The end of the semester is here, and that means class reflection and evaluation time. I must say I feel this blog assignment added a lot to my class experience. First of all it's great to have such unique homework assignment for a math class, it makes the class less boring, as for as math classes go. Most students don't like long lists of problems to do for required homework, I know I don't. The blogs were a great alternative. In relation to the focus of the class, the practical teaching techniques, it helps see math in a different way. Up until this point I've looked at math from the student's point of view, I know my opinions on math (not a fan) and the critical thinking the blog posts give are really helpful in thinking like a teacher. I don't know if I'll continue blogging, but I enjoyed the experience. As far as the idea of using it in my own classroom, I feel the critical thinking behind some of the posts may be more appropriate for older students, secondary and high school. I'm more geared toward english, so I feel I may be a bit harsh.
All in all I think the blogs were a great contribution to the class. It really shows how math doen't have to be all arithmetic problems. It's a great opportunity to think differently and creatively and I feel I gained a lot, though I don't think it would be appropriate for an elementary setting.
Monday, December 17, 2012
Sunday, December 2, 2012
Geometric Constructions
A compass is more than just a tool for drawing circles. I remember as a student the first time I used one for that purpose, it was so cool. Later in school I learned all the other things a compass can be used for. Who knew something that made circles, when also used with a strait edge, can also be used to make triangles. That just blew my mind.
It is important to know how to use a compass and strait edge to create angles because with just these two tools, you can accurately make any geometric figure. As early as ancient Greece mathematicians were using these tools to solve geometric problems. In these times though, the compasses were collapsable, that is, they would close as soon as they were moved, and would not hold its radius. A Greek mathematician named Euclid formulated three famous geometry problems that for centuries went unsolved. The basis of these problems were to solve them using only a strait edge and compass.
the three problems are:
1.Squaring a circle
2.Doubling a cube
3.Trisecting an angle
It wasn't until a few thousand years later that it was proven these constructions are impossible to make using only a strait edge and compass.
In elementary geometry, we only go so far as to construct angles, triangles and bisectors, with these tools. Yet these same tools have been used for thousands of years to solve (or not solve) much more complex problems.
It is important to know how to use a compass and strait edge to create angles because with just these two tools, you can accurately make any geometric figure. As early as ancient Greece mathematicians were using these tools to solve geometric problems. In these times though, the compasses were collapsable, that is, they would close as soon as they were moved, and would not hold its radius. A Greek mathematician named Euclid formulated three famous geometry problems that for centuries went unsolved. The basis of these problems were to solve them using only a strait edge and compass.
the three problems are:
1.Squaring a circle
2.Doubling a cube
3.Trisecting an angle
It wasn't until a few thousand years later that it was proven these constructions are impossible to make using only a strait edge and compass.
In elementary geometry, we only go so far as to construct angles, triangles and bisectors, with these tools. Yet these same tools have been used for thousands of years to solve (or not solve) much more complex problems.
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