In Memoriam: Grant Wiggins

I was shocked and saddened at the sudden passing of renowned educator Grant Wiggins earlier this week.

I can’t say that I knew Grant well, but I felt like I did.  Through his prolific blogging and tweeting, Grant shared his philosophies, passions, and provocations with me and thousands of others on a regular basis.  And, of course, Understanding by Design has made a real impact on education.

Grant had strong opinions about teaching and learning, which were rooted in a lifetime of experience in schools and classrooms all over the world.   He reveled in being provocative, in challenging teachers about what they do and why they do it.  But he did so in a way that demonstrated a great respect for the work of teachers and students.

Grant argued publicly and passionately for reforming education.  The word “reform” carries a lot of negativity these days, but I came to understand that Grant’s notions of reform were not political:  they were genuinely about teaching, learning, schooling, and student experience.  And they were directly connected to both research and practice.  While I didn’t always agree with his positions and prescriptions, I always learned by listening, and I always went away thinking and reflecting more deeply about my own views.

I feel fortunate to have had some opportunities to interact with him personally, through our blog-exchanges, and via email and Twitter.  I learned a lot by talking and arguing with him, and can honestly say he has had a significant impact on me as a teacher.  Even today, I’m still mentally drafting responses to things he wrote or said.

He will be missed, both personally and professionally.  His spirit will continue to influence what I do and how I do it, and for that I will be forever grateful.  I’m sure many others feel the same.

A memorial for Grant Wiggins can be found at AuthenticEducation.org.

Cavalieri’s Principle and 3D Printing

These 3D printed objects served as an excellent starting point for a classroom conversation on Cavalieri’s Principle.

3DP and Cavalieri

Each shape above is an extrusion of the same square.  In the middle, the square moves straight up; at left, the square travels in a complete circle from bottom to top; and at right, the square moves along a line segment and back.

The objects all have the same height.  Since at every level they have the same cross-sectional area, by Cavalieri’s Principle they all have the same volume!

Cavalieri’s Principle is a simple but powerful idea, and one that can be easily demonstrated around the house.  Here are some other examples using CDs and CD cases.

 

05/21/2015 — Happy Derangement Day!

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:

20150521

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.

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