By Dennis Muldoon, LLA Mathematics Teacher
Education has a lot of buzz words, perhaps more than any other part of our society. Everyone’s looking for that 21st-century, blended-learning, disruptive, student-centered, innovative, data-driven learning experience.
The buzz words can be a little much for me sometimes, but the new ways of thinking about education that they represent are often very exciting. My favorite development in the education world right now is the transition from STEM (Science, Technology, Engineering, and Math) to STEAM (the ‘A’ stands for Art). Allowing my students the chance to demonstrate their knowledge in an artistic, creative way seems to create a lot more buy-in from them, in addition to generating some awesome products to hang around the school.
Even more exciting, though, is the opportunity to mix in some modern digital media tools, so that students are not only flexing their creative and mathematical muscles, they’re learning a new technology as well, something that will likely benefit them later down the road. In this post, I’d like to share with you some of the STEAM-y projects my students and I have worked on this year.
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My most recent (and to me, most exciting) project was sparked by an observation of a student doodle. My 3rd period Algebra class was learning about linear inequalities, and had gotten pretty good at them. One of my students got a little creative on a classwork assignment, using his pencil and eraser to make a cool pattern in the shaded region of his graphs.
When I saw this, I thought it would be a neat opportunity for students to throw a little graphic design into their graphs. Having taken a course on Adobe Illustrator in my graduate studies, that seemed the best tool for the students to use. I bounced the idea around with a colleague, and made a plan to try elevating the doodle to a polished artwork.
I began the assignment by giving the students an Illustrator file with an artboard already set up with a graph on the bottom layer. I asked the students to create two linear inequalities of their own choosing on the graph, and to include the written inequality on the graph where the shaded region would go. Then they had to use Illustrator to create the shaded regions, one with a solid color fill, one with a geometric pattern, and each one on it’s own layer. Finally, I asked them to put themselves into the solution region, where the two fills overlap.
Students worked with our Digital Media instructor who helped them make some great photos of themselves, and they used the ‘clipping mask’ function to fill the solution region with their pictures on yet another layer. The beauty of using multiple layers was that they could turn off the lines they had made and the graph I had given them, so that only their filled regions were visible. This gave their projects a nice, clean look, but I could still turn those bottom layers on to evaluate their work.
Their finished projects came out great, each one unique, and the students seemed a lot more excited to create their project with professional-level digital illustration tools than they might have been if we had only worked through these problems with rulers on graph paper. With that said, I imagine an analog version of this project using tracing paper and color or collage might be exciting if digital tools weren’t available.
The students’ final reflections showed me just how much the project reached beyond mathematical problem solving, and required them to make good aesthetic decisions that rely on strong technical proficiency:
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Constructing clinometers (sometimes called an inclinometer) and using them to find the height of tall objects has been a part of my Geometry curriculum for several years now. In the past, I’ve asked my students to document the process at Instructables.com.
This year,I wanted to try something new. I split the class into two teams, gave each one a flip-cam, and asked them to make an instructional video that could teach a viewer how to use a clinometer. I left the specifics entirely up to them, only giving them some general guidance when they asked.
After walking out to make some measurements of the tall statue at the front of Treasure Island, we returned to school where the students used Adobe Premiere to edit their videos. At least one person in each group had used Premiere previously, and so they were able to edit their videos with only a little bit of support from me. Their finished products were impressive: They were able to show off both their mathematical knowledge and their video production chops, including in their videos things like voice-overs, title slides, and music that fades down when the narrator is speaking.
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This project really grew out of a desire to show my students the Geometry that exists outside the classroom. On a nice, sunny day we went for a stroll around Treasure Island with some cameras, and I asked my students to take pictures of things that were congruent. When we returned, I gave them a brief demo on how to use Adobe Illustrator, and then asked each student to choose their favorite photos and use the software to highlight the congruent shapes they saw. The images above were created by students in a couple hours, and helped visualize the notion of congruence.
Pink Pyramid, created by Marie, Danna, Leila, and Laversa.
Green Prism, created by Jhon and Angel
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For this project, we were inspired by the work of artist Aakash Nihalani, who used tape to create two-dimensional designs that appeared to be three-dimensional. I wanted my students to think about how 3D shapes would look from different vantage points, and so I asked them to create their own faux-3D tape art on the walls of the school. Working in teams, they created several designs, each spanning a corner of the hallway. Each installation only creates a complete image if the viewer is standing in one specific place at a specific eye-height, which my students marked with an arrow on the floor and an icon on the wall to show the height.
We definitely hit some speed bumps on a few of these projects, but for the most part I was very happy with the way they all came together. I love putting these tools in front of the students and seeing what they come up with. All of these projects are things that I will try again next semester, and the challenge I’m setting for myself is to create even more great ways to integrate the S,T,E, and A into my M.
Dennis Muldoon has been teaching mathematics at Life Learning Academy since 2012. He is currently pursuing a Master’s degree in Instructional Technology at San Francisco State University.