Like the saying, “teaching is learning”, while I investigated the topic
plane vectors and reorganized them for teaching, I could have an
opportunity to solidify my understanding about the topic. When I tried
to use technology to create an mathematically meaningful unit, I
on keeping its mathematical and pedagogical fidelity as well as
promoting students’ interests with visual effect. Initially, I was
challenged at finding the better technology for the topic. Among
several types of technologies that I experienced, I chose Geometer's
Sketchpad (GSP) software and I thought about how to use it in order to
maximize students' understanding and motivate them. However, I’m not
sure yet if there would be better software than GSP for it.
I found the topic I chosen was a little difficult to
see dramatic effect with using GSP. One reason can be lack of time
given to me, but I guess that is mainly because the topic does not
require complicated cognitive process in students' minds. It requires
basic geometrical knowledge, operation laws for adding, subtracting,
and multiplying quantities, memory for cosine laws and so forth.
That is to say, without using tools, the topic can be well learned by
students, compared to other topics. Nonetheless, I could see some
advantages in that students not only can save their time to investigate
vector operation, find operation laws, and understand basic concepts
but also can reinforce their learning by confirming their conjectures
using the vector tool provided by GSP function with visual effect.
The more I investigate GSP to represent mathematical
ideas, the more I need to learn about it to do so with knowing
functions provided by GSP. I was thinking about what software would be
the best and what is required to visually represent the ideas of three
dimension vectors to help students' understanding. I think we can find
some ways to do it by using GSP although much time is needed. The scope
of GSP use has gone beyond my expectation until now.
I believe that developing teaching resources with
using technology, which is German style research, “stoffdidaktik”, can
provide a direct and practical contribution into teaching and learning
environments. I found NCTM e-examples about the topic vectors were poor
at touching the main concept for the topic. Such works, therefore, are
needed for the all mathematical topics. That is one of the important
parts that mathematics education courses provide in terms of the needs
of the times.