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?

Why “maker” seems so appealing…

In the education world, “maker” as a vocabulary word seems very trendy, but the thought behind it really isn’t new. We learn by doing. We do by creating. The ability to create within the content requires connections among a variety of different related content pieces and often testing and trouble-shooting which are themselves tasks that require pretty significant understanding.

So, it shouldn’t surprise us that creative activities seem valuable from a learning standpoint.

What is significant is how satisfying they are for our students… 0r at least the advocates would have us believe. I was able to be a learner today in an all-day session regarding maker-style learning and this quote by Mark Hatch certainly got my attention.

“Making is fundamental to what it means to be human. We must make and express ourselves to feel whole.”

A Google search of the quote revealed a second part of the quote:

“There is something unique about making physical things. The things we make are like little pieces of us and seem to embody portions of our soul.” (Quote found here.)

That’s a pretty powerful statement. There aren’t a lot of areas of education that will evoke words like “soul” and phrases like “fundamental to what it means to be human.”

And it makes sense. Let’s remember that each of our students (and each of us) were CREATED. We were literally made by a MAKER. And we are not just made, but we are made specifically in the image and likeness of that maker. We are created to be creators.

“Then God said, ‘Let Us make man in Our image, according to Our likeness.’ ” (Genesis 1:26) This quote, by the way, is uttered just after God the Creator had made the universe and everything in it. Our Lord, Himself a maker, created humans and said “Let Us make them in Our image…”

So, it should not at all be surprising that a day spent making is much less likely to feel like a day wasted. Perhaps our souls recognize that the time spent making is time that is bringing us closer to the image in which we were created. Time spent being who God made us to be. A chance to be our best selves.

And isn’t that our job as educators? To help our students be their best selves?

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?

The Value of Opening Your Doors

Have you ever heard a teacher say something like “Yeah, you know administrators make all these rules and policies, then I close my door and do whatever I think is best”?

Ever heard that? Or something that basically means the same thing?

There’s a lot of different directions that could take, of course, with that as a starting point, but I want to focus on “closing the doors”.

Let’s look at this at several levels. Often “closing the doors” represents an attitude as much as it describes a physical state-of-being. “Closed doors” implies that we don’t want people seeing us do what we do. (Or perhaps, at least, only certain people.)

But it also creates risk. “Closed door” teachers often don’t see their classroom practice compared to other teachers. This stifles innovation, collaboration, public relations and other essential components of schools in search of consistent improvement.

It follows, then, that one good first step toward improving innovation, collaboration and public relations in a school is to open the doors. Let teachers explore each others work, let the community see what goes on. And not just see, but explore, participate, and engage.

Yesterday I saw that attitude on display at Cavanuagh STEAM in Lansing, MI (follow them on Twitter @CavanaughSTEAM ).

 

School hasn’t started yet. It begins the Tuesday after Labor Day, but already the doors were open, the teachers were ready to give the community a chance to explore their classrooms.  Parents were given a chance help shape the direction of the projects their students will be completing and provide opportunities for authentic audiences for student work. One kindergarten teacher had a small block-based  maker activity ready for the incoming kindergartners. She reminded me as I chatted with her prior to the event that this was many of her students’ first school experience. She clearly wanted to make a good first impression.

The event, “Family STEAM night” gets repeated 4 times per year. After the first one, subsequent evenings have a strong emphasis on showcasing excellent student work and giving each teacher a chance to highlight some of the outstanding experiences their students explore in the classrooms.

Their doors are open and they invite the community to come in and join them. Sadly, I had to leave before I got to see what it looks like when they do. I look forward to the next Family STEAM night when I can see the halls filled with parents and students getting to see first hand what it means to be a student at @CavanaughSTEAM.

Birds at an #EdTech Conference

One thing you certainly can’t say about #TeamJXN (Made up of Kellie DeLosSantos, Alaina Sharp and Ann Smart) is that they aren’t outside-the-box thinkers.

“Outside-the-box” is certainly well on it’s way to cliche status these days, but despite that, it still has a perfectly functional and relevant meaning. And at an EdTech conference, where so much of what we are learning about is touted as “outside-the-box”, what does it actually take to live up to that?

Birds.

It takes raptors at lunch.

Simple Leadership Advice

I’m going to attempt to model this my internalization of a bit of advice that I received recently.

Leadership is about trust. You want your people to trust you?

