Understanding Teaching Philosophy & Instruction

This section of my website shares what research says about teaching math and my personal philosophy as a future educator. Mathematics Instruction highlights current teaching practices, equity, and mindset, while My Mathematics Teaching Philosophy explains my vision for supporting students and helping them build confidence in math. These sections will grow as I continue learning in my coursework.

Mathematic Instruction

In recent years, the way math is taught has shifted, especially in elementary classrooms. Instead of focusing only on memorizing steps or facts, teachers are now encouraged to help students really understand the “why” behind math. This means using things like visual models, hands-on tools, and real-life examples so students can see how math works and how it connects to the world around them. For younger learners, this kind of approach builds a stronger foundation and makes math feel less intimidating and more meaningful.

Another important part of math instruction is equity.  Research shows that when teachers provide support, encouragement, and multiple ways for students to solve problems, it helps level the playing field. Every student deserves the chance to feel like a capable mathematician, no matter their background or experiences.

Research also highlights the importance of developing a mathematical mindset. When students believe they can get better at math through effort and practice, they are more likely to keep trying, even when it’s tough. Teachers play a big role in shaping this by praising effort, encouraging “productive struggle,” and making it clear that mistakes are a natural part of learning. For elementary students, this mindset can make all the difference between seeing math as stressful and seeing it as a challenge they can overcome.

Overall, today’s math instruction is about helping kids feel confident, curious, and capable. By focusing on understanding, equity, and mindset, teachers can set students up for success, not just in math, but in learning as a whole.

Madison's Teaching Philosophy 

As a future educator, I want to build my math classroom on a foundation of love, patience, and encouragement. I know what it feels like to doubt your abilities in math, and I never want a child to feel “not smart” because of a struggle. Even now, I sometimes face that feeling myself, so I want to be the kind of teacher who reminds students that their worth and intelligence are not defined by how quickly they solve a problem.

I believe that math should challenge students through productive struggle, where they work hard, stretch their thinking, and learn to persevere, but without the anger or sadness that can come when the struggle feels overwhelming. My role as a teacher will be to create a safe, supportive environment where mistakes are seen as opportunities to grow and where every student feels confident enough to take risks.

In practice, this means using a variety of strategies to reach all learners. I want to make math interactive, visual, and connected to the real world so students can see its value beyond the classroom. I also want to emphasize collaboration and discussion, so students learn from one another’s thinking and feel part of a learning community.

Equity is central to my philosophy. Every student deserves to feel capable and supported, no matter their background or starting point. I will celebrate small successes and provide different pathways for students to show what they know.

My ultimate goal is to help students develop a positive mathematical mindset, believing they can grow, improve, and succeed.

Above all, I want to be the teacher who helps students love learning, trust themselves, and see math not as something scary, but as a tool for problem-solving, discovery, and confidence!


References:

“Mathematics Teacher Educators’ Conceptualizations of Equity.” AMTE, amte.net/connections/2020/11/mathematics-teacher-educators%E2%80%99-conceptualizations-equity. Accessed 5 Sept. 2025. 

“Positive Conditions for Mathematics Learning: An Overview of the Research.” Learning Policy Institute, 7 July 2025, learningpolicyinstitute.org/product/positive-conditions-math-learning-brief.