Fun with The Magic Octagon

So, we are wrapping up our unit in Geometry on rigid transformations, which means it is that wonderful time of year when I show the students Dan Meyer’s The Magic Octagon!

Seriously… have you seen this? (Go through it like a student. Pause it to make your first prediction.)

The Magic Octagon from Dan Meyer on Vimeo.

Isn’t that cool? Not sure whether you predicted correctly or not (I did not the first time), but I’ve used this video with 6 or so geometry classes and the results are somewhat predictable. 85-90% of the class guesses 10:00. Most of the remaining voters choose 7ish:00 and get called crazy.

Then they see the answer and they JUST… CAN’T… BELIEVE IT!

“Wait… wait. How does one side go clockwise and the other side go counterclockwise?

“No. Run the video again. What did I miss?

That would be a 10-out-of-10 on the perplexity scale, when, like 85-90% of the class gets the math problem wrong and that suddenly becomes a motivator!

Then as they start trying to figure it out, they start making lots of hand gestures, which is surprisingly helpful to them and

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Then they don’t want you to move on. They want two more minutes to talk about it. Then a classmate starts explaining it. Not all of them get it the first time, but some of the demand to have it explained again.

Then they move on to the second rotation and they feel so confident. You ask for explanations. They give them… quickly. Quickly because they can’t wait to see the answer. And then they did.

And those who got it right cheered! Quite loudly.

Then a boy stopped us and offered a sequel.

“If the front side arrow is pointed at 5:00, would the other arrow point at 5:00, too?”

He turned the tables enough close to the end of the hour that we left with that question unanswered.

 

And I fully expect a couple students to have something to say about it tomorrow.

Kids, I’ll tell you why you need math…

So I was at Kroger and I was thirsty.

I went to the cooler to pick out a 20 oz. Coke. $1.69. Reasonable. About what you’ll pay most places, at least around these parts.

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But I had some more shopping to do. So, I kept walking. Gathering the items on my list.

Then I saw some 2-liter Cokes. (Remind me. Which is a bigger amount of Coke? 2 Liters? or 20 ounces?)

The 2-Liter Coke was priced at “2/$3.00″. (Which, I’m pretty sure is less than $1.69.)

(Oh! And you don’t have to buy 2 to get that price. Kroger is awesome like that.)
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I get pricing a little bit. I worked concessions at a college football stadium for a while (true story, by the way). I know the shtick. It’s upselling.

“For an extra quarter, you get almost double the pop!”

But this isn’t like that.

You have to buy 4 twenty-ouncers to fill a 2-liter. 4! You include the 10-cent bottle deposit here in the great state of Michigan, and that’s over $7.00!

2-Liter? $1.50

This isn’t even close.

Kids, THAT’S why you learn math.

Student Blogging: Off and Running

After the encouragement of a few folks (among them, Hedge (@approx_normal), Zach (@z_cress), and Jennifer (@RealJMcCreight)), I decided to move forward with my admittedly medium-rare idea to have a class start a blogging community. I needed their encouragement because I hadn’t ever SEEN anything like this done before in math class. I’ve seen examples at the elementary level. I’ve heard about English teachers doing this, but the benefits of active engagement in a blogging community to a class of math students was purely hypothetical.

So, with that in mind, I decided to leap (and then look at where I was once I landed.)

curious? alg2point0atphs.wordpress.com/

I decided to leap…

I sold it to them in this spirit: Algebra II is the last math class that Michigan specifically requires high school students to successfully complete in order to graduate. That makes Algebra II the series finale. This is the last season. A sitcom that they have been watching daily since 2004 begins it’s final season this fall. They have spent more than a decade learning different kinds of mathematics and Algebra II is where we show off how it all fits together. We are able to reveal where it was all leading.

The blog acts as an extension of that. If they are going to take anything of value from the dozen years of math we lead them through, they are going to have to internalize their experiences. The blog is going to give them an opportunity to make visible a portion of that internalization.

Here are the structures I am using:

I am requiring a single post per week, along with a single meaningful comment on another person’s blog per week. A post should be between 150-500 words (because they asked). This is designed to enter them into the world that I know exists for more bloggers than just me. That is, becoming observant of the world around you thinking what you might write about. (The first topic I asked them to write about was the most enjoyable math-related experience they can recall in math class.)

They are required to follow all of their classmates’ blogs. This ensures that their WordPress homepage readers are displaying recent posts.

I have a rubric that I will be following to hold student’s accountable for actively participating in the blogging community.

