For the past two weeks I’ve been doing some really deep thinking. Enrolled in a curriculum foundations course, my class of 20 or so educators has been working hard to understand and reimagine the perplexing puzzle of curriculum design. There were times I was grateful for the chance to hear so many perspectives, times I lamented not taking a course like this earlier in my career, and times I was confident with my conclusions only because of my years of experience. Truthfully, there were moments I wondered why I was spending my sunny summer days in a classroom instead of at the beach – but as the final pieces fall into place – I am proud of my effort and intensely satisfied with the journey.
The Task
Early in the week our facilitator gave us an overview of the course requirements and projects. One stood out: The Artifact. We were asked to create something: a product that, when viewed later, would trigger the learning from this course. Eventually displayed in our classrooms, it would be a reminder of the most powerful take-aways and aha moments we experienced these few weeks. Interesting. I liked the sound of this one.
Our learning was structured around the examination of curriculum design through eight lenses: curriculum theory, postmodernism, critical theory, methods and models, tools and techniques, persona, motivation, and assessment. We completed activities to gain a deeper understanding of what these lenses entail. We identified challenges in our profession and searched for the root causes from each vantage point. Together we discussed solutions, reflected on our practice, and made plans for our own redesign with these lenses in mind.
As we made our way through the week, the artifact idea swirled around in my head. What would I make? Can I focus on these lenses and also make something math-y? A few ideas started to take shape. I would make a math puzzle. The pieces would stand for the essential components required to make a complete picture. But what was the complete picture? What did it represent? A well composed curriculum design plan? A successful math classroom? A well composed curriculum design plan for a successful math classroom? Something else?
While I wasn’t sure about all the specifics, the puzzle idea felt right. If all the necessary components fit nicely together, you have a sum that is greater than the parts. Puzzlers often use a variety of strategies and methods to reach the desired end point. And of course, with a puzzle, the process can be collaborative and fun and just as satisfying as the finished product. So yes…a puzzle. But not a typical puzzle with only one solution. That would not have the parallels I needed. Depending on the community of learners, the plan for a successful learning experience changes…sometimes drastically. The puzzle had to have multiple correct and creative solutions that include all the pieces. It had to be fun and appealing and invite play without being intimidating. Puzzlers should want to interact with it in their own way and figure out an end result that would be satisfying to them, but I should also offer prompts for users to examine, challenge, and test.
A few puzzle options seemed to fit nicely with my plan: 3D Pentominoes and Soma Cubes. I’ve been wanting to create both for a while after following the adventures of Mark Kaercher and others on Twitter. Perhaps this assignment will give me that needed push to get going.
The Product
I tried to visualize my ideal finished product. It would be a beautiful (fingers crossed) 3D pentomino puzzle. Pentominoes are the 12 unique ways that 5 squares can be arranged edge to edge to create a polygon. Then they can all fit together to form different rectangular solutions. 3D pentominoes just take this idea and make the pieces 3D – cubes instead of squares. Having twelve little structures to work with meant that I could have each one represent one of the lenses discussed this week and still allow room for other factors that might be specific to the math classroom. The pieces resemble and are often named for letters of the alphabet. Should I assign a lens to each? There’s a “P”…that could be postmodernism or maybe persona? Or could it represent product models versus process models? If the “P” represents Persona, maybe I could find mirror tiles or stickers to use on the faces to represent students seeing themselves in the design. Or would reflective or sparkly paint work? The “U” could be UDL…my mind was overrun with ideas and possibilities. I was getting bogged down with the details and the bling before I had the structure. Maybe I’ll think about those specifics later…
The super cool thing about pentominoes is that they can fit together in many different ways. One solution is a 6 x 10 rectangle, another is a 15 x 4. What other combinations exist? I remember the great math-y conversations I have had with students when playing with pentominoes in the past. 3D pentominoes take it up a notch, opening up the possibilities for discussion and investigation even further. Beyond my given prompts, students playing with these pieces might make a completely different creation that just looks or feels cool by interacting with the parts. The more we play, and test, and challenge, the more we can understand how the parts relate to each other and a more complete view of the possibilities can be realized. Yes. This fits nicely with my math ideals and my learning this week. With my finished product visualized, I was ready to plan out the process.
