On the Job Training Part 2: Framework for Teaching with Technology

In the previous post, I have shared with you about our two on the job trainees (OJTs) whom I trained for six weeks. They are currently studying BS in Secondary Education major in Mathematics. They are going to graduate next year and one of the requirements to graduate is a 6-week on the job training related to teaching. This is different from their internship where they will teach in actual class.

During the first week, my goal was to familiarize them with the theories in teaching mathematics with technology. This will give them a theoretical background of technology integration and would help them develop lessons with a framework in mind. One of their readings is the Technological and Pedagogical Knowledge Framework (TPACK) by Khoeler & Mishra (2006). The TPACK suggests that there are three types of knowledge are needed to teach mathematics (and other subjects) with technology effectively: technology, pedagogy, and content. I will be posting the details of this framework later. To give the trainees a bit of context and history, I also let them read the origin of TPACK which is Shulman’s Pedagogical Content Knowledge (PCK) (Shulman, 1986).

Technological and Pedagogical Content Knowledge (Mishra & Koehler, 2006)

I let the two OJTs summarize the article and at the end of the week we discussed the framework. I asked their opinion of the frameworks, their advantages and disadvantages, and how they think the framework can be used in teaching mathematics. There was no time for them to read more articles, so I incorporated Ball’s Mathematics for Teaching Framework during our discussions.

By the end of the week, the two OJTs were excited since during the next week, they would be exploring GeoGebra.

For those who are interested to read the articles I mentioned above, I have listed the references below.  The source of the image can be found here.


Koehler, M., & Mishra, P. (2009). What is technological pedagogical content knowledge (TPACK)?. Contemporary issues in technology and teacher education9(1), 60-70.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher15(2), 4-14.

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.

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