Videos

I just got finished watching the side splitter video proof. Overall, I am very impressed with the students work. There were a few minor errors but the major ideas were correct. It's great to see that pre-service teachers are getting such great exposure to technology. I'm sure their students would much rather watch a proof created in sketchpad than one that the teacher writes on the board. And this is an idea that I will sock away for when I teach geometry.

Class on the 16th...

I really enjoyed last Monday's class. Much of the material was review for me but it was much needed review as some of my details on proofs are a bit fuzzy. I think the activities were great and are something I would definitely like to do with my class if I ever teach geometry. So overall, it was an edutaing class!

NCTM Research Chapters

I read both of the chapters from the NCTM book this week. Once again I am stuck but what a difficult job elementary teachers have. The idea of having to teach something as basic as using a ruler is mind boggling to me. Teaching calculus sounds like fun to me but teaching measurement sounds like a nightmare. I am very thankful that there are talented teachers out there who enjoy teaching things that I don't think I could.

Masters Project

Well, I think I have finally settled on a topic and it's not one of the original three ideas I had. I've decided to try to reproduce known fractals using sketchpad and maybe see if I can come up with some on my own. Since I have no idea what I will be teaching next year, I figured these would be fun to show my students in any class.

Reaction to Slavit Article

I really enjoyed the article by David Slavit. I think it was admirable that he wanted to create some abstract reasoning skills in younger students. The article also underlined the importance of discovering learning in mathematics. However it also highlighted how difficult it can be to allow time for discovery. The activities outlined are wonderful and allow students to form their own ideas about the principles of triangles and polygons. However the activities also show how much class time would be taken up by such activities. As outlined it would take several days to cover the congruence and similarity theorems. Unfortunately, teachers simply don't have the time to cover very many topics in this way. However I think it could be very beneficial to choose a few topics to cover in this manner because it allows students to make much stronger connections with the material.

Spring Break

I will be on spring break from around noon on March 6 until March 15. Only two weeks away! My only real plans are to go home to Illinois and finalize some wedding plans and have my first dress fitting! Besides that I hope to catch up on some work and some rest.

My reaction to the assigned article is ...

that the authors were right about many things. Students typically understand concepts much better when they are able to make real world connections, like with the sprinkler and the amusement park. However I think there was one aspect of the article that was absent that should have been present; how the activities went in the authors' classrooms.

I was disappointed that they choose not to discuss the students' reactions to the activities or the students' performance on the activities as compared to the more traditional assignment. I think it would have been interesting to do this a more of a comparative study. Students could have tried the more traditional activities and then the more real-life activities . Or have one class try one assignment and another class try the other assignment. This would have given the authors more concrete information about the success of less traditional assessments/assignments.

Finally!

I finally got the custom tool option to work for number 4 of explore more on page 101. I can now construct a string of successive midpoint triangles very quickly. Woohoo!

Masters Project

Right now I am torn between three ideas for my masters project. I thought it would be a lot of fun to create a house in logo or sketchpad and animate it. However I did want to come up with a more original ideas too.

Another idea I've had so far is to create a series of Christmas tree ornaments that display relationships in geometry, like parallel lines, vertical angles, and concentric circles.

The last idea I had was to recreate a series of board game boards (such as checkers/chess, darts, Monopoly, and Clue) using geometric constructions.

Right now I'm not sure which idea I'm going to choose but I'm looking forward to the project. It's going to be fun!

Frustrated

Right now I am extremely frustrated with Geometer's Sketchpad. I have been trying for a few days now to create custom tools and still cannot get it right. When trying to create a tool that will make a regular hexagon, all I can get to tool to do is draw a line segment. I thought I followed the directions from the help menu but simply keep coming up with line segments. Ahhhhh!!!! I'm about ready to give up the struggle except making tools would probably be useful in the future. With a full arsenal of tools, I'm sure I would be able do more in sketchpad. Plus, it would probably be something very useful to show my students when they use the program. So for now at least, I guess the battle continues. If it's not settled this afternoon, the situation might escalate into a war!

Vocabulary

I've always felt that mathematics is one part language and one part science. Geometry is no exception to the rule. Vocabulary plays an essential role in geometry. Students can easily get confused if they aren't up-to-date with the vocabulary. Concepts in geometry usually build on previously learned vocabulary. Trying to teach students about 3 space is difficult if they do not first understand the number line and coordinate plane. By using vocabulary at higher level than all students understand, it can make learning extremely difficult for students (as we read in the van Heile text). By using vocabulary at a lower lever than is appropriate, students won't be able to properly discuss geometric topics. Teachers must toe a fine line with making the vocabulary sufficiently challenging yet accessible for all students.

Technology

Technology has become a way of life. People are much less likely to turn to a newspaper to get the days headlines than they are to turn to the internet or TV. We are constantly flooded with information thanks to the technology that is available. Because of this, students are harder to reach the the old tried-and-true ways of teaching mathematics. I will admit, I was the same way in high school. I remember always having to bring my geometry kit with me to class. It included a straight edge, compass, and protractor, among other things. And while I remember being forced to carry it back and forth to my locker, I don't remember actually using it in class. However nine years later, I still remember using geometer's sketchpad to discover what it meant for a graph to have a "hole" and what a limit truly was.

Logo can be just as influential in teaching students about the basics of angles and lines that teachers often take for granted. So often angles are taught as a rotation of a ray from standard position to its terminal position. Because of this, it seems like many students don't really understand angles. And students are able to connect as much with the material because of the techology gap. Logo can give students a chance to test there ideas and get immediate feedback as to whether or not they are correct. Rather than having to wait to get homework or tests back, they can instantly see their mistakes and triumphs. They also get to make mistakes in a very safe environment. There isn't a buzzer or big red checkmark when they make an error. If things don't work out exactly as planned, they can simply start an new sketch and try again. These features make Logo a very useful tool that I hope to employ in my classroom.