Thursday, July 16, 2015

Projects: theory versus practice

This is the first of a few blog posts that I want to write as reflections on this year. One of the topics that I'm thinking about and would love to get feedback on is the use of independent projects in teaching math. I understand that projects aren't a well-defined entity, but are somewhere on the spectrum past tasks (aka problems) in terms of self-direction, depth, and length of time.

Here's a little visual of how I imagine traditional problems compare to tasks to projects:

I am much more comfortable operating in the "task" or problem space: there are a limited number of routes and answers and they can more obviously be connected to specific content that I would like students to learn. We can have productive discussions and students can learn from other approaches and how they relate to their own. 

Projects are a more challenging space for me to navigate. I feel like I won't predict all the different possible things that students might choose to investigate, and I'm not always sure what they're going to learn or how it's going to connect to the content of the course or to what other students are doing. There is also greater potential that some students will go off in totally unproductive directions or into a space neither of us understands, and I will not know how to help them make sense of what they uncover.

Students are preparing to launch M&Ms using a launcher they designed after creating a mathematical model for the launch in a unit on quadratic functions. This project was actually pretty structured, so probably not technically a project.

I am also generally unclear how tightly projects should connect to course content. I often use tasks as a way for students to explore and learn specific mathematics, but because projects are more individualized and go farther and deeper, students engaging in them will tend to learn different things and often not ones within the narrowly defined boundary of the course. I have seen teachers basically separate the course into two clear portions: content and projects, which are done separately and often have little to do with each other. Personally, I am not a fan of this because it tends to push content instruction to more traditional methods as a time saver and students see two conflicting ways of doing math. But trying to make projects an integrated part of the curriculum means that I can't always use ones that are really open and need to have a sense of each student's direction and how it connects to the course.

This is a pattern created by a student for a project in the series and sequences unit. Some students got a ton out of this project, others created simple linear patterns and went on with their day. How do I make sure that everyone is appropriately challenged with open projects?

The other aspect of projects that has been hard for me to manage is time. My students can't just be assigned a project and complete it individually (I guess if that were the case, the project is probably not sufficiently challenging). They need time to figure out how to explore, to get feedback on their ideas and attempts to communicate those ideas, and to get unstuck and make sense of what they find. It is really hard to find projects that will appropriately challenge all of my students and then make enough time and provide the right amount of support to have them be valuable, positive experiences that promote learning and self-confidence. Additionally, they take much more time to grade and provide useful feedback on because students have gone off in totally different directions and learned varying amounts and types of math. How can I use a common rubric? How can I assess a student's work that seems so much less productive than another student's, but perhaps, the first student actually worked harder and learned more? 

Solar cooker project completed by students in @michaelpeller's class. Hopefully next year, this will be a collaborative project between Math and Engineering.

Clearly, I think they are worthwhile to do, but there are many things that can go wrong and I need to really think harder about the purpose of projects and the optimal frequency for doing them in my classes. Ideally, the math teachers in my school would discuss this as a department and come to a consensus on these questions and create a project thread that went through all of our courses and spiraled and built on work from prior years. In an ideal world, projects would also cross disciplines and leverage students' strengths and interests.

I have so many questions about how to do this... what are good starting projects? How can I get better at supporting and providing feedback on projects? How do I help students learn to better manage their time and work more independently/cooperatively on projects? If you have had some success with projects, please share any resources, both print and digital, that you have found helpful. If this is something that you'd like to work on next year, let me know and we can trial and error together!


  1. For me, "project" is a pretty broad term, but I generally take it to mean that students are 1)doing something that asks them to use and apply their skills, and then 2)presenting their work in some way. Both of these ask students to take their learning to the next level - to practice skills, synthesize learning, and then to articulate their thinking in some way.

    Like you, I struggle with providing enough project structure to keep all students challenged and productive, while leaving enough room to allow for students' interests and some choice. But I feel like the best learning that I've seen from my students has come from project work. When they have a driving question, and they know that they are presenting their work to an audience, they have been consistently more invested. Handing a problem set to the teacher just doesn't hold the same weight. Even asking students to make a poster forces some analysis and synthesis.

    If you haven't seen it, Kyle Moyer and Zack Miller gave a nice Global Math Department presentation last year ( about the kinds of projects they design. I used "Booming Populations" with Algebra 1 students last year with great success.

    Thanks for sharing this challenge. Looking forward to reflecting more together as this evolves for you next year.

    1. Hey Nat! Sorry for the long delay in replying - somehow missed this earlier. I totally agree that projects have the potential to drive learning to much deeper levels than other types of activities. Something that I thought about recently is that even for students who maybe struggled with a project and didn't accomplish as much as I hoped, it was actually still a valuable learning experience and they are better prepared to get more out of the next project that they tackle. The only way for students to get better at doing projects is to do projects and the only way for me to get better at supporting their work on projects is to keep including them in my curriculum and reflecting on that process.

      This post was actually inspired by working with Zack Miller this summer and seeing the structures that he put in place to help students do the "Booming Populations" project. That's a great example of a project in which learning goals are clearly defined, but students still have some personal choice. It's been much harder for me to find projects that do that for other topics. Maybe it's time to start a database of projects, kind of like the one we have for 3 act tasks at