As the school year comes to a close, I’m finishing grading the third project of the year that my Honors Precalculus students completed. As always, I’m blown away by the reflections that the students write about how the project period went for them. I also do need to put a grade on their work, so I’m looking closely at what they did, wrote and created. I am so pleased to see how many kids did something really interesting in exactly the type of exploratory fashion that I hope to see.

As an example, two groups chose to study Markov Chains. They had seen some probability and a little bit about matrices. It was a hard topic to tackle and try to understand, let alone explore and push and do more with it. One pair of kids started by looking at weather data and how likely we were to have a rainy day followed by another rainy day, versus sun or fog. They pulled data, analyzed it, made predictions, asked more questions, and explored. They asked hard questions and tried to answer them. The other group studying Markov Chains started looking at games, as well as economic applications. One student ended up using her programming knowledge to write a virtual Chutes and Ladders game that models your moves based on rolling a die and the probability of moving to a certain position on the board. The game included the ability to be played in 100,000 batches, to collect experimental probabilities. Another group was interested in probability so they created a video teaching about the basic probabilities in poker. They did some additional exploration of the mathematical differences between five-card poker and seven-card poker. The best part about that project was how much fun the kids had who did it; they spent more time doing this work just because it was what they wanted to be doing.

[As a total aside, this makes me think of a way to motivate homework. If I can create learning experiences that make students want to do more exploration “after hours”, then I don’t actually need to ever assign homework. The kids who want to do it, can. I’m not sure where that nugget leads but it’s an intriguing thought.]

Last year, we did three projects as well and the timing felt fine. This year, it was too many. Due to schedule, we didn’t complete the second project until early March. Then, we needed to start the final project in time to share out at our school’s Math Exposition Night. Therefore, doing the projects one month apart (not counting vacation time) felt too close together. I knew this was going to less than ideal and I even felt a bit apologetic as I announced we were starting yet another project. It is a testament to the great group of kids I’m teaching this year that they were willing to dive in again just because I’d asked them to do it.

It is only now, as I read and have time to process some of what they students wrote, that even though I felt like this project was too much and wish I had made a different plan, my kids think differently. One person wrote, in answer to how the structure of the project period work with your own strengths as a student:

“The structure provided allowed us to go into depth with our topic because we had so much freedom. In previous projects I was wary of the freedom that we had because it was difficult to get started and go in to depth on the projects without instruction but this time around I knew what to do to be successful during the project period because of the past experience. The peer review day also helped cater to my strengths because I was able to take the constructive criticism and apply it to the project to help improve it.”

Another person wrote “I feel as though I didn’t take full advantage of the project structure until this project period. I always tried to make a project plan before starting to know what I need to explore but this time I didn’t make a plan and rather just decided what I wanted to explore as I did the project. I discovered and explored a much more diverse plethora of ideas through this structure and I ended up enjoying the project a lot more thoroughly because I was doing what I was passionate about learning more about rather than what I thought would be most useful in my project. This played to my strengths as a student because I wasn’t planning every step and I could explore what I wanted to, even if it was outside of my comfort zone, and this allowed for the product of the project (the artifact) to be much more detailed yet simultaneously broad with having covered so many aspects of [my topic].”

Someone else shared: “My first project dealt with fairly simple math and I was more reluctant to push myself beyond what I already know. I think that each project period I have been able to push myself further in thinking of new things to explore beyond what we have covered in class. I think this project period was the most successful for this because we chose a topic that I had never even heard of before.”

Lastly, a student wrote: “I feel as though I have gotten more comfortable going outside of my comfort zone and using the projects to enjoy maths explorative side. I was in a habit at the beginning of the year to plan everything out before I began, whether it was a project or approaching a problem. This project series has brought me to realize that when working a hard or long math problem it is not always the most effective strategy to plan your attack before beginning, often times success comes from exploring and trying many different ways to solve a problem before discovering the most effective way.”

In the end, it seems my “mistake” worked out fine. I am finally seeing the growth and type of work that I am hoping to see by taking this time. By dedicating such a significant amount of class time (in and out) to the projects themselves, I think my students can see the value I am placing on this type of exploration. I am continuing to tweak how I do things but I feel like I must be heading in the right direction to see more groups whose work feels like a great future project exemplar. Now on to writing down those ideas to save them for next year!