Reflection: Diverse Entry Points Compare and Contrast Graphs of Rational Functions - Section 2: Investigation and New Learning


I have now tried teaching this lesson two different ways. The first year, my students compared and contrasted the graphs of the functions without access to graphing technology. The second year, they used graphing technology to make the comparisons. To be honest, I still am undecided about which is better, mostly because I think there are advantages to each strategy. 

When students did not have access to graphing technology, this task took much longer (obviously) and students spent much more time figuring out how to choose inputs, and calculating outputs, and plotting points, which took forever. On the other hand, I think that they do get a deeper understanding of how the function actually works by going through this process, but I have no real evidence of this. I am still curious about whether or not that is true.

When students were able to use graphing technology, they could figure out how the different parameters affected the graph in almost no time, so this was much more efficient. However, I am not sure that they would be able to graph one of these functions without the technology and I feel that to truly master a skill, you would be able to do it on your own, without requiring technology. 

 I am still torn about this--I want to use the advantage that technology gives us, but I don't want to lose any of the engagement with the actual numbers that might foster a deeper understanding. 

  With or Without Technology?
  Diverse Entry Points: With or Without Technology?
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Compare and Contrast Graphs of Rational Functions

Unit 6: Rational Functions
Lesson 8 of 10

Objective: Students will be able to compare and contrast the graphs of rational functions in the form y=a/(x-b)+c and describe the differences and similarities of these graphs using academic vocabulary.

Big Idea: Engage students in the higher-order thinking task of comparing and contrasting rational function graphs using academic vocabulary while reviewing all essential skills of the unit.

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Math, Precalculus and Calculus, rational function
  70 minutes
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