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Enhancing Math Learning with GeoGebra Learning Objects


Introduction to the

Learning Object

The GeoGebra learning object I developed bridges the gap between abstract mathematical concepts and practical understanding by leveraging interactive and engaging tools. Specifically, this resource focuses on exploring quadratic functions in the form y= a(x− h)^2+ k, supporting research that emphasizes the importance of dynamic visualization in math education (Saha et al., 2010). By providing students with a hands-on opportunity to manipulate variables and observe their effects, this learning object fosters deeper conceptual understanding.


Learning Objective

The learning object aims to help students analyze and interpret how changes in the parameters a, h, and k affect the 2D graph of a quadratic function in vertex form. Additionally, students will establish general rules for how the parameters a, h, and k transform the 2D graph and apply these rules to new graphs. Lastly, students will explore the graph of the quadratic function in 3D and consider real-world objects shaped similarly. This process builds a foundation for connecting mathematical concepts to real-world objects and applications in future lessons, aligning with best practices that emphasize interactive, learner-centered activities to promote conceptual clarity (Kay & LeSage, 2009).


Content of the Learning Object

The learning object includes a step-by-step instructional guide for students to explore quadratic transformations using GeoGebra. Starting with a standard quadratic equation, students can input the equations of the functions or adjust sliders corresponding to a, h, and k to see immediate changes in the graph. There are four main prompts, which include:


  • Guided Activities, where students will observe how changes in values for a, h, and k affect the graph of quadratic functions.

  • Parameter Manipulation, where students will establish the general rules for how a, h, and k transform the graph of quadratic functions.

  • Apply and Verify Transformations, where students will describe how transformations will be applied to new functions before graphing them in GeoGebra.

  • Exploration and Connection, where students will transition to the three-dimensional graphing tool in GeoGebra to explore quadratic functions in 3D before identifying real-world objects that exhibit the shape of the function.


This focused 2D exploration ensures a solid understanding of foundational concepts before transitioning to a brief exploration of the function in 3D. Such an approach supports research that interactive tools enhance student engagement and comprehension in mathematics (Dickinson, 2016). By maintaining a primary focus on 2D, the activity balances depth of understanding with opportunities for extended exploration, fostering conceptual clarity and engagement. The 3D graph provides a visual connection to real-world parabolic structures, enhancing spatial reasoning and reinforcing the practical applications of the learned concepts (Salinas & Pulido, 2016).


Design Considerations and Insights

GeoGebra AR was chosen from my VR/AR proposal for its robust features, ease of use, and alignment with educational best practices. Research highlights the effectiveness of interactive learning objects in improving conceptual understanding and retention (Saha et al., 2010). The design process prioritized accessibility and interoperability, ensuring the learning object integrates seamlessly with other educational tools and platforms.


In addition, Canva was selected as the tool to design learning object. It was chosen for its versatility and ability to create visually appealing content that enhances learning, supporting the need for materials that are not only interactive but also engaging and easy to distribute. Research underscores the value of aesthetically pleasing and accessible learning resources in capturing attention and improving learning outcomes (Papastergiou & Mastrogiannis, 2021).


Interactive, Accessible, Engaging, and Reusable Features

The learning object integrates the strengths of both Canva and GeoGebra to create an interactive, accessible, engaging, and reusable resource. Canva was selected for its pre-made, visually appealing templates, which ensure the content is colorful, organized, and engaging. Canva's templates are easily editable, allowing instructors to customize the learning object for different classes or topics as needed. Furthermore, Canva’s public sharing options make the learning object widely accessible, ensuring students and instructors can easily access the content through a simple link without requiring a subscription (Canva, 2024).


GeoGebra complements Canva by providing interactive graphing tools that allow students to manipulate the quadratic function y= a(x − h)^2 + k in real time. Links to the web version of GeoGebra calculators are embedded in the Canva-designed learning object, ensuring accessibility for students who may not have the GeoGebra app on their devices. This feature ensures that all students, regardless of their device type or technical proficiency, can engage with the activity.


By combining Canva’s visually engaging design with GeoGebra’s interactive graphing capabilities, the learning object promotes conceptual clarity and active participation. The seamless integration of these platforms makes the resource reusable for various lessons, from introductory algebra to advanced applications in calculus, and adaptable to diverse instructional needs, ensuring its long-term value in enhancing student learning outcomes.


Accessing the GeoGebra Learning Object

Interested in seeing the learning object I created? Check it out! I'd love for you to test it out and send me your feedback.


To access my learning object,

  1. Visit the GeoGebra Learning Object in Canva

  2. Open GeoGebra by either using the:

  3. Read and complete sections 1 - 3 of the GeoGebra Learning Object...and have fun!


    Caption: Image of GeoGebra Learning Object


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References

Canva. (2024). Canva design tool. https://www.canva.com


Dickinson, B. D. (2016). One-to-one mobile devices in rural school districts: A mixed methods study investigating the impact of Khan Academy on mathematics achievement and teacher pedagogy. Northwest Nazarene University.


Kay, R. H., & LeSage, A. (2009). Examining the benefits and challenges of using audience response systems: A review of the literature. Computers & Education, 53(3), 819-827.


Papastergiou, M., & Mastrogiannis, I. (2021). Design, development and evaluation of open interactive learning objects for secondary school physical education. Education and Information Technologies, 26(3), 2981-3007.


Saha, R. A., Ayub, A. F. M., & Tarmizi, R. A. (2010). The effects of GeoGebra on mathematics achievement: Enlightening coordinate geometry learning. Procedia-Social and Behavioral Sciences, 8, 686-693.


Salinas, P., & Pulido, R. (2016). Understanding the conics through augmented reality. Eurasia Journal of Mathematics, Science and Technology Education, 13(2), 341-354.

 
 
 

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