As a prospective teacher, who is a senior student in a five year Integrated B.S. and M.S. Program in Teaching Mathematics in Faculty of Education, Boğaziçi University, my internship in Robert College has been one of the most intense experience throughout my undergraduate study. I deliberately use the word ‘intense’ since I was extremely exposed to many educational technology tools and their effective usage in classrooms. A ten-week long internship program with class observations of 8 block lesson hours per week and practice instructions of 2 block lesson hours had great impact on my teaching experiences. What makes my experiences great is that I have observed and learned how to use TI 84 graphing calculator, interactive white board, Google Apps, Web2.0 tools and many more things in classroom instruction. In this article I’d like to share some of the key facts I have observed so far.
As teachers, first thing you need to consider is to be sure that your students are ready for the tasks you will cover in the lesson. Creating an environment where students learn new concepts by building up their own conceptual knowledge brings true learning. Assessment is also a key factor to plan your lessons and should provide you enough data to understand to what extent you have reached your expected goals for the students.
When it comes to assessment, you need to think both the capability and the time efficiency of your method. As an example, in one of Mr. Firat’s classes I have seen that Google Docs could be used as formative assessment tools to provide students with immediate feedback on their performances. Thanks to BYOD, all students have access to a Google Form in which there are many questions. As soon as they answer a question they receive a feedback which shows how good their performance is by providing the statistics of performances in the class. Since Google Docs allows teachers to integrate online grading tools using scripts, such as Flubaroo, teachers can send individualized feedback to each student in seconds. Thus, students get the opportunity to monitor their progress throughout the learning process, which encourages them to take the responsibility of their learning.
I have observed that in Robert College teachers have developed many skills while integrating technology tools and applications into their curriculum. Their curiosity and enthusiasm in learning and improving themselves by developing innovative instruction strategies have made me inquisitive and enthusiastic to improve my teaching skills as a prospective mathematics teacher.
One of my colleagues has discovered the magical world of augmented reality and asked me which apps I have installed to my iPad. I have prepared a file for him and wanted to share it with you as well. If you are new to AR you can think of it as a layer you put between reality and your eyes by using your mobile device’s camera and screen. You can insert images, videos, anything you want onto that virtual layer.
Among those my favourites are Aurasma, colAR Mix, ChromVille, Anatomy 4D and Star Chart. By the way I need to say that Qrafter and i-nigma are QR Code readers and generators. QR codes are still popular so you should have these kind of apps.
Below you can find the links to the websites or iTunes pages for the apps. Most of them work in both iOS and Android.
The Brain AR , Blippar , Elements 4D , Enchantium , Layar , Qrafter , i-nigma , Augment , Sekai Camera , AR Media , ChromVille , colAR Mix , Anatomy 4D , Star Chart , Sun Seeker , DAQRI , SnapShop , Junaio , Wikitude , ZooBurst , acrossair , Aurasma
Multitasking can be simplified as doing more than one task at the same time. This is something our students and we do regularly. We all think that there is no problem in multitasking because everything works fine and whenever we come up with an error we consider it normal. After all we are human and humans can make errors. In an overall approach the idea sounds right but there are some people who claim that multitasking increases the probability of doing errors and they have concrete scientific research results. Let me give you two examples which will clarify the situation:
1) Writing an English essay while talking on the phone with your friend (about a movie etc).
I can hear that you are saying this is a bad example because nobody does this and you are right. If two or more actions are continuous then people tend to focus on only one task. This habit is broken when it comes to driving. Many people unfortunately risk lives by texting or talking on the phone while driving.
2) Writing an English essay and checking an SMS message.
Now this example is the reason of all those discussions because the second action is not continuous. You checked the message, replied it and it took only 10 seconds. You think you can continue where you left off but actually you can’t.
While trying to study at home students get occupied by the small tasks coming from their cell phones, laptops or tablets. They think that they can manage the process but this is scientifically impossible; brain can not multitask. Below you can find some resources which support this fact.
From Brain Rules Book – Attention
Beliefs That Make You Fail – Part 1 (check 3:10)
An Infographic With Statistical Facts
A really good article by Kendra Cherry – The Cognitive Costs of Multitasking
A different approach to the discussion via TeachThought – Teachers: The Real Masters of Multitasking
In my previous article I tried to explain the reasons behind why GeoGebra is so popular all around the world. As I explained before, it ensures the interactivity in the lessons and enhances the teaching and learning of mathematical concepts. However, using it appropriately and effectively is more important than knowing what it is. In the second part of my article, I will provide examples of the use of GeoGebra in different areas.
