The GeoGebra file featured in the gif above was created by past participant Yan Huang

'Further Your GeoGebra Skills' Course

The dynamic nature of the files/applets had the students' 'hooked' straight away. The fact that they were engaged (from bottom set year 9 to Extension1 (prelim)) speaks volumes to the ability of a half decent GeoGebra file to engage students. The bottom set year 9's asked meaningful questions about surface area and volumes of prisms and responded with insightful answers to questions posed. In fact, one of the most unlikely lads in the group found a glitch in the file. He asked, "why is it that the prism has a surface area of 2 faces when h=0?, I thought it wasn't 3D if h=0, where's this second face come from?" "Good questions and well observed (I'm fixing this)

The Extension 1 class certainly had aha moments with the files they were exposed too. Initially, the 'Pi's the Limit' was very successful in the students' exploration and consolidation around the concept of limits. This investigation then further revealed its relevance to the students when they tackled curve sketching (pre-calculus) of rational functions with asymptotes (vertical, horizontal and/or oblique). The curve sketching file was successful in conveying the concept of how certain functions approach asymptotes from particular directions (above/below). Visually, students could see how the trace approached the various asymptotes; with the embedded spreadsheet providing immediate numerical data to validate their observations. However, it wasn't easy to toggle between zooming in/out and back to the original perspective. To compensate for this I had to create a 'Desmos' file to really exaggerate this idea of approaching a certain value (asymptote) but never quite getting there. Ideally, I'd like to be able to incorporate this facility into the GeoGebra file, to make the learning experience a little smoother, instead of jumping from one file to another. Although successful, I felt it a bit clunky and potentially unnecessary.

Moving forward, besides the benefits of exploring GeoGebra in this course, I found the screen-casting aspect of the course invaluable! I see myself now 'in the creation studio', making more instructional/demonstration videos for my students. In addition, I discovered that I can embed these videos into OneNote, which is absolute gold in terms of the enhancement my pedagogy. Although it took me out of my comfort zone and initially I found the process time-consuming and cumbersome, I have come out the side more confident and motivated to utilise this frequently in my teaching.**Noel Ornelas, St Augustine's College, Nov 2018**

The Extension 1 class certainly had aha moments with the files they were exposed too. Initially, the 'Pi's the Limit' was very successful in the students' exploration and consolidation around the concept of limits. This investigation then further revealed its relevance to the students when they tackled curve sketching (pre-calculus) of rational functions with asymptotes (vertical, horizontal and/or oblique). The curve sketching file was successful in conveying the concept of how certain functions approach asymptotes from particular directions (above/below). Visually, students could see how the trace approached the various asymptotes; with the embedded spreadsheet providing immediate numerical data to validate their observations. However, it wasn't easy to toggle between zooming in/out and back to the original perspective. To compensate for this I had to create a 'Desmos' file to really exaggerate this idea of approaching a certain value (asymptote) but never quite getting there. Ideally, I'd like to be able to incorporate this facility into the GeoGebra file, to make the learning experience a little smoother, instead of jumping from one file to another. Although successful, I felt it a bit clunky and potentially unnecessary.

Moving forward, besides the benefits of exploring GeoGebra in this course, I found the screen-casting aspect of the course invaluable! I see myself now 'in the creation studio', making more instructional/demonstration videos for my students. In addition, I discovered that I can embed these videos into OneNote, which is absolute gold in terms of the enhancement my pedagogy. Although it took me out of my comfort zone and initially I found the process time-consuming and cumbersome, I have come out the side more confident and motivated to utilise this frequently in my teaching.

I started out with the intention of using GeoGebra to demonstrate concepts dynamically. As I constructed files, I found myself being engaged in a lot of exploratory activity myself. This was a real bonus as I found myself making discoveries that resulted in increasing my own depth of awareness of areas related to functions. This included realisations of the reasons why students develop misconceptions.

My students were positive about the GeoGebra demonstrations. However, I found an interesting consequence. What happened quite often was that students were more inclined to ask questions. This, I believe, was because the answers were often readily accessible by utilising the dynamics of GeoGebra. I asked students about them being more inclined to ask exploratory type of questions. My four students conveyed that they were more confident to ask questions when they could see the answers not far from their grasp; also, they were able to identify questions they might not have seen while doing more traditional “book work” type activities. They relayed that questions were more likely to occur to them while experimenting with the dynamic attributes of GeoGebra. This was especially the case with circular, exponential and integration functions.

I believe that GeoGebra would have been an even more powerful tool had the students had prior experiences with using GeoGebra. As senior students, with a highly packed curriculum, there was little time to make them proficient with the program.

While I used GeoGebra essentially demonstration with exploratory elements, I intend to extend my repertoire to files that lend themselves to greater self-discovery.

As an overall observation, I felt that by using GeoGebra, the students engaged with the learning process in a new and exciting way. It was very rewarding to see how the students discovered many of the principles themselves which I feel has resulted in deeper understanding and learning. I was impressed by the students' level of engagement each time GeoGebra was used. It led to much group discussion and shared ideas. I felt this was a very worthwhile exercise, especially for the couple of students who went further and started to investigate what else GeoGebra has to offer.

I started with a bunch of investigative files that allowed the students to discover the principles of constant and variable rates of change. At first the students struggled to get used to the different tools used in GeoGebra, but they were soon playing around with them and learning as they played. It was fantastic to see how engaged the students became in discovering what each file had to offer. Some of the brighter students then started to suggest different ways of setting up the files.

I then used my GeoGebra files to show the students how to relate velocity-time graphs to position-time graphs. Once again, some of them started to come up with their own files to demonstrate this concept. I definitely found that by using GeoGebra to explain how to sketch velocity-time graphs, the students found the process much easier to understand when they could see the resulting graph being formed step by step.

The final file I used was Differentiating by First Principles. This activity required the students to create the file using the steps listed in the file. They were fully engaged in this process and by all accounts thoroughly enjoyed being able to create the file and then to play around with it.

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