Monthly Archives: September 2011

Homework this week: “free-choice time”

Does that title shout “paradox” to you? It certainly did when I said it aloud, but it’s true. “You pick” was the homework I actually assigned every day this week. On purpose. I didn’t even write it on paper.

I’ve been talking a lot about the importance of student choice and control in posts like this, this, and this one, but I’m not alone. On his own blog, Steve Miranda has described time and time again ways in which student interest controls almost everything at his school, and has lead to incredible growth and ability in its students. Saint Ann’s bestie, Justin Lanier, is posting all sorts of goodness specific to implementing student choice in his classroom. Check out his blog, I Choose Math, for more of the same. In my case, “free-choice time” is very quickly becoming the most invigorating, most engaging, and most successful part of my fifth grade math class.

This weekend, Anna Weltman, Justin, and I are offering a session on student choice at EdcampNYC. I figured it was time to put up or shut up, and I am very proud to share what’s happened so far.

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How does it work? [The Specifics]

Themes of experiential learning, identity, choice, differentiation, exploration, and personal insight have been playing in my head for a couple years, but this year, they’re starting to harmonize. Justin gave me the structure I needed to feel really good about allowing more student freedom, so now every Friday is “free-choice time” for my fifth graders.

This amounts to a quarter of our class time, so it might seem like a terrible idea to let kids do this much whatever they want. Another math teacher and others have voiced concerns along these very lines, and I expect parental skepticism, but here’s what’s making it work so well.

“If you were the only person in charge of what math you learned, what would you spend your time doing? What goals would you have?”

That’s how I introduced free-choice to my fifthies, and they got it. It isn’t about doing whatever they want. It isn’t about doing what I think they should. It’s about figuring out what they think is good to do. What kinds of math make them happy? What kind of math is hard? How do they want to grow? Where do they want to improve? What do they want to create? How do they want to share their work?

These are the questions they take on in their journal each week as they prepare for Friday, setting specific goals to pursue during their time. These goals fall into categories like toys and puzzles, making community, problem packets, making art, computer programming, games, online problem sets, and reading and writing. They’re arranged in bingo card fashion to give kids some visual record keeping for their year and accomplishments.

I am lucky to have enough autonomy that these are all things I’ve spent class time on in the past. I am even happier to have students take them on by choice. In fact, it makes the time spent much more directed and efficient, because everyone is personally connected to their work.

Over the weekend, students write a reflection in their journal, telling the story of their experience, considering their goals, and setting new ones. During the week, I read them, take notes, and share my thoughts privately with each student. Lather, rinse, repeat – the feedback cycle goes to work – and on and on we go.

So far, I would say it has been a wild success. If an administrator called me in to shut it down, I would literally beg for a chance to continue.

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So what’s happened so far? [Highlight Reel]

Lots of people are getting into programming by playing lightbot. Having difficulty knowing which way to turn, one girl walked through the room as the light bot and improved her spatial intuition. Another student (who said she hated math) walked around the room helping her classmates with light bot while I made cuboctohedra with three others.

One kid watched youtube videos to make an origami dragon. Another spent the last ten minutes watching Vi Hart videos. We talked about how I could help him make a video of his own.

Lots of people are using Khan Academy to speed up their multiplication or practice other computations – proof that when kids are asked to take control they won’t just waste their time. This is especially good, because I’ve seen goals on everything from exponents and times tables to decimals, percents, and algebra.

Last week a student logged on to try some three-digit addition. “Whoa!” he said, seeing how hard these problems were, “well this is what I asked for!” He took a deep breath and dove in. Now THAT is personal investment! I couldn’t possibly have designed an arithmetic lesson that would garner focused determination the way this simple choice did.

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What are the kids saying? [Journal Excerpts]

“I feel like I have learned so much about math in the past two weeks.”

“I’m pretty sure from now on I will do something math-related every night.”

“I always thought math was the worst subject, but I’m beginning to think I was wrong.”

“I really felt like a mathematician this week, but it was hard.”

* * *

For these students (many entering the year disinterested in math) class has been completely transformed. It’s fun. It’s hard. It’s different. It’s what they want it to be! They are realizing they are mathematical, and they can choose to amplify this part of themselves.

That’s a flipped classroom!

This week was three-days long, and no Friday means no free-choice time, so I assigned it as homework. I’ve done this in years past, but inside the framework we’ve set up this year, it’s going so much better! They came to me with proud stories of accomplishment and improvement. The types of problems they solved, their Khan Academy streaks, the levels they reached on lightbot, etc.

These are their stories, and I’m so proud to be helping my students live them!


Humans did that! (and you could too)

A vague childhood memory pops into my head fairly often, and the event’s subsequent effect on my thinking surely appears daily. This thought of mine is confirmed and reinforced everyday, because I sense it in almost everything I see and hear, the way I suspect religious faith is reaffirmed in the faithful. It’s become my very favorite thing about the world, and I’m certain of the enormous impact it’s had on my learning, and yet I wonder how present it is in our schools today.

Here’s the gist – Humans did that.

