Teaching Together: Participation and Diversity in Mathematics Education

Introduction: Defining Resilience through Diversity in Life and Teaching

Growing up as the grandson of immigrants on one side and a rural farming family on the other, I learned that individuals are inherently shaped by their communities. On the Slovenian side, my family in Haughville, Indianapolis, shared everything—from traditional foods like potica to the values of cultural pride and communal responsibility. On the farming side, I witnessed the power of shared labor in Harrison, a small town on the Indiana-Ohio border. Here, humility and resourcefulness were essential; success depended on teamwork and practical knowledge.

These dual experiences taught me two crucial lessons: that education and skill are both valuable and even more powerful when combined. A brilliant academic may struggle with hands-on tasks, while practical skills can inform and enrich academic work. Together, these complementary forms of knowledge build individual and collective resilience.

In mathematics, this principle is echoed in the balance between internal diversity and redundancy. Internal diversity equips us with various tools and perspectives to tackle problems, while redundancy ensures the system continues even if one part fails. Applied to teaching, this “diversity principle” underscores the importance of varied skills and perspectives to handle classroom challenges. Teaching, as in life, is not about avoiding adversity—it’s about building the collective resilience to thrive despite it.

The Collective Power of Diverse Skills

"We all should know that diversity makes for a rich tapestry, and we must understand that all the threads of the tapestry are equal in value no matter their color." ~ Maya Angelou

There is immense strength in combining different perspectives and talents. On the farm, the success of a harvest relied on collective effort and trust. Whether we were planting or bringing in the crop or getting hogs to market, everyone’s role was essential. I’ve never been more aware of this trust than when a 650-pound sow fell into the manure pit, and my uncle, by marriage, handed me a rope as he was going in to get her out and said, “Start pulling if you feel me stop moving.”? This same principle applies to teaching: the most effective educational environments are built on collaboration and shared expertise.

Every educator brings a unique set of skills to the table in teaching—some are experts in classroom management, others excel at curriculum design, and still others can connect with students in ways that make learning come alive. Together, these strengths make up the “diversity principle” in education, specifically mathematics-for-teaching. Just as diverse skill sets help a farm thrive, a collective approach to teaching mathematics also ensures that all students benefit from a rich, multidimensional learning experience. We can and will all need to contribute.?

It’s important to remember that the craft of teaching is never static; it evolves over time as educators gain new insights and experiences. As a teacher matures in their practice, their role on a teaching team will shift, but their contributions remain critical. This collective work—co-creating lessons, sharing classroom strategies, and reflecting on teaching practices—allows us to continuously grow and improve as educators. It allows the dynamic nature of teaching to be approached pragmatically and with empathy. All teachers will tell stories about mathematics, but they will change over time as their expertise evolves.

The Solidarity of a Teaching Collective

“Collective action remains the best way of renewing the march towards the great trinity of liberty, equality, and solidarity.” ~Guy Standing

Solidarity in teaching means working together toward shared goals, fostering collaboration and mutual support. This collective responsibility is crucial, particularly in environments where resources are limited and the challenges of teaching can feel overwhelming. In the modern classroom, the complexities of education—from navigating student needs to dealing with limited resources—are challenges that should not be faced alone.?

Unfortunately, the number of educators entering the field is dwindling, weakening the values of cultural pride and communal responsibility overall. Research, such as that by Beltman and colleagues (2011), shows that collaboration and strong interpersonal relationships are key protective factors for teachers, helping them endure and thrive in the face of challenges. The solution to this issue isn’t just recruiting more people to the profession—it’s about creating clear pathways for those already in our communities and schools to become part of the teaching collective.

My academic journey laid the foundation for this understanding. Initially, my research focused on improving success rates in post-secondary mathematics courses with notoriously high dropout rates. However, I realized that creating solidarity among professors was challenging. It wasn’t until I turned to students that I saw the power of collective action. By building peer learning centers, I created spaces of trust, support, and collaboration where students helped each other succeed. There was a shared cultural identity and a location that united the diverse people that shared it. This solidarity translated into real results, with student engagement skyrocketing.

So, what does solidarity look like at your school or in your local context? In our schools, teachers need the opportunity to study mathematics together. This breaks down barriers between “content experts” and those with other valuable teaching skills, fostering a true sense of solidarity. By working together—co-creating lessons and supporting each other in the classroom—teachers build the resilience needed to face the inevitable challenges of teaching. When creating the right teaching team, looking for all the same types of mathematics teachers would be like recruiting a basketball team stacked with stellar point guards and nothing else. The right team—one that values diverse perspectives and skills—ensures the team's solidarity to respond with strength when adversity strikes over time.

Reaping the Harvest: Mathematics Is Grown from What We Sow

The phrase "reaping the harvest" is an idiom that means to experience the results of one's actions or the actions of others, either positively or negatively. The idea of “reaping the harvest” mirrors the outcomes of teaching: success comes from collective effort, careful planning, and shared responsibility. In farming, I learned this lesson well when trying to grow blueberries. You will not get blueberries if you do not get the right soil mix of nutrients and acidity. You get a lovely plant but zero fruit. But how can this be practically accomplished in teaching??

