Just a thought, but outside mathematics education, our students encounter
(in newspapers, TV, and magazines) data pairs and graphs as representations
of functions before they ever see the symbolic representations that we
study in the classroom. It makes sense to me that the math classroom should
mimic this process. This makes functions in symbolic form the last
representation our students study -- and then the most thorough. Graphing
calculator technology like the TI-83 make our work with data pairs and
graphs of these data extremely simple and understandable, even at the 7 -
8th grade level.
As for the question "But how do students know where the graph comes from?",
this also blends well into the data - graph - symbol approach. When we
teach in the context of real-world situations (data pairs), mathematical
ideas are much easier to teach and are easier to understand.
Related data pairs can be used in many different ways to help teach
understanding of mathematical ideas. For example, function behaviors such
as increasing, decreasing, maximum, minimum, rate of change, zeros, etc.
are best taught using data pairs students may relate to -- because of their
life experiences. Developing mathematical concepts in the context of
real-world problems often starts with data pairs. Each type of function
studied in a course can first be introduced in class with data pairs that
can be modeled by the function. With the TI-83 and its list features, we
can even explain the connection between data pairs and the mathematical
symbols (functions) that model them -- not using the black box approach.
Ed Laughbaum
_________________________________________
>(snip)
>
>The question I have for readers of this list; do you
>think it's OK for students to use Graphic Calculators
>while they are in high school???
>
>Regards,
>
>The Old Pro
>
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