Activity 1. Please follow the instructions listed below:
Click on the following link to download latest version of GeoGebra. GeoGebra’s official website.
Write “(x^2+y^2-1)^3 – x^2y^3 = 0″ into the input bar and press enter. Be aware that you have already constructed a curve on the window easily.
Right click on the curve and select Object Properties from the popup menu.
- Click on the Color found in the second place in horizontal menu and choose the “red”.
- Click on the Style found in the third place in the horizontal menu and set the value of Line Thickness Slider for 9. Be aware of the changes on the curve in terms of color and style.
- Click on the twelfth icon in the Tool Bar. Use Zoom In Zoom Out and Move Graphics View to get the clear view of the curve.
- Click on Close which is in the upper-right corner of the child window to close it.
- Click on File located on the upper-left corner of the GeoGebra parent window.
- Choose Save from the drop down menu.
- Name your GeoGebra file as Activity 1 and save your file.
Figure 1. Plotting graph of (x2+y2-1)3-x2y3=0 in GeoGebra
Now you are finished. Below, you can see some other examples I created to represent how GeoGebra can be used in different areas.
As you can see from examples GeoGebra can be used to encourage discovery and visualize mathematical concepts. I’d like you to take a moment and try to find areas at which GeoGebra can be used to enhance learning. If you visit the GeoGebra forum site you can find examples, teacher discussions and many more useful resources.
I came to the end of my article here. I’d like to add that I am one of the researchers who make studies on GeoGebra. I have just completed my thesis study which aims to develop worksheets including activities similar to Activity-1 so that high school mathematics teachers can use GeoGebra appropriately and efficiently in teaching and learning of geometry.
Finally, I would like to thank Emre Fırat for his helpful comments and sharing my article on his blog.
Today I have received an email from Google telling me that I can start using Classroom. I was waiting for this for a long time and I’m very excited to be able to work on Classroom before September. I logged in to my account and started working on it. Below I’m sharing my first presentation on Classroom For Beginners.
If you have no idea about what Google Classroom is let me explain it very quickly; if you are a user of a Learning Management Sytem like Moodle, Haiku or Edmodo you can start forgetting about them. Google Classroom will take their places. If you don’t use an LMS or don’t know what it is you can think of Google Classroom as a platform where you can organize your Google Drive content in a better and easier way. You will be able to assign and follow tasks, publish announcements etc. Here is an excerpt from the site classroom.google.com ;
“Classroom weaves together Google Docs, Drive and Gmail to help teachers create and organize assignments quickly, provide feedback efficiently, and communicate with their classes with ease. And it lets students organize their work, complete and turn it in, and communicate directly with their teachers and peers.”
Recently I have been informed that International Teacher Development Institute (iTDi) (http://itdi.pro) is launching a MOOC for TEFL teacher development training on WizIQ which is an online education platform where you can learn and teach many topics. You can find more information about WizIQ at www.wiziq.com
The MOOC is scheduled to begin on July 20, 2014 and it will help teachers in the following way:
- Learning how to make their own education materials
- Designing interactive classroom games
- Discovering how to create projects, and set up a blog
- Learn about the latest education apps, using social media in class & more.
There is a very rich list of presenters and participants will be able to choose from a wide range of sessions. Moreover all the participants will be awarded Certificates of Participation issued by WizIQ and certified by iTDi.
Last week I had a small vacation with my family. The hotel we went to was a big one and there were lots of tourists coming from different countries. The hotel was located in the southern part of Turkey where the weather is extremely hot during summer. Since I have a 2 year old son I had to spend noon time inside the hotel and I was not the only one. Families who wanted to protect their kids from warm sun were there as well. I started observing how other families are spending their times with their kids and what I saw was like a scene from a horror movie. In a room full of kids (and parents) almost everyone were turned into zombies by smart devices. Since I can’t publish their photos with you I’m sharing the following pics from 9gag to give you an idea.
My followers know that I’m a tech-savvy person and I can’t live without internet and my smart devices. But even I have boundaries. Except summer I’m very busy and I can’t spend enough time with my family. This vacation is a perfect opportunity for me to catch up with them so why would I waste my time in front of a tablet screen playing games or tweeting all day. Of course my job follows me every time even during the vacation and I need to be online but the time I allowed to myself is limited to 30 minutes for the whole day.
