GeoGebra Applications in Secondary Education.

Look at the two shapes below and intuitively compare them. What do you notice?

From initial thoughts, I'm sure that you classified the two shapes as the first being a parallelogram and the second being a rectangle. However, what if I told you that the rectangle is a special type of parallelogram. Let's compare:

Parallelogram:

• Two sets of congruent sides and opposite sides are parallel

•  Diagonals bisect each other and two adjacent angles are supplementary

Rectangle:

• Opposite congruent sides and opposite parallel sides

• Congruent diagonals and four right angles

Through the GeoGebra, you can take your rudimentary knowledge and understanding of shapes and compare them through the parameters of geometry. Based on the comparison, we can confirm that a rectangle is indeed a special type of parallelogram.

GeoGebra Implications in Secondary Education.

Looking specifically at the 2019 Alabama Mathematics Course of Study, especially the Grade 8: Geometry with Data Analysis section, GeoGebra aligns naturally with several standards. For example: Standard 22 encourages students to verify experimentally the properties of rotations, reflections, and translations (Alabama State Department of Education, 2021). From this standard alone, we are able to see how GeoGebra gives students a live, interactive canvas to manipulate shapes and draw conclusions based on movement and data—not just abstraction. 

Additionally, the insights from Shaughnessy & Burger’s “Spadework for the Future” remind us that mathematical visualization is a powerful cognitive skill. Their emphasis on spatial reasoning and hands-on engagement emphasizes how visual and dynamic experiences foster deeper understanding of structure, symmetry, and patterns. GeoGebra builds this visual intuition, letting students pose their own problems, test conjectures, and receive visual affirmation or correction—essential for developing true mathematical thinkers. In the article, they classify of user engagement and mathematical thinking into fives levels known as "Van Hiele Levels" (Shaughnessy & Burger, 1985). Each level from zero to five depicts the steps it takes to achieve true mathematical thinking. Starting from visualization, analysis, informal deduction, formal deduction, and rigor. GeoGebra explores each level more providing users the opportunity to become proactive thinkers by level three truly understandings and not memorizing geometric relationships. 

GeoGebra empowers students to see math, move math, and truly grasp math. In today’s classrooms, this tool allows for the   exploration, visualization, and connection of mathematical ideas more deeply than ever before. Whether you're guiding users through the geometry of dilations or analyzing volume data, GeoGebra aligns perfectly with the Alabama standards—and more importantly, with how students learn best. Its integration into geometry and data analysis standards can transform passive learning into active, inquiry-driven discovery. With proper support and thoughtful implementation, this tool can help us meet the call for engagement in math education—one draggable point at a time. 

References:

• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author. https://www.nctm.org/uploadedFiles/Standards_and_Positions/Principles_to_Actions/

• Alabama State Department of Education. (2021, June). 2019 Alabama Course of Study: Mathematics (Rev. ed.). Alabama Achieves. https://www.alabamaachieves.org/wp-content/uploads/2021/03/2019-Alabama-Mathematics-COS-Rev.-6-2021.pdf

• Shaughnessy, J. M., & Burger, W. F. (1985). Spadework for the future: Priorities for geometry and learning. In E. G. Begle (Ed.), Learning and teaching geometry, K–12 (pp. 212–226). National Council of Teachers of Mathematics.