Mathematics and Media

Math, math everywhere…It’s in the beat to the music on the radio, the speed my car travels as I zoom home, the statistics of the presidential poll on the nightly news, the calories and carbs we count for each meal…the list goes on and on. One thing that I think is important to note is the distinction between numbers and math. Room 319 designates the room a class meets in, as opposed to Room 320, but is there really any math involved? Of course this goes back to our discussion on what is mathematics.

As far as the use of math in the public domain, let me preface my comments by saying that I am an ostrich and very much disconnected from the media so my comments may be a little elementary. In the media we hear of math largely in the form or statistics and probability (for those that distinguish between the two). We hear about the probability of rain and sunshine in the nightly weather report. Commercials are filled with statistics on the likelihood of pregnancy, cancer, heart disease, adverse reaction to a medication, etc. We here about the popularity of individuals based on “polls” (I put it in quotes, because no one has ever called me and asked my opinion, have they called you?) Often though the math is done for you and the message is explicated stated or implied to you. Often the observer does not do the math, but simply accepts the reporter’s remarks as fact. I think that is one of the beautiful things about constructivism. If we will really get a hold of this concept, we can produce future generations that will critically think about what the media portrays as fact.

Limitations on Student-Centered Learned

One of the biggest problems I have encountered in trying to implement student-centered learning is students’ unwillingness to think for themselves. Students have been programmed not to think. Often I have made the statement that I didn’t learn to think until I got to college. Students were told how to do a problem and expected to follow the procedure. (Again that’s what I liked math, right?) Those that could grasp the procedure were fine, the ones that couldn’t were left behind. By the time they get to middle grades they don’t even try. Our textbook has been so empowering though. Even for me, I’m learning things. I want to go back to my school and teach these basis operations again – the student centered way. We spend so much time in our curriculum re-teaching the same old way, and students still don’t understand it. When I see the strategies in the book, I am totally buying into it. The way I plan to engineer the shift from limitation to constraint is to first recognize that this is prevalent. Secondly, I plan to begin with something simple, like an addition problem where they can’t use traditional methods. By giving them something early that allows them to be successful, I believe this will empower them to continue to try.

The effects of constructivism on my thinking

The idea the math is not simply a set of standard rules and formulas is one of the most radical, maybe even revolutionary, ideas that I have heard. I liked math because I thought it was so structured, so black and white, so clear cut. I thought the objective of math was to get the right answer. I liked it because it did not appear to be subjective. This class has caused me to rethink my ideology. In ways it has pulled my foundation right out from under me. But the interesting thing is that I don’t feel like my world is falling down. Just as quickly as the old ideas are crumbling – or at least let’s say the fallacies and inconsistencies are become apparent – new ideas are forming to replace them.

As I have previously stated, I tried to implement the new constructivist ways (although I didn’t know that’s what it was called at the time), but I also tried to keep the traditional way as well. I wanted to live in both worlds, but that will not work.

A constructivist classroom looks like ordered chaos. Students are engaged in mathematical discussions and activities. Each group may be doing something completely different in their efforts to hash out their ideas. It is such a contract to traditional classroom where at any given moment you should be able to hear a pin down. It is also different because it eliminates the plug-and-chug approach. The importance is not solely on obtaining the correct answer, but obtaining and retaining the key concepts needed to derive the correct answer. Oh, how I long for this in my classroom.

June 14 - My Student and Teaching Experiences in Mathematics

My experience in my mathematics has been very much along the traditional lines. While I was a student in middle school and high school, my math classes followed much of the same routine. The teacher went lesson by lesson from the textbook, we copied notes and were assigned nightly homework problems. The next day, we would discuss the homework from the previous night, then proceed to learn the next lesson. This was not very hard for me because generally it was memorization of a formula and plug-and-chug from there. When I did question the why (in geometry), I had a teacher that could not answer the “why” in terms that I could understand.
When I started teaching last year, I went into the classroom with the preconceived idea that teaching mathematics was just like I had learned it. I do not recall ever hearing the word manipulative before I started teaching and I certainly didn’t have a clear understanding of how to implement them in my lessons. When I was introduced to GPS, I loved it, but had a very hard time implementing it in my classroom. I felt like I still needed to teach the students the procedures/material first, then give the problem-solving task. In addition, I had late afternoon math classes and a lot of discipline problems. When I would try to do problem solving task they generally flopped.