 

Already, this has allowed us to consider a variety of different relevant topics that are not normally relevant to a math classroom, but are darned interesting to talk about. The value of pictures and story-telling in conveying meaning, the consideration of audience, the use of images and movie clips, digital citizenship, etc.

It has worked to make the class more holistic, which needed to happen if we are really going to take the series finale approach to this course. There’s value in that because the last 10 years of math class haven’t just been about math content. They’ve been about math habits, problem-solving techniques, specific tools, vocabulary, and a variety of technology. To focus purely on content would be to miss an opportunity to help them make sense of all of those experiences.

And to solidify those things is to provide a springboard to launch the students into an opportunity for spin-offs once this required Michigan math series has reached its conclusion.

Here are the handouts I used to introduce the blogging community to the students. None of these handouts stood alone. All of them were given as part of a large-group question-and-answer session, so keep that in mind as you read them and notice details left somewhat vague.

Handout 1

Handout 2

Handout 3

Making an effective first impression

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My geometry students explored Dan Meyer’s “Best Circle” on Day 1.

 

It is customary to start the year by helping the students understand their role as a member of our math community. So customary, in fact, that toward the end of the day, it seems most students have seen 3, 4, or perhaps, 5 different “here are the procedures and policies in my classroom” lectures.

I choose a different approach for two reasons. First, I feel like the students are appreciative of the chance to do… something… anything… other than listen to another description of the classroom policies and procedures (which, aside from late work policies and grade categories, are probably pretty darn similar teacher-to-teacher anyway). And second, there’s only so much value in telling students stuff.

It’s usually better to show them.

 

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My ALG 2.0 students explored Dan Meyer’s “Toothpicks”.

 

My classroom expectations are almost all focused on the effective learning of mathematics and being an effective member of a mathematical learning community. I could lecture them about what this looks like. Or I could let the students group together in teams of 3 or 4, give them a mathematical task, and let them explore. Consider it “Classroom Policies and Procedures LIVE!”

In case you’re curious, these are the expectations for each member of our mathematical community.

1. We stay on task.

2. We seek out the tools that we need.

3. We ask questions instead of quitting.

4. We are responsible for having something to offer to the team, and then our the team to the class community.

5. We make sense of the answers we get, examining if both the answer and the procedure for getting it are reasonable.

 

If every person in my classes did that, we’d be just fine. Always.

 

The problem with Day 1 is that you have to be very, VERY careful assuming ANYTHING about the background of the students coming into your classroom. I was fortunate that my ALG 2.0 class was almost entirely made up of students whom I also worked with in geometry. This is rare. In general, I don’t start gaining a real understanding of each group of learners until I’ve watched them explore math tasks the first couple times.

So, this is when you make the entry point to activity as low as you can get it. Up the mathematical intensity only once you are sure everyone is still on the same page. This is when you establish norms. Remind them to get back on task. Require a contribution from each group. Gently ask follow-up questions. Offer the students a variety of resources and then brag on their creative and effective use (even if it is something as simple as using multiple colors to organize work).

Central Park by Desmos is a perfect fit, by the way. As are the activities from the pictures.

It’s important to take advantage of the opportunities given to you as a teacher on Day 1. After all, you never get a second chance at a first impression.

And if Day 1 goes well, when the student’s are shaking off the summer rust, then imagine all the fun we’ll have on Day 2!

For the start of this school year, I am excited about…

It’s Labor Day and in Michigan that means that school starts tomorrow. Every school year comes with its own challenges. It also comes with a great deal of excitement.

I am excited to be getting a second try teaching Algebra II (which is coming in two different versions: Algebra II, the one-year version and Algebra IIA, the first year of a two-year version). The first try was clunky and unorganized. Having three sections will help as it is nice to have multiple tries at the same lesson, which wasn’t the case the first time around.

I am excited to be starting geometry again. Last year’s course got really backed up because of the incredibly intense winter that easily cost us a month’s instruction.

I am excited to (finally) make Desmos and Geogebra a regular part of my instruction. I am glad that teacher.desmos.com exists. (Does anything like that exist for Geogebra?)

I am excited about the chance to explore the possibilities for student math blogging. My school’s one-to-one program makes that possible. I am very thankful for that.

I am excited to meet a new group of young people. I am also excited to get a chance to work with some students for a second year, as we worked together to learn geometry last year.

I am excited about the new teachers that we brought into our community this off-season. So far they have brought a lot of energy. Energy is nice to have around, I’ll tell ya.

I am excited for a couple of my colleagues who accepted new positions for this school year. I’d say both moved upward and in a direction that will serve them and their educational communities very well.

