Tag Archives: Math

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!

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)

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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.

“We shouldn’t be teaching that!”

I recently read a terrific post by John T. Spencer about personal connections and reading. “Personal insight” is becoming a central goal of my teaching, so the post stirred some thoughts in my head. Is personal connection a reading strategy? Two skeptical teachers say no. They won’t waste their time with it.

John also describes his own experiences getting to know the Founding Fathers. In school he learned mythic tales about superheroes of patriotism, full of great deeds and honor. In college he read Howard Zinn’s counter-narrative, which John realized was merely a “smear campaign.” He was unsatisfied until he read Founding Brothers, which gave him a sense of nuance and paradox as well as personal identification with these historical figures.

It all got me thinking about what should be taught in schools. Reading strategies? Personal connections? Evolution? Creationism? What about our nation’s founding? Which story should we teach? What about Math? Computations? and on and on we go…

Can you guess what I think?

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John recounts this story:

I’m in a staff lounge when a teacher says, “Are we supposed to have them make personal connections?”

“I don’t know. I don’t even think that’s a reading strategy. It’s nice. It’s a great byproduct of reading, but it’s not a strategy.”

“I’m not sure it will be tested. How do you test that? I’m not going to spend my time teaching personal connections when they can’t read as it is.”

“I know. I need kids increasing in fluency. I think all this mumbo jumbo about personal connections is why they’re not reading more.”

Given current legislature and prevailing approaches to school, I can’t blame these teachers for focusing on “increasing fluency.” Obviously, this is something we all want, but I think they have the relationship backwards. Personal connection isn’t a “byproduct” of learning. I could say a lot here, but let me leave it at this: Personal connection is the best way I know to create historians, artists, designers, writers, mathematicians, and experts of all kinds.

This, though, is about what we should teach.

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The way I was taught, the way I see it, teaching History is about doing history – reading, thinking, researching, rethinking, formulating opinions and theses, supporting them, and responding to the criticism of your peers. This is what historians do, and in this way, History class is about making “historian” a part of the student mind and identity. It isn’t about internalizing the correct view of our nation’s founding.

Likewise, teaching Science is about the history and practice of the scientific method. English class should be about making language a central and vital part of your life, the way you speak and communicate, not satisfactorily mastering ______. My Algebra 1 students and I agreed; The product of school isn’t the degree conferred or the facts you can recite. The product of learning is the alteration of your thinking. Can you think like a mathematician? A writer? A scientist? Do you?

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But seriously, should we teach Creationism or Evolution? Isn’t that a hugely important question for curriculum? No. Not really. Let’s teach students the importance of thinking, and let’s help them strengthen their ability to do it. The questions they take on and the results they land upon (for the time being) should be completely their own.

Finally, math. Math class is a place to become mathematicians – wondering, asking, thinking, researching, formulating ideas and questions, sharing solutions and proofs, and responding to the criticism of your peers. This is what mathematical fluency really is – the ability to think like a mathematician.

As John put it, we see “the Founding Fathers as proper nouns, enshrined in ideological monuments, inaccessible to a postmodern man.” We do the same to mathematicians, when in fact, math is now and has always been done by humans like the ones in our classroom. Let’s get busy doing math.

Is a square a rectangle? Which definition should we teach? As my friend Justin told me, “teach the controversy!” Teach thinking.