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Content Knowledge
When developing a lesson, the first step is to thoroughly understand the standards and the mathematical concepts students are expected to learn. A meaningful lesson plan begins with unpacking the standards to identify skills, core ideas, and supporting concepts. In the concept map shown on the right, I demonstrated this process by breaking down the standard into smaller subconcepts and showing how they connect to one another. This helped me understand not only what students need to learn, but why these ideas are important and how they build toward deeper mathematical understanding and possible misconceptions.
This also demonstrates my own content knowledge in the subject matter I will be teaching. Throughout my education coursework, I have completed assignments that required me to analyze standards, connect them to instructional decisions, and justify instructional choices using learning theories studied in Knowledge and Learning (K&L). For example, creating the concept map reflects principles from constructivist learning theory, which emphasizes that students build knowledge by connecting new ideas to prior understanding. Graphic organizers such as Knowledge Packages and concept maps helped me organize the structure of the content, plan coherent lessons, and ensure that instructional activities aligned with learning goals.
By engaging in this type of analysis, I showed that I can not only understand the mathematics behind the lessons I teach, but also plan instruction that supports student learning in a thoughtful, structured, and research-based way.
Historical Importance
Before coming to college, I honestly had very limited knowledge about the history of mathematics beyond the quick-recall facts. Taking Perspectives of Mathematics and Science completely changed that for me. I learned about the founders of algebra, geometry, and other major ideas, and I began to understand how these mathematicians shaped their societies and pushed human understanding forward. Seeing how math developed over time helped me realize that it isn’t just a set of rules, it’s a story of people trying to make sense of their world.
This is something I plan to bring into my own classroom. I want my students to see that mathematics has a historical foundation and that the concepts they learn today grew out of real problems, cultures, and innovations. Showing students the historical importance of our content helps them understand the why behind what they are learning. It also helps them see how mathematics connects to the big ideas of the discipline: problem solving, modeling, reasoning, and using patterns to understand the world.
Modeling
Mathematical and scientific modeling plays a key role in helping learners make sense of real-world systems by creating simplified representations that can be analyzed, tested, and revised. Through modeling, students learn to uncover relationships, make predictions, and evaluate how accurately a model reflects reality. Whether analyzing a natural phenomenon or an engineered process, modeling encourages inquiry-based thinking and helps students move beyond calculations toward understanding how and why a system behaves as it does.
My preparation for modeling was strengthened through coursework such as Functions and Modeling, where I practiced posing real problems, determining relevant variables, making assumptions, and analyzing data to draw meaningful conclusions. These experiences helped me learn not only how to build a model, but also how to justify design choices, evaluate limitations, and interpret the model in context, skills that are directly transferable to classroom instruction and student project design.
To demonstrate these skills, I developed a mathematical model estimating the environmental impact of paper usage within the MSUTeach program. Using real usage data and published forestry yield estimates, I calculated how many trees are consumed annually by departmental printing and compared this amount to the estimated tree population in the Daniel Boone National Forest. This model allowed me to evaluate our ecological footprint, assess the model’s assumptions and accuracy, and make data-driven recommendations for sustainable practice. The full project can be found below.
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Formal/Informal Reasoning
As a Mathematics Education major, I have taken several courses that require me to formally communicate mathematical reasoning through proofs. These assignments have helped me justify solutions and clearly explain the logic behind mathematical arguments. I am currently enrolled in the College Geometry sequence (MATH 370 and MATH 371), where I am developing a deeper understanding of geometric foundations and learning how to construct and extend geometric theorems.
One proof I completed that is highly relevant to high school mathematics is a proof of the Pythagorean Theorem using similar triangles. This approach provides conceptual justification that is accessible to students while demonstrating formal mathematical reasoning. For this proof, I used a direct proof, which is the most appropriate method because the conclusion follows logically from known triangle similarity relationships without the need for contradiction or indirect argument.
Topic Connections
Mathematics is a discipline that naturally connects across subjects, and my MSUTeach experiences have shown me just how broad and meaningful those connections can be. Math serves as a backbone for many areas whether we are quantifying historical trends, modeling scientific processes, or using mathematical language to understand the laws of physics. Throughout my coursework and teaching experiences, I’ve seen how prerequisite skills are built into these applications.
One of the clearest examples came from my Project-Based Instruction class, where I taught an architectural design lesson. At first, many students questioned how this could possibly be math. But as they explored scale, triangle properties, perimeter, congruences, and structural constraints, the mathematical thinking became obvious. Experiences like this help students see mathematics not as isolated procedures but as a tool for solving real problems in meaningful ways.
Moving forward, I plan to continue designing opportunities where math is integrated into authentic contexts, especially those that students might not initially associate with the subject. Whether through connections to art, science, technology, or everyday decision-making, I want my students to recognize that mathematics is not just something done on paper, it is a way of understanding and interacting with the world.