EFFL in Action: How Math Medic Lessons Sparked Curiosity and Confidence in College Algebra

Jennifer Caldwell is a mathematics professor at Mesa Community College who believes that true learning happens when students feel both challenged and supported. Her classroom is a community built on curiosity, confidence, and connection—where mistakes are part of the process and laughter is part of the lesson. Outside the classroom, Jennifer loves cheering on her daughter at volleyball tournaments, hiking through Arizona’s desert trails, rollerblading for fun and fitness, and experimenting with new recipes in the kitchen.  She lives in Chandler, Arizona with her husband and daughter.

---

When I first stumbled across Math Medic, I wasn’t searching for activities to use in my community college classroom—I was at the kitchen table with my daughter, who was working on her AP Precalculus homework. Her high school teacher is fully invested in the Math Medic program, and as I listened to her slightly frustrated musings, I was struck by the thoughtful, conceptually rich questions she was grappling with. These weren’t your typical “plug and chug” problems. These questions asked her to think, to reason, to make connections. Then I noticed the “Math Medic” icon at the bottom of the page. I did a quick Google search… and it was love at first sight.

As a community college math professor, I wasn’t sure how a curriculum designed for high school would translate to my college algebra students, who bring a wide range of experiences, goals, and (sometimes) a bit of math anxiety to the room. But the core philosophy of “Experience First, Formalize Later” (EFFL) resonated with me instantly.

The idea that students should wrestle with ideas, collaborate, and build their own understanding before being handed a formula or definition? That felt like the kind of learning that sticks. I knew I wanted to move away from front-loading notes and toward something more active, more thoughtful—more human. So I decided to experiment with Math Medic lessons in my College Algebra classroom.

Spoiler alert: I’m so glad I did.

This post is a reflection on what that experiment looked like in practice—how I modified the materials to fit a 16-week semester, what surprised me along the way, and most importantly, what my students gained from learning in this new way.

Why I Wanted to Try Something Different

Over the years, I’ve noticed a familiar pattern in many of my College Algebra students. They arrive in my classroom with a transcript full of math credits, but often without a strong sense of mathematical understanding. They can recall procedures, but they struggle to explain why those procedures work—or when to use them. Many have internalized the idea that math is about memorization, not meaning.

As much as I love teaching math, I started feeling frustrated with how much of my class time was spent talking at students, rather than working with them to build understanding. I’d explain a concept, we’d work through a few examples, and then students would try problems on their own. It was tidy and familiar—but it wasn’t generating enough moments of discovery I wanted for my students.

When I saw how Math Medic lessons invited students to dive into rich, collaborative tasks right from the start, something clicked. I realized that my students didn’t need more carefully polished lectures—they needed more space to think, talk, and make sense of math for themselves. The EFFL model gave me a structure for doing just that.

What EFFL Looks Like in My College Classroom

By the time I introduced Math Medic lessons into my College Algebra classroom, my students were no strangers to productive struggle. They were used to me answering their questions with another question and working through unfamiliar problems before I had officially “taught” anything. Whether they liked it or not (and trust me, reactions varied!), they had come to expect discovery learning as part of our classroom culture.

But the part of the EFFL model that was new—and a little uncomfortable—for me was the idea of having students present their thinking to the class and using that as the main way to debrief and summarize a lesson. It’s not that I didn’t see the value in students learning from each other. In fact, I loved the idea. But in the back of my mind, I was always calculating time: We only have 16 weeks. We only have so many minutes in each class period. Can I really risk running out of time to “cover” the important takeaways?

That’s where I had to shift my own thinking. Instead of rushing to fill in gaps or wrap things up neatly, I started trusting the process—and my students. I still provided clarification when needed, but I gave them more opportunities to share their reasoning, identify patterns, and lead the conversation. We didn’t always have time for every student to share every thought, but we did make space for students to make the learning visible—on the board, in small-group conversations, and in full-class discussions.

One of my favorite moments came during the "How Much Does It Cost to Tile a Pool?" activity. I asked a student—someone who often doubted herself and regularly discounted her own abilities—to come to the whiteboard and share her work. She had a thoughtful approach to the problem, which focused on understanding the composition of functions in a real-world context. To everyone’s surprise (hers most of all), she was a natural. The explanation wasn’t perfect, but it sparked a cascade of student “aha” moments that no polished lecture could have produced. That’s when I realized learning was happening because I stepped back, not in spite of it.

Her explanation helped clarify the concept for the whole class, and the discussion that followed was rich and engaged. From that day forward, she jumped at the chance to present her work during other activities—and even told me she wanted to start a YouTube channel to explain math concepts to others. 

Adapting the Materials for My Context

While the Math Medic lessons were designed with the high school calendar in mind, I found them to be remarkably adaptable for my college students—with just a little rethinking. The most obvious challenge, of course, is pacing. In a 16-week semester, there’s less time to linger with extended exploration, revisit, or spiral back, so I knew I’d need to be intentional about how I used class time.