Speak plainly and keep your word.

By speak plainly, I mean say what you mean in a way that designed to be heard and fully-processed by those who hear it. Trust corrodes when those you are leading feel the need to constantly read between the lines of your statements.

By keep your word, I mean if you commit to doing something, then do it.

The advice I received was from Mark Wilson, but his was directed at goal-setting. Goals should be simple and easily understood. He didn’t mean that they should be low-level goals. But they should be able to be stated simply.

All of our students will be safe in our school.

All of our freshman will successfully complete all of their classes.

All of our new students will get a complete orientation to our school community before they attend a single class.

These are not-simple goals, but they are stated simply. That makes them easier to follow. Easier to implement. Easier to assess.

And it also makes it easier to keep your word. Here’s what I said I would do. Did I do it?

Well, if your goals sound more like this…

“To support the ever-dynamic pressures of a 21st century global economy, we will consistently find new and innovative learning experiences to blend with classical best practices to provide the highest-quality academic pathways for our diverse learners to produce successful work- and college-ready graduates.”

… then it becomes quite a challenge to evaluate whether or not you did what you said you do. This goal is not necessarily more complicated than “All of our freshman will successfully complete all of their classes”, but it is much less likely to become the unifying slogan around which we focus our energy. And isn’t that the point of stating the goal?

 

To close, all of this talk about speaking plainly has me thinking of this delightful scene from Shrek the Third

 

 

The Transfigurative Work of Schools

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Photo credit: Deviant Art artist Jeixnox – used under Creative Commons

 

I know that not everyone places as much stock in the teachings of The Bible as I do. I also know that there are some risks with teachers interpreting their role as classroom leader as overly similar to the role Jesus played in his time on earth. All of that being said, I was recently moved to reflect on how the role of our Lord as teacher could provide some lessons to us as we engage the work of educating young people.

This reflection needs a story.

I had a student some years back who struggled his way through geometry… twice. The first time it didn’t work (for a variety of different reasons). He was a pleasant boy. Fully engaged in the social aspects of class. He was a willing partner or group mate, didn’t mind talking in front of the class and practically ALWAYS listened to the words I was saying. He came to me first as a 10th grader and a struggling math learner. His skill set wasn’t strong. His perseverance also wasn’t strong. He had scraped by in math classes before he made it to geometry. Geometry seemed to be where he hit his limit.

As his struggles mounted, he began to disengage. The absences started to become more frequent. Then he got sick. I spoke to his mom. We made a plan. He eventually got better and started coming back to school, but the plan didn’t stick. By June, he had mastered barely half of the learning targets for Geometry and it became clear that I couldn’t recommend him for credit. He understood. His mom understood. I never liked having to do that.

And, due to the limitations of our system, he ended up back with me, right back where we started the next fall. This time he, as a junior, was a bit more out of his element. His other friends had advanced to the next course. And a fresh batch of last year’s freshman (now sophomores) mixed with this year’s freshman were now surrounding him. He parked into the back corner. Sat by himself. Would rock back in his chair. Still paying attention to every word I said.

As was my custom with all of the students who I have to see a second time, I like to go back and talk to him. See, I misspoke earlier. We weren’t exactly right back where we started. In addition to the half-ish of learning targets he’d once mastered, he and I knew each other. I knew his mother. I remembered him telling me what his summer was going to look like. I followed up on that. He knew I had young kids. He followed up on that. It wasn’t like last fall. It was different.

So, he sat in the back. We agreed that the absences were the primary problem last year. That my goal was, for as much as I enjoyed having him around, to never have him in my class again. And in order for that to happen, he needed to be in school. He committed to that and to his credit, he kept his word. He came to school a lot more, missing a few days here or there. There weren’t too many gimmicks or cheesy incentive programs. (although, he became one of the guys I could really count on. There is a benefit to having a kid who doesn’t mind being tardy to his next class. When the bell sneaks up on you and you need someone to help rearrange desks and clean up construction paper scraps, a guy like him was handy to have around. Don’t worry. I wrote him late passes to keep him out of trouble.)

But he continued to sit in the back and keep to himself. Eventually, that changed some. I paired him up for think-pair-shares with some fairly safe partners. And he kept learning geometry. A “C” here, a “B-” there, a “D+” somewhere else. Most of the time he was passing. Sometimes he wasn’t. Some quizzes or tests he needed to try twice, but he did. Sometimes he couldn’t stay after school, so he’d go in the hallway to do it. No big deal really. I was just happy he was coming to school.

