Module 2: Perceiving

 

 

Re-Imagining the Perception of Graphical Representations of Linear Equations

 

 

 

 

 

 

 

 

 

 

 

 

         

 

The cognitive tool of perceiving is the means through which we understand a certain theme or artifact of a given topic.  This could be visual perception, aural, touch, taste, or even a mental perception imagined completely within the mind.  Algebra is a mostly abstract field of study due to its nature of taking the concrete, generalizing it, and then utilizing these generalizations in order to solve new problems or discover new information.  I specifically looked at the topic of reading graphical representations of linear equations for my topic area artifact.  A graph of an equation takes the abstract equation and gives it a visual representation and therefore when observing linear equations it is traditionally a visual experience.  We can see the slope of the line and understand that this is communicating a rate of change between two variables.  Where the line crosses the intercepts is an important observation to make of linear equations as well because it tells us where we are starting at in the case of the y-intercept or it tells us the root of the equation when we observe the x-intercept.  When observing linear equations we also can alter the equations and observe movements of the graph.  For example, as we increase or decrease the slope in the equation the angle of the line will rotate and be increasing at an upward angle from left to right as the slope increases or as we decrease the slope the line becomes less inclined from left to right until it passes the horizontal threshold and begins to decrease from left to right.  We can also change the y-intercept of an equation and observe as the line moves vertically up or down. 

 

Being that reading graphs of linear equations is primarily a visual experience I decided to re-imagine the perception of linear graphs to be an aural experience in addition to the visual.  I wanted to communicate the idea of how a greater slope means a faster or greater rate of change.  I measured the beats per minute of a song I acquired on a royalty free music website called Bensound.  I then used the free audio editing software Wavepad to change the speed and pitch of the music to higher and lower beats per minute.  Knowing these rates, I was able to use the free software Geogebra to graph the linear equations relating to the different versions of the song.  Finally, I organized the music and graphs into a presentation, which combined the visual and aural senses to enhance the understanding of rates of change in graphs.

 

This new imagining of graphs of linear equations allows people to take a visual image and perceive it aurally.  Using music, however, goes beyond just stimulating the sense of hearing because music is more complex than just a sound and has the power to elicit emotions from the listener.  Thus the listener/observer can actually see, hear, and feel the slope or rate of change of the equations and graphs.  This produces a deeper and richer understanding of slope and its graphical representation.