ASU MTE 494 - Overview (3 pages)

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Overview



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Overview

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Lecture Notes


Pages:
3
School:
Arizona State University
Course:
Mte 494 - Topic: Advanced Methods Teaching Math Secondary Schools

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Days 2 3 The mathematics behind what I intend to teach In a nutshell the concepts behind the mathematics that will be introduced to the students will be the formal definition of a function having a limit as x approaches infinity namely the statement f x has a limit L as x approaches infinity if and only if for every epsilon greater than zero there exist a real number M such that if x is greater than M then The key notion from this statement is the understanding that after a certain point on the graph if the function does indeed have a limit the subsequent points should be restricted or bounded between a certain error or tolerance Indirect to these concepts students will be very briefly introduced to reading math symbols and translating mathematical expressions e g into written sentences although this is only a minor stepping stone to the overall concept of a function having a limit as x approaches infinity Ideas I want my students to learn and the ways of thinking I want them to have I want my students to be thinking about limits in the way the statement is written There s a certain order to reading the formal definition written above i e first one must consider any epsilon greater than zero next they have to see if such an M exist et cetera I also want students to think about the behavior of the functions at certain values of x s which in this case for limits a x approaches infinity I want my students to consider the function only after certain M values What they should be tuning into is the fact that the function remains bounded for a lack of a better word around the limit value after a certain M value Moreover I want my students to understand that this M value isn t anything inherently special Certainly at times for many functions M may be defined as an odd messy function of epsilon but the important thing I want my students is understand is that we only need just one M value for every epsilon to work by work I mean that the function stays bounded between for x M



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