Activating the student-learner (emphasis on active)

I always found it tricky to get students up and out of their seats meaningfully. I know that cooperative learning manuals are full of ways to get students meandering around the classroom, but I always liked to try to make sure that the movement was meaningful as a tool to help them learn the content.

In the past week, I’ve seen two examples of meaningful active learning in the realm of Geometry. And as it happens, both are from my neck of the world.

One comes from Tara Maynard who teaches middle schoolers in Zeeland. Her post on “Dance, Dance, Transversal” plays off the mechanics of Dance, Dance Revolution while putting the students in an experience of having to know the different angle pairs coming out of parallel lines cut by a transversal.

Photo credit: Tara Maynard

Photo credit: Tara Maynard

The thing I like about this is that in the end, this is a vocabulary exercise, but Tara has found a way to use movement and activity to add some life to it in a way that fits pretty naturally. This is a nice pairing. And, as she states in her post about the activity, she pairs the students up so that one can watch the feet of the other to make sure they aren’t making mistakes and reinforcing poor understanding. She also includes the file so that your students can play, too!

The other comes from a pre-service teacher at Central Michigan University. Tod Carnish used Twitter to share a nice idea to help students explore geometric transformations. And as much as it hurts for me to say nice things about Central folk (Go Broncos! #RowTheBoat), this seems like a pretty solid idea.

Transformation Tweet

Sticking to the idea that transformations are really just the organized movement of vertices, why not have those movements represented with the students acting as the vertices? Think of the ways that one could use this as an introduction to function notation of the transformations? Characterizing the movement by it’s vertical and horizontal components?

Nice thing about these two fine educators is that they love to share. If you have questions about their work, or want to drop them some props, I’m sure they’d love to hear from you!

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Why do we collect student work?

 

 

 

For a couple reasons, I’m sure. Here’s one of mine: to turn it around and let them see it.

Best Proof Snip

 

“Here are four proofs written by your classmates. Which of them is the best? Why? Which of them comes in second place? What would the second place proof need to change in order to tie for first?”

 

Such good conversations arise when students explore decent examples of their own work compared to their classmates. And they don’t have to be time-consuming. If the work suits it, you could create a 5-minute opener comparing just two pieces of work. It can be a wonderful way for a student to recognize his/her own mistakes without me, as teacher, having to reveal them. Such recognition is a wonderful evidence of internalization of the content… real learning that can be used to solve problems.

 

Why do you collect student work?

 

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.

Okay… I solved it, but how’s that math?

Its on these warm, spring days that some learners tend to start checking out. They recognize our typical reviewing and recirculating attempts to help students recapture some learning before the last tests and exams. But some of them learned the content the first time. Essentially, this time of year can bring with it a lot of down time for our students who learn the fastest.

That’s when I like to pull out my old college textbooks. I spoke before of the power of ungraded bonus problems. If interesting and placed properly, they can provide powerful opportunities for thinking simply for the sake of thinking. I like to give them a window into math that “doesn’t look like math.” After all, most of the content that K-12 mathematics includes has some commonalities that students get used to. They’ve gotten used to “what math looks like.”

Today, four groups got a problem that I adapted from one of my undergrad courses that I took at WMU with Dr. Ping Zhang who, along with Dr. Gary Chartrand co-authored this book which was the textbook for the course I took.

The problem is adapted from Example 1.1 from Chapter 1. It asks the students to create a schedule for 7 committees that share ten people. Now, the purpose of the problem in the book is to give a simple example of how a graph can be used to visualize a complex situation. Often the way a problem is mathematically modeled can change the intensity of the solution process.

 

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Figure 1.1 from Page 1

 

The reason I like to give this problem (and problems detached from the K-12 curriculum in general) is that in May, to curious students, these problems tend to hit the perplexity button just in the right spot. In fact, all the students looked at the handout at first and were unimpressed. Until I asked them to read it… then, they seemed to just want to see what the answer looked like. As one student put it, “It seems really easy at first, then you get into it and it’s actually harder than we thought.”

Graph theory is about creating visual representations. I didn’t want to ruin their experience by pigeon-holing them into trying to represent this they way I knew they could. And given the time, that didn’t stop this group from creating a similar idea. Not with a graph, but they did use crayons.

 

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To hear Kailey explain: “We just gave each person their own color. Then we knew we could have two committees meet at the same time if they didn’t have any colors in common.” That isn’t different thinking, really. Just a different representation.

I enjoy the conversations that come out it. No grade. Just doing math for the sake of thinking about something that’s interesting. It’s especially interesting to students like Katie who said, “Okay… I solved it, but how’s that math?”

 

Reference

Introduction to Graph Theory (2005) Chartrand, G., and Zhang, P., New York: McGraw Hill

My experiences with Kahoot!

