Eureka! and Mathematical Thinking

This weekend, David Leschinsky, Eureka’s founder and owner, was in Atlanta for the tenth biennial “Gathering 4 Gardner.” This event celebrates the life and accomplishments of math and puzzle whiz Martin Gardner, whose many achievements in popularizing mathematics and recreational puzzle-solving we have previously discussed in this blog post. Fans and professionals from around the country and the world come together at this conference to give presentations and share new discoveries and inventions.

David was at the Gathering to exchange notes with the many puzzle enthusiasts he’s become friends with over the years, and discover new books and puzzles to bring into the store – and there will be plenty of cool new merchandise here in the next few weeks as a result! But he was also there to present on the topic of mathematical thinking: how, in its many forms and varieties, it applies to our daily lives, and how games – both solo and multiplayer – can improve and even transform our aptitude for it.

Mathematical thinking isn’t just a matter of figures and equations. It’s a whole array of mental processes that allow us to take real-world problems, and create abstract models of them in our minds, which we can use to break the problem into manageable pieces and understand how different aspects of the problem relate to one another. Whenever we pack a suitcase, organize our schedules, decorate a room or maneuver a sofa through a house, we are using mathematical thinking. On a higher level, mathematical thinking is the set of essential tools we use to address problems and craft strategies in a huge variety of professional endeavors: engineering, population studies, demographic models, economic models, business plans, graphic design and all the experimental sciences, among many others.

One crucial ability in mathematical thinking is known as “flexibility of mind.” Often, in addressing a multifaceted problem, we have to create an abstract model in our heads, and then abandon that model in favor of a new one as we delve deeper into the problem – in short, we need to be able to shift perspectives to balance different needs. For example, imagine you have to set up a school cafeteria for an after-school event. You might first address the issue of space: how will you set up tables and chairs so that there is enough room for everyone, people don’t feel crowded, and people can move between different exhibits or activities. That would suggest one set-up for the room; but then you might address the issue of time. Say you have several speakers who need to give presentations throughout the night; how will you arrange their seating so that they can easily address the whole room? What if there are posters that need to be visible to all attendees? How should you arrange the room to comply with fire codes? What if children and adults have different activities and need different areas? When you combine the solutions to all these models to arrive at a compromise that suits the whole, you are demonstrating flexibility of mind.

One of David’s constant interests has been matching individual aspects of mathematical thinking to particular puzzles that help to build those skills. For the Gathering 4 Gardner, David expanded this idea to address games as well as puzzles. His chart of popular games matched to different kinds of mathematical thinking can be found here.

Building your mathematical thinking skills has daily applications in your life, increasing your flexibility as a thinker and your ability to visualize complex problems as aggregations of simpler problems, and to recognize patterns between diverse problems. If you’re curious about games and puzzles that can help improve your mathematical thinking skills, stop by Eureka and ask us about our favorite games that translate abstract skill sets into tangible objectives.

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