Problem of the Week
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Check out the Alumni comments by scrolling to the bottom of the page! Problem of the Week has been a special feature of Princeton Friends School since its founding in 1987. All third to eighth graders take POW as a separate class that meets about once a week in sections grouped by age. Generally all students receive the same problem, and students are encouraged to work with classmates, friends, family members and teachers. This helps create a community interest in math. I strive to find problems that are fun, accessible to our third graders, provide some skill practice, offer challenges to even our most experienced eighth graders, and illustrate some important concept in math or reflect an important part of math history. Pascal's Triangle is a typical example, as it begins with just adding whole numbers, and its repetitive nature and rapid growth often fascinate younger students. Yet this same problem offers older students an opportunity to work on binomial coefficients, combinations, and advanced topics in number theory. Over the course of a year, I try to include problems that will call on different problem-solving strategies, illuminate different areas of math, and reflect our annual central study theme. Our current practice is to introduce a problem in one class, use the following class meeting for collaboration and discussion, and then in the next class hear what students have discovered and introduce the new POW. Please get in touch with comments, questions, and suggestions for new POW's! I can be reached at (609) 683-1194 x22 or richard@princetonfriendsschool.org. Dave Gibson is my co-teacher, and he can be reached at (609) 683-1194 x51 or at dave@princetonfriendsschool.org. -- Richard Allen Fischer For access to all other POW's that have been posted, click here. Problem of the Week NOTE: Documents may be downloaded in PDF format. Printing
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Please look for this in your browser. If you don't have Adobe Acrobat Reader, click the image below to download it. What Alumni Say about Problem of the Week"Almost every week I use ideas I first encountered in Problem of the Week. The most startling thing is that the best and most fun questions I address in my research more closely resemble POW questions than any homework or tests I have ever done; open-ended, discovery-oriented and, at their core, uncluttered." -- Josh G, PFS Class of '93, graduated from Harvard College and is currently a grad student in astrophysics at Berkeley. "From POW I have learned how to approach a problem -- to step swiftly away from intimidation, dive whole-heartedly into the thick of it, even knowing full well that the outcome may not necessarily be finding the solution. Perhaps the only result will be a mapping out of the contours of the problem -- uncovering new inlets and crevices leading on and on to new questions. But what is more exciting than simply going exploring? POW has given me a great deal of self confidence which I'm not sure I would otherwise possess. I know that you will never actually know if you can do anything unless you throw your whole self into trying." -- Megan J, PFS Class of '95, graduated from Yale College and will be attending medical school at Stony Brook. "I was actually thinking about POW the other day when talking in my education class about creating a vibrant learning environment in schools. So often the only math that people are exposed to until high school or even until college is a series of exercises in reproducing what the teacher tells them -- given an operation or procedure or formula, kids are asked to solve set problems with set answers, which are then evaluated as "right" or "wrong". This kind of mechanical reproduction of correct answers is the only image that kids have of the whole field of mathematics. To me the value of POW is that it exposes people from such an early age to the idea that math is a field of creativity, investigation, exploration, unsolved problems, art, games, music, puzzles, and so on and so on. I remember spending hours and hours in fourth grade doodling shapes in my notebooks trying to find a map that couldn't be colored with only four colors. In POW, math is presented in its full depth, and students are pushed to be creative, artistic, innovative, ambitious--and the concept of "right" and "wrong" is hardly emphasized at all. This exposure to the true depth and vibrance of math starting in elementary school I think is absolutely essential, and will serve students wonderfully as they go on to study more math or any other field in which creative and innovative thinking is important." -- Rebecca B, PFS Class of 2000, is a student at Swarthmore College, majoring in math and linguistics. |
