Isn’t Geometry an Art?

The things I do to get the students to learn geometry...

The things I do to get the students to learn geometry…

By the time most students arrive in my classroom to take geometry, they have seen Math 7 and Math 8 (which are two sides of the same pre-Algebra coin) and Algebra I. The stated goals of this sequencing is to “prepare the students with the necessary algebra skills to be successful in Algebra I (and later on in Algebra II) and also to be successful on the state tests (currently the Michigan Merit Exam, soon to be replaced by the Smarter Balanced Assessment).

And then there’s geometry…

And our textbook decides that it wants to teach this class right in line with the sequencing pattern: right between Algebra I and Algebra II comes “Algebra G” or Geometric Algebra. I’ll admit it makes some sense. We have spent several years training our students to “do algebra.” Typically that includes plotting points, graphing lines, solving equations and systems, and manipulating functions. If that has been the environment for the last three math classes, then, for the sake of the students, it would make sense to keep the model the same, right? Consistency and predictability breed success, right?

But what’s the risk? Well, as I’ve talked about before on this blog, the Algebra taught in most places is significantly lacking in it’s ability to engage students. So, while the theory is that our students come in well-prepared and well-trained, the reality is that most students come in with sensitive pressure points and calluses similar to someone who has walked for three years in the same pair of shoes. While the shoes are certainly familiar, they might also be smelly and worn out. The ankle support might be gone and the students have learned how to walk funny in them to avoid the blisters and shin splints that have plagued them in the past.

Is this any less geometry then having the student solve equations?

Is this any less geometry then having the student solve equations?

Perhaps what some of them need is a new pair of shoes.

Today’s learning target is getting students to be able to visualize cross-sections and 3D shapes made when 2D shapes are rotated around specific lines.

To approach that, I started with this activity and I noticed very quickly that the students started “walking funny.” I had asked them to put on their old Algebra shoes and the predictable disengagement started setting in very quickly. I wasn’t going well. Following the Dan Meyer Model, I could find at least three indicators that I was doing math education wrong.

Then something dawned on me: Why do we insist that students do algebra all the time? Geometry is the measuring of the earth, a true down-to-earth, visual math. Why can’t it be art?

So, we changed things up. I had them all get a piece of paper and I acted like an art teacher. I put stuff on a stool and had them draw what they saw.

Engagement hit 100% fairly quickly, especially once I struck a pose and asked them to draw me (see the pic at the top).

If 100% are willing to do this, and 40% are willing to graph lines, which is a better math activity?

If 100% are willing to do this, and 40% are willing to graph lines, which is a better math activity?

Apparently, the new shoes I gave them to wear were a lot more comfortable and many more of them were willing to follow along the path. Content-based discussion and collaboration began to happen without me telling them to do so. As a result, when we had to discuss how the activity supported the learning targets, the connections were much better.

Then I gave them back the original handout (which, for the record, I still think is a good handout), and the students did much better with it the second time.

So, I ask again: why do we insist on turning Geometry into an Algebra course? It doesn’t seem like it has to be. Our current textbook says it has to be, but the textbook only has the authority we choose to give it. (See The Blessed Textbook Conflict if you want my take on the authority of textbooks.)

Today’s activity would suggest that if we are willing to consider what a class would look like if we really wanted the students to simply learn geometry, perhaps it would look more like an art class instead of a math class.

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