When we think of mathematics, we often picture chalkboards filled with equations or students silently solving problems at their desks. But this semester challenged that image and offered a powerful alternative; one where technology redefines what’s possible in the classroom. As a future educator, I’ve spent the past few months exploring how digital tools can not only support but revolutionize the way students interact with math. Through hands-on investigations, thought-provoking readings, and reflective practice, I’ve come to see technology not as a distraction or luxury, but as an essential component of meaningful mathematics instruction. My understanding of technology in the mathematics classroom was limited to calculators and online homework platforms. Now, after engaging in multiple investigations using GeoGebra, Desmos, and Google Sheets, my perspective has shifted entirely. These tools have transformed my approach to teaching math by making it more visual, interactive, inquiry-driven, and student-centered.
What follows is a reflection on what I’ve learned, how my perspectives have changed, how technology can be purposefully woven into instruction, and why it’s such a valuable asset for meeting today’s educational standards and students' needs.
How have my views on using technology in the mathematics classroom changed across the semester?
Before this course, I considered technology an optional extra, something to use when time allowed. Through the lens of GeoGebra, however, I saw how it makes abstract geometric concepts tangible. By dragging points and watching triangle centers dynamically shift, I began to see math as something alive. GeoGebra empowered me to manipulate shapes, uncover patterns, and understand relationships like never before. Desmos, too, took algebra from static equations to animated, adjustable models. And Google Sheets helped me understand patterns in sequences and functions through interactive tables and graphs. Technology went from accessory to necessity in my instructional thinking. Also, from one of our readings, Hollebrands and Lee (2008) argue that dynamic software allows students to focus on patterns and structure instead of procedural steps. This aligned perfectly with my experience in the GeoGebra investigation and others when exploring the dimensionality of shapes.
Incorporation starts with intentional design. GeoGebra, for example, provides a canvas for students to construct and test geometric relationships. Its real-time feedback transforms a simple triangle into an exploratory investigation. In Desmos, sliders helped students understand slope and intercept without being told what they meant. One powerful investigation used Desmos to compare linear functions by adjusting parameters in y = mx + b, making the steepness, flatness, and direction of lines instantly clear. Meanwhile, Google Sheets became a "math lab," where we explored sequences, growth models, and recursive vs. closed formulas. Investigations like "Choose Your Allowance" and "Dealing with Quadratics" allowed us to model arithmetic, geometric, and quadratic sequences. Adjusting just one cell would cascade changes throughout the table, fostering real-time, visual feedback and pattern recognition. The key insight? These technologies aren't about shortcuts; they're about building mathematical intuition. The key is purposeful integration such as using tools not for the sake of novelty but to enhance student understanding and engagement. Another example is in our Triangle Center Investigation using GeoGebra. We explored how the centroid, incenter, circumcenter, and orthocenter behave under different triangle configurations. Instead of passively memorizing definitions, we interacted with and constructed these points, developing intuition about when each might be useful (e.g., placing a stadium equidistant from cities). Adiitionaly, in “Using Technology to Support Students’ Mathematical Thinking” by Hollebrands & Lee (2008), the authors stress the importance of dynamic technology in shifting students from instrumental (procedural) to relational understanding, a recurring theme throughout the duration of our course work.
GeoGebra aligns beautifully with the Grade 8: Geometry with Data Analysis standards. For instance, Standard 22 encourages students to explore properties of rotations, reflections, and translations. GeoGebra allows students to test these concepts visually and experientially. Similarly, the Desmos activities we conducted tie directly into Algebra I Standard A1.23, where students investigate transformations of functions such as f(x) + k and k*f(x). Using Desmos, we visualized these transformations in real time, promoting understanding through interaction. With Google Sheets, standards related to modeling real-world problems and analyzing functions come alive. We explored linear, exponential, and quadratic patterns through spreadsheet formulas, adjusting variables to test outcomes. The investigations supported Mathematical Practices such as MP1 (Make sense of problems), MP2 (Reason abstractly and quantitatively), MP5 (Use appropriate tools strategically), and MP7 (Look for and make use of structure).
What are some major insights from the investigations this semester?
One of my favorite moments came during Investigation 3.2: Throw Down, where Desmos helped us explore a ball's motion when thrown downward versus upward. Questions like “How fast would you have to throw a ball to keep it in the air for 10 seconds?” sparked meaningful conversation and experimentation. It wasn't about getting the right answer, it was about understanding the behavior of parabolas, symmetry, and motion. Through GeoGebra, I realized that shapes aren't isolated facts to memorize but dynamic relationships to explore. Through Desmos, I saw that algebra isn't about plugging numbers but discovering patterns. Through Google Sheets, I experienced how spreadsheets can shift student thinking from passive to proactive allowing them to construct formulas, analyze change, and validate models.
This semester has shown me that technology isn't just something to add on after a lesson but it's a vehicle for delivering the lesson in a deeper, more meaningful way. GeoGebra, Desmos, Google Sheets and others are not just digital tools; they are bridges that connect students to the heart of mathematics. They empower students to see math in motion, make sense of relationships, and think critically. As I move forward in my teaching journey, I plan to integrate these tools not as optional extras but as core components of student exploration and understanding.
Mathematics is no longer something we just do, it's something we can see, test, and bring to life. And that, to me, is the true power of technology in the classroom.
Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to support reasoning and sense making. National Council of Teachers of Mathematics.
Hollebrands, K. F., Laborde, C., & Sträßer, R. (2021). Teaching and learning mathematics with dynamic geometry. In S. J. Cho (Ed.), The Proceedings of the 13th International Congress on Mathematical Education (pp. 351–358). Springer.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
Shaughnessy, J. M., & Burger, W. F. (1985). Spadework for the future. Mathematics Teacher, 78(2), 130–135.
Alabama State Department of Education. (2021). 2021 Alabama Course of Study: Mathematics. Montgomery, AL: Author.