The Power of the Slider – Understanding Math through Geogebra

Among the hated subjects in schooling is math. It is difficult and challenging. You need to be gifted to be good at it, or understand it easily. I may perhaps agree with the former, but I beg to disagree with the latter. Recently I found a very useful tool in making math easier to understand. It is among the fruits of technology, so my apology goes to the oldies- those who weren’t fortunate enough to have fruits available for harvest then.

Now for those who hate math, I would like you to meet Geogebra (merge of geometry and algebra), an application program designed to simplify matters concerning numbers and graphs. They say the best things in life are free. Geogebra is pretty much one of the best things- it is a freeware. You may download the program from this site: http://www.geogebra.org.

The program looks like this:

 

Looking at it you may have thought it will not be easy to use the program. In this article, I do not intend to teach equations or programming, as you may have also guessed they are needed to make this program work. In just about anything, we want only the best. I thought of extracting perhaps some of the best of this program and that is what I am to lay down for you. Thus, this article is practically for everyone- teachers or students, lovers or haters of math.

This program work much like usual Windows programs do. There is menu bar and toolbars whose purpose can be seen by pointing your mouse over them.

 

I argue that the key in optimizing this application is working on the slider. The slider is found in one of the toolbars. Selecting it and clicking on the drawing pad (the white area, where the coordinate plane is), a window pops up asking for some values. Upon accomplishing the form, a horizontal segment (or vertical) with a point on it appears. The name you give on it serves as a variable (whose value dynamically changes when you drag the point).

 

The idea is that whatever math concept you may have failed to imagine or verify, you can clearly see with the use of the slider. The slider, serving as a variable, shows how a certain graph or function behaves as we change the values (or drag the slider). You can make as many sliders (or variables) depending on the need of the function or graph. As an example, we use slider to study the graph of the sine function (one of the trigonometric functions). To graph the sine function, we simply type the function at the bottom of the screen where the “input” is. Pressing enter gives us the graph of the sine function.

 

We verify this true from our trigonometry class in high school. The graph of the sine function is a wave. What we want to know is how the sine wave behaves if (1) there is a multiplier “a”, (2) there is a divisor “b” in the angle, and (3) if there is an addend “c”. Thus, our function is redfined as “f(x)=a sin(x/b) + c”. We can only wonder how these three variables a, b and c affect the sine wave. With the slider, however, this will be clear. Now, as we have a slider “a” already, all that’s left is to construct two more sliders and redefine the sine function. Redefining the function is done by right clicking the function on the left and seleting “redefine”.

 

With the sine function redefined, we note that the function is actually moved from the free objects folder on the left to the dependent folder. This is because the graph of the function this time depends on the values the slider have. Our graph is now dynamic.

 

We can move any of the sliders to see the effect of changing the values of the multiplier/addend to the sine function. For instance, increasing the value of “a” gives the wave more altitude. Hence, the graph is taller. Setting the value of “b” close to zero makes the period shorter, thus the graph repeats right away.

 

This is something we may have not understood well in our trigonometry class before. With geogebra, it is easy to see and understand the concept. Among the other topics you may want to explore using the slider are: the circle, the line and its slope, the parabola, and so on. They key is the slider. For the line concept, you may create slider for slope and intercept.

I am still new to this program but upon discovering the slider I thought I found the main feature. The slider makes graph dynamic. If students of today are learning through pictures, they will certainly learn more seeing something that moves. This is technology today, providing what we perhaps can only imagine before. This is geogebra, redefining the teaching and learning of mathematics. This is the power of the slider.