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Lesson Design & Implementation
All of the lessons I design and teach are rooted in students doing the thinking. I intentionally build each lesson from the Kentucky Academic Standards and the Standards for Mathematical Practice so inquiry is at the center of student learning rather than an add-on. By setting up tasks where students explore patterns, test student ideas, and make sense of concepts before ever given formal explanations, students take an active role in constructing their own understanding. I also draw heavily on their interests, experiences, and cultural backgrounds, whether that is designing a home that reflects their identity or analyzing real community data. When students recognize themselves in the work and see that their ideas matter, their participation becomes more sustained and meaningful.
Inquiry Design & Assessment
When I first started designing lessons in Step 1 and Step 2, my planning was heavy on doing the IM material when I was focused on making sure I covered the content instead of really understanding how students were making sense of it. By the end of Step 2, things started clicking for me. I finally understood why we were doing inquiry tasks and what it meant to connect everything back to the Kentucky Academic Standards and the Math Practices. Once I got into CI and PBI, I really started to see the point behind the design process, lessons needed to be aligned, intentional, and centered around students doing the thinking. That’s when I began building lessons around exploration, patterns, connections, and giving students space to try ideas, talk through them, and revise their reasoning.
As I grew, my assessment methods shifted too. I moved away from just checking for right answers and instead started using things that actually showed me what students understood, exit tickets tied to the standard, student reflections, asking them to create their own definitions and examples, and having them find mistakes in sample student work. These assessments helped me see how well students were meeting the learning goals and gave me evidence of their thinking, not just whether they could follow steps. When I chose resources or activities, I checked them against the standards and asked myself if the task really matched what I wanted students to learn.
Revising lessons became a normal part of my planning. I looked at what went well, what confused students, and what parts needed more support or structure. I always tried to think: how can students learn better next time? In Knowing & Learning, learning about how novices and experts think helped me see why scaffolding and inquiry need to work together. That directly shaped my Novice/Expert Project and taught me how to design lessons that support students as they move from surface-level understanding into deeper reasoning. My growth from Step 1 to PBI shows how I moved from just delivering lessons to actually designing inquiry-based learning experiences where students take ownership of their thinking.
Technology
Throughout my planning and teaching, technology has played a major role in creating an engaging and accessible mathematics learning environment. In this lesson, students use Pear Deck on their Chromebooks to complete warm-ups, explorations, and reflections in real time. This technology allows me to monitor student thinking instantly, check in on misconceptions as they occur, and make instructional decisions during the lesson rather than after it. Pear Deck also encourages equitable participation, since every student contributes an answer rather than only a few students responding verbally. For the goals of this lesson: communicating strategies for the area, demonstrating reasoning, and showing decompositions, the platform is highly appropriate because students can draw directly on the figures, annotate thinking, and share multiple approaches that I can display to the whole class.
In addition to Pear Deck, graphing paper and virtual drawing tools help students manipulate shapes and visually test decomposition strategies. The ability to move, trace, and redraw areas supports spatial reasoning and conceptual understanding, especially for students who struggle with visualization. For students who need tactile support rather than digital tools, physical cut-outs are provided, ensuring that technology enhances learning rather than becoming a barrier. This variety of approaches allows all learners to practice composing and decomposing shapes in ways that make sense to them.
Across my MSUTeach experience, I have used a range of technology from a teaching standpoint. Jamboard, Desmos, and Pear Deck have allowed me to shift from teacher-centered instruction to environments where students collaborate, explore problems, and communicate mathematical reasoning. These tools have supported inquiry-based instruction by allowing students to make predictions, test ideas, and justify conclusions using digital evidence rather than static notes.
My experiences as a student in courses such as Functions and Modeling Research Methods, as well as my research experience in the summer, have shaped, and will continue to shape, how I use technology as a teacher. In those settings, I regularly used mathematical tools such as Excel, Desmos, GeoGebra, and RStudio to analyze patterns, create mathematical models, and communicate conclusions. Using these tools firsthand helped me understand how technology can make abstract mathematical ideas visible and easier to interpret. Because of that, I want to bring similar experiences into my classroom so students do more than follow procedures; they explore patterns, test ideas, and make meaningful sense of their findings.
Technology strengthens my instructional goals by helping students move beyond simple computation into communication, visualization, and reasoning. Whether students are using Desmos to generate graphs, Pear Deck to explain their thought process, or virtual manipulatives to test decompositions of area, technology gives them multiple entry points into high-level mathematics. My objective is not to use technology for its own sake, but to make learning more interactive, reflective, and accessible, preparing students to use the same types of mathematical tools that real mathematicians, scientists, and researchers rely on today.
Multiple Representations
In my Algebra II lesson on exponential and logarithmic functions, students learned that logarithms are the inverses of exponential functions through coordinated linguistic, non-linguistic, enactive, iconic, and symbolic representations, and the effectiveness of this approach is strongly supported by research. Linguistically, students began by describing real-world situations involving repeated growth or decay to build intuitive meaning. Enactively, they used manipulatives and interactive tools to model how exponential processes can be reversed, giving them a physical sense of what it means to “undo” repeated multiplication. Iconically, students examined graphs of exponential functions and their corresponding logarithmic inverses, noticing how the curves reflect across the line that exchanges inputs and outputs. Symbolically, they then expressed this inverse relationship in formal algebraic terms. The Sarry (2020) study found that learning through multiple representations significantly strengthens mathematical literacy and conceptual understanding because students are able to translate among verbal, visual, physical, and symbolic forms rather than relying on symbolic procedures alone. By intentionally connecting these representations throughout the lesson, students were able to internalize the idea that logarithms emerge naturally as the inverse of exponential change, illustrating exactly the kind of representational coherence the research identifies as essential for effective mathematics instruction.