Even though I’d like to share my thoughts on technology and its effects on adults the focus of this article is kids. Our lives are not as plugged as theirs and during this vacation I became certain about it. Unfortunately kids were using smart devices not only noon time but whenever it is possible; during breakfast, lunch, dinner, on a sunbed etc. In the absence of school, kids have the freedom(!) to use these devices all the time. Some parents tried to resist their kids’ demands on playing with these devices but in the end they always lose the fight. Just when I thought the situation is hopeless I realized that they were unplugged during the hands on activity times arranged by kids club animators. This was a good sign. No one was forcing them and they seemed to enjoy being unplugged.
Now, the situation and the questionin our minds is clear: What can parents do during vacation to help your kids get unplugged? Here is a list of some ideas and some of them include using these devices;
1) The very first thing that parents can do is unplugging themselves. Parents are role models for kids so why can’t kids play with an iPad while their parents can?
2) Second thing can be making daily schedules for different activities. There is plenty of time to do activities during a vacation so why not use this precious free time? Before your trip search the websites (like education.com) to collect holiday activities.
3) Don’t forget to arrange some time to let your kids get bored. Getting bored is perfectly normal and essential. I know it sounds weird and crazy but one of the problems that today’s kids have is this; they can’t get bored. They can access various types of smart devices and internet anytime. They don’t have time to listen to their inner voice and think about the events in their lives.
4) Breakfast, lunch and dinner times are very important for a family. The communication between family members shouldn’t be interrupted with TV or with a smart device and this is true for all members of the family.
5) It is not possible to get unplugged 100% but you can set rules for everyone. You can set the time spent on these devices, install/uninstall certain apps etc.
6) These devices can also be used as a substitute to other tools. For example instead of carrying physical books you can download them to your device or you can read your daily newspapers. They can be your music player as well. This can be a good time to exercise encouraging your kids to resist the urge of playing games only and using these devices more productively.
7) These devices can be a part of your family activities. Use them to take pictures. At the end of the day you can get together and play with these images using photo apps. Create collages, family albums etc. and save them to share with others.
8) Another activity might be creating a digital vacation journal. Every member of the family can write and comment on eachother’s thoughts about the holiday. This may increase the collaboration among the members of the family. Besides it will be digital so it can contain photos, videos, audio files, links to websites etc. which is much more fun and preferable for kids.
GeoGebra is a dynamic mathematics software developed to make students, from primary school through university level, understand mathematics and science better. Created in 2001 as the thesis study of Prof. Markus Hohenwarter for his Master’s Degree at Salzburg University, GeoGebra is used by students, teachers and researchers in 190 countries, translated into 62 languages (Hohenwarter & Fuchs, 2004; Lavicza, 2014). In order to share materials created by using GeoGebra, GeoGebra Institutes were established in different countries (Lavicza, 2014). Today, there are 153 GeoGebra Institutes in 85 countries (Lavicza, 2014).
As you can see GeoGebra becomes more and more popular every day. More than 1.000.000 people visited the official website of GeoGebra within only a month (Lavicza, 2014). At this point, you might wonder why Geogebra is such a popular tool. Actually this question encouraged me to make a research about it and I’d like to share my initial findings below.
1. GeoGebra, is a free open source dynamic mathematics software (Hohenwarter & Lavicza, 2007).
2. Since it is a free to use , students and teachers do not encounter licensing problems when they attempt to use it; and they can use it freely both in the classroom and at home. (Lavicza & Papp–Varga, 2010).
3. GeoGebra is constantly being upgraded by various researches. In my interview with Dr. Zsolt Lavicza on January 2014, Dr. Lavicza mentioned that it will be possible to collect data through GeoGebra and analyze the collected data using GeoGebra.
4. GeoGebra is a single package that includes geometry, algebra, statistics and mathematics (Lavicza, Hohenwarter, Jones, Allison, & Dawes, 2010).
5. GeoGebra allows us to correlate computer science and physics in secondary education (Guncaga, Majherová, & Jancek, 2012).
6. Haciömeroğlu, Bu, Schoen and Hohenwarter (2009) addressed the research question of how we as teacher educators provide rich learning experiences to help prospective teachers develop Technological Pedagogical Content Knowledge (TPCK) and enable them to design appropriate activities and describe pedagogical strategies for the effective teaching and learning of mathematics with technology. The results indicated that not only drawing mathematical objects and figures but also creating dynamic activities help teachers develop their TPCK (Haciomeroğlu, Bu, Schoen, & Hohenwarter, 2009).