* * *

The strange recursive process that is memory recall/storage has muddled the exact details, but this is the story as I can remember it now. My parents and I were at a movie (perhaps a drive-in), seeing something semi-scary like ET or Ghostbusters (except it was neither of those), and I got sort of scared. My best guess is Indiana Jones and the Last Crusade, which came out when I was six. At one of the bloodier or more potentially frightening moments, I looked to my dad for support. “It’s not real,” he said, “those are just actors – just normal people pretending.”

This made good sense to me, because both of my parents were actors, and I had spent plenty of time in the theater world. I could pretend, and if I looked at the screen just right, I could see it for what it was – some humans doing some stuff. (or even just light on a screen) As this thought propagated more and more in my brain, I realized that I could choose at any time to snap out of it and break almost any illusion. This surely figured prominently in the formation of my religious beliefs, because, as I told myself, books like the Bible were obviously written, edited, and republished by humans.

More than that, I learned two hugely important lessons. I could control my mind, and if they could do that, so could I. When I watched a clown juggle, when I listened to the Beatles sing, when I wanted to fix my bike, or write a song, or build a ramp, or flip off a diving board, these powerful thoughts pushed me through it.

Knowing that humans like me did every amazing thing in this world comforts and empowers me.

* * *

The season premiere of Boardwalk Empire blew me away last Sunday, and during the opening scene there it was. A terrific old song from the 20’s played, and I started thinking about the people who made this music. Firstly I realized this was a new recording made probably only months ago – arranged and performed by people in LA. This amazed me, and I imagined the mostly normal life of this singer. Then I thought about the original songwriters. What was it like to write that song? I’d love to hear their false starts and alternate lyrics and to know the series of choices they made in its creation.

The same is true of mathematics, and I love that! Every shred of math is the product of human thinking. Whether you see the mathematical process as invention or discovery, everything in these books was put down, just so, by people like us. Is zero in the set of natural numbers? Is it even? Is it positive? Is 1 prime? Humans decided the answers! (and they don’t all agree.)

This is part of what drives me so crazy about standard mathematics; Students are constantly trying to figure out what “they” are asking, when we should be the ones asking. We have the ability to do mathematics the same way mathematicians do, (albeit on our own terms), so why aren’t we doing it?

* * *

Look around you. Everything you see, from the size and design of the room you’re in down to the buttons, knobs, and handles of every object was conceived, designed, and built by humans. Everything we see is the result of conscious choice on the part of empowered, thoughtful people.

How does school help students become these people, when it offers them very little choice at all? You must take this class. You must read this book. You must reduce your fractions. You must show your work… and on and on.

In rethinking the way we teach young people, this point seems potentially vital! I want to show my students the overwhelming effect of deliberate human choice on the shape of our world, and I want to show them that they can be a part of that process. By helping students make choices, I can teach them to take control of their lives, and to shape their own little world.

Social media and misconceptions

I’ve realized more and more how truly powerful the internet is for learning, if you want it to be. This is why I am so pleased to see that Google+ is available to the public today. Aside from its innovative privacy settings and excellent video chat, Google+ is social media right there with your gmail, google docs, and reader. (If you don’t have some of this stuff, you may be missing out, especially if you seriously want to get into something.) Google+ and Twitter are now central to the way I grow as a mathematician and a teacher. I once heard, “Facebook is for the people you went to high school with. Google+ is for the people you wish you went to high school with. G+ is for people you want to talk with over coffee, and Facebook is for people you wouldn’t meet for coffee if they were in the same town.

Two great places for exchanging ideas are the #edchat and #mathchat on Twitter. Tonight’s question was, “If you could clear one misconception about mathematics and/or teaching it, what would it be?” (Share your own in the comments?) I found this more enticing than my Field Theory class, so I fired a few off. Thought I’d share this mini-manifesto. (140 characters at a time)

* * *

must change misconception: geniuses do real math. Otherwise math is math class.

you have to get As and 800s to do math or like math.

you’ve gotta climb the ladder to get to the good stuff in math.

you need the high school math to do ______ And you definitely can’t study topology until ______!

you’re either an applied person or a pure math person. Bleh.

math is math class and homework should look like homework.

you really need to know algebra for the real world.

fractions are wrong if their not reduced.

practice is the best way to get better. (personal experience actually is)

you have to play the role of “teacher” to get class to work.

must change misconception: “there are problems I need to solve, and I need someone to show me how to do that.” – Salman Khan! No joke!

“they” write the problems. I just answer them. Can we tell what “they’re” asking?

must realize: math is made by humans like the ones in the classroom. So let’s make math.

must change misconception: it’s ok to say “I’m so dumb at math. I’m not just not a math person.” especially for kids

stick to the book or you’re in trouble (aka I don’t trust you)

go with your first instinct. Your second is wrong (aka don’t trust yourself)

you need the teacher to learn math. You need school to learn math.

texting in class is bad. (I’m in field theory class enjoying this much more)


oh ok. Boo! Too many to choose. How about this one: you can tweet forever without battery death. (I have to go)

* * *

Lots of old thoughts there, and I could include links to old posts, but this is already too self-indulgent.

The preponderance of general misconceptions about math seems so overwhelming and frustrating at times. A large part of my teaching is an attempt to give math a good name with my students by showing them mathematical traits and habits already within them. This is my little force against the mathematical boogeyman. I’m glad I got some of that off my chest.