Wednesday, October 23, 2013

Mission #3: What Else is Happening Out There?

So it's week 3 of the Explore the MathTwitterBlogosphere extravaganza. Our task was to look through some of the really cool sites they had curated and find one that inspired us. Waiting for my computer to back up before I shut it down and headed home, I started looking through the list. 101 questions is cool and fun, although I haven't yet found anything I can apply. Estimation 180 is a fantastic idea, but I've been feeling crunched for time in class (the wandering mathematical discussions that I indulge because they're awesome, while cringing at the time that passes!) and don't think I have space for it.

Then. Oh my goodness, you guys. THIS. Visual Patterns. 3 figures. Different kinds of patterns. Some of the diagrams aren't even sequential! Some are 3.D.

This was the first one. I can't even tell what's happening! How many squares were being added?! I had to sit back down, grab a piece of scratch paper, and figure it out.

And then I did.

And then... I CHECKED IT. ON. THE. WEBSITE. See how they asked me how many squares were in step 43? Bam. No waiting until the next class to see if they got the right answer. It's right there.

So then I had to open my computer back up and change Friday's homework. B period Math 1 (9th graders, Algebra-level), you are about to figure out Pattern #109. Granted, I'm going to also make them document their thinking on paper. Because I'm more interested in their process than the answer for the 43rd figure. Does that take away from the coolness of doing mathematical thinking on an outside website? Not sure that it does, or that I care too much.

I'm excited because this is right in line with what we've been doing - finding rules and patterns. But it's presented in a different way than they're used to, and as I always tell my students, "you know I love when there's more than one way." They've pretty much mastered linear patterns at the point (we're halfway through our first term), but they need practice and periodic reminders, which this is perfect for.

Plus there's a nice variety of kinds of number patterns, from my initial investigation. So I'm going to lead them in slowly (Friday's Pattern #109 is linear and it gives them the first 3 figures). Freshmen can respond in interesting ways to change. "Wait, I was supposed to click on the link to open it?" So let's make the math super familiar at first.

Then maybe Pattern 82. Still linear and give them the first figures in order, but with legos. So that's fun. Then Pattern 111. Still linear, but the change in x, if you will, is no longer 1. Then maybe Pattern 103, a smooth quadratic. Pattern 102, a more tricky quadratic (in the category of "well, it's not linear, so try quadratic. Close, can we make it work?"). Then hit them with Pattern 108 - quadratic, but way above their level to figure out algebraically, so they have to use the shape. Back to a more reasonable quadratic with Pattern 101. Go to Pattern 95 - a straightforward cubic, but in THREE DIMENSIONS? Throw in a Pattern 107, which looks nonlinear perhaps (it's made of squares after all) but isn't. Pattern 29 which is in context so therefore trickier to apply strategies that may have become rote. Have them pick one - who can find the most interesting pattern that we haven't done yet?

Okay, now they're probably tired of the site. But spread out over several weeks, some in class and some at home, and the discussions we're having are about how you found the pattern. What was your strategy? Did you draw the next one? Make a table? How did you decide what kind of pattern it was? I'm betting we develop an even stronger toolbox of pattern-seeking and rule-finding strategies. And that is what I'm all about.

A non-Math 1 pattern

Just for fun, look at this one.
I found the table pattern (adding cubes). And that leaves us with a constant fourth difference. So this must be a 4th degree function. I could find it in a huge system of equations. Is there a better way?

Saturday, October 19, 2013

Exploring Twitter

So this week's Mission (number 2 for those keeping track at home) over at Explore the MathTwitterBlogosphere was to use my Twitter account, @LauraVHawkins, for math good. And now, I reflect!

One thing that I learned to appreciate was the power of the hashtag. Not just to be clever, it turns out. Adding #MToBS to the end of my tweets made them reach a whole new audience. Look and see my most successful tweet (by some measures):
2 Retweets and 3 Favorites! All from people who were not previously following me! So that's cool.

Tweeting a conversation is a bit too quick for me right now, though. I replied to a tweet about using the textbook less in class, and they replied back to me, and I... let it just lie there. And it seemed too lame to respond a day later, so...

Oh, but it was interesting to spend the week in a "How could I Tweet this?" state of mind. I do that sometimes with Facebook. When something super cool happens that I want to tell someone about, I start thinking about the status update I may write. Last weekend, we went to an amazing brunch at Lazy Bear underground restaurant. Not only was I dancing in my seat at the deliciousness of every course, (because there were so. many. courses), but I also took a picture of each course.

Want to see? Of course you do.

So one of my thoughts and hopes is to approach my math teaching more like other aspects of my life in terms of social media. What can I capture in words, photos or video to help me remember, celebrate or reflect on later?

Here's one attempt (inspired by 2 absent student). How do we find the solution to this problem using the rectangle model? (Where 2y^2+2y is the area of a rectangle, and 2 is the "length" so we just need to find the width.) I sadly didn't record it right the first time, though. So this video is missing the reactions of the first time around, but still cool. And that is what I will leave you with. Happy Weekend!

3.4A Problem 3 with 3D rectangle from Urban School of San Francisco on Vimeo.

Sunday, October 6, 2013

Math is Happening When?

Hello world! Welcome to my first entree into the world of blogging about my experiences teaching math. (You can see my first entree into the world of blogging about other things in my life here, if you're curious.) A little bit about my teaching history, for context:

Palo Alto and Namibia, Peace Corps

I started my teaching career as a long term sub in my hometown of Palo Alto. There, the wonderful Sue Duffek was my mentor, who I clung to tenaciously, since I had no teacher training at all. After that, off to Namibia where I taught Maths and English in a small village near the Angolan border.

Look at Meme Laura! Imagine trying to get good math done on that tiny blackboard with a limited chalk supply. The classroom looks pretty nice, and it was, except for the lack of electricity or running water on campus. During the rainy season, things were rough. It's hard to learn when you're wearing those same thin uniforms, but soaking wet and cold. Also you don't have a pencil.

San Francisco - Public Charter School

After 2 years there, I came back to the US and started teaching at a wonderful charter school, here in San Francisco. I had the privilege of working with some amazing educators there, including Mark Isero (whose Classroom Kindle Project is as an inspiration for the power of technology, hard work, and social media to benefit students). And my students there were amazing as well - truly remarkable assortment of young people. LHS taught me more about teaching in my 5 years there than I could imagine learning in any other school.

San Francisco - Small Private School

Aaaand, during those 5 years I worked so hard that I almost burnt out. I met my now-husband, and decided I wanted to be able to be in my personal life a bit more. The Math Gods smiled down on me, and I jumped at the opportunity to be able to teach with the most amazing math educator I have ever known, Henri Picciotto. They were also looking for someone to step into his enormous shoes and attempt to lead the department as he entered into retirement from full-time teaching. So now here I am, in my 4th year teaching at a wonderful small private school in San Francisco (and 3rd year as the Math Department Chair). 

This year, one of my goals was to continue to get more involved in the online math ed community. So when the inspiring Dan Meyer advertised the folks at Explore MTBoS who have created 8 weeks of missing to do just that, I signed right up! And here I am, writing my first blog entry!

Wish me luck.

What about the title, though?!

Also, my title come from one of my most-used reminders to students, "Life is happening now." Copyright my friend Lindsay Stiegler, a fabulous personal trainer who does not support just sitting there when you could be running a lap, or thinking about math.