Logo Success

I just had my 4th graders use Logo for the first time and they LOVED it! I gave them a quick overview of the basic commands and then just let them experiment. They worked in pairs, which I think was very helpful, and even my most unmotivated students were totally into this. After they were comfortable moving the turtle around, I challenged them to make a shape. One pair of girls made a square within a couple of minutes. That impressed me! Other groups were eventually able to make a square, rectangle, and some even got really close to making a triangle. Their success with this program makes me wish I had tried it earlier. We are moving onto some Algebra concepts for a couple weeks, but later I will be teaching area and perimeter so I will definitely be using Logo at some point during those lessons.

Slavit Article

I just finished reading the Slavit article and it, again, stresses the importance of exploration of geometric concepts. I remember learning about these properties in high school and I recall that I was told they worked, probably shown a proof that I didn't understand, and required to memorize them. I also remember that I promptly forgot them when the semester was over! I agree with Slavit that triangle similarity should be explored and investigated so that students have a better understanding of the concept. However, it seems to me that the activity would probably not go quite as well in a middle or high school as it did in the college course. Even though the students in the course had probably not worked with triangle similarity since high school, they had done something with it before and would have at least vague recollections of that. These concepts would be brand new to middle or high school students and I think they would struggle with the ideas a little more and perhaps need a bit more direction in exploring the triangles. I do like the idea of using Sketchpad to explore this because it will show the students how side lengths may change but angle measures do not, and that is something that is difficult to do with straws or pencils.

Spring Break

My spring break is March 23-27. I am visiting my best friend in Wisconsin who is due March 3rd with her first baby.

Article Reaction

I fully agree with the article on finding triangle centers. I believe that students often need to have a real world situation in order to understand geometry, as well as most other mathematical skills and concepts. Upper level geometry, in particular, can often lead to the the famous "When I am ever going to use this stuff?" question. By engaging students in problems like the sprinkler and amusement parks question, they can see a real world use of angle and perpendicular bisectors. This motivates students and encourages them to explore the concepts much more than a textbook lesson and worksheet on a skill that seems unnecessary.
I am always trying to think of real world examples to use in my math lessons for elementary students. Some things are obviously easy like addition, subtraction, rounding, and area but other things are more difficult. How do I convince 4th graders that they need to know prime numbers? Other than, "Because you will need that information in middle school!" I think that finding these investigative type of problems is difficult, especially for the elementary level. If anyone knows of a good resource with LOTS of investigative problems for K-5, please let me know.

The Definition of Polygons

My objective today was to teach the definition and properties of a polygon. If I'd chosen to use our textbook (the dusty thing that sits on my shelf) this lesson would've been quite quick because I would have simply read the definition to the students, given them some examples like a square, triangle, and regular pentagon, and assigned them a simplistic worksheet. HOWEVER...I chose to have the students create the definition and properties on their own. I used a "Are/Are Not" chart where the Are side has examples of polygons and the Are Not side has non-examples. I started with a simple triangle and rectangle on the Are side and an open triangle on the Are Not side. As a class (I only have 10) we began discussing what the columns had in common. The students quickly agreed that one property is "closed". I added some more figures, had more discussion, and students came up with "straight lines", "flat," and "3 or more sides." After about a half an hour of discussion on these examples and non-examples, I finally gave the word polygon to the students and discussed that the Are column are called polygons and follow the rules that they created. I then had students draw a figure of their choice in either column and justify their reasoning. They did well with this activity. I'm hopeful that this will be more meaningful to the students and that they will be able to recall the information later in the unit. Heck, I hope they can recall it tomorrow!

Random Thought

Without intending to, I identified 1 of my student's VanHiele level today! We were doing a daily review before my lesson today and one of the questions asked about a square pyramid. I showed the class a square pyramid and asked why it was a pyramid as opposed to a prism or something else. One boy said, "Because it looks like a pyramid!" Internally, I chuckled and thought "Hmm..VanHiele Level 0!"

Technology

As I explored more with Logo this week, I discovered that I had to think more than I thought I would! Many of my predictions were incorrect, and I realized that this program was very useful for making students really consider what they are telling the computer to do. For my 4th graders, I think that Logo will be a little bit difficult for them because they are just starting to learn about angles. I will use it, but probably towards the end of the unit. I will, however, definitely be using Sketchpad as much as possible. I think that it helps students explore a lot of geometrical concepts and the dynamic aspect of it really motivates them. We are fortunate to have a SmartBoard at my school, so I am hoping to bring that in and allow students to work with Sketchpad in that manner.