Monday, May 26, 2014

Creating a Tessellation

In class I was not having much luck creating a tessellation, so I decided to work on that for my weekly work this week. I went to the "Islamic Tessellations" link and chose to look at a YouTube video on "How to Make an Islamic Tessellation." I went through the video, and thought it might be easiest if I just do it on dot paper. However, it was a lot harder than I thought and I decided to switch to Geogebra shortly after, which make it a lot easier since I was using so many circles. 

I started out by making a central point with two lines perpendicular to each other, and where the lines intersected I made the center of my first circle (this is shown in my screenshot below).

I then began overlapping circles in the way shown in the video I watched. I went all way across the screen and up and down the screen.

I did this by making the center of the first circle a point on my next circle. This created the flower-like pattern in the center of the circle, which I really liked. It doesn't really show to continue to repeat the flower pattern in the video I watched, but I chose to continue you the flower pattern to kind of make it my own design. 

I then added lines that ran through the center of flower petals. these lines were at a diagonal, and were parallel to each other, and then I added another set of parallel lines that were perpendicular to the first set and also went through the center of petals. I also made a square with the polygon tool to enclose the flower inside of it.

After I titled with the smaller circles, I decided to overlay larger circles of different colors in the same pattern. I decided to have a little fun and made different color patterns as well, and it ended up looking pretty cool.

I added more circles and scrolled out a little so that I could add more lines to intersect the petals like I did before. I also messed with the colors again.

Lastly, I wanted to make polygons around my bigger flowers like I did with the smaller flowers. I also hid all the points when I finished just for looks.

I was struggling to come up with an idea for a tessellation in class, but watching the video on how to make tessellations really helped me to understand how to make the tessellations work in Geogebra. The video gave me an idea of how and where to start, and then I was able to come up with my own creation just by having a little direction. I am really happy with the way my tessellation ended up looking, and I am glad I had fun creating it, rather than getting frustrated. 

Thursday, May 8, 2014

What is Math?

So what exactly is math? Often, math is seen as a subject that not many people have interest in. Its complexity can be overwhelming, and one bad impression with math can often turn people away. When I think about what math is, it is hard for me to give a formal definition because it a very broad concept. There are so many elements and components of math, so it can be taken in many different directions. It is also subject of interpretation of the person defining it because it is so broad. Some have much different ideas as far as what is math and what isn't math.

It is so hard for me to try to even think of a formal definition of what math is. However, if I was to have to give some kind of definition, I would say that math is the discovery of patterns of change that help us to explain things that happen in the world around us. It can use a range of levels of thinking, from logic and reasoning to simple calculations and calculations using algorithms. There are so many parts that I know I did not talk about, but we could be here forever discussing the amount of information that math encompasses. So, to me, math is a very broad topic containing many larger topics within it, and it focuses on the patterns among the topic of study. From this, we can explore the change in things all around us. 
The top milestones in the history of mathematics that I feel like effect me the most, based on the fact that I am going to be a teacher, is kind of hard to narrow down. There are so many important milestones in the history of mathematics that will effect me as a teacher, and have effected what I am going to eventually teach, but I think there are definitely some that I can say are going to make the explanation of a pattern much easier and things that will aide my students in their discoveries with math. So, if I was going to give a top 5, I would say they would be...

1. Algorithms: These are an important tool to teaching lower elementary and middle school math. It is obviously most important that when using the algorithms with students that they actually understand why and how the algorithm works, but once they do, they can make computing in mathematics that much easier and less time consuming. 

2. Modeling in Mathematics: I don't know if this tool is really considered an important milestone in the history of mathematics, but I definitely think that it is an important tool for understanding mathematics and that is why I mention it. Modeling in math gives a picture or imaging explanation of a problem. In teaching math, I cannot express how important it is for students to be able to do this! It helps with their reasoning and understanding so much, and benefits the teacher as well, by giving us a look at how they were thinking and reasoning with the problem. 

3. Pythagorean Theorem: This is important in my mind, because this is one of the discoveries that I am sure I will be teaching a lot, when it comes to geometry. This makes it easier for students to work with triangles while learning geometry. 

4. Euclid's Theorems: These are important, again, because they help students reason with shapes in geometry. It gives students this idea of reasoning with shapes through components that they have. It helps to see congruence in shapes, and gives a concrete reason why they are or are not congruent. 

5. Calculator: This seems like a silly one to put on, but calculators are such a useful tool to us while doing math. Sometimes they are overused for simple calculations, but they can be so helpful for making math more efficient, especially time wise. There is so much that we can do with them that is helpful to us, and therefore, is an important milestone in math history.