Innovative Approaches: Bringing Math to Life Through Project-Based Learning
If you’re a K–12 educator, you’re likely familiar with the ways in which project-based learning (PBL) can enhance content that is uninteresting or challenging for students by sharing it in a more engaging way. Unlike the traditional “stand and deliver” lesson format — in which the teacher lectures and students listen — PBL is designed to connect students to concepts and skills through authentic, hands-on experiences. By bringing PBL into math, students are able to go beyond textbooks and formulas and solidify their understanding of mathematical principles and concepts with real-life applications of skills.
In this blog post, we’ll explore the essence of project-based learning in math and provide practical tips for creating impactful PBL math projects.
What Is Project-Based Learning?
Project-based learning, as defined by President of PBL Global Thom Markham, Ph.D., is a method that seamlessly integrates 21st century skills — such as communication and teamwork — into core academic subjects. This approach provides a tangible connection between academic concepts and their practical applications.
Project-based learning activities start with a question, encourage thoughtful inquiry and self-reflection, and allow students to collaborate to problem solve. Another way to describe this approach is “learning by doing.” The one commonality between all PBL engagements is that they have a clear connection to real-world scenarios or challenges.
“I used to struggle to get students engaged in analyzing the ‘standard’ spreadsheets I provided in my math lessons. Now, with the SmartLab, students design an experiment, collect unique data in Excel, analyze the data in class, and publish the results. Students are so much more motivated to analyze data grounded in their unique experiments. I have also noticed that their thinking is deeper, their questions are better, and the collaboration causes a depth of rigor not seen in my class previously.”
Why Use Project-Based Learning in Math?
In the context of mathematics, PBL involves students working in teams or small groups to design and execute projects with real-life applications that illustrate mathematical principles.
PBL doesn’t just help students who feel challenged by math — even some of the strongest math students struggle with the practical application of math skills. Project-based math engagements can bring critical relevance to math concepts, challenging students to solve real problems authentically while preparing them to navigate standardized tests and problem solve in the real world. No matter their academic strengths or interests, learning to creatively solve problems is critical for students’ success in their future personal and professional lives.
Using PBL in K–12 mathematics instruction enables learners to:
- Make abstract concepts concrete
- Experience productive struggle and practice perseverance
- Use reasoning to solve problems
- Practice creativity, self-expression, and innovation
- Develop a deeper understanding of math principles in real-world applications
- Construct viable arguments and give/receive meaningful feedback
- Model their learning visually through presentations, graphs, diagrams, etc.
- Identify and use appropriate tools and technologies to solve problems
- Build critical thinking and problem-solving abilities
- Collaborate with their peers and practice communicating their ideas
- Iterate and redesign solutions to work toward efficiency
When students have the opportunity to use academic concepts to solve practical, real-world problems, they can feel as though what they are learning matters — which has a direct impact on their motivation, engagement, and learning retention. This can be especially helpful for students who dislike the subject or feel as though math just isn’t for them.
Using math in PBL also provides opportunities for differentiated learning by providing students with different access points, inspiring different ways to engage with course content, and allowing them the flexibility to choose the tools and resources that will best help them solve problems (all of which are applicable to life beyond school). Overall, this approach allows for more equitable access to learning.
“We incorporate science, history, math, reading, and writing in the SmartLab HQ. The activities can be open ended allowing the students to come up with their own outcome, or they can be solved multiple ways allowing the students to learn from their classmates.”
Tips for Creating PBL Math Projects
Academic standards provide an ideal jumping-off point for any type of academic engagement. Coupled with clear learning objectives, teachers can develop and implement project-based lessons that guide students in achieving a specific goal while still leaving room for creativity and unique engagements with the course material.
When creating PBL activities for math units, keep the following tips in mind:
- Name the problem: Ask students to explain, in their own words, the particular challenge they’re trying to solve through their work. This ensures that everyone is on the same page and answers the eternal question: “Why do we have to know this?”
- Clarify the standard or learning objective: As the teacher or facilitator, you need to be sure the problem students identify is relevant to their learning goals as much as it is relevant to them personally. Effective lesson design always begins with a specific end in mind, even when the students are in the driver’s seat.
- Authenticity is paramount: Projects should be connected to students’ interests, current events, or their daily lives. Doing so will hold their attention and invite meaningful engagement with the course content.
