On the Job Training: Using GeoGebra in Teaching Math

For the last several years, our Institute has been accepting on the job trainees from nearby universities. These trainees are undergraduate students taking up bachelor’s degree in education. As for our group, we are accepting students who are taking education major in mathematics.

This year, we have accepted two students who are on their third year of university studies. I have been handling them already for three weeks of their 6-week course. In this post and the next several posts, I will be sharing our activities during the training.

During our first meeting, the two students shared that they wanted to deepen their understanding on content and strategies in teaching mathematics. Since my specialization is on the use of technology, I have designed their training with the focus of integrating technology in teaching mathematics. This includes familiarization with various theoretical frameworks used in teaching mathematics using technology, using a software in creating teaching and learning materials, and developing lessons with technology integration. Once a week, we also discuss key content topics in high school mathematics and various ways to teach them.

The GeoGebra Interface (via Wikipedia)

At the end of the training, the students are expected to develop applets and lessons using GeoGebra. They will implement the lessons with me and my colleagues as audience. After the implementation of the lesson, we will comment on how the lessons can be improved.  Their last task is to revise the lesson. Their major output is a lesson plan.

For those who are not familiar with GeoGebra, it is free software that can be used for teaching and learning mathematics. You can download it here and there are various tutorials on learning the software here. GeoGebra is available on Windows, Mac, Linux, iOS and Android operating systems.  You can use it on laptops, tablets, and mobile phones.

Helpful Resources in Learning Latex

I am being serious of using Latex to the point that I’m going to use it to create our next booklet at work and in my next presentations, so I began learning about it a few months ago. In this post, I’m going to share with you the resources that I have been using in learning it which I found extremely helpful. For those who have not heard about Latex yet, it is a typesetting system that can be used for creating professional and technical documents. Most mathematicians use Latex in publishing their research papers. The image below shows a Latex code and its output.

Click image for full view (via Wikipedia)

To create equations like

x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}

on websites or blogs, you need to have some basic knowledge about Latex codes for mathematical expressions.

To create Latex documents, you need two things:

  1. An editor where you will type your code
  2. A distribution (compiler) which turns the code into a readable document

For the editor, I use Texmaker because it is both available for Windows and MacOS. I use Windows at work, while may personal laptop is a Mac.  For the distribution, I recommend using Miktex for Windows or Mactex for Mac. Texmaker, Miktex, and Mactex are all free software!

Learning Latex

For learning the basics of Latex, I highly recommend Michelle Krummel’s tutorials on Youtube. Honestly, you only need these tutorials for learning the basics. The tutorials include creating and formatting simple documents, typing mathematical expressions, using packages and macros. There is also a tutorial on creating Beamer presentations. We will talk about Beamer in another post.

Other tutorials can be found on Overleaf’s Documentation page. Overleaf is an online and collaborative Latex editor. I have used it for a few days but I preferred TexMaker.

You only need those two resources to learn the very basics of Latex. I strongly suggest that you finish Michelle Krummel’s tutorials first.

Compass and Straightedge Construction Using GeoGebra

In Geometry, the term construction refers to the ‘drawing’ of geometric objects such as lines and circles with only the use of compass and straightedge. Construction does not allow measurement of both lengths and angles. The earliest study of Geometry, particularly parts of Euclid’s Elements focused on “building” Geometry based on compass and straightedge construction. In the following discussion, we will refer to compass and straightedge construction as simply construction.

 

Compasa and Straightedge

Compass and Straightedge

Using dynamic geometry software (DGS), we can extend construction to computers, tablets, and mobile phones. In this post, we will learn how to use GeoGebra to mimic construction. For those who do not know about GeoGebra yet, it is a free multi-platform mathematics software (not just a DGS) that can be used for teaching and learning mathematics. You may download it here and if you want to learn about it extensively, I have created numerous tutorials on how to use it hereContinue reading

You Can Now Graph Using PhotoMath

Three years ago, I wrote a post about Photomath, a software capable of scanning and solving equations using phone cameras. I haven’t used the software in a while, and recently discovered that it also has added a capability of graphing functions. It can now graph polynomial functions, rational functions, and trigonometric functions, exponential functions, and logarithmic functions. Recent improvements also allows solving for exponential equations, derivative, integrals, and limits.

Shown below are some examples. I scanned handwritten equations of functions and graph them.

To use Photomath, just open it, click the Camera icon and point to then expression or equation.

 

To view the graph, click the red rectangle containing the equation at the bottom of the screen.

Aside from the graph, the output also shows some important information about the function such as its x and y intercepts, domain, minima/maxima.

I think Photomath is a very good software that can be used for learning mathematics. Students can use this app to verify answers and also to explore graphs. Photomath is a free app and is both available on Android and iOS.

Calculators That I Use Nowadays

I have shared several decent calculators and graphing tools in this blog, but in this post, I’m going to share the calculators that I actually use nowadays. The calculators I use depend on the task that I’m doing. I use my phone for short and simple calculations, but if I’m studying or working for an hour or more, I use an actual calculator to avoid distractions. Here are the four calculators that I use most of the time.

1.) Calculator (Mac)

When I’m using my laptop, I use the default calculator app of MacOS. This app allows the user to choose among basic, scientific, and programmable modes. It also supports base 8, base 10, and base 16 number systems. Personally, I only use the basic and scientific calculators and I have not tried the programmable calculator yet. 

2.) Google’s Calculator App (Android)

Google’s calculator is a simple and beautifully designed app for basic calculations and scientific calculations. It can store previous calculations. I like the simplicity of this app, so I use it most of the time for basic calculations when I’m using my Android phone. This app is compatible with WearOS.

3.) Advanced Calculator FX991 (Android). This is a paid app but I really like it because it mimics the interface of an actual calculator (see image below). I’ve been using it for six months and so far, I really liked it.

4.) Casio FX991 ES Plus. Aside from apps, I also keep a Casio 991ES Plus. It’s not that I wanted to buy this calculator,  but it was the only decent calculator in a store the time when I wanted to buy one. So far, so good, I’ve gotten used to it. I think I will be using it for a long time.

That’s all. Maybe you can share the calculators that you’re using in the comment section below.



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