7. Using GeoGebra and interactive whiteboard together enhances the understanding of mathematics (Lavicza & Papp-Varga, 2010).
8. GeoGebra develops students’ conceptual understanding and problem solving skills (Bulut & Bulut, 2011).
9. Students in mid-secondary grades can investigate real world problems with GeoGebra (Bu & Schoen, 2011). Since students can build a bridge between abstract mathematics and real world situations, mathematics will be more attractive and meaningful to them.
8. Teachers can use it to demonstrate and visualize mathematical concepts and prepare enriched materials (Hohenwarter, 2004).
9. “Dynamic geometry software allows the creation of geometric constructions and other dynamic figures (e.g. function graphs) by using the computer mouse and a variety of geometric tools and menu items” (Prenier, 2009, p. 32). Hence students are able to watch the variations in the geometric shapes and explore their properties when they use the dragging facility of GeoGebra.
10. In addition to the reasons explained above, the users also can set the color, transparency or thickness of constructions, and insert a picture into their GeoGebra file.
Figure 1. Main parts of GeoGebra
In the next article I’ll present some activities using GeoGebra. If you have any questions or comments regarding use of GeoGebra please feel free to contact me via email.
Hamide Akkoca, MA
Tarsus American College
Email: [email protected]
Bu, L., & Schoen R. (2011). Model centered learning: pathways to mathematical
understanding using GeoGebra. In Lingguo B. & Robert S. (Eds.), Using dynamic geometry to bring the real world into the classroom (p. 41–46). Boston, USA: Springer.
Bulut, M., & Bulut, N. ( 2011 ). Pre service teachers’ usage of dynamic mathematics software. The
Turkish Online Journal of Educational Technology, 10(4), 294–299.
Guncaga, J., Majherová, J., & Jancek, M. (2012). GeoGebra as a motivational tool
for teaching and learning mathematics, informatics and physics. In M. Billich (Ed.), Mathematical IV: scientific issues (p. 53-62). Ruzomberok, Slovakia: Verbum.
Hacıömeroğlu, E. S., Bu, L., Schoen, R. C., & Hohenwarter, M. (2009). Learning to
develop mathematic lessons with GeoGebra. MSOR Connections, 9(2), 24-26.
Hohenwarter, M. 2004. Bidirectional dynamic geometry and algebra with
GeoGebra. Retrieved from
Hohenwarter, M., & Fuchs, K. (2004). Combination of dynamic geometry, algebra
and calculus in the software system GeoGebra. In Computer algebra systems and Dynamic Geometry Systems in Mathematics Teaching Conference.
Hohenwarter, M., & Lavicza, Z. (2007). Mathematics teacher development with ICT:
Towards and international GeoGebra Institute. In D. Kuchemann (Ed.), Proceedings of the British society for research into learning mathematics (p. 49-54). University of Northampton, UK: BSRLM.
Lavicza, Z. 2014: http://prezi.com/5c29843f3lgq/serbia-community-research- geomatech-april-2014/.
Lavicza, Z., Hohenwarter, M., Jones K., Allison L., & Dawes M. (2010).
Establishing a professional development network around dynamic mathematics software in England. International Journal for Technology in Mathematics Education, 17(4), 177-182.
Lavicza, Z., & Papp – Varga Z. (2010). Integrating geogebra into IWB
equipped teaching environments: preliminary results. Technology, Pedagogy
and Education, 19(2), 245-252.
Prenier, J. (2008). Introducing dynamic mathematics software to mathematics
teachers: The Case of GeoGebra (Doctoral dissertation). Retrieved from Google Scholar.
 Please, check the link: http://www.geogebra.org/cms/tr/download/
We are experiencing a transition from 20th century to 21st century in education. We have been discussing 21st century skills, curriculum change, new pedagogical methods, educational technologies etc. Lots of ideas, theories are on the table and due to enormous speed of change in technology more is on the way. While we are focusing on the big picture we are missing (or maybe ignoring) some little things which might seem insignificant but actually has an enormous effect on teachers’ lives.
