Editing of Old Articles

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.

Understanding the Meaning of Absolute Value

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. » Read more

The Dancing Triangle and Its Applications

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.  » Read more

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