{"id":10119,"date":"2014-01-10T01:36:23","date_gmt":"2014-01-10T07:36:23","guid":{"rendered":"https:\/\/uwm.edu\/news\/?p=10119"},"modified":"2015-11-12T08:27:54","modified_gmt":"2015-11-12T14:27:54","slug":"math-circle-taps-kids-creativity-in-problem-solving","status":"publish","type":"post","link":"https:\/\/uwm.edu\/news\/math-circle-taps-kids-creativity-in-problem-solving\/","title":{"rendered":"Math Circle taps kids\u2019 creativity in problem-solving"},"content":{"rendered":"

 <\/p>\n

\"\"<\/a>
William Hegelmeyer and Michael Vayninger work through a problem together.(Photo by Ryan Allsop<\/em>)<\/figcaption><\/figure>\n

If you\u2019ve never thought of math as a creative art, you\u2019re probably not alone. But three Letters and Science professors will disagree with you. Gabriella Pinter, Chris Hruska, and Boris Okun, all professors within the Department of Mathematical Sciences, teach middle and high schoolers how to find creative solutions to unconventional math problems through the 51ÁÔÆæ Math Circle.<\/p>\n

At each of Math Circle\u2019s weekly sessions, the professors use an entire hour to pose one or two problems to the youth. They do not suggest a method; they do not even promise that there is an answer. They do, however, guide the students in brainstorming ideas, working together as a class, and recognizing the underlying patterns and principles involved in the problem. What\u2019s more, this circle has a point.<\/p>\n

\u201cIt\u2019s giving them a feel of what it is like to actually do real mathematics,\u201d said Hruska. \u201cOr any real science,\u201d added Okun.<\/p>\n

A different kind of classroom<\/strong><\/p>\n

\"\"<\/a>
Chris Hruska, Associate Professor of Mathematics, works math problems with Georgia Kundrat and Ruba Sager. (Photo by Ryan Allsop)<\/em><\/figcaption><\/figure>\n

Real-world problems of any kind, they said, are rarely as straightforward as the ones you find in a textbook. The Math Circle complements classroom experiences by posing open-ended, frequently abstract questions that encourage young students to draw on a variety of skills, including their own ingenuity, to approach the problem.<\/p>\n

One problem they discussed involved dominoes and a chessboard. They took a chessboard \u2013 an eight by eight grid \u2013 and removed two opposite corner squares. They then asked the kids to cover the board with dominos so that every domino covered exactly two squares. The problem is admittedly contrived, but it\u2019s also more difficult than it first appears.<\/p>\n

Pinter, Hruska, and Okun make a point to distinguish the experience of the Math Circle from that of a traditional classroom. Aside from the unusual problems, they also deliberately remove common classroom elements. \u201cThere\u2019s no homework, and there\u2019s no commitments that you have to do something by a certain date,\u201d said Hruska. \u201cThey come if they are interested, and if they continue to be interested they continue coming. And if they are not interested, they just don\u2019t come back.\u201d<\/p>\n

The professors further distinguish their program from a math class by focusing the teens on learning to articulate the root of a problem \u2013 why an approach does or doesn\u2019t work \u2013 rather than only coming up with an answer. For example, it turns out the chessboard problem is impossible, and most students reach that conclusion after much trial and error. But explaining why it\u2019s impossible means understanding the fundamental predicament behind it, which the professors try to draw out of the students through discussion.<\/p>\n

The 51ÁÔÆæ Math Circle is the only math circle in Milwaukee, though the idea is not entirely novel. It happens to be a common extracurricular activity in eastern European countries, and immigration from those countries since the 1990s has brought the tradition to the United States. Today, math circles are scattered throughout the country, usually attached to a university and a bit more prevalent on the East and West Coasts than in the Midwest. Both Pinter and Okun, who grew up in Hungary and Russia, respectively, attended math circles as kids and said that their own positive experiences were major factors in initiating the program here. They\u2019ve patterned this math circle after ones they enjoyed but have also incorporated ideas from successful math circles they\u2019ve researched as adults. The goal in the 51ÁÔÆæ Math Circle has always been to help youth develop critical thinking skills and confidence in approaching situations they haven\u2019t encountered before.<\/p>\n

\u201cIf you\u2019re afraid that \u2018Oh, I don\u2019t want to do this problem because I don\u2019t know how to do that type of problem,\u2019 then you won\u2019t be very successful in your adult life no matter what career you\u2019re in,\u201d said Hruska.<\/p>\n

\u201cFrom my experience,\u201d said Okun, \u201cmost of my classmates in math circles didn\u2019t go into math careers, but they were successful in other areas. The point is to develop some sort of analytical thinking which is important in many careers.\u201d<\/p>\n

In other cities, math circles sometimes operate differently to meet different needs. One based in Madison, for example, functions to generate interest in math careers by presenting students unusual but true problems in math history as a lecture series similar to the 51ÁÔÆæ Science Bag. Other circles are gathering places for educators interested in brainstorming new ways to teach traditional subjects in their classes.<\/p>\n

Teaching creativity<\/strong><\/p>\n

When asked how she would like to see the 51ÁÔÆæ Math Circle grow in the future, Pinter responded that she would like to extend the program to elementary school students. She believes in the importance of showing students early in their education that math relies on creativity and diverse thinking. And though funneling kids into math careers has never been the purpose of the program, she feels that more students would choose to pursue those fields if they recognized this.<\/p>\n

\u201cThese students who are typically very creative and who can put things together in interesting ways \u2013 they cannot use their creativity in the math classroom, typically, so they turn to different things like music, for example, where they can freely express their creativity. I think you can do that in math also, but they don\u2019t see it,\u201d Pinter said.<\/p>\n

Creativity is important to math because not all problems are solved with an equation. For instance, one way to explain the chessboard problem is to take a Sharpie and color one half of a domino black and leave the other half white. You do this to show that no matter where you place the domino on the board, it\u2019s going to cover one black square and one white square. You realize, then, that opposite corners of a chessboard are always the same color. This means when you cut two corners out, you\u2019re stuck trying to cover a board that has more squares of one color than the other with dominoes that can only cover an equal number of each. It\u2019s impossible, but it takes a little creativity to explain why, and that\u2019s the real point of the problem.<\/p>\n

51ÁÔÆæ Math Circle runs throughout the school year on Wednesday nights at 5:30 p.m. in room E424A of the Engineering and Mathematical Sciences (EMS) building. Anyone interested is welcome to attend; however, problems are selected to be most appropriate for students in grades 7-12. More information can be obtained by contacting Gabriella Pinter at gapinter@uwm.edu<\/a>.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

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