Mathematics and Multimedia has been silent for the past four months because I am busy, but I have silently edited old articles. I will continue editing and one of the improvements that I am planning is to integrate GeoGebra applets in some of the articles since GeoGebra can now be directly embedded in WordPress posts. As many of you already know, I have numerous tutorials on how to use GeoGebra. In addition, I am also updating the tutorials using the current version of GeoGebra. There are many new developments particularly the integration of augmented reality.
I started this blog 9 years ago and, so far, I have written more than 1000 articles. Many of them are on using GeoGebra and many also contains discussion about mathematics content from elementary school to university mathematics. Numerous times, I have also introduced apps that can be used for teaching and learning mathematics. The complete list of all the posts can be found in the Archives page.
Starting today, I will be sharing more about mathematics teaching and mathematics ago. I had been hesitant to share my thoughts about them because I felt that I was not qualified to do so. Recently, I have realized that maybe, there are a few things that I can share from more than one and a half decades of teaching and training. Hopefully, this blog will be of help to younger teachers or at the very least a trigger for reflection and discussion.
One important concept in algebra that we learn is the distance between two points on the number line. In particular, we study the distance of a point that corresponds to a number to the point that corresponds to 0. In the following figure, the point (or circle) on the left represents 0, while the point on the right represents 5. To simplify our language, we will use coordinates to refer to its corresponding point on the number line. For instance, we will use -8 to refer to the point that corresponds to -8.
Looking at the number line, it is easy to see that 5 is 5 units away from 0 and that -8 is 8 units away from 0. We can also see that 0 is 0 units away from 0. The distance of a number from 0 on the number line is called its absolute value. Hence, the absolute value of 5 is equal to 5, the absolute value of -8 is equal to 8, and the absolute value of 0 is equal to 0. Continue reading
I started using an Android phone three months ago and since then, I have been searching for some apps that would fit my needs as a teacher. One of the apps that I have been using which was really useful to me is Foldersync. It enables you to sync your cloud storage with your local mobile phone storage. You can also use it with your phone’s SD card.
What I like most about Foldersync is it enables you to sync a specific folder and not your entire cloud storage with your phone. In my case, I only have a 64GB storage, so I did not want sync my entire Dropbox to my phone because it will take up a lot of space. I use a specific folder to sync my electronic books folder on my Dropbox and my phone.
Foldersync at Google Play Store
Foldersync supports the following locally and on the cloud: updating of files, copying, moving, and deleting files, and creating files and folders. Although I have not tried it yet with other cloud storage, it works perfectly in my experience with Dropbox. It has a free version (the Foldersync Lite) which contains ads and it also has a premium version. I’ve been using the free version for three months already and I am perfectly satisfied with it.
Foldersync is also compatible with Google Drive, Amazon S3, Godaddy, Amazon S3, OneDrive, OneDrive for Business and many others (see full description on Playstore). It is available for Android users and can be downloaded from the Google Playstore. There is also a very detailed setup guide at the How To Geek website.
In the figure below, lines l and m are parallel lines. What can you say about the areas of triangle ABC and triangle ADC?
The distance between two parallel lines is equal at any point, so the two triangles have the same altitude (can you see why?). Further, the two triangles have a common base, therefore, their base lengths are equal. So, the areas of the two triangles are equal. In fact, you can choose any point P on line l and the areas of the triangle ACP will always equal to the areas of triangles ABC and ADC. We like to call this triangle the dancing triangle because using an applet, you can dance it by moving P without changing the area. In the applet below, move points B and D to dance the triangle. Continue reading
I’ve been really busy in the past months due to my studies. In this post, I am going to share to you one platform that I have learned in one of my courses.
One of the platforms that we used in one of my courses this trimester that might interest teachers is Canvas. Canvas is an online platform that can be used for peer review. Using Canvas, students can comment on other students’ homework such as term papers and essays. Here’s how Canvas works:
1.) Teacher and students create their Canvas accounts.
2.) Teacher creates a course/classroom.
3.) The students join the course/classroom
4.) Students submit work in Canvas.
5.) Students comment and give marks to other students work.
One of the interesting thing about Canvas is that the teacher can set the comments anonymously. Aside from the comments, students can also give marks based on the rubric created by the teacher.
I have not explored the full capability of Canvas yet, but I think it is a very good tool for peer review.
It’s FREE, so you should try it.