At first, I considered reducing the amount of scaffolding in the handouts or condensing the worksheets to make them fit more neatly into our time constraints. But then something changed my mind. We were working through the lesson titled "What’s Your Domain Name?", and as the class wrapped up, I noticed one of my students flipping ahead to the Check Your Understanding questions on the second page. We hadn’t gotten there yet as a class—and honestly, I didn’t think we would that day—but he was eager to apply what he had just learned about domain restrictions and interval notation to more challenging functions.

That moment reframed things for me. I realized that the pacing built into the EFFL lessons wasn’t a problem to solve—it was part of the magic. These lessons gave students a reason to keep engaging beyond the proverbial bell. Momentum and curiosity spilled over into the next class period. Some students even came back the next day ready to debate the trickier questions on the back side of the page, excited to compare ideas and test their thinking.

So instead of stripping things down, I leaned into that sense of “unfinished business."

I became more flexible with lesson flow, sometimes letting a rich discussion push a lesson into the next day. I focused less on “covering” everything and more on creating space for real understanding—even if that meant we didn’t always get to the formal definitions or the practice on the second page of the worksheet

In the end, adapting the materials wasn’t about shrinking them to fit my schedule. It was about recognizing which parts sparked the most curiosity in my students—and making sure I gave those moments room to breathe.

What My Students Gained

Over the semester, it became clear that the Math Medic lessons were shaping how my students thought about learning math itself. One habit I encouraged from day one was the importance of making meaningful notes for their future forgetful selves. I urged students to write hints, reminders, or any “gems” that resonated with them—little jots in the margin of their notebooks that might help them later when they revisited the material.

After a class discussion about the importance of truly understanding math vocabulary (it’s not just about the numbers) sparked by student curiosity and questions, many students took this advice to heart. They began keeping notebooks filled with “aha” moments and connections that spanned across lessons, creating their own personal maps of understanding.

This became more than just note-taking—it was a reflection of growing ownership over their learning. Just short of tear-worthy and definitely a teachable moment, I even gave bonus points to students who were willing to share their note-taking strategies with the class. This unintended but welcome side effect of the EFFL lessons helped build a community of learners who supported one another beyond solving problems.

Beyond improved study habits, I saw students become more willing to ask questions, experiment with different approaches, and justify their thinking. They learned to embrace struggle as part of learning rather than a sign of failure. Quiet students found their voices, group discussions grew more thoughtful, and the energy in the room shifted toward curiosity and confidence.

While academic gains in fluency, problem solving, and connecting concepts were evident, it was the development of a mathematical mindset—a trust in their own thinking and a willingness to persevere—that I found most rewarding.

My students didn’t just get better at math; they became better mathematical thinkers.

Why I’ll Keep Using Math Medic

After piloting the Math Medic lessons this semester, I can say without hesitation that this approach has earned a permanent place in my body of teaching. The EFFL model—Experience First, Formalize Later—aligns beautifully with how students learn best: by wrestling with ideas, collaborating, and making sense of concepts instead of memorizing formulas.

The lessons sparked curiosity, encouraged deeper thinking, and built a classroom culture where struggle was seen as a natural and valuable part of learning. While adapting the pacing for a college semester has been a challenge, it’s also been a rewarding process that has helped me rethink how to prioritize understanding over coverage.

I have to highlight one more powerful aspect of these lessons—they help students see real-world connections within college algebra competencies. Abstract concepts become relevant, and students engage more deeply as they connect new ideas to their everyday lives. One of my favorite moments this semester came from an adult returning student—someone with the wisdom and curiosity of a grandmother and a natural “What’s in it for me?” lens. During "How Much for a Bagel and Cream Cheese?", she had an unforgettable lightbulb moment. As we worked through possible prices for bagels and cream cheese, she suddenly grasped the meaning of dependent systems—and the importance of independence when seeking a unique solution. Midway through the activity, she burst out (loud enough that I swear the whole campus heard), “I get it now! That’s why one line would lay right on top of the other!” Her breakthrough not only lit up her understanding but also deepened the learning for everyone in the room. That’s the magic of EFFL—it helps students make sense of math in ways that are contextual, visual, and truly meaningful.

Most importantly, I’ve seen firsthand how these lessons build students’ confidence and mathematical mindset—qualities that go far beyond any one course or exam. And with the collaborative support of the Math Medic team, I’m excited to keep refining how I use these materials in the community college environment, especially as I work alongside colleagues who are eager to incorporate this approach into their courses as well.

Does anyone else out there use these materials in the community college classroom? What has your experience been? How have you been able to effectively use these lessons as intended in a condensed time frame? I’d love to hear your stories and strategies.

In short, Math Medic has not only enriched my students’ learning experiences—it has enriched my teaching practice. I’m looking forward to continuing this journey and sharing more insights as we grow together.