Fawn Nguyen, a middle school math teacher who has a great blog where her fun personality shines through (I think it’s her personality…I’ve never met her!). Just the other day, in one of her posts on her blog Finding Ways to Nguyen Students Over, she struck a chord with me when she dissed a book that I have so far avoided in favor of more interesting reading about MATH (what does that say about Fawn and me??)
She wrote: “Jesus. I’d rather stick needles in my eyes than read another page of Fifty Shades.” Then added “… makes me want to kick someone. Since when does the word THERE get italicized so damn often?!” My kind of gal. She then mentioned that she was reading a new book on Ramanujan and said she’d send a copy to the first person who emailed her. On a lark, I emailed her, although the post was 2 hours old. I got an email back that another reader, who responded in 5 minutes, had already won. Ah, the cutthroat world of the blogosphere. I had just barely had time to recover my composure after my defeat when I got another email from Fawn saying she had sent me the book anyway! I like Fawn!
Today, I read Fawn’s new post about an idea for a site that featured growing visual patterns. She has now set up the site with it’s own domain name http://www.visualpatterns.org/. So far there are 21 patterns posted. Definitely worth checking out.
In her visual patterns post, she linked to a previous post discussing a lesson where she had her students create pattern posters. The post included a very interesting discussion with a student who had an equation y = 4n – 4 that worked for the pattern, but the way he had organized his pictorial representation led to the equation y = 4(n – 1). It’s worth reading this conversation and witnessing a good teacher at work. I’ve copied the conversation between Fawn and Chris below. However, it’s worth looking at the whole post which includes the lesson handout.
The following is copied from Fawn’s post Patterns Posters for Algebra I
I’m now working with Chris. He has this pattern:
His sketch of the 13th step looks like this:
At the bottom of his paper, I see he has this expression for the pattern:
Our conversation goes something like this:
Me: Okay. Show me why the “plus 4″ in the expression?
Chris: Hmmmm. The equation works.
Me: I didn’t say it wouldn’t work. I just want to see where “plus 4″ is in your sketch. Let’s take a look at your sketch for step 13 here. How did you get “4n + 4″ from the drawing?
Me: You’re right! Your expression works. That’s good, Chris! But your sketch doesn’t match up with it… Think about what I mean by that, I’ll be back.
About five minutes later, I return to Chris’s desk, “How are you doing?” He says, “The ‘plus 4′ is the 4 corners.” Yes!!!! So as I talk with him, he realizes that these two sketches jive more with “4n + 4,” and he’s able to verbalize that whatever step number you’re on, there’ll be four groups of it around the square, and the “plus 4″ is for the 4 corners.
We go back to his original sketch of step 13 and come up with a general sketch.
And he is able to write an expression that would represent these sketches better:
Then I ask, “Well, are these two expressions the same?” Chris looks at me like I need a refresher course on how to distribute.
In this exchange, Fawn moved the student towards realizing that the two representations didn’t match via questioning, not telling. By my reckoning, her teacher moves elicited the student to display many of the CCSSM Practice Standards:
# 1 Make sense of problem and persevere in solving them.
# 2 Reason abstractly and quantitatively
# 3 Construct viable arguments
# 6 Attend to precision
# 7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning
Thank you, Fawn, for developing a good lesson, sharing it with us, sharing student work and conversations, and for taking it a step further by creating a website devoted to visual patterns.