The Process
The first thing I needed were cubes. Lots of cubes. The ones I purchased at the local craft store were not going to work. A quick measure confirmed what my eyes had suspected. These cubes were not quite cubes…fine for other crafting but a disaster for this project. I needed to start from scratch. While my awesome husband, Kyle, cut some 1 inch cubes from a 2 by 4, I assembled my other materials and made a schedule of what needed to be done each day so I could meet the deadline. I was ready to work.
Kyle piled 70 cubes in front me. Perfect. Enough for my twelve little 5-cube structures and some extras in case I had to redo a couple. Once I had my cubes sanded, I assembled my pieces and glued them in place. They were now 3D pentominoes. I lined them up assembly style and set to work with my schedule in mind. Today they had to be primed and painted. That’s when I started to notice some interesting things…
Some structures were easier to paint than others. Some structures required a different brush. I started with the simplest piece and attempted to apply that process to the others – nope my skills didn’t translate. Figuring out what worked best for my complicated structures, and handling them first would have saved me time and built my skill set faster. I made assumptions about what paint colors would work best and which might require additional coats. I was wrong. Trying to stay on schedule, I attempted to get a second coat of paint on too soon…it didn’t stick. In fact, I had to sand and start fresh when I tried to do too much too soon. I started out with the same plan for each piece but quickly had to adjust. The tools, process, number of coats, and wait time between coats was different for each structure. I didn’t give up (even though I had a cool idea involving a Jenga game in my back pocket in case of disaster). I examined the progress carefully for each piece during each stage to make sure my efforts were successful. I made sure they had what they needed before I tried to move them on to the next step. I continued to adjust my timeline and rework my plan. I talked about it with my husband and I checked in with my girls. How do you think I should handle this piece? How long between coats? The others had an extra coat – does this piece need one too? In the end, the pieces didn’t all go through the same steps at the same time…but they all got there. When I really tuned in and allowed some flexibility with my plan, I could figure out what each piece needed and when they needed it.
In the end…
I did it! Process and project complete.
I have come to realize that these sweet puzzle pieces are all the little personalities that I consider when designing learning experiences. Some soak up the learning quickly, while others need more time or alternate tools and techniques to have the same result. Some are so complex that I need to expand my skill set and try something different and new to have the desired result. I have to choose my materials and methods with this in mind.
The complete picture is my ideal learning community. Everyone is beautiful and unique. Everyone has a space and we are all connected, considered and valued. Interacting with this puzzle will remind me that there are many ways we can all fit. The typical 6 x 10 x 1 rectangular prism is the solution I know well, but what others are out there? What learning and experiences do I need so that I can reimagine how we can all fit together?
You could argue that my 3D Pentomino Set is not really connected to this course at all. This was something I’ve been wanting to create for some time – this assignment just gave me an excuse to do it.
And, well – that’s true…or it was true. Pentomino puzzles represent a lot of what I value in math instruction: Have stuff to hold in your hands. Play. Play your own way then try out a method your friend suggests. Invite everyone in. Try given challenges and stick with it until you can be proud of your endpoint. Talk about your creations with a friend and ask questions about their work. Reflect on the process. This is how I operate…how I already operate. So how is this course reflected in my work?
The act of creating these pieces and reflecting on the process represents the act of consolidating my new learning and will guide my practice moving forward…
Decide on the desired end result. Plan out the steps you may need to reach that goal but be flexible. Know when to ask for help. Make sure everyone is primed and ready for the learning to come. Consider the needs of the complicated or exceptional first in designing the necessary steps to reaching your goal. What are the different tools, techniques, and methods that might be needed? Have them ready. Remember that taking small meaningful steps in the right direction is faster in the long run than having to backtrack or begin again. All these ideas have become solid. They are in the brushes I used, the paint that I chose and the glue that holds everything together.
Over time the paint may fade. The wood may warp and the pieces may no longer fit together the way I want them to or think they should. This will be the time for a new puzzle…a chance to reconsider the make-up of my new classroom community. Who are all these little people? What do they need to be successful? What does success look like now? Our learners change and their needs change. Reimagining and redesign is a necessary component in all aspects of education. We need to continually respond to the changing needs of our learners and dream up new ideas of what education could and should be.
This puzzle was a challenge and a delight – just like each and every learning community I have had the pleasure to lead. I’m proud of my beautiful finished product. But for me, it was the reflecting I did throughout the process that was the most meaningful. I am hoping that I continue to examine curriculum design from the eight lenses we discussed these last two weeks. But, like all things, some lessons will stick and others will not. As long as I keep students at the center of everything I design, the pieces of the puzzle will fall into place.
JoAnn Sandford Math 