Kahoot Student Front

A teacher across the hall (@nolink10) encouraged me to try Kahoot!

So, a Spanish teacher across the hall from me encouraged me to try “Kahoot!”. Kahoot! is a online quiz maker that works a lot like pub-style trivia. A teacher makes a quiz. Students log into get a chance to take the quiz. The question goes up on the screen and students try to get it right. Get it right quickly, you get many points. Get it right slowly, you get less points. Get it wrong, you get no points.

So, knowing the typical doldrums that the “last-day-before-a-unit-test” can fall into, I decided to try it as part of my test review. So, here’s how I used it: I posted 9 trig problems around the room. Students paired the students up and sent them around in 90-120 second intervals to solve each one. I encouraged them to show as much work as humanly possible to the point of being excessive. (This is an instruction that often gets ignored.)

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This part took about 20 minutes.
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Then, I fired up the ol’ projector and sent the students to kahoot.it. The quiz had a pin# they had to enter when they arrived. Then they could choose a nickname. (I’d advise some fairly clear boundaries on the nicknames. Just sayin’.)

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Then the questions came up on the screen and they could use their laptops, tablets, phones, or wi-fi enabled tech to answer. After each question, the correct answer is revealed and they got a chance to ask clarifying questions. It is possible to set multiple answers correct. The next question doesn’t appear until the teacher clicks “next”. The standings are updated and displayed after each question, too.

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So, what did I think? Well, the students sure enjoyed it. Although, I am curious how much learning got done. I suppose we’ll have the the test to offer some insight into that question. Also, one negative is that if the student device goes to sleep, Kahoot! kicks them out of the quiz. In one larger class (32 students), students were having trouble reconnecting and only about 17 students finished all nine questions. That wasn’t the case in my other class (of 22).

The students get to rate their experience after the quiz is done. Ratings were generally (but not all) positive. Also, the teacher gets an opportunity to download an Excel file that reports out all the data including the answers for each student (whether they finished or not), the breakdown of answers for each question and the student survey results. That is a nice piece.

I would encourage you to chime in if you have experiences with Kahoot! or something like it. I feel like tools like this can be useful, especially in BYOD schools.

“Ugg.. I don’t get ANY of this…”

I like working with teenagers for a lot of reasons. One such reason is because it is usually quite easy to get bold, absolute statements out of them.

For example: “I don’t get ANY of this.” (emphasis not mine…).

It’s tricky business handling that statement because most of the time, the author of that quote genuinely feels that way. That doesn’t make the it true, but if he or she is already feeling like all the attempts at math are turning up wrong, combating their perception by simply saying it’s false is probably not the best approach.

I enter into evidence the following photo:

 

See it? He made the same mistake twice.

See it? He made the same mistake twice.

I gave these two problems as part of a short formative assessment. I saw the answers shown above a bunch. Most of my classes were lamenting the assessment because, “They don’t get any of this.”

Which, as I said above, couldn’t be farther from the truth. Those two answers show quite a lot of understanding, actually. There is a single mistake that led to incorrect response in both cases. That student was unable to distinguish the shorter leg from the longer leg. That’s it. Fix that and the answers get better.

And when I show them the answer to those two, many of those bold, absolute thinkers are likely going to think, “Yup, I knew it. It’s wrong. I knew I didn’t get any of this.”

At least I know that going into the discussion. Now, if I can just convince them that understanding is a spectrum more than a light switch.

Coke vs. Sprite – One Class’ Response to Dan Meyer’s #wcydwt Video

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Almost three years ago, I highlighted the Coke vs. Sprite video that @ddmeyer made. It is a very intriguing question (which glass contains a greater amount of its original pop) without a clear answer.

Today, I let a class give it a go and here’s what they came up with.

First, they chose to model it with integers. Said one student: “I pretended it was a jar with 10,000 marbles.” 2014-04-03 11.07.36

Then they assigned “a dropper-full” to be 100 marbles. So, the first dropper took 100 red marbles and placed them into the jar with the 10,000 green marbles.

Now we assumed the stirring made the mixture homogeneous which meant that there was a consistent 100:1 green-to-red marble ratio in the right jar. So, when we pull another 100 marbles to put back, (with a little bit of rounding) we pull 99 green marbles and a single red marble back into the left jar.

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A little number crunching reveals (at least in this model) that there would be 9901 original-colored marbles and 99 other-colored marbles in each jar.

My original assumption matches their investigation. It seems (at least by this model) that at the end of the video, each glass is containing equal amounts of their original soda.

Another teacher Chris Hunter (@ChrisHunter36) also battled with this video and created an excellent read about his experiences. Check them out.