Toothpick, Vampire and Domino Sequences
(Clifford Pickover, 1994)
Recreational mathematics is on the fringes of mathematics, but its real worth is in mathematical pedagogy. Vampire Numbers are a perfect example. They are ridiculous. Most mathematicians would not take time to look at them because they lead to little else of interest. They’re a DEAD end.
But like a lot of recreational mathematics, their true home is in the classroom where their weirdness is an asset.
P.S. Clifford Pickover created the Vampire sequence. The other sequences were created by others. You can find them on the Online Encyclopedia of Integer Sequences.
God made integers, all else is the work of man.Leopold Kronecker
Standards for Mathematical Practice
MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:
MP1 Toughen up!
This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.
MP3 Work together!
This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.
MP6 Be precise!
This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.
MP7 Be observant!
One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.