Reflection:

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 focused 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 by 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.