John Koker, mathematics professor and dean of the College of Letters and Science at the University of Wisconsin Oshkosh, gave the commencement address at the University’s midyear ceremony Dec. 18.
Here is a transcript of his speech:
“Congratulations to all the graduates! Celebrate and be happy — you have earned it.
“Over the years, I have worked on numerous mathematical and other types of problems, and I have learned a lot by working on them. My definition of a problem is simply ‘something you don’t know how to do.’ Because, if you knew what to do, you would do it, and thus, you wouldn’t have a problem. Our individual experiences determine what situations are problems and which aren’t.
“I have learned that all problem solving starts with the problem solver being stuck (since a problem is something you don’t know how to do). Being stuck is a natural and honorable state during the problem-solving process. I have learned that being unwilling to stay stuck helps a lot in the problem-solving process. I have learned that we can all become better problem solvers and that we need to develop a healthy frustration about being stuck. Frustration should be confronted rather than avoided — to avoid frustration is to avoid learning.
“I am going to give you three problems and then discuss what I have learned from them. You choose: Listen to me or work on the problems.
“Problem No. 1
“Rosemary can paint a room in five hours, and Fred can paint the same room in seven hours. How long will it take them to paint the room if they work together?
“Every time I assign this problem, someone says the answer is six. I respond, ‘Rosemary can do it in five hours. She gets some help, and it takes her six?’
“Recently, this problem made me think of my mother, who would often enlist me to help with a household chore. I would follow her around, dawdle and loudly sigh. Eventually she would say, ‘Go out and play. I can do this faster myself.’
“Everywhere you look, there are problems that need to be solved — in business, in government, in education — problems surrounding the economy, diversity, and our communities. We may think that the trick is to hire or elect smart individuals to solve these problems for us. However, a recent study at Carnegie Mellon University revealed that might not be the answer.
“Researchers found that collaborative groups who conversed easily with equal participation were more efficient and produced better results in problem-solving situations than groups dominated by individuals. It may take longer as we work towards solutions and compromise, but it is more effective and satisfying.
“According to a September 2010 Pew Research Center Publication, about half (49 percent) of us say we most admire political leaders who stick to their positions without compromising, while slightly fewer (42 percent) say that we most admire political leaders who make compromises with people they disagree with.
“There are many instances where we chose to do nothing rather than to work with others. When confronted with a problem, work to create a supportive atmosphere of questioning and challenging. Continue to develop the ability to work cooperatively and effectively with others in ways that respect the contributions from all participants.
“Problem No. 2
“A drawer of Tom’s dresser has five brown socks and seven black socks. Without looking, Tom reaches into the drawer and picks a sock. He checks the color. He repeats until he has a pair of socks — that is, at least two socks of the same color among the socks he has picked. What is the most number of socks that Tom would ever need to draw so that he can be sure he has at least one pair of socks?
“I always thought this was a silly problem. Maybe since I know, as a math teacher, I can get away with wearing two socks of different colors! So what’s the point? The problem does have some ‘real world’ features — how many of us have an odd number of socks of a given color?
“I am sure many of you have asked, ‘What’s the point?’ in response to a number of experiences here — both inside and outside the classroom.
“While you work to reach your career goals, I challenge you to find your role in a diverse, democratic society and world community, to have a greater appreciation for the fine and performing arts, and to develop your ethical and moral sensibility. Continue to develop the skills and knowledge to succeed professionally, to participate in communities and to enhance your whole-life experience.
“Many of your college experiences were designed to have a problem-solving focus and were intended to have you reflect on processes rather than memorize facts or answers. Problem solving, while provoked by contradiction and tension, is something in which we all need to be engaged as it empowers us to think deeply and act constructively. My college education is the foundation that supports most of my work and play. Each and every day, although my college days are long ago, I find new answers to the question ‘What’s the point?’
“The ‘point’ is to help you prepare for life after graduation. And to me that means further education and lifelong learning, civic leadership and community engagement, a successful career, and opportunities to pursue your passions and hobbies.
“Problem No. 3
“Art rolls a pair of dice and gets a five. Art, who made a large bet, continues to roll the dice. He wins if he rolls another five before he rolls a seven. What is the probability that Art will roll a five before he rolls a seven?
“I am not sure what luck is. Some say it’s a combination of circumstances or events operating by chance to bring good or ill to a person. I raise the ideas of luck and chance because sometimes it seems we continually deal with problems that are apparently brought on by chance or by external forces, rather than our own actions. Sometimes it feels as if we continually have bad luck.
“At this beginning, I challenge you to take the initiative. At times you may feel that your values, ideals and what is most important to you is under attack. You may feel pressure to become more accommodating and follow the crowd. Sometimes you will feel uncertain how to proceed. Remember, being stuck simply means you have a problem. You will need to choose. Do you want to stay stuck and leave things to chance? Or do you want to shape the future, cause change and solve problems?
“While working on a problem, give yourself credit for little successes and a lot of credit for larger successes. If you focus too long on how many times you were stuck and frustrated, you may begin to believe you are unable to solve the problem. Expert problem solvers become stuck and frustrated more often then they reach the aha!
“Much of life can be viewed we as an open-ended problem-solving activity and, as such, cannot be reduced to template or algorithmic behavior. There are many unanswered, open questions that you will encounter. Learning is about finding one’s way through the unfamiliar and making sense out of it.
“While the unknown lies ahead, today is a time to pause and celebrate. You solved a big problem. You’re graduating. When you hear your name called, be proud. And realize your name is being called because of your hard work and persistence, not because of luck!
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