Player 1 passes a penny to player 2 who then passes

Info icon This preview shows pages 20–24. Sign up to view the full content.

View Full Document Right Arrow Icon
each has a single penny.  Player 1 passes a penny to  Player  2,  who  then  passes  two  pennies  to  Player  3.  Player  3  then  passes  one  penny  to  Player  4,  who  passes  two  pennies  to  Player  5,  and  so  on,  players  alternately  passing  one  penny  or  two  to  the  next  player who still has some pennies. A player who runs  out of pennies drops out of the game and leaves the  table.  Find  an  infinite  set  of  numbers  n  for  which  some player ends up with all  n  pennies.  Putnam, 1997
Image of page 20

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Problems 5. What is the expected length of a standard  NHL shootout where the probability of each  shooter scoring a goal is 1/3?  AMTNYS : Jan ’07
Image of page 21
Looking Back As a student… Math is about exploring problems. “School math” is necessary for “real math.” Problem solving is not random. Problem solving is developable. A positive attitude promotes clear thinking.
Image of page 22

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Reflections (Looking Back) As a prospective teacher… Finding problems genuine to students is key. Teachers must model effective strategies. Students should learn how mathematics’ great  thinkers approached problems historically. Struggling through problems helps teachers  empathize with struggling students. A positive attitude promotes clear thinking.
Image of page 23
So, what now? I will…. …explicitly teach the tools and tactics and model the self- questioning techniques learned from my research. …develop a repertoire of creative problems to assign for extra  credit, in addition to more innovative homework. …encourage students to investigate problems genuine to them. …foster an environment of creativity and risk-taking. …incorporate the mathematical history of content into lessons. …continue to solve problems and work independently.
Image of page 24
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern