Category: Article

Playing with GeoGebra Augmented Reality

Augmented Reality in education is relative new but developing rapidly. Sometimes in mathematics class, especially on geometry topic, students have difficulties to understand because they have to imagine in a three-dimension way. AR allows the students to see the real world with virtual objects. The students can also see geometrical virtual objects like a cube, a cone, a pyramid or a sphere in 3D superimposed with the pictures of a cube or a cone in 2 dimensions in a textbook. This will help the students to visualize for better understanding.

Beside it is engaging, another thing from “Why use AR” is promoting rigor and relevancy.

GeoGebra AR application includes several examples of 3D math objects that you can place on your table, floor or any flat surface around you. However, for right now, GeoGebra AR only can be downloaded in IPad or IPhone with iOS version 11 and above.

Place math objects on any surface, walk around them, and take screen recorder from different angles. Also, guided activities lead you to discover math in the real world by taking screenshots from different perspectives.

Now, GeoGebra AR also includes “New” 3D objects that can be modeled and built by each and everyone of us with just using two surface functions or even more surfaces. For example, my “butterfly” model below is inspired from Tim Brzezinsky’s model (Tim is an Independent Mathematics Education Consultant Educational Technology Content Developer/Author Accredited GeoGebra Trainer). I add two functions,    as the butterfly’s wing and    as its body.

While, my donut (aka Torus) is from

Have fun with building as many models as you want!! 😀

Also, I got my inspiration from this. After my water bottle fell and the water spilled, I remember again the surface functions from Tim, that looks like a bottle.  Now, here is the spilled water from the “AR Bottle” 😉

My new collections (added September 2018):

 

Some Equations:

Triangular Prisms:  and  

Cone:  

Sphere:  

Pringles:  

 

Challenge!! Can you find more equations to create your 3D shapes?

TEST – But Given Answer Key (?)

This topic “Permutations and Combinations” is one of the topic that most of my students don’t like (me too 😯 *whoops*). But for some students who are really excel in Maths, of course, no problems at all. Lucky me, having them in my class.

When the topic of your mathematics class is not just like calculating and using formula, then, it will more challenge you how to teach them.

In your explanations, it is not just “must be in clear”, but you should also recognize your students’ understanding level. Some of them grab the concept in easily, but some of them hard to translate the meaning of the words. How can you make them differentiate between arrangement and selection, for example, in one problem. For me, I see difficulties to make them understand it.

Beside this topic is hard to explain, a good thing always appears on the other side. When you see your students get excited after finding the answers (similar situation and reaction when they can show trigonometry identities problems), you will satisfy and feel success teaching them.

To make them excited during the test, in one section of my test paper, I attached the answer key (without working process) on each question. Instead of asking them to answer, I want them to explain how to get the answer, in any methods.

They were happy, you know, test but answer key was given? yeaaayy. They tried to find the answers, they used any methods, to match it with the given one. They are allowed to do that, of course. However, at the end, marks will be given based on their explanations, why they chose that way.

After I distributed the test paper back to them, no one complaint about the test score. Although, there were some students provide the answer same with the given one, but the process was wrong, they will not get the marks on that question. They knew and realized, that they “created” the “not logical” working that came up with the same answer 🙂 .

This is interesting, isn’t it?

In one side, you trust your students to find any methods with any working process to get the answer same with the answer key given by you (for me, it is actually exercising their critical thinking) while in the other side they will try as hard as they can to get it.

These two pictures are captured from two students who provided their answers with complete explanations (structural and also wording).

Solve “Ed Southall” Maths

Last week, I answered the challenge question of basic mathematics given by Ed Southall @solvemymaths, the author of “Yes But Why?” and “Geometry Snacks” in his twitter timeline.

Here is the question:

What fraction is shaded?

My reply was late. But, I still did that, because I did many times answering maths questions that were appear in my timeline. Some people had already answered in correctly, some just gave up immediately and replied with funny responses and some did wrong.

Few days after that, I found my name spotted by thisisinsider.com as one of the users whose rose to the challenge.

Ed’s question has gone viral. He caught up by many medias from UK. The famous Ed should be proud, however, I also proud and very happy because my name was spotted in the media…. hahaha 😀 I am joking that I am famous now. #eh

The idea of giving question in social media, is always interesting. It depends on the purpose of course. As a teacher, you can use your social media to challenge your students with questions. Make the link between you and your students. See how your students will response on it. As Ed, he wants to spread the fun of learning mathematics, I believe, he regularly challenge people by his (not so hard) questions, actually, but will make people to think before answer. Including me.

This is fun and very useful, to make friends in social media from other countries, and see what people think about many things, especially in educations.

 

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