Revelation

  Today, I started teaching function notation to my Algebra I classes.  They got as far as learning to take the value given and substituting it into the equation to get an answer.

After class, I realized I need to take this one step further by having students connect the input and output as giving a location on a line.

I fear I am guilty of teaching functions, function notation and linear equations as separate entities rather than showing their relationships.

I found a wonderful chart, I wish I had to introduce functions. It gives examples such as selecting K on a snack machine after putting money into it (input), the machine processes the information, and a Twix candy bar comes out. (output) or A zero on the phone is pushed (input), the phone sends a signal to a receiver (process), and the operator answers (output).  Practical examples of input, process, and output.

By introducing the topic this way, it identifies prior knowledge that can be built up.  It is easy to relate this to the value for x being the input, substituting the value for x and doing the math in the equation, with the output being the answer.  Once students learn function notation, the next step would be to relate this to a graph. 

Since functions and graphs are related it is important students be taught the two together so they get a chance to understand the connection.  In addition, its nice to relate function notation with an actual value representing a point on the graph to that point. 

When I went through my teacher training program, the world still treated this topics as separate topics.  In fact, most of the math I taught was taught in isolation from other mathematical topics.  So as I read, think, and reflect, I find more and more connections I try to share with my students.

Once I get students used to thinking in terms of function notations, functions, and graphs, I want to take them to the next step showing the four ways points can be represented but I hope to do it so they see the representations are related. 

I'll let you know how this goes.  I'd love to hear your thoughts.  I'm off.  Have a great day.