Then, in late May, I was able to show him that he was mathematically in the clear. He had learned enough geometry to pass and could prove it to anyone who asked. We high-fived and I called his mom to make sure she knew. She was excited. He shrugged it off. Mostly, it seemed he wanted to verify that this meant that he didn’t have to study for the final (as was his custom). I rolled my eyes at him and told him that he should see it as a chance to show off how different this year was to last (as was my custom).

In reality, it was a compromise. He tried a few problems. The ones that were easy for him. Left the harder ones blank. But, on the last problem of the test, he wrote something that I’ll never forget.

“It’s been a great two years. Thank you for not giving up on me.”

He put it at the very end. Last question after about a dozen that he’d skipped. He knew that I’d look at every single question. (I told you. He listened to everything I said. After two years, he probably knew me as a teacher better than I knew myself. He probably could have written my evaluation more accurately than me.)

I didn’t expect that. What if I told you that a kid would fail geometry, have the same teacher the second year, just barely pass, and would THANK the teacher at the end? I didn’t get many thanks from those students. Heck, I didn’t get many thanks from students who had great experiences in my classes.

But it helped me to realize something. Teaching isn’t about accepting students as they are and leaving them be. It’s about accepting the reality of where a kid is and helping them become more and better versions of themselves. Perhaps our job is to help transfigure our students.

Eastern Christianity commemorates the feast of the Transfiguration of the Christ in late summer. You can read about it if you’re unfamiliar. It’s in Matthew, chapter 17. In a nutshell, Christ takes His three closest disciples up to the top of a desolate mountain and begins to radiate a light brighter than any of them had ever seen. Moses and Elijah appear also. He did this for a variety of reasons, but the most important reason was that this light wasn’t new. It wasn’t something that Christ had only recently found, acquired, or learned. This was something that was always inside of Him, it was always a part of Him. He needed His disciples to understand that. They needed a full understanding of the reality of their situation. One commentary considers it “a foreshadowing of His future glory.”

When the disciples came down, their resolve was set. They had (quite literally) seen the top of the mountain and knew that their goal was to get back there again. They’d seen the glory of Him whom they were following and knew that if He was willing to share it, they were willing to work to receive it.

As I was reflecting on the story of the transfiguration as I read it today, I noticed some connections to the way that teachers relate to the students in their classrooms.

Each of these children has “a future glory” built into them. There’s a potential that is always there. It’s a part of them, built into the very fabric of their humanness. Our job is to give them a chance to see a foreshadowing of that future glory. To give them a view of the potential they have. To help them to see that it exists and is worth fighting for, worth working for, worth sacrificing for, worth struggling for.

It would have been easier for me leave that boy to his struggles, move him on (either by flimsily passing him or casting him off to another teacher). It would have been easier for him to simply quit the second year as he did the first year. The struggles build up. There were times he wasn’t passing, even in the second year. At those moments, he needed to decide why year two was going to be different than year one. Not me. Him. He needed to know.

And while I didn’t know it at the time, he knew it was different because there was an adult who, as he put it, wasn’t giving up on him. Who believed not in what he was, but in what he could become. Who was able to foreshadow his future glory. Quite literally, there was a portion of that student who was transfigured during geometry class. And I didn’t know it was happening. The day-to-day becomes ordinary and the students are numerous enough that you don’t recognize what is happening moment-by-moment. But when he had a moment to reflect, he recognized what had happened. And I’m glad he did because now, I do, too.

That’s our role. We are in a human development industry. There is an often-unspoken understanding that development means that at the beginning, people aren’t what they should be. And they need guides to become fully developed. Many of our students don’t come to our rooms as their best selves. They’ve become convinced of things that aren’t true. They’ve drawn conclusions from experiences that are interpreted through blurry lenses. As a result, they are confused. They look to the world around them and they often don’t find help. Many of the modern social messages are contradictory and confusing. 140-character answers are plentiful, but real help often takes much more time. The messages from the media don’t help. What helps are caring adults who, as my student put it, won’t give up on them.

That’s where our job begins. We get these young people and we need to take them up the mountain. Show them why their future selves are worth struggling, fighting, and sacrificing for. We need to foreshadow their future glory. Because in so doing, we accept that our task is no less than to transfigure these students a little bit at a time.