(This is the final post in a two-part series. You can see Part One here.)
The new question-of-the-week is:
How can project-based learning be used in math class?
In Part One, Bobson Wong and Larisa Bukalov shared their responses.
Today, Suzie Boss, Chris Fancher, and Telannia Norfar contribute their ideas.
Suzie Boss is a PBL advocate and author who has collaborated with teachers around the world to design engaging projects:
When I facilitate workshops with teachers about project-based learning, one question inevitably surfaces: “What about math?”
In their recent post, “Using Project-Based Learning in Math Classes,” Bobson Wong and Larisa Bukalov acknowledge some of the same reluctance that I often hear from math teachers, such as the pressure to teach (and practice) procedural skills, concern about the time that projects require, and why PBL is a better fit for subjects like social studies or science.
These are legitimate concerns, but they shouldn’t make the math classroom a PBL-free zone. Students deserve to experience mathematics as a way to engage with their world. They need opportunities to apply their understanding of math concepts to problems that matter to them and to their communities. That’s what PBL offers.
Where can math teachers find opportunities for engaging projects? Here are just a few ideas to jump-start your thinking.
What’s nearby? Your own campus can provide the context for authentic projects. Help students identify problems that math can help solve, such as reducing food waste, increasing energy efficiency, redesigning playgrounds, or improving pedestrian safety. Addressing any of these challenges would require problem solving, reasoning, communication—all important process standards for mathematicians to master.
What’s newsworthy? The news is filled with statistics, mathematical predictions, and graphs and infographics. Leverage current events to find out which topics interest your students and then help them find the math in the issues they care about. For example: How could they use data in a public-health campaign to increase COVID-19 vaccination rates among specific populations in their community? As financial advisers, how could they help small business owners struggling to reopen after pandemic shutdowns? As engaged citizens, how would they advise government officials (in areas such as public transportation, housing, libraries, or other services) to use their budgets to improve the lives of young people? As media critics, how can they draw attention to issues that are underreported?
For any of these questions, think about the audience most likely to be interested in students’ arguments and solutions and help your students use the power of math to make compelling presentations.
Who wants to collaborate? Find out which of your colleagues (outside the math department) are planning upcoming projects. Brainstorm opportunities to integrate math learning goals. Your students might serve as consultants for students in another content area by designing a survey, analyzing data, making predictions, or doing math modeling of proposed solutions.
Finally, don’t overlook the importance of reflection in project-based learning. Encourage your students to think about how math projects challenge them to persevere, think creatively, and build on their peers’ ideas to reach better solutions. In a blog post, Francis Su offers more suggestions for helping your students see themselves as mathematical explorers “who have the habits of mind and confidence to solve problems they’ve never seen before.”
Chris Fancher is a retired math and engineering teacher. Telannia Norfar is a high school math teacher. Both work with teachers to perfect the PBL process. They co-authored Project-Based Learning in the Math Classroom and can be found at MathPBL.com:
We have each been training teachers in the project-based-learning process for about 10 years. We honed our own skills in the classroom teaching math in the public school setting. Math teachers love to tell us what is going well and what they struggle with in attempting to use PBL in their classrooms.
When planning a PBL unit, we ask teachers to use PBL Works’ Gold Standard PBL Elements. Yet it is through that lens that math teachers often struggle to find a way for them to “do PBL.” What we say to them is to rethink each of the elements. The elements are just things that great teachers do. Let’s explore the elements from a PBL teacher’s perspective.
Challenging Problem or Question and Sustained Inquiry - In math, it is easy to challenge our students with a tough problem. But can we challenge them to explore something that can be sustained over a long period of time? We encourage teachers to keep their projects in the 10- to 15-class-hour range when they are starting. But when teachers are told that they have to spend a couple of weeks with just two or three standards, they rightfully push back and say they can’t afford that much time away from their curriculum-pacing guide.
PBL teachers don’t go outside of their pacing to do a project, they teach their content inside of the project. So we tell teachers to look at a time in their school year when they can devote the time needed for a project. We recommend once in the fall and once in the spring to plan for a full PBL unit. Teachers can then plan their calendar around these two spots in their pacing guide.
We think teachers should be striving to keep the day-to-day environment filled with opportunities for students to wonder and ask questions. Peter Liljedahl’s book Building Thinking Classrooms in Mathematics, for example, gives teachers the tools to create that environment. When students know they will be expected to critically think and work collaboratively, every day, then it is easy to extend that to the day-to-day work flow of a project.
Critique and Revision and Reflection - When a teacher offers multiple opportunities for students to be assessed, then revision and reflection should naturally follow. The switch we ask teachers to make is to rethink who is doing the assessing. It should be a mixture of teacher, peers, and content experts. If student work is going to be assessed, then they should be given an opportunity to make revisions and reflect on the process. Inside a project, the work-revise-reflect cycle continues.
Student Voice and Choice - It is hard for us to imagine not giving students options within the normal class period. Teacher-preparation programs often do a disservice to future math teachers when they show the “I Do, We Do, You Do” process. Too often, the “You Do” part means do it exactly the way the teacher did it. When a teacher is comfortable with their content, then they can allow students to try different ways of coming to an answer. This allows for students to critically think, be creative, and make mistakes. The beauty of a project is that students can explore ways to create their final product. They might choose to create a video, write a story or poem, or build a 3D object that helps explain their interaction with mathematics.
Authenticity and Public Product - The two elements that are the most impactful with getting students to go deeper with their learning are authenticity and public product. While it is easy to find a way to get authentic mathematics with data and geometry, teachers struggle to create extended explorations in other mathematical areas. Quite often, there needs to be a second, or even third, content area that helps focus the authenticity. Experienced PBL math teachers look to their peers to find a common area where the math overlaps with another content area.
When students know that they will be solving an authentic problem and that they will be presenting their work to the public, they raise their game to meet the challenge. And, whenever we can give students the opportunity to present to experts and get honest feedback, then students are the beneficiaries of truly authentic learning.
Example Project - HS Geometry: Create a tire display for a local tire store. The display must be a triangular prism that can hold four tires. The entire display must fit inside a 10' X 10' area. A model that will fit on an 8.5" X 11" in paper will be made and will be used for a presentation to the manager of the tire store. Students learned about inscribed circles in a triangle and created equations to explain the scale used for their model.
Conclusion - When teachers are tied to a curriculum-pacing guide, it is hard to do a project containing all of the Gold Standard PBL Elements. These elements are key components to successful PBL but are also key components of great teaching. Teachers should strive to use them in their normal teaching practice and find the time to create a rich learning experience for their students a few times each year.
Thanks to Suzie, Chris, and Telannia for their contributions!
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