Friday, April 20, 2018

Teach 180: Some Kindness (Day 144)

My daughter was getting her wisdom tooth out today. (Yes, only one.  I had four and her father had none.)  That meant that I was not at school.  However, I had a sense of how the school day started, because my daughter got a text from her friend.  On the table in the senior lounge were little slips of paper with each senior's name.  Every single senior.  Typed next to each name was a kind statement about them.  My daughter's read: you're sweet and sassy at the same time. you really care about people and want the world to be a more pleasant place

It was clear that they were written by a classmate, as some referenced a specific school event or growth and maturity over the course of the student's high school years.  If people shared kindness like this with each other on a daily basis, even a weekly basis, our world would be a better place.  Whoever the anonymous student was that did this, if you are reading my blog, I say "Thank you for taking the time to recognize what makes each student special and sharing it.  Your words will have a lasting effect beyond those simple strips of paper."

Thursday, April 19, 2018

Teach 180: Powers of i (Day 143)

Today I was visiting another teacher's classroom for an informal classroom observation.  They were talking about complex numbers and started to work with powers of i.  When I have taught complex numbers in the past, we calculate powers of i by noticing the pattern.  We recognize that there is a cycle of 4 and that i to any power can be determined based on where you are in the cycle.  In this class, the teacher was showing the complex plane for graphing complex numbers as she was talking about powers of i.  Then it dawned on me.  Why not visually represent powers of i and consider the cycle of 4 by seeing the complex number move around the complex plane?

Was there a Desmos Activity Builder lesson that already did this?  I did a quick search and came up empty.  That's when I created this in Desmos - Powers of i. If you hit the play button in line 6, you can see the power increasing by 1 and the number being plotted in the complex plane as it cycles, 1, i, -1, -i...  Here is an short screencast to show the animation.

Two things that would make this better are for the powers to display in a little box on the complex plane, as in i12, i13, etc., and for the coordinates of the point to be displayed as i, -1, -i, 1, etc. as the point moves around the screen.  Looks like I'll need to get into the computational layer of an Activity Builder for that.  Then, I would need to think about what questions to ask students.  Perhaps it is just as easy as "What do you notice?"  "What do you wonder?" and "Can you use this to find i103?"

Wednesday, April 18, 2018

Teach 180: GMD Shoutout (Day 142)

If you haven't heard of the Global Math Department, then you are missing out.  It is educators sharing their ideas, free of charge on Tuesday nights at 9 PM EST.  Topics are varied and include teaching ideas, assessment, technology and more.  Plus the talks span multiple grade bands.  I coordinate the hosts for each session and often serve as host myself.  Hosts help with tech glitches and moderate the chat room.  We have had some big names in the math education world present, including Matt Larson (NCTM President), Denis Sheeran (Hacking Mathematics), Michael Fenton, James Tanton, Rose Mary Zbiek, Dan Meyer, John Stevens (Classroom Chef), David Wees and others.  Sessions are recorded and you can access any of them once you join the GMD for free.  If you are interested in presenting a session or helping with hosting, please post a comment to this blog entry.