Thursday, March 25, 2010

NCTM Article Number TWO

Hudnutt, B.S., & Panoff, R.M. (2002). Mathematically appropriate uses of technology. On-math, 1(2), 1-5

The main idea of this article is that technology should be used in classrooms because it can help students accomplish tasks they couldn't do otherwise. Students can use technology to see what happens to equations when algebra gets complicated and when it comes to the point that the arithmetic is hindering the teaching. When studying probability the computer can compute thousands of cases in seconds, when it would have taken a student hours to do the same thing. Students can explore lots of graphs and observe how changes in an equations change a graph very simply on a computer. The same effect may have been muddled in having to make so many graphs by hand had the students not had access to such technology. The author acknowledges that technology can have it's downsides with technical difficulties, but overall it is beneficial in the classroom.

I think technology is beneficial in the classroom. I think it allows students to explore complex ideas in a shorter amount of time. As was stated in the article, sometimes students forget what they are actually looking for and get lost in complex algebra. I am not saying that technology should replace arithmetic, but I definitely think it should be used in the classroom for exploration and for teaching the big ideas of what is going on at that point in the course. I have observed lots of classrooms with advanced technology for my 276 class and it is amazing the things we can do in with math and technology. The teacher can make perfect shapes that can show exactly what they were trying to show. This technology can also help with students who have IEP's and need the notes from class. The teacher can simply print off a copy of everything shown in class. All this and more are reasons I know technology is beneficial in today's classroom.

Thursday, March 18, 2010

NCTM article

Switzer, M.J. (2010). Bridging the math gap. Mathematics teaching in the middle school, 15(7), 400-405.

This article had two main ideas, first there is a gap between elementary and middle school learning, and second there are ways to bridge that gap. The author addressed the issue of a gap by stating that middle school experiences don't connect with elementary experiences. Often times middle school teachers don't quite know their students' prior knowledge. He did recognize that even though middle school teachers will often have a basic idea of what the students have or should have learned in elementary school, the school structure differences and other factors make it hard to communicate between elementary and middle school teachers. One of the ways he mentioned that can help fill this gap is for middle school teachers to become better acquainted with their students' prior knowledge. A way to do this is to encourage middle and elementary school teachers to work together and communicate students' learning. Much of the paper consisted of algorithms and methods to teach these algorithms that would help students better transition into middle school, thus helping to bridge the gap.

I agree with the author that there is a gap between middle and elementary school, and there are multiple ways to bridge that gap. More than just a gap between middle school and elementary school, there can be a gap between middle and high school learning of mathematics. From my own experience going into middle school is hard enough but sometimes the teachers presented material in a way we had never seen before in elementary school. Had they started with the math we knew and built off of that I would have felt much better equipped to learn. I found that to be the same when going into high school. For example I remember getting into high school and feeling as though I had never learned slope before. However I had learned it in middle school, it just wasn't taught the same way as it was in middle school so I had a hard time making that connectoin. Some of the ways this could have been fixed were mentioned in the article. It would be beneficial for the middle school teachers to communicate with the elementary teachers. This could have both schools working to better student learning in order to have a smooth transition between schools. Along with that I think that teachers should make an effort to figure out what their students know, and then build off that knowledge.

Haley Bly