Tags: art, beauty, nature, science
Happy New Year everyone! WordPress has just informed me that my blog received about 6,700 views in 2012. Given that 600 people reached the top of Mt. Everest in 2012, we could say that it would take 11 years for all of my viewers to climb Mt. Everest…but this would be ridiculous (yet entertaining) logic. See you next year!!
Argyll Halloween 2012. (This is a link to our school slide show from the day.)
We had the most wonderful day yesterday here at the Edmonton Campus. Thanks to all the families that stopped in to celebrate with us. And a special thanks to my Math 30-1 class. You were so understanding of all the disruptions from our on-site celebration.
Some of you asked how I did my hair for Bellatrix LeStrange. Well, it was a two hour ordeal. My hairdresser sprayed and teased and curled my natural hair. Then we inserted four extension clumps from the dollar store. More teasing and back combing and spraying. Then we cut some strands from the extensions and hot glued them to bobby pins. Those became the tendrils that hung over my face. All of this took place on October 30, so I had to sleep very carefully!
What does this have to do with math? Not much. It’s about fun and indulging in the playfulness of Halloween. And I suppose it brings to mind two ideas that strike me as important.
One, math IS fun. In my teaching, I try to impart my love of playing with mathematics, from testing ideas with outrageous options to using math to create interesting stories and images.
And two, in the words of Maya Angelou:
“I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.”
Last week, I saw Maya Angelou live at the Winspear. She reminded me about how important it is to engage in celebrations as a community. For many, Halloween may seem like a distraction from learning. But I see it as a platform to build strong and lasting relationships. I loved the opportunity to improvise with elementary students, to notice the efforts they made on their costumes, to honour a cultural tradition together, and to show how I can be silly…. and, of course, “evil”.
Michael: I don’t understand why it is that when I reflect y=lxl-4 about the y-axis, the only invariant point is (0,-4). I think they are all invariant, because the reflected graph and the original graph are identical.
Me: Well, I see what you are saying. It looks as if nothing changed so you are concluding that none of the points moved. But in fact, the left side became the right side and the right side became the left. Do you see?
Michael: Not really.
Me: Okay, I am trying to get inside your mind to understand what you are thinking.
Michael: And I am trying to get inside your mind.
Me: Hmmm…. Oh, how about this. What if a doctor cut off both my arms –I know this is gross but it is all I can think of. And he sews my right arm on my left side and my left arm on my right side. Aside from the thumbs going the wrong direction, I could look unchanged to many people. (Secretly knowing that this analogy was very bad, but keeping hopefulness in my voice, just in case.) Now do you see?
Me: That was horrible, I know. Oh wait. Here it is. What if I switch my earrings? The earrings have switched places but my appearance does not appear different. We KNOW that the earings switched places, it just LOOKS like nothing happened. The invariant “point” in this analogy is everything else on my head. Only the earrings switched.
Michael: Okay, I got it. So, only (0, -4) is invariant, because it is on the line of reflection?
Me: Yes…. Sorry about the story about my arms. That was a terrible idea.
Me: Molly, if we have 9 strips of bacon, and three people, how many to do we get each?
Molly: (without hesitation) Three.
Me: How do you know? (in the distance, we hear Jack interject “I would get four!”)
Molly: Because I can count by threes. (Again, in the distance, ”I would get four!”)
Me: You did not hesitate! I think that means you may have been dividing. Nine divided into three equal groups makes three in each group. (Switching to my now neglected child.) Jack do you remember when you had just turned 6 and I purchased two cookies to share between you, Molly, and me. You were worried about how we would share. I asked you what we should do and you said, without any pause, 2/3 each. That was amazing for a 6 year old. You were even able to tell me how you got that number.
Jack: That is easy. You just divide each cookie into three pieces, because there are three people, then give each of us two pieces.
Me: That is exactly what you said then! I had been thinking that Molly and I would share one and you could have the other.
Jack: You mean I got less cookie because of my good math?! That sucks…. Molly, if mom did not have any bacon, how many would we each get?
Molly: One of us would get 4, probably you, and one of us would get 3. No wait, that is seven. One of us would get 5 and one of us would get 4.
Me: What if you each got four and you split the extra one?
Jack: We would each get 4 and “one and a half thirds”. (Grin)
I smiled with huge math teacher/mother pride. It is important to notice when math is part of your daily life. Sharing things is a lovely space for doing work with fractions.