Building (math and science) Knowledge

KevaTweet
There are different types of knowledge. To know how a square is defined is different than knowing how to identify one. These are different that knowing how to draw one with ruler and paper. Or construct one with compass and straight edge.

A square is a pretty simple example, but when it comes to ramps, bridge, exploring mass and rotation, there’s being able to answer questions about it, and then there being able to build object to create examples, non-examples, and solve challenges. And it can help to have the right tools.

My office recently got a set of Keva Planks. Now, I’ve gotten to see these blocks in action a number of times and they are pretty cool. First, there is almost no learning curve. The blocks are all exactly the same. There’s no connecting pieces or fasteners or adhesive. There’s nothing to them. But with them you can build ramps and towers, polygons and prisms. They set up easily, the clean up easily.

Full-disclosure: They aren’t free. (Cheapest place I’ve found them is Amazon… 400 blocks for $90). Ordinarily, I don’t make a point to advocate for expensive tools, but in this case I think it could be money well spent based on the needs of the location. Also, they are durable and shareable. One department or grade level team could probably make good use with one to share.

Anyway, it’s worth looking in to as they allow us to explore types of knowledge that we otherwise might not be very well equipped to explore. (Particularly with those Next Gen engineering practices that are starting to become a reality in many states.)

For another look, here’s my latest podcast: Instructional Tech in Under 3 Minutes #5 – Keva Planks.

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Proofs (and writing) are difficult

The moment I started to have success helping student really learn how to write proof in geometry was the moment I realized that”The Proof” is nothing more than a persuasive essay converted to math class. It’s disciplinary literacy. And thinking of them as mathy-style essays can help us isolate some of the reasons the students struggle with proof in general. My experience leads me to think that many of the struggles are the same the ones the students experience with writing outside of math class. They don’t understand the structure, they don’t appreciate the value of honoring their target audience, and they don’t understand the content well enough.

Luckily for us, the ELA department has often hit those three points really hard. As math teachers, we just need to help the students bridge the gap.

What’s the structure to an essay? Thesis, supporting paragraphs, conclusion. Or, in math, “Given angle a is congruent to b, I’ll prove that segment a is congruent to segment b. Here’s the evidence I’m using to support my claim. And here’s what I just proved.”

Who’s the target audience? In math, it’s often either someone who doesn’t understand or someone who disagrees with you. That explains why you need to back up each statement with theorem, definition, or previously proven statement. Take nothing for granted or you’ll lose your reader.

And as for content? Well, have you ever read an essay from someone who plain ol’ doesn’t know what they are talking about? The best structure in the world isn’t going to save them if they can’t define the words they are trying to use.

So, when it comes to proof-writing, I think we math teachers need to appreciate that “writing” really is at the core of it, and the better we make that connection explicit to our proof-learning students, the more likely they are to be successful. And perhaps there’s a role for some meaning collaboration between high school math and ELA departments.

And with that, enjoy the latest “Instructional Tech in Under 3 Minutes” discussing, of all things, writing.

New Podcast: Why I love this picture

So, I get the pleasure of supporting a different school community than I have been these past couple of years. As a part of that work, I have decided to start a short video podcast. (The Geogebra post was the first episode.)
Occasionally, that means I’ll be borrowing “thegeometryteacher” content and podcasting new life into it. This is one of those examples. I originally posted this last fall…

 

Here’s the picture…

2016-11-15-09-06-34

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.

A long-awaited solution (featuring Geogebra)

So, a while back, I posted “Circles from Cedar Street” with an intriguing (at least to me) picture designed to kick off the conversation about rotations.

Then, I left it alone. Like, literally. I didn’t solve it. I should have solved it. I let you down.

I especially let guys like Dan down, who also found the problem intriguing. Sorry about that.

But I realized today that it’s never too late to make it right. So, using Geogebra, here’s is one possible solution to the Circles from Cedar Street problem from back in August of 2013.

Why I love this picture #2

A while back, I discussed why I loved this photo. It’s possible that I have a series starting here (sort of like I have with “Real or Fake”. Anyway…)

MathPhoto

Today’s photo is a beautiful example of tech integration because the tech is actually integrated. Integrated with what? Well, in this case, with manipulatives.

See? The student has the problem presented online and will record her answer online, but there clearly is no expectation that the work will be fully digital. Which is a good thing because it can be difficult to ignore how effective manipulatives can be in helping student model and visualize mathematical topics (in this case, 3-D images. She’s building a rectangular prism given the front, stop, and side view.)

That’s why I love this picture.

The Blessing of the Broken Tech…

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I was reminded this week of the risk of good tech. It’s easy for good tech to take on greater value that it deserves. Teachers… good teachers… sometimes remember that tech is a tool that needs to be wielded with the skill of a discerning educator in order to be effective.

And so, sometimes when the technology isn’t working right, you get a reminder that the teacher ultimately makes the decision about how a tool gets used and, thus, whether a tool is effective.

This week it was a teacher who was struggling with the audio of a video. The video was designed to accompany their math content and, under normal circumstances, there would be a temptation for the tech to BECOME the instruction for that lesson.

But then the audio broke…

So, the visual parts of the video simply became props for the teacher. She could still use the tech, but it could no longer stand alone. It was frustrating moment, to be sure, which I understand because the emergency-lesson-plan-rewrite isn’t usually the favorite moment in the life of the educator.

But, if we allow ourselves to be opportunistic and learn from all circumstances (#GrowthMindset), then we see that the technology going down can help us see the areas in which we are becoming too dependent on the tech. And then we can learn to rebalance those areas. And the constant striving for improvement is the hallmark of the type of learning we should be consistently modeling for our students.

Why I love this picture…

I want to tell you why I love this picture.

2016-11-15-09-06-34

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.