Editor’s note: This week’s post is by Isaac Alexander with additional reflections by Michael Colombo.
Rachael Ayre teaches a high school algebra course at Montgomery High School in Santa Rosa. Her class is tough: it consists of students who’ve struggled with Algebra in the past and are hoping to graduate this year. Rachael turned to the Makerspace team to help her develop new ways to get the students engaged. We suggested that the class reinvent its standard math classroom (inside a portable) into a highly functional, inspiring “math through making” lab environment. After gaining administrative approval and funding with the help of Anastasia Zita, we began working with Rachael to guide students through the process of redesigning their classroom.
Over four weeks, this Makerspace transformation project began with two design/planning days where students envisioned their future classroom. Later, during two field trips to local hardware retailer Friedman’s, students selected and purchased their materials and hardware. After that, there were two or three in-class workdays where students began construction in three phases:
- Phase One: East design wall, South tool wall, and storage area
- Phase Two: North and West walls
- Phase Three: Design and build the classroom fixtures; e.g. moveable multi-use work surfaces, a work bench, design table, and even an up-cycling of twelve remaining standard student desks and their attached chairs (these will be blank canvases for the students to reinvent as they see fit).
The students plan to cover the existing walls with a combination of whiteboard, pegboard, magnetic, and cork board surfaces. These new surfaces will allow every inch of wall space to be used for organization and storage, or flexible surfaces for hashing out projects, transforming almost 1000 ft² of unused space into a blank canvas for their creations and their creativity to be developed and displayed.
Transforming their classroom in this way has demonstrated to the students the practicality and usefulness of math, as they plug real-life numbers into the equations they’ve been learning in class. The students have been learning new skills as they do the building themselves. The steps include math in all aspects through measurement, design, material acquisition, and installation.
The students began by clearing a space around the edges of the room so they could measure its dimensions. The students went to this task, at first, begrudgingly, like a chore. In their reluctance, one student volunteered, “Why can’t we just use math to figure it out?” After some serious persuasion to move the furniture and books, they quickly started measuring. The students measured the length, width and height of all the walls at all the corners. We were all surprised to see the actual height was different than our math would suggest. The students learned that in the real world, portables are not perfect geometric solids and don’t always get built symmetrically.
The outer dimensions were recorded and students began to measure the features of the walls (i.e. windows, doors, air vents, etc.) and their respective distances to each other and the edges of the walls. While measuring the dimensions of the south wall’s window one group of students came across a curious discrepancy. The calculated overall height of the south wall using the sum of the distances of the floor to the bottom of the window, the height of the window, and the distance from the top of the window to the ceiling, did not match another group’s measurement of the southern wall’s overall height. We asked the students, “What do you think is going on here?” They looked at me expectantly, thinking I had the answer to the riddle. I responded to their looks, “I don’t know the answer; I’m just as confused as you.” Their expressions changed from expectant to puzzled.
After finding a stepladder they quickly found their measurement of the height of the south wall corresponded with their previous mathematical calculations. Again they looked at me to see what that data meant, to which I said, “I don’t know, what do you think it means?” One student yelled out, “It was Andy! He messed up [the measurements] the first time!” From across the room we heard a murmured “nu-uh!” Another shot back, “Math doesn’t lie. Plus we just measured it!”
Having double checked all the measurements, students drafted scale drawings of each wall on butcher paper. The drawings were then posted on the whiteboard and students answered Rachel’s questions about surface area and other mathematical features of their room. Students surprised themselves with their own engagement in learning algebra, and they spent the remainder of the class intently sketching out ideas in the Maker’s Notebooks they will maintain for the year.
Opportunities to connect math and making are abundant. One day when we visited, Rachael’s 12 students started by reviewing their homework. It’s a classic math problem, as in the image at right. A circle rests within a square and the solution is to find the empty space between. As Rachael jumps from one student to the next, it becomes apparent that nobody has completely solved the problem. But Rachael recognizes that a few were quite close, and combines their work into an explanation of the solution.
Once the students understand the homework, they move into the next activity. They dive into a box full of high-quality tape measures to grab one. But before using their treasures, they want to decorate them so the tapes don’t get mixed up. The students make circular labels, applying what they learned about inscribing circles in squares in the previous night’s homework. What had started out as an abstract math problem now becomes concrete! The students use their new tape measures to turn a 3 x 5 label into a square, then they calculate the radius of the circle that will be inscribed upon that square with a compass. Along the way, students have questions. Instead of answering them outright, Rachael encourages them to use a tool – grab an iPad, use your phone, figure it out somehow.
After some hard work and a little cajoling, the students have embellished and bedazzled their tape measures. Now Isaac steps in to explain the basics of using a tape measure to the students, which will come in handy next week when they go to Friedman’s Home Improvement to buy materials.
Next post: The students go on a field trip!