- Chunk it up: Break units into manageable chunks to ensure your students can pace themselves, make mistakes, ask questions, and ultimately have a productive learning journey.
- Think ahead: Even the youngest students benefit from lessons that connect to real careers or future pursuits. Connecting abstract concepts to concrete outcomes also opens up cross-curricular opportunities, such as exploring how a marine biologist uses data collection and statistical analysis when studying invertebrate populations, or how race car drivers use speed and acceleration or gear ratios to improve their performance.
- Different is good: Design or select challenges for which there is no “right answer,” such as devising a budget for a lemonade stand. Math has the reputation of being restrictive, but when given the opportunity to use different approaches or produce different solutions, students can better understand math’s versatility.
- Pause and reflect: Make time for students to pause, review their steps, talk through challenges, iterate, revise, and reflect on what they’ve learned. This helps with learning retention and recall for future lessons.
- Share the results: Sharing their learning and giving and receiving feedback benefits both the students presenting and their peers. Seeing how others approached the problem and what conclusions they made is an invaluable learning experience that demonstrates the cognitive diversity present in every classroom.
“All the coding activities we did in the SmartLab HQ helped me in my math class. I like that there are different levels to choose from—I worked my way up to the intermediate level!”
Challenges of PBL in Math
As with any subject, teaching math through PBL presents unique challenges — but small adjustments can make a big impact on the overall student experience. Consider these three common challenges and their possible solutions.
- Demands of standardized tests often force teachers to cover content quickly in a traditional, lecture-based instruction model, limiting the opportunity for customization.
Solution: Instead of “teaching to the test,” identify the ultimate learning objective and have students come up with their own problems to solve to get there.
Alternatively, you can present students with a problem to solve using fundamental concepts, but allow them to choose the method of engagement — hands-on, with a partner, connecting it to a personal interest, exploring a new application, or a holistic combination.
- Math textbooks and lessons often follow a linear path of instruction without room for interpretation.
Solution: Build in time for unstructured exploration upfront, during which students can test out procedures or tools, discover and make connections, identify questions, and otherwise play with the concepts being presented. Allow students space throughout the learning process to pause, explore, make observations, ask questions, and reflect, both independently and collaboratively. - Even some of the strongest math students struggle with the practical application of math skills.
Solution: Instead of ending with the solving of an equation, challenge students to solve a real-world problem using their math skills. Make it fun and interesting by connecting the problem to a real application or their personal interests. (This also works with students who are typically disengaged from math.) Ask students to articulate the problem in their own words and identify the tools they’ll need to solve it, then challenge them to find efficiencies to improve the process. Bring it close to home by posing a problem that affects them directly — ask them, “How will finding a solution improve your life or the lives of others?”
Examples of Project-Based Learning Math Projects
In a SmartLab, math is integrated with other core subjects in project-based activities called “project starters” to help students contextualize their learning. This integration aims to make concepts more approachable and fun and help students see the practical application and relevance of mathematical concepts in broader and more meaningful contexts.
Project starters also serve as a jumping off point where students can apply learned skills and knowledge in other applications/contexts. This jumpstarts their curiosity and opens opportunities for future skills application, which can foster career ideas or connections.
Take a look at these project starter examples with a math integration (you will need a SmartLab LearningHub account to view these):
- Pixie: Exploring Patterns (Elementary School): Students create original art through patterns and explore mathematical concepts such as symmetry, rotation, and reflection.
- Bridge Designer: Bridge on a Budget (Middle School): Students use the engineering design process to design and build a bridge, then apply mathematical concepts to determine cost and budget changes.
- Alternative Energy: Home Efficiency Exploration (High School): Students collect data on their own home energy usage, then analyze their data and propose changes to increase their energy efficiency.
“The student experience in our SmartLab has positively transformed our school’s learning culture. Students become empowered and engaged as they apply content standards through the skills of critical thinking, curiosity, and collaboration.”
All of these projects integrate mathematical concepts in an authentic way that connects to students’ interests or lived experiences. In a SmartLab, math isn’t just fun — it’s meaningful!
Explore our STEAM + PBL programs for K–12 learners here.
Case Study
Improving Math Scores at a Denver Elementary
Find out how a SmartLab HQ helped grow standardized test scores.
