Problems for Entertainment and Enrichment


Over my years teaching mathematics at many levels, I accumulated a number of quirky puzzles related to math. Most are accessible by simple arithmetic. A number can be used as an introduction to related mathematical topics. I am sharing these as a potential classroom resource.

Two cautions: Regrettably, I did not consistently collect source information nor did I check publication rights. Many of these date back a number of years, and I no longer remember whether or not I’ve verified the solution.



Some people consider the depression year 1930 unlucky because the sum of the digits totaled 13. What is the next year in which the numbers will again total 13?  (Otto P. Kramer, Games Magazine, Feb. 1983) 



Relations Between a College's Administration and Professional Staff



Recently our college had a difficult time bargaining a new contract for the faculty. Rather than get into the particulars of contract issues, I would like to focus attention on what has happened to the state of relations between the professional staff and the administration. The negotiating process exacerbated an already tense relationship. I do not pretend to understand the priorities of the administration or the financial position of the institution, but I do understand education and how the education process works.

 Education and training are the product of our college. They are what we “sell.” The number of students who come through our doors depends directly on the quality of that product. Good education comes from good educators working together to create high caliber classes and innovative curriculum. A major role of administration is to foster and enable this cooperation by providing resources, coordination, and leadership.

 Developing quality, innovative courses requires time and energy outside of the classroom. Few educators are satisfied to teach the same material the same way year after year. Good teachers constantly look for new techniques to motivate students so they get the most out of class. Besides, doing the same thing every semester is boring. If instructors’ natural innovation and creativity are going to be harnessed for the good of college as a whole, the administration must give its faculty resources, coordination, and leadership.

A “warm body” in front of a class (or behind a computer for an online course) can deliver course material, but is that a quality product? Unfortunately all too many of our classes are delivered by adjunct instructors. For some subjects this is a benefit because the adjuncts are practicing professionals who bring current, specialized knowledge into our college. However, it also means students are exposed to a very mixed bag of quality. Full time faculty can help mitigate this problem by creating model courses and guidelines to support high standards. This cooperation takes resources, coordination, and leadership.

 In my years in education, I have seen both good and bad relations between administration and professional staff. Some administrators have had a very poor relationship with our educators. No trust existed. Faculty edured administrators who had little interest in our college’s reputation for delivering quality education. Innovation was mandated to keep up area rivals. We followed no strategic plan for advancement as an institution. Internally, an us-versus-them attitude created a weak institution which delayed important advances at our college.

An adversarial relationship does not vanish overnight. Faculty suspicion and distrust of management linger after a new president and his or her administration take over. When a college’s leadership is not trusted, initiatives and innovations are reflexively opposed. It takes time and effort to cultivate a positive relationship with the professional staff. Unfortunately, mistrust and antagonism can be reignited all too easily.

 I am close to the end of my career in education, but I am deeply worried about the future of our college as an innovative educational institution. The poisonous atmosphere created by the recent difficult negotiations has deeply affected attitudes of our professional staff. While our educators still innovate, and will implement on an individual basis. There is no collective plan; No vision.

 Creativity and innovation take time and energy. Unfortunately the current crisis over collective bargaining has sucked time and energy out of this institution to no good end. How long will it take to rebuild a positive, trusting relationship between the leadership and the professionals who deliver the educational product? When will our educators be able to work with our administration to provide the best possible education to students in our service district?

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