Physics, a helicopter and cameras

First watch this (and be amazed… well, if you’re anything like I am.)

So, when the students can get past the idea that there is some foul play involved, then it becomes a wonderful opportunities to discuss the idea of frequency.

Frequency is an odd discussion because it’s got a strange unit. The “per time” can be a little challenging for students to wrap their heads around.

And the opportunity that this video provides is that here, we don’t need to immediately concern ourselves with the quantitative value of the frequency (maybe 300 RPM for the helicopter rotor, for example, or 5 frames per second on the camera), but we can begin with the qualitative value of the frequency (that the frequencies, whatever they are, are the same.)

And then it opens the door for them discussing some quantitative issues. For example, the fact that the standard unit of frequency (the “per unit time”), obviously isn’t constant. So, the helicopter rotor is RPM and the camera shudder is typically in frames per second (at least, I think. Not a photographer…) So, you’ve got some nice dimensional analysis opportunities.

Where could you take this next?

One thing’s for sure, I’d hate to waste a video like this. Fully captivating, and it only costs your 30 seconds of class time.

Source: I owe TwistedSifter credit for blogging about this video first.

Perplexity and how it appears…

Here’s a video (by Derek Alexander Muller) I think you should watch.

 

The critique of #flipclass aside, I’m intrigued by the way the narrator describes the value of “bringing up the misconception”. It’s almost like a thorn that creates some discomfort that only learning will relieve. This gets close to Dan Meyer’s use of the word “perplexity”.

From Dr. Meyer: “Perplexity comes along once in a while. What is it? It’s when a kid doesn’t know something, wants to know that thing, and believes that knowing that thing is within her power. That right there is some of the most powerful learning moments I’ve ever seen – so powerful that it’s really hard for me as a teacher to mess those up.”

There’s power in perplexity. I’ve seen this in my classroom on multiple occasions. It’s important to remember that there’s three distinct parts to creating what Dr. Meyer is describing. First, there needs to be something worth knowing. Second, you have to create the want. And finally, we need to empower the students so they feel enabled to know that thing. What Dr. Alexander suggests is that becoming aware of your misconception seems unsettling (leading to claims that videos were confusing), but also leads to more learning. The discomfort fed a drive to resolve the discomfort.

The tricky thing is that misconceptions are a tool you can use when they are available. Science provides a particularly fertile ground for misconceptions because so much of it is drawn from experiences many of us have regularly. Alexander uses the model of a ball flying through the air. This video uses the phases of the moon and the seasons.

The potential for misconceptions is necessarily lightened when there’s no misconceptions, so the quest for perplexity in math needs to take on a different look, proper planning and timing, and different strategies for when perplexity isn’t an available option. (Preconceived notions are just as good at times. After all, we ALL think we know something about squares!)

It’s like Dr. Meyer says, those wonderful perplexing moments only come along once in a while. We foster those moments when we have them, try to create as many as we can and we do our best every other time.

 

Math Talk by Necessity: a 4-year-old’s story

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My 4-year-old is chatty. And while he will occasionally talk to himself, he’d much rather talk to you. And to him nothing is more frustrating than not being understood.

So, he’s realized that he needs detail. Words like “lots” or “just a little” or “soon” are easily misunderstood. Like when Dad says, “Hang on, dinner will be ready soon.” He’d prefer to have a better understanding of whether you mean 30-seconds soon or 10-minutes soon.

The math teachers among us see this as adding units to your answer. We ask our students, “What was the final speed of the car?” We don’t expect them to say, “fast.” We’d prefer something like “54 m/s”. So would my 4-year-old. “Soon” is too loose a word.

Except, most of the typical units don’t mean anything to him because he is still developing his understanding of what “a mile” is. First, that it’s a unit of distance. Second, how far is one of those. These two things are essential to making meaning out of a statement like, “Well, the store is 6 miles from here.” Without those, statements like “This box is heavy. It’s, like, 6 miles!” are not uncommon around my house right now.

But yesterday, something new happened. Together, he and I made Alton Brown’s Hot Cocoa Mix . To go from ingredients to a drink, you have four units of measure. (cups, teaspoons, tablespoons, and ounces)

So, midway through as we were chatting about this and that… together making the distinction between teaspoons and tablespoons… why two cups of one ingredient looks so much different than two teaspoons of another… stuff like that. Then, we came to the part where we needed to scoop the mix into the mug and I handed him a “scooper” and he says, “I need two… two… of THESE, but I don’t know what it’s NAME is? Dad… what’s this one’s name?”

Did you catch that? There was a step forward in that.

He knew the number wasn’t enough. “Put two in there” is really easily misunderstood. That would be a problem. Two of what?

He also knew that it totally mattered what “name” he gave the scooper. If he called it “a cup”, he risked calling it the wrong thing. Two cups of mix makes a totally different amount of hot cocoa that two tablespoons. And both could be called “a scoop”. (Two scoops from the coffee can is different that the two scoops of raisins on the cereal box.)

