Technology

Technology:
I really enjoy using technology as a learning tool and so do my students (most of them). I have enjoyed working with Logo. Although it seems slow at times, it makes me think visually. I find myself picturing the turtle in my head and thinking about the direction I should make him turn. It also makes me think in my head about how far I should rotate the turtle to achieve the angle or direction needed. I also find that if you are precise when working with the drawings the activity encourages mental math. I find my self using multiple mathematical ideas such as the Pythagorean theorem to know how many turtle steps to take.
Logo:
I think this program would be useful in both middle school classes and in high school geometry. It would help students visualize the geometrical ideas and place them in control of creating the shapes. In order to correctly produce the shapes using logo students will have to understand the basic ideas and properties of the shapes.
GSP:
I have used GSP in the past and really enjoy working with the program. I used the program when I taught in middle school. We would use it to explore properties of shapes and their area and perimeter. I used the program to show students a proof for the Pythagorean theorem. We also used the program to look at transformations of objects. It was helpful to use the coordinate plane as a background and then we could look at rotations, translations, and reflections.
Vocabulary:
Vocabulary in Geometry is important just like it is any other class or setting. If we are a football game and you don't know what a first down is, then you are in trouble. If you don't know what a QB or a receiver is then you aren't going to understand the game. When you find yourself in a setting where you don't know the vocabulary it seems as though everyone else is speaking in a different language.
I find that some of my students are this way. On the surface it just appears that they don't understand or aren't trying. However, if I start asking questions, I find that the student has no idea what we are talking about. He or she doesn't understand the terms that we are using and therefore can't follow the discussion, activity, or examples. I also find that students may know a word or its definition, but they don't understand how to use it or what it really means. Example....I asked my Pre-Algebra students early in the year "what is area?", several of the responded by saying "length times width." I said, "no, that is the formula for finding the area of rectangle, what is area?" They again said "length times width." Many of students have partial understanding of concepts or ideas that we talk about on a regular basis in the classroom. This particular lesson wasn't even about area, it was just using area as an application of the idea. In conclusion, vocabulary is very important and it is important that we (teachers) meet students at their current level of understanding and work upward. As said in the Van Hiele article, if you speak in level 2 to someone who is currently in level 0 they won't understand what you are talking about regardless of how well you are explaining the idea.