The one that I’d like to share with you is about digitalising our notes. As mobile devices occupy more and more space in our school life more of our notes and materials are getting digital. This situation leads us to a very important problem; “finding the most efficient filing system”. With physical materials it is easy to put your notes together under different folders and arrange them in shelves. But when it comes to digital notes, things don’t work smoothly.
The main reason of the flaw is still having physical notes and materials. I don’t know you but I still couldn’t finish the transition of my notes and materials to the digital world. When you stop for a moment and think about this it doesn’t make sense. It seems that both types can be kept and organised easily but somehow it doesn’t work. I sometimes can not find necessary documents whether they are digital or not. Thanks to technological solutions (laptop, tablet, flash disk, cloud storage etc.) number of places I should look at increases. Even these platforms are synchronised continuously still I encounter problems.
Another reason is the instability of the apps and programs we use. Papers, files, folders have not changed much and we learned how to use them efficiently in time but their electronic versions keep on changing. User interfaces (UI), features, pricing conditions, synchronization methods, policies,… everything is subject to change anytime. When you just get used to it bam! you receive an update and something you liked a lot is gone or changed for ever. Not updating apps and softwares might seem to be a solution but actually that’s not. If you don’t update your device it will be vulnerable to malicious attacks and if you update only system files for security concerns the apps won’t be able to work flawlessly with newer version of the system. Assuming that you resist and did not update anything. That’s fine but how do you think your device will act when you install a new app which is programmed according to the latest software version of your device? So as you see updating and changing the apps is inevitable.
Another problem is the excessive number of digital tools. It is a known fact that people are discouraged when they are given a lot of choices. If you make a search on “note taking apps” or “lesson creation apps” you will understand what I mean. Although I have mentioned a negative situation I see that many teachers I talked to prefer to stick to their initial choices unless they come up with a different tool which creates a real difference for them. So it seems like problem is solved, right? Well, unfortunately not. A teacher prefers to use the tool A and another teacher uses B, another one uses C and so on. They create notes and materials, share it with students and expect (not force) them to use the same tool. Now this is a real problem because it includes students as well. We consider students as experts when it comes to use computers and mobile devices but actually they are not because we want them to use these devices for academic purposes and they don’t know how to do that properly. So teachers using different tools are not making their lives easier. This problem is not like the others because it is manageable and could be solved through communication among administration, coordinators, IT department and teachers.
How can we manage this process and pass through the transition with less damage? Let me keep the answer of this question for the next article.
“??Internet of Things?? What?” This is the first reaction I get from my colleagues. They don’t like to hear technical-technological terms and it takes me a while to convince them to think over it. Internet of things is a concept not directly related to education system today but it will be a part of it eventually because it will have a major role in our daily lives.
Let’s start with the definition of “regular” internet. You use it every day for multiple purposes. It’s on your computer, on your mobile device but can you write down a clear definition for it? Please pause for a moment and try it.
If you are done please compare your answer with the definition given in Wikipedia:
“The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite (TCP/IP) to link several billion devices worldwide. It is a network of networks that consists of millions of private, public, academic, business, and government networks, of local to global scope, that are linked by a broad array of electronic, wireless, and optical networking technologies.”
This is what I understand from this definition;
- The Internet is a global network system.
- It connects computer networks worldwide.
- It follows its own protocol to link devices.
- Every institution has its own network and internet connects these networks together.
- It does its work using different technologies like wireless systems.
To my understanding Internet works like this; Google has a network which includes an emailing service. Internet helps me to connect my computer to Google’s network and use Gmail. That’s it. Not very complicated right?
In 1998, Reza Raji asked a good question: “What if the Internet was allowed to go beyond connecting desktops and laptops and could somehow be tied to the devices around us?”  Inspired by that question let me change the above definition:
“The Internet of Things is a global system of interconnected things (daily objects) that use a protocol suite to link several billion things worldwide. It is a network of networks that consists of millions of private and public networks, of local to global scope, that are linked by several networking technologies.”
Here is an example to make it less technical. Think about a smart home where electiricity, heating system, refrigirator, garage door everything is controlled by a remote control or a voice recognition system. This is a local network of things. Assume that you have a similar network in your office. These two networks are separate but when you connect them to each other you will have an internet of things. With this connection all these things act like one single system. They are physically separate but digitally one.
It is obvious that Internet Of Things will have a major role in our daily life and it will shape the future. Next step for us is to start discussing how it will affect school life and educational technologies. Below you can find two great (and short) videos to help you understand the concept better.