AL, Comical

 

AL, Logical, available on Kickstarter until March 5th!

Perhaps the question that have come up the most in discussing AL, Logical with people:

Why a comic book?

Time passes between panels, and it's especially good when we are seeing problem-solving. Something happens. She's THINKING. 

The reader's perspective can be quite different than in prose. Xavier (coauthor, pencils, inks, colors and letters!) is especially strong on showing action instead of telling about it. When the house is moving, we don't see the house changing, we see the elder god seeing the house changing (we see it in its eye). It's humanizing.  Comic books help you to take the perspective of the people in the story. We see AL the way the mathematician sees her, and vice versa. 

And then there are all the joyful little visual tricks he does, like "hey there" backwards in Chapter 4. Fun, but also serves the story. It also offers the reader a chance to notice. Also in Chapter 4 there are a lot of clocks. What's happening with them? 

A big part of our impetus for writing the book is that I see math as being all about problem solving, and he sees art as being all about problem solving. And he does a lot of problem solving throughout the book, which gives readers two ways into AL's problem solving experience.

In a sense, the comic book format literally allows the reader to see math how we see it. 

This might be just because we are a comic book loving family (well, 3/4 of us and one patient parent), but comics are a story form that invites rereading. Even a 70ish page comic like this one is about like three issues of a comic book. Readers have taken from a half an hour to an hour to read it, almost inviting you to pick it back up, look at specific pages, see if the beginning makes sense with the end... go where your attention takes you. Partly because of the story, and mostly because of Xavier's art, the comic really offers a lot of chances to make connections as a reader, and to notice AL making connections in her thinking and experiences.

There are some other math comic books (see the list at the end of the AL, Logical page on the blog), but this one is pretty distinct from those. As fond as I am of them! In our comic, we really worked to make it about the narrative, not a math lesson in disguise. While still having fun, real mathematics.

Please take a look, and help us spread the word.

PS> My previous blog post about the book goes into some of the relevant frameworks behind the math content and the math processes we get to see in the story.

AL, Logical

 The mathy graphic novel I wrote with my high school art teacher son Xavier is up on Kickstarter!

The Kickstarter has a lot of information about the story, so I'll geek out here a bit more.

We started with the protagonist: a middle school student who knew she wasn't a math person. The haunted house idea came along pretty early. And a pretty cosmic haunted house with some Cthulu near relatives peeking in.

One of the frameworks we built the story around are the Van Hiele levels of geometric reasoning. This let AL develop and tackle more complex problems as the story progresses.

Though AL does more than geometry as she's tackling problems from all different kinds of math.

A lot of math comics are directly trying to teach some specific content. This comic is about trying to show the experience of doing math. The framework that helped the most for this is from Tracy Johnston Zager's Becoming the Math Teacher You Wish You'd Had. These chapters...

3: Mathematicians Take Risks

4: Mathematicians Make Mistakes

5: Mathematicians are Precise

6: Mathematicians Rise To A Challenge

7: Mathematicians Ask Questions

8: Mathematicians Connect Ideas

9: Mathematicians Use Intuition

10: Mathematicians Reason

11: Mathematicians Prove

12: Mathematicians Work Together and Alone

... really give you a great feel for what doing math is.

All this might make it sound dry, but the focus was on the story. Very inspired by stories like The Phantom Tollbooth, and our love for comic books, we were glad to see that the beta readers found it fun.

More about the story and other mathy comics in the AL, Logical tab, and of course at the Kickstarter!

Who WIns?

 I'm teaching our Statistics and Probability for K-8 Teachers for the first time. Had excellent support and suggestions from Jenna Laib, colleagues Jon Hasenbank, David Coffey and Hope Gerson, and from Stephanie Casey and ESTEEM folks.

Working out bit by bit what we're going to do. Luckily I get to teach it again next year...

We just finished our first week, and I loved how the Day 2 lesson worked out, so I wanted to share it and think about it a bit. I miss the reflection of blog writing about my teaching!

On Day 1 we had started exploring measures of typical. We got out the unifix cubes, and did a bit on how could we make the distribution more fair. It took several rounds of give aways, but we got there. Some tubs of 252 and some with 251. Then each person built a stack as long as their first name. We organized from shortest to longest and thought about how to answer "How long is a 323 student's first name?" We had initial estimates, then talk went to median and mean. We retooled and did full legal names. Much bigger range, but a surprisingly dominant mode. So there was another consideration. Our emphasis was not the number you said to answer the question, but why you would say so.

Each day one of the teachers leads a Slow Reveal Graph, and Day 2 Tessa started us out on Disney Princess Baby Names, so energy was pretty high. If they had to name kids with Disney princess names they'd go with Belle and Aurora. Yvette's great question was what can you say about this without calculating?

Good discussion. I added in that since all of them had 7 elements, we could just look for a total instead of dividing. Some good call backs to Day 1's discussion of mean and balancing or distributing.

Then the main activity. They used NRICH's great millisecond timer tool and each collected 5 points of data for trying to hit 10 seconds exactly. They each found their median and mean, and thought about what would make a better measurement of who was best at estimating 10 seconds. Uniformly, each table decided on the mean. I raised up the idea of how some sporting events use your best score. They decided that they wanted to include outliers, that consistency matters.

The NRICH page that got me started on this idea had a set of data for discussion, which they credited to the great Don Steward, from his awesome Median blog.

Anna	Ben	Charlie
31	36	37
26	19	32
32	39	24
27	36	32
29	20	30

Typically great prompt from Don. They all found Ben had a mean of 30, though they all thought he was the worst of the three. People were divided over whether Anna or Charlie should win. People liked Anna's accuracy, but others were compelled by Charlie's spot on 30 seconds. They had time to propose a new summary statistic to answer the question of who is best.

One table proposed |mean-30|+|median-30|+range, low score wins. Another table proposed just the best score, tie broken by 2nd best time. Voting was mostly in favor of the more complicated statistic. But definitely the Charlie fans wanted best time. 

And then the breakthrough moment! Someone said 'What if we just totaled up how far each guess was from the target?' Absolute deviation! I tried to play calm and cool, and gave them time to think about it.

Revoted, and people went 22/24 for the absolute deviation. My inner teacher was screaming.

They reevaluated their own times using this metric, and decided on a table representative for the class champion. Then, a class championship, three rounds. Very exciting, started close, and then someone ran away with it.

In their summary, lots of great discussion about variation, mean, median and their limitations.