I absolutely love teaching high school geometry especially when it comes to the topic of transformations in the coordinate plane. Teaching this unit always makes me want to collaborate with our art department to create a cross disciplinary project based approach to understanding the concepts of reflections, rotations, translations and dilations in the design process.

A few months ago I came across Tilman Zitzman’s (@tilmangeometrydaily.tumblr.com and simply tweeted “hmm this site gives me an idea for a project in my math class.” To which a good friend Steve Dickie (@falconphysics) responded:


Now this seemed too compelling not to try. Design in Geogebra, advertise, promote, and sell on Cafepress. This seemed like a great way to authentically engage and evaluate student understanding and creativity.

Fortunately for me I have a good friend Mike Fenlon (@mfenlon44) who is a national trainer for the Buck Institute of Education (BIE.org) and he was able to help me through the design process of this project. Here is where we landed:


Project hook: A video/skype call from Tilman himself to talk about his tumblr and how he designs. This was AWESOME! He was AWESOME! Let me just say for being bugged and twitter stalked by me he totally put himself out there and created a 12 minute video for students he has never met and absolutely knocked the ball out of the park. THANK YOU Tilman!  I encourage all of you to buy a kick-a** t-shirt from Tilman.

Viewing the video entailed active listening and jotting down the answers to questions like “Where does Tilman find inspiration?”, “How does he design?” “What emerging patterns do you seen in his designs?” and “What common geometry terms do you hear him referring to as he talks about hiswork?”

Following the video we developed our driving question:

Driving Question: How can we create a geometric t-shirt design that could be a best seller on cafepress.com?

Need to knows: After viewing Tilman’s website and video students were tasked with jotting down as many descriptive terms and ideas that came to mind throughout the viewing process.  Such terms as:  “2-Dimensional”, “overlapping”, “lines”, “repeating”, “circles”, “arcs”, “color” etc.


From here students were placed into groups of 5-6 to decipher their 1-3 word descriptors and place them into larger themes such as “shapes”, “reflections”, “growing”, “repeating”, color, etc.

Our goal here, which I believe is one of the major goals of PBL, was to have students develop the content strands relevant to this project and their end product.

This was a struggle. I knew the standards that my students needed to work through but could I really expect them to say “Mr. DiLaura, I believe we will need to develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments, thereby meeting common core standard HSG-CO.A.4”  Alright so I added that last part to make it obvious no student would ever say this.

In the end, I fed the students most of the content descriptions I was ultimately hoping they would pick up on. That probably disqualifies me as a true PBL’er.


Tap to download and open iBook 100MB file

Content delivery. One of my major concerns with PBL is the shift of focus from content mastery to product design. Don’t get me wrong, that is one of the things I love about PBL, yet I live in the tension of making sure my students have access to quality instruction and opportunity to build fluency in problem solving.

To ensure these things I built a multi-touch book for my students to be able to read, view, interact with and practice the concepts we were talking about and working with in class. This allowed me to free up some of our face to face time to explore designing abstract geometric work with our iPad apps.

Product designing. Students were allowed to use Sketchbook Express, Geogebra, and Kaleidopaint to design in. Next year I will not allow students to use Kaleidopaint and I will make sure we spend more time designing in Geogebra. The potential for connecting designing in the coordinate plane and the effects of transformations is immense when using Geogebra.

After the first week of learning about translations, reflections, and rotations students submitted their first draft of artwork. As a class we performed a gallery walk in which students gave feedback to each other on their work. They were encouraged to list things they liked in addition to things they thought the student could do better.


Here again I was a bit disappointed. I didn’t set great ground rules or perhaps my expectations were too low. Students were too nice to one another in their reviews, and as a result students didn’t feel a big need to iterate on their work. In other words, the majority of students performed how they always performed. The did just enough to get by and I hated that.

So this is where I found myself. Half way through a project that I thought would be really sweet. And some did love it. They rocked it.  But for the majority of others it was one more hoop to jump through. I was dumbfounded. I fought to understand the answer to these questions.

Was their no motivation to publish their artwork and see if they could make money or were they calling my bluff?

Was their lack of effort secretly telling me that they were uncomfortable with demonstrating knowledge this way? That they’d much prefer to be told to do numbers 1-25 on page 345 and that it was due tomorrow?

Or do they need to be unlearned from how they’ve learned over the years? Is PBL so vastly different for them that they need to be given permission to do things differently?

Or did I just blow it? (most likely) Did I not set something up right from the beginning and therefore not make it possible for my students to succeed?

In the end. I came to the conclusion it was a little bit of all of the above. There are definitely things I need to do to set my students up to succeed. But at the same time accountability and ownership lies on the shoulders of students. I will definitely repeat this project in years to come but will modify my approach, follow through with posting student work on cafepress.com (I didn’t end up doing that this year) and I will make sure we spend more time designing in class with Geogebra.

Any PBL experts out there wanna shoot holes in this project or offer constructive feedback I appreciate your thoughts.


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