In mathematics, participation means more than just being present in the classroom—it requires actively engaging with fellow educators, parents, and students to create a dynamic learning environment. Teachers are not mere transmitters of pre-existing knowledge; they are vital participants in the creation of mathematics as a living, evolving discipline. As Davis and Renert (2013) argue, teachers co-create mathematics through their choices: which concepts they emphasize, how they frame them, and how they engage their students in the learning process.

Participation also extends to parents, who help shape their children’s mathematical understanding through their attitudes and conversations about the subject. The stories we tell about mathematics—whether of fear or fascination—become the seeds from which students’ understanding grows. The harvest reaping is based on the choices made by teachers and parents regarding the stories we tell about mathematics. These choices directly impact the soil fertility into which we are planting mathematics and the resultant harvest to come.

"Mathematics is the music of reason." ~James Joseph Sylvester

If your past participation in mathematics was complicated, then equating mathematics to art or music might rightfully sound bizarre. So let me tell you a story.

My first experience of mathematics as the same as music was discovering what my Grandpa called a 3/4/5 rope, which was frequently used around the farm. What is a 3/4/5 rope, you ask? It is a rope with lengths measured precisely at three feet, four feet, and five feet. Good name! Why these lengths, you ask? It's the way, in the field, to ensure that you can lay a perfect 90-degree angle for a fence row. When fence rows run for long distances, being off just a bit can cause real problems. How did it work, exactly? When I asked that question in the field, I got a look that I would characterize as questioning if I had left my brain in the barn. However, this is where the music comes in. Music has a pattern; it touches our souls and is memorable. It fulfills your desire, a job to be done at that time. Sad? Then, you love the tragic song because it is helpful for you to better understand your emotions. The chorus is a section of a song repeated at least twice and contains the song's central message and tone. The chorus of the 3/4/5 rope is that it always works. It's repeatable, dependable, and memorable. How?

The lengths of 3/4/5 make a perfect Pythagorean triple, which means that the lengths of a triangle of any measurement with those lengths of sides (in that measurement) will make a perfect right triangle. This means the angle opposite the side of length five will be the right angle. Always. The tool is built from what has been called the Pythagorean Theorem. Pythagoras, the Greek philosopher namesake, was credited with it because he was the first to prove it always worked. However, dependability came about in human consciousness significantly earlier through the Babylonians, Chinese, and Egyptians, dating back to before 1800 BCE. They were writing it on clay tablets, so it was memorable. The music of mathematics exemplifies the diversity principle of teaching. As a tool, it has a balance between diversity and redundancy. It is the human ability to make a highly creative problem-solving technique repeatable, dependable, and memorable. Participating in mathematics means both doing and knowing these things. To teach is to be able to tell that story.

Connecting the GROWTH Framework: Teach with Peers (T)

“Tell me and I forget, teach me and I may remember, involve me and I learn.” — Benjamin Franklin

The “T” in the GROWTH framework, Teach with Peers, emphasizes the importance of collaboration in developing mathematics-for-teaching. At MathTrack Institute, we believe meaningful collaboration is the foundation of teacher resilience and the key to creating dynamic, effective learning environments. We embed this ethos into our professional development, licensure, and apprenticeship-to-degree programs. Our models are job-embedded, meaning we do not want to separate academic and applied teaching skills. Participation requires both and is built together through a productive framework to guide collaborations.?

Participation in mathematics education is not just about following a curriculum—it’s about actively engaging with colleagues to co-create lessons, share strategies, and reflect on teaching practices. In GROWTH, this might look like discussing the best manipulatives or activities for teaching a complex concept or exploring multiple representations of a mathematical task. For example, this activity from research (Izsak, 2008; Izsak et al., 2012) can engage diverse educators on fraction multiplication. Which of these images shows:

The answer is that all of them do, but they show it differently. A discussion on this topic exposes educators to different layers of understanding of how teachers would teach fractions, operations on fractions, and the meaning of the multiplication operation. Diverse perspectives are invaluable when working with diverse levels of learners.?

Collaboration helps teachers develop the mental and emotional stamina needed to persist through adversity. This fosters a sense of community—an essential factor in preventing burnout and isolation, common threats to resilience. For example, I’ve seen firsthand the power of collective resilience in farming when a neighbor farmer had a life-threatening health scare. All the farmers around him (including me) rallied and helped harvest his fields before the first snow. Similarly, working together, educators are more likely to find solutions to their challenges, preventing burnout and isolation. This collective effort strengthens the teaching profession as a whole, ensuring that we continue to grow and evolve as educators.?

Conclusion: The Power of Teaching Together

Much like farming or the immigrant values of cultural pride and communal responsibility, teachers thrive on collaboration, resilience, and shared effort. Teaching is very hard. The GROWTH framework’s Teach with Peers (T) highlights how participation and the diversity principle are key to building resilience in the face of challenges. By engaging with fellow educators, embracing diverse skills, and sharing the responsibilities of teaching, we not only enhance our individual practices but build the collective strength necessary to navigate the complexities of education. Teachers, in a way, do need to survive teaching. It is fundamental to understand that the mathematics that we all work together to expose children to is the only mathematics that will often exist for them long into adulthood. Together, we can create the kind of learning environment where both teachers and students thrive, cultivating a future where mathematics is accessible, meaningful, and enriching for all. Music to my ears.?