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VR Math classroom
VR Math classroom
Kaurialan lukio, Finland
The Math VR classroom took place in Upper secondary school Kaurialan Lukio in Finland. 10 Czech students attended the programme, accompanied by two Czech teachers. The focused group of students was mixed up with local students.
The math workshops introduced the use of mathematics programs in virtual reality and augmented reality. Ready-made worksheets were planned for the students, based on which exercises were done.
In the first workshop, students were able to explore geometric problems in virtual reality using GeoGebra Mixed Reality and VR sets. The objects and questions were in virtual reality and the answers were thought together in small groups of 3-5 students.
In the second workshop, various objects were modeled using GeoGebra's 3D tool and GeoGebra AR. Students were able to measure real objects and program 3D models of them based on the measurements. The mathematical models were then taken to augmented reality for examination. Using augmented reality, students compared the programmed model to a real one on a flat surface.
At the end of both workshops, we had thorough feedback conversations. It was said that sometimes geometrical tasks are not easy to visualize. In virtual reality, you could walk inside the objects, and move or rotate them. Virtual reality seems to be helpful for challenges in geometrics especially.
Both VR and AR environments were seen as helpful tools and nice variety alongside regular studying of math.
VR Marth lesson 1
VR Marth lesson 1
Teacher´s name: Markku Pohjola
Home school: Kaurialan lukio
Age range: Not specified
Subject: Mathematics
Topic: Mathematical objects in VR
Topic 2: Sierpinski pyramid model in VR
Topic 3: Basic geometry tasks in VR
Grade level: 1st, 2nd
Number of students: <20
Aims of the lesson:
The aim is to study mathematics in an unconventional way in VR using GeoGebra Mixed Reality.
Lesson objectives:
Students will be able to solve mathematical questions in a virtual environment.
- Geometrical problems
- Easy examples, like sorting different geometrical objects
- More difficult examples, like calculating a volume for 4th Sierpinski fractal pyramid
Resources and materials:
- VR set with GeoGebra MR. 1 set for 2-3 students.
- Computer, iPad, or some device to stream that is seen in VR (1 for 2-3 students)
- Questions are written on paper to solve for students
Instruction:
- Students are split into pairs (preferably, groups of 3 will do as well) and every pair gets a VR set with GeoGebra installed. We also need a device to stream what is seen in VR.
- Guiding to „how to work with GeoGebra“ is needed (moving in the area, zooming and moving objects, etc.)
- Pairs will complete prepared tasks together
Assessment activity:
- After the tasks are complete, discuss the problems and possible difficulties in them.
Follow up:
- There are multiple pre-made questions in GeoGebra MR itself. Students can study them to deepen their understanding of maths.
- Also there is a graph you can draw mathematical functions with. The drawing needs more advanced knowledge of two-parameter functions.
- Questions can be made more difficult. Like, what would be the volume of Sierpinski fractal, when the order goes to infinity? What is the mathematical equation for the Sierpinski pyramid?
Reflection / Evaluation/ Reminders:
- Students might feel uncomfortable calculating math in virtual reality. There is no calculator in the software, so students might have to take off the head-mounted device at times and solve problems on paper (or computer).
- Using GeoGebra MR needs a certain amount of space for each pair.
AR Marth lesson 2
AR Marth lesson 2
Teacher´s name: Markku Pohjola
Home school: Kaurialan lukio
Age range: Not specified
Subject: Mathematics
Topic: Mathematical modeling in AR (augmented reality)
Number of students: <20
Aims of the lesson:
The aim is to model practical objects with mathematical functions in augmented reality using GeoGebra AR
Lesson objectives:
- Make a function of a coffee mug with computing in GeoGebra.
- Examine that object in augmented reality (with a phone or iPad).
- Compare the real object and the object made out of functions in AR.
Resources and materials:
- Computer with GeoGebra installed
- iPad or phone with GeoGebra AR installed
Instruction:
- Students are split into small groups (2-3 preferably)
- There will be a step-by-step guide on how to proceed with mathematical modeling.
Assessment activity:
- After the tasks are complete, discuss the problems and possible difficulties in them.
Follow up:
- You can basically model a lot of different common things. Students can try different stuff and put them in AR. There are easier shapes in GG (balls, cones, etc) that can be easily drawn and exported to AR.
Reflection / Evaluation/ Reminders:
- Mathematical functions may be complex, however, they work nicely. Understanding those functions would need deeper understanding. Thus a paper guide and personal guidance are needed.
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