A toolbox that is truly full

When I think of a math activity that really flexes it’s muscles, I’m reminded of the activities that could reasonably be solved multiple different ways with no method being preferable on the surface. These are tricky to create (or to find and steal). They are also somewhat taxing on your students (especially if they aren’t used to this kind of problem-solving). It requires a more intense, higher-order level of thinking.

photo credit: Jo Fothergill - Used under Creative Commons

photo credit: Jo Fothergill – Used under Creative Commons

Many schools are reaching the stage where students are carrying around smart devices. Increasingly schools are issuing them (we are up to 4 districts in our country that are now 1:1). Also, in many districts, students can be trusted to bring smart phones in with them. With all of these devices available, it seems like we could integrate a new set of tools into our tool box for consideration. We should design activities that allow the students some control over what mathematical techniques they choose to employ. But increasingly, it’s making more sense to also allow the students some control over what tech tools they are making use of.

That is a nerve-racking idea for some, especially since as soon as students start dabbling in technology that the teacher is unfamiliar with, they become their own tech support. There is a very real (and perfectly understandable) anxiety over students using technology pieces that the teachers aren’t familiar with. But we could flip that on it’s head.

First, we could model some of the tech pieces that we are familiar with.

Consider an activity where in the students use a Google Form to poll their classmates, then enter the data into a Desmos sheet to do the analysis. The formative assessment of the analysis could be done on Socrative or Google Forms.

I mean, this is a standard math task: Gather some data, represent it visually, analyze, and produce a product to submit to your teacher. What makes this different it two-fold: First, some of the more annoying parts are going to be relieved by the technology (namely recording the data, plotting the points, and drawing/calculating the best fit line… those are also the parts that create barriers to our students with special needs). Second, you are giving the students meaningful experience using their technology for something that makes their school work easier and more productive. (Imagine that… both easier and more productive… both…)

One of the goals of an activity like this is the students gaining an appreciation of the roles of each of those different technology pieces, in the same way as we give them specific prescribed practice with the math skills to gain comfort. But it should stay there in either case. At some point, the students need to build in a working understanding of each of the tools in their tool box – math, tech, or otherwise. (I was even vulnerable to whining… the right kind… used at the right time. Proper tool for the proper job.)

Then, when we unleash our students to solve a problem by any means necessary, with a proper foundation underneath them, we run a much lower risk of them choosing something completely off-the-wall. Students might replace our technology with choices of their own, but if they know that we have a standby that will work, then often the replacement is something they find more useful… and it might be something we’ve never seen before… and they might be able to teach us how to use it.

And never underestimate the power of allowing a student to be the expert in the room once in a while.

Full disclosure: The data that I plugged into the Google form came from here. Many thanks to cpears93@stu.jjc.edu who is named as the owner on the site.

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.

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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There is one thing that never seems to fail…

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This is going to be a short blog post, but it comes with a request.

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I was reminded today that there is nothing quite as powerful the department of meaningful student engagement as allowing students to set things on fire.

 

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But I’m a science teacher these next two weeks and come fall, I’m a math teacher again. This begs the question: What opportunities are there to allow students to set things on fire meaningfully in a math classroom? (Think Geometry or Algebra II)

 

I need ideas people! Let me know what you got!

Thoughts from Outside the Education Community

Dan Carlin (@dccommonsense or @hardcorehistory) is not a professional educator. He is a podcaster about politics and history. His podcasts are fantastic. A ton of substance in manageable doses, and he is a fantastic story-teller. He describes himself as a “fan of history” as opposed to “historian” because calling himself a “historian” would create academic structures that would keep him from adding a lot of the sensational pieces to his history podcasts that make them such awesome listening. Historians and academics might consider that irresponsible and reckless. But, he’s got something like 500,000 people currently waiting part III of his current series on World War I. Dan Carlin is clearly not a professional educator.

And yet, Edutopia decided to post a short column by him that they supplemented with a podcast that Dan recorded directly addressed to the Edutopia community. It’s worth recognizing that Dan does a fantastic job of recognizing some problems with history education that are consistently problematic in the math arena, too. From the podcast, about a minute in:

“… we teach it the same way we always did, except we’ve learned over and over, haven’t we, that the vast majority of people don’t like it taught this way. And they don’t remember it. And because they don’t remember it, any rationale you have for why it has to be the way it is because people have to learn these things goes right out the window, right? Because if they don’t retain them, they didn’t really learn them.

Maybe they were good students, studied them for the tests and got a good grade, but they didn’t keep that information a couple years later. It’s like learning a foreign language that you don’t keep up on, right? It doesn’t matter if you took Spanish back in high school if you don’t remember how to say anything, you know, ten years later.”

Educational professional or not, that is a pretty accurate observation of the major symptom plaguing education today. Many teachers I talk discuss how unprepared the students are for their particular class. This problem isn’t a secret. And it isn’t new. (Sam Cooke Sing-along anyone: “Don’t know geography… don’t know much trigonomety…“) In the podcast, Dan urges that the education should be less about what we teach and more about how we are teaching it.

From about the 10:00 mark.

You have to awaken a desire to continue with the subject, and not just in an educational sense, but in their lives – to have an interest in the past. Allow them to choose the subject and you’re halfway there. If a kid’s into motorcycles, let them do a report on the history of motorcycles. They will quickly come to understand how that motorcycle they admired in the showroom window today came to be. They’ll understand the value of knowing the past about any subject, right?

If you have a person in your classroom that’s interested in fashion – same thing. The history of fashion’s a wonderful subject. It’ll teach you how we got to where we are now in terms of fabrics, and colors, and styles. You’ll be able to recognize, “Oh, I see a little bit of ancient Egyptian influence in that dress I saw the other day on the runway.” This is how you begin to teach people that the past is infinitely exciting if you get to pick the subject.

… They can learn all the social studies aspects of these stories down the road, if it matters to them. If it doesn’t matter to them, they’re never going to learn it anyway. Now I don’t know if teachers have any control over this in the classroom, and I realize this doesn’t give them many tools to use, does it? But the truth of the matter is that if we’re going to teach history in a way that less than 10% come out knowing anything 5 years down the road, we’d be better off using that time to teach math.

 

Now, Dan recognizes his limitations as an adviser of educators, but he brings a lot to the table of value – and not just in the teaching of history. Replace history with math in most of that quote and you’ll find that his sentiments are still pretty applicable.

Why are we teaching math? What are we doing to put students in a position to leave us with anything of value to take with them? We’ve known for years that students often forget the math they study in school. (I am reminded of this every year at parent conferences when the parents remind me how little they remember of their high school math.)

So, why do we continue to do what we’re doing? Why are we spending so much time at the top levels stressing about WHAT we should teach and so much less about HOW we should teach? What should the goals of math class be?

The goals of math class are perplexity, problem-solving, organized logical reasoning, creativity within constraints, patience, persistence, perseverance, the ability to guess well, and then to design a way to check the accuracy of the guess…

THESE are the reasons for math class. THESE are the long-lasting takeaways. THESE are the things that make math class useful to 100% of the students. And THESE are things than can be taught regardless of the content. You can teach those things with linear functions, or visual patterns, or number lines.

And it’s okay that the advice came from a “fan of history” and not an educator.