Today we celebrate a Derangement Day! Usually I call a day like today a Permutation Day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:
The numbers of the month and day are a derangement of the year: that is, they are a permutation of the digits of the year in which no digit remains in its original place!
Derangements pop up in some interesting places, and are connected to many rich mathematical ideas. The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion. Derangements also figure in to some calculations of e and rook polynomials.
So enjoy Derangement Day! Today, it’s ok to be totally out of order.
I personally enjoy writing, and as a math teacher I love getting my students writing about math.
One of my favorite writing assignments for students is math-themed haiku. The rigid constraints of haiku make it an easy exercise, it allows students to access and interact with mathematical ideas in a different and creative way, and the elegance and efficiency of the form evoke the character of mathematics itself.
Here are some selections from this year’s Geometry class. Enjoy!
A rhombus and rectangle
Also known as square
A polyhedra’s paint job
An unfolded thing
|Two, the same as two
A number equals itself
For a point, a line, a plane
At the base of math
|As some things, unknown
The things we can’t do alone
Some things just seem to work out
So we find out why
Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.
This is our third Permutation Day of the year, and we’ve got a few more coming up.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
One of my guiding principles as a math teacher, as I articulate in this TEDx talk, is to provide students with tools and opportunities to create with mathematics. Few things are as aligned with that principle as well as Geogebra, the free, open-source, dynamic geometry environment.
I’ve integrated a lot of Geogebra work in my Geometry class this year. I use Geogebra assignments to assess basic geometric skills, to connect old ideas to new, and to explore geometry dynamically.
But much like geometry itself, once you master a few elementary rules in Geogebra, you can create amazing and beautiful works of mathematics.
Below is an example of some wonderful student work from this year. After an introduction to polygons, students were given two simple ideas for creating new objects from polygons: constructing diagonals and extending sides. I gave students some technical tips on how to color and polish their final products, and invited them to be creative. As usual, they did not disappoint.
Students, and teachers, need more opportunities to create with mathematics. We’re fortunate to have technologies like Geogebra that offer us those opportunities.
I’m excited to announce that I have been invited to speak at the 2016 Kansas City Mathematics Technology Expo!
For 25 years, the KC Math Tech Expo has brought together mathematics teachers from the college and secondary level to discuss technology and teaching. This year’s conference will be held October 7th and 8th at the University of Missouri, Kansas City.
I’ll be giving the Invited Address on Saturday, and mathematician and 3D-printing expert Laura Taalman will be giving the Keynote on Friday evening. You can find out more about the conference here.
I’m looking forward to connecting with teachers through mathematics and technology in Kansas City this October!