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?


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

Looks kinda like this…


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


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.