving’s Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving’s Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He received the World Federation of National Mathematics Competitions Paul Erdös Award in 2014. He graduated from Princeton University in 1993.

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