Finally, he figured out that this thing had a name. That I knew it. That he needed to know it and that it wouldn’t work to make it up. If he is going to communicate this amount to others, he needed to know the ACTUAL name of this scooper. Not his preferred name.

There you have it. Math talk by necessity. Lends credence to the notion that if you put students in rich enough environments, you won’t have to mandate good math talk. They simply won’t be able to communicate effectively without it.

Now, we just have to deal with the fact that when Chef Alton says “two tablespoons”, Dad tries to measure accurately while the 4-year-old would prefer that mean “the maximum possible amount of hot cocoa mix that the tablespoon will transfer to the mug.”

Why I love this picture…

I want to tell you why I love this picture.

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I took this picture this morning in Lansing, MI during some wonderful small group math talk. There is one device, an iPad, with an Osmo setup attached to it.

So, here’s why I love this picture.

There’s tech and…

… manipulatives and whiteboard markers and collaboration. Tech fits among the variety of tools available. It’s not the best tool unless it best supports the learning. And sometimes other tools work better. And in this case, the students were being led into learning with all the different tools.

The activity is built around the social nature of learning. 

The kids are clearly sharing their answers with each other and the teacher… there is a constant back-and-forth, sharing ideas and discussing them. They were seeing each other ideas, but…

Their strategies aren’t all the same. 

One girl is using an array. One girl is using groups of three. One girl wasn’t quite sure what to do (so it was a good thing she could see the other two girls’ work.)

The teacher’s hands are off. 

The students are doing the reaching, arranging, manipulating. Remember, the one that does the work will be the one that does the learning.

That’s why I love this picture. it captures so many wonderful things about the right kind of teaching and learning.

The Beauty of Geometry

Every now and again, I take the opportunity to simply opine on the beauty of geometry. Math gets a bad rap because of it reputation of being cold, lifeless, functional and academic. (Some folks aren’t helping this by proclaiming that the arts are what we do to enjoy school and math is what we study to get paid later on in life.)

Don’t get me wrong, there certainly are academic ways of discussing art, music, iconography, fashion, design. There’s technique and vocab to all of these areas. Students of these disciplines are still students who must study, but their exploration isn’t saddled with the atmosphere that math is. In math, it is often believed, the box is set; the boundaries drawn. The math frontier is closed. There is no need for exploration when there is nothing to explore.

I’ve always felt like geometry has the capacity to challenge those notions. Kolams, quilts and origami help students understand the aesthetic value of straight lines, precise measurements, perfect circles and right angles. Sometimes, you have to build them to complete your understanding of them. That process alone can bring with it its own supply of feedback. When you are trying to create something visually appealing, often times, the eyeball becomes the expert in the room, not the teacher. Attention-to-detail and technique become valuable without encouragement.

At a recent professional learning opportunity, I was given some time to play with KEVA planks. So I did. The planks are all congruent rectangular prisms. So I placed one on the table. Then I placed a second on with a slight rotation (the diagonal intersection points were designed to sit right on top of each other, but the counter clockwise rotation was determined by the next block being placed so that the vertices were placed on the preceding blocks’ short-segment midpoints. It ended up being about 10 degrees.)

That all sounds pretty mathy (and probably somewhat unclear since I’ve never had to verbalize the process before). But the resulting tower is pretty cool-lookin’ (at least I think.) I simply love when objects with straight lines and right angles are arranged to look like curves. This can happen in algebra as well. As a teacher, of course I don’t know if my students will share my fascination, but fascination isn’t the goal. It’s tough to measure and, besides that, it’s fickle.

I’d encourage you to look for opportunities to change the cold, academic atmosphere surrounding the math. How can we warm this wonderful subject up? We used to take advantage of those tricky days right before a long break and do art projects. Thanksgiving Origami, or build a Christmas (or holiday… or wintertime) scene using nothing but triangles.

 

What ideas do you have?

Maker Geometry – What can blocks do for you?

So, today I got to play with blocks called Keva planks. A set of Keva planks are nothing more than a whole bunch of congruent wooden rectangular prisms. You can build towers, mazes, bridges, and… of course… geometric shapes.

So, a task came to my mind. Let’s suppose we were going to take the planks and make the smallest possible cube.

  1. How many planks would we need for the combined widths to match the length of a single plank?

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The answer’s five, by the way. So, each face is 5 planks wide (which is a single plank long)

Looks kinda like this…

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So, naturally… now we can calculate stuff. Like surface area and volume. But to do that, we’ll need some numbers.

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So, in my haste,  I clearly did a lousy job of lining up the blocks on the measuring tape. Sorry about that. Not exactly a deal breaker, but annoying.

But since maker materials are becoming more common, I figure you might prefer your students pull their own measurements.

There are a couple of ways that I could see variations of these: different shapes (different kinds of prisms, for example). I could also consider challenges like, given x-number of blocks, who can build a figure with the largest volume or a flat shape with the largest area?

Keva blocks seem like a low-risk, high reward manipulative simply because the start-up would be so quick. What could you do in your class with a set?