Tag Archives: Math

Imbalance Abundance

I’m really happy to see how many people have been excited by these imbalance problems.  The entries continue to roll in for my imbalance problem writing contest.  You can check them all out here, and I’ll continue to update that page.  I’m so happy to see other people’s ideas stretch my thinking and help me see what’s possible.  This is just really fun.  I have some early favorites, but I won’t give anything away just yet.  Hopefully I’ll get more submissions.  maybe YOU will make one.

I’m noticing all sorts of techniques for solving them.  In fact, I learned something from a recent submission and it inspired three new puzzles of my own!  I hope you enjoy.  I’d love your feedback.

Imbalance Problem 13 20130330-224605.jpg 20130330-224612.jpg
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Real World Math (Dan Meyer and stuff)

I spent a really invigorating and exciting day at EdcampNYC on Saturday, surrounded by passionate, motivated, active educators. I just want to thank everyone who came, especially the attendees at my session, Student Choice in the Classroom.

The sessions were posted by people who could facilitate, but not necessarily in response to attendee interest, and some were left underwhelmed by the offerings.  If I were designing EdcampBK, for instance, I would include a way for session requests – probably a quick and dirty version of class planning at PSCS.

I just wanted to grab these underwhelmed adults and say, “see how boring stuff is when it isn’t what you want?  That’s how our students feel everyday!”

* * *

At the end of our student choice session, I had a conversation with a teacher about her daughter, who was very interested in becoming a math teacher. The daughter spent lots of time in college preparing for this, but she decided to enter the business world instead, and come to teaching later in life.

“If I’m going to tell these kids about all of the real world applications of math in the business world, and all of the life and career paths that include math, I’d better have some experience with it first,” said the daughter.

Math is so COOL! Right?

First of all, if she just wants the money, I get it. No blame. No shame. I’ve seriously considered selling out lots of times, especially with student loans rocking my monthly budget. On the other hand, she brings up a good point. You don’t even need to look at a textbook like this to know that questions of “real world applicability” are always being asked. In the face of “when am I ever going to use this?” many teachers see winning over students and convincing them of relevance as hugely important for gaining their buy-in.

They’ve got that right!  Personal attachment and investment are what drive personal growth, but this is a very artificial look at math in the real world. Let alone that shade of orange and the hodge podge cover full of unrelated stuff, I suspect no one actually sees the world this way.  Ugh.

* * *

Here’s a better vision of real world math.

Dan Meyer is a former teacher, now doctoral fellow at Stanford working on curriculum design. You can check out his TED talk, but I’ll summarize. Dan’s trying to recontextualize mathematics by using videos and photos of REAL scenarios – the kind you can actually see.

Here’s a classic problem, revamped and improved.

You show that, and then ask the students what they’re wondering. “Does it go in?” perhaps. You can read all about Dan’s “three acts of a mathematical story” here, but act one should grab hold of the audience with something truly compelling. I’m all about that, for sure, but let me be critical.

Sometimes I get the feeling that Dan is close to merely repackaging the same old product in a more exciting way. I applaud his work and effort, but this is still pretty dull. Dan’s stuff is distinct from that textbook cover in two ways; It’s authentic, and it’s actually compelling (though not always and not for everyone). Furthermore, lots of teachers simply must teach this stuff, by law, so I’m extremely happy that he’s helping them do that, but the “math makeover” we need is about much more than repackaging.

It’s about the mathematical process (Dan gets this), and it’s about student interest and their questions. I get the sense that Dan only kind of gets this one, because the videos speak so directly towards one or perhaps a few very specific questions.  I try, instead, to bring students to mathematically rich and accessible environments, in which an abundance of questions can be pursued along various routes. This helps students develop the mathematical instincts already within them, on whatever terms they can negotiate.

* * *

But here’s what rocks about Dan Meyer and what I think “real world math” really is.

Dan is a very passionate mathematician, and he is sharing compelling math, directly from his own experience.  Seeing math in the world is something he actually does, and to share that with students is to help them do it themselves. If my kid were in his class (not that I have one), I would be thrilled that he got to learn from a passionate and empowered math nerd.

That’s what’s real about math in this world.  There are real human beings, called “mathematicians,” that spend a considerable portion of their time engaged in mathematical thought – asking questions, answering them, revising, explaining, sharing, tinkering, analyzing, wondering, dreaming, playing, failing, succeeding, and on and on.  This is what I want to share with students. Math is something that people do, including me, and it is something that they can do as well.

This is what I want to tell that daughter. You don’t have to go into business to understand real math. Simply immerse yourself in a mathematical life, be a mathematician (in your own way), and you will have plenty to share. The sad fact is that school-math discourages this notion by implying to students that math is math class (or for geniuses), particularly because so many so-called “real world applications” are wholly artificial and pseudocontextualized.  Furthermore, school tells us we need teachers, texts, and problem sets to do math, when this is far from the truth.

Real world math is simply mathematical thinking. It’s personal, it’s real, and it can happen to all of us.

[Recursion]: Video Feedback

I’ve been playing with video feedback since I was kid hooking our shoulder VHS video camera up to a little black and white TV in my grandma’s basement. I have a document camera that plays through the computer in my classroom, so I can achieve the effect anytime, these days. All I have to do is point the camera at the screen and play. My students LOVE it, of course, as does just about everyone who experiences this in person. There is something deeply fascinating to us about this mechanical system observing itself. Infinity? What’s going on in the middle of that screen?

Homage: Drawing Hands

It’s the same effect you get when mirrors face each other, but the camera enhances this in several ways. You can twist and move it, creating incredible and surprising results. The camera/display combo makes small alterations each time the “image” is sent through the loop. As a result, the image deforms, one generation at a time. The color, the shapes, the detail, just about everything is slightly transformed through this recursion, similar to the evolutionary process that shapes all life.

In fact, I see feedback systems as a ubiquitous mechanism in the world. “Memes,” increasingly well-known, are the mental structures, analog to genes, whose interactions affect our ideas, or perhaps even constitute human thought. (Hofstadter’s I am a Strange Loop is all about this.) I’ve never fully explained my choice of “Lost In Recursion,” but perhaps it’s starting to come through. It refers to my own thinking, as well as to our schools – a troubled yet robust, self-perpetuating system, surviving minor alterations, awaiting revolutionary demand for change.

Homage: The Creation of Adam
(out of recursion, life and soul emerge)

By writing this blog, reading others, engaging in conversation on Twitter, and simply sharing my thoughts, I believe I’m taking part in the dynamic collision of ideas that is already shaping education reform and change in our country.

I hope my students will take active roles in this as well, but it won’t happen just by mastering material, meeting standards, passing tests, following directions, or going to the right colleges. It happens when you start sharing ideas, communicating, taking control, pushing back, and effecting change within these systems – most importantly the one inside your own brain.

Thanks to Justin Lanier for helping me take these photos. You can see more pics on the Lost In Recursion flickr page.