How Geogebra Contributes to Middle Grade Algebra I Students' Conceptual Understanding of Functions

The current study examined how GeoGebra contributed to middle grade Algebra I students' conceptual understanding of functions. In order to gain a deeper understanding a case study approach was utilized. Vinner (1983), and Vinner and Dreyfus' (1989) concept definition and concept image framework was used to analyze the students' function definition. O'Callaghan's (1994) component of translating was used to analyze the students' comparison of different function representations, and his component of modeling and interpreting was used to analyze the students' use of functions to model relationships between quantities. The following results were derived from the analyses. Having more correct concept images of functions through GeoGebra could also bring about a more correct definition. The dependency upon the concept definition to verify if a given example was a function could not contribute to the concept image. In order to gain correct concept images more integration of technology into algebra instructions was crucial to explore and interact with more function models. GeoGebra was an ideal environment to perform a transition among the representations. All three cases were able to understand how the given real-world problems transformed to GeoGebra simulator and the reverse procedure. The role of instructor was very important to guide and facilitate the learning. The results indicated that verification and exploration of more functions on GeoGebra contributed to a better conceptual understanding of a function definition. The advantages of GeoGebra were obvious for the translating component. The real-world problem scenario could be better modeled and interpreted via a simulator on GeoGebra and the need for algebraic symbolic manipulations could disappear.