I am excited to roll out the math club this year at our school. Our first task will be to design and test the m&m’s project.

There is a lot to be excited about. What are you excited about? I hope to hear back from you. Drop me a comment (or a link to your own blog post).

My Most Recent Thoughts About Student Blogging

I have spent the last few months processing this temptation to integrate student blogging into my instructional practice. I have some medium-rare ideas. And some Iron Chef colleagues who do a nice job of focusing my thoughts and cooking medium-rare ideas. Like this very evening in a conversation with two such colleagues:

 

 

Like… bingo. That’s it.

 

So, here’s are my goals. Here’s what I’d like to accomplish:

A. I want to give the students a meaningful way to explore math topics, or think mathematically when they aren’t in my classroom. I don’t trust traditional homework problems to achieve this goal. I think there is value in understanding that in class we spend an hour exploring thoughts and ideas that have real value during that hour and the other 23 hours of the day. I’d like to create SOME mechanism that enforces that.

B. I want to give the students a chance to develop their own voice when talking, writing, and reasoning mathematically. Too often, I use gimmicky phrases, memorized lingo, and rigid vocabulary to guide student language. There are wonderful reasons for this. But, I want them to develop their own voice, too. I’d like to see them develop their own ability to verbalize a mathematical idea and…

C. I want to open the students’ ideas up to each other and to the greater math and educational community. I feel like this will offer a level of authenticity that simply having the students submit their work to me wouldn’t. Also, I want them to be able to think about the mathematical statements of another student and respond. I want to break away from this idea that the students produce work simply for my review. A mathematical statement isn’t good and valuable simply because I say so.

I think blogging can do that. I am sure other things can do that. Perhaps other things that are easier. Or less risky. Or have undergone better battle-testing. Or…

 

And as for the second question. The evidence would be a gradual improvement in the math discourse in class. More people talking, and talking better. Explorations becoming richer. Questions becoming an increasingly regular occurrence. Students trusting each other, and themselves, and not looking at me as the lone mathematical authority in the room. We would begin to talk and explore together, and sense-making would become a bigger and bigger part of what we do.

I told you. Medium-rare ideas.

I’m hoping that some more of my Iron Chef colleagues will take my ideas, season them, finish cooking them, and help me turn them into an action plan.

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My advice to the newly “en-Twitter-Blogged” (reflection on #edcampmm )

Today I got to meet a lot of folks at EdCamp Mid-Michigan in Charlotte, MI. Some of them are seasoned tweeters and bloggers (Elizabeth Wellfare – @ealfoster or Tara Becker-Utess @t_becker10, for example) and some are just starting out. A couple of people got set up with their very first Twitter handles today. Welcome. I talked to a couple folks who are interested in starting their own blogs (or rethinking the way they use the blog they already have).

Now, that EdCamp is over, we start the “now what?” stage of all the new stuff we learned.

What are we going to do with it?

How intensely do we want to attack it?

How is it going to be useful to us in the practice of constantly improving as educators?

All of these are fantastic questions. We discussed some of these issues already, but I want to offer a bit of encouragement and advice.

First, don’t be afraid to be selfish. (I believe Dan Meyer – @ddmeyer gave this same advice a few weeks back). By that, I mean that you are likely going to take a WHOLE LOT more than you give for a while as you start out in the world of twitter and blogging. That’s okay.

The first major idea is trying to decide what you want the Twitter feed or the blog to do for you and your professional practice. Sometimes the first step in that is seeing what other people are doing. How do they tweet? What do they tweet about? How do they use #hashtags? What do they blog about? What types of blogs/tweets are interesting for you to read?

Tweet and blog about the stuff you find interesting. Your blog and your tweets should AT LEAST be interesting to you.

Second, keep at it. When you first start tweeting/blogging, chances are that you (and a very few other people) are going to be the only ones reading. That’s okay. That changes over time. The more you write/tweet/interact/question/comment/favorite the more you will find people who are trying to do the same things you are doing. And THAT is what you want. You want to begin to form a network of people who are all trying to support each other in common goals.

Now, if you are brand new to this, follow me at @hs_math_phys. When you start your blog, tweet me the link to your blog. I look forward to reading your ideas and thoughts.

Finally, if you want a nice network of people who want to read your thoughts, check out The MathTwitterBlogoSphere homepage for a ton of GREAT bloggers and tweeters. Don’t let the name fool you, it’s not just for math teachers. There are takeaways for educators of all makes and models. They are good people.

Welcome to our world. Please don’t be a stranger. And Please, let me know what I can do to be helpful.