Schultz, K. T. (2009). Soft drinks, mind reading, and number theory. Mathematics Teacher, 103(4), 278-283.
In this article, Schultz describes the experience he had giving his students an opportunity to experience proofs as more than just verification of what they already know. The students in his class were amazed by a mind reading game that used arithmetic of multiple digit numbers to correctly guess a selected number. Having figured out for himself the math behind the magic, Schultz used the curiosity of the students as an opportunity to teach them a different aspect of proofs, using them to find answers and gain understanding. With a little guidance the students were able to figure out the mind reading trick and then proceeded to prove the process to further understand the process. They learned what properly constitutes an accurate mathematical proof and the lesson demonstrated an example of the necessity of a proof naturally arising to gain understanding.
I agree that learning of proofs as a source to gain understanding is very important and useful. The students curiosity seemed to really motivate them to find the answer they were looking for. I am very impressed with Schultz ability to recognize a golden opportunity to get a confusing concept through to his students and to pull through.
Thursday, March 25, 2010
Thursday, March 18, 2010
#6
Switzer, J. M. (2010). Bridging the math map. Mathematics Teaching in the Middle School, 15(7), 400-405.
Switzer talked about Bridging the Math Gap between elementary, middle, and high school math by building off of what students have already learned. In order to do this, teachers must know what and how their students have learned in previous schooling. This is necessary for students to be able to make connections between concepts from different math classes. Hence, middle school and high school teachers must understand what knowledge their students are starting with and build from there so students are able to see how to use what they already know.
I agree with Switzer's ideas and, as a student, I understand that learning based on information already learned is encouraging and makes new material much easier to understand. I just wonder what a teacher should do if they do not think that the way their students have been taught is the most effective way. I guess, they should determine whether or not it would benefit the students to switch or try to correct what the students have learned to what they believe is the better way.
Switzer talked about Bridging the Math Gap between elementary, middle, and high school math by building off of what students have already learned. In order to do this, teachers must know what and how their students have learned in previous schooling. This is necessary for students to be able to make connections between concepts from different math classes. Hence, middle school and high school teachers must understand what knowledge their students are starting with and build from there so students are able to see how to use what they already know.
I agree with Switzer's ideas and, as a student, I understand that learning based on information already learned is encouraging and makes new material much easier to understand. I just wonder what a teacher should do if they do not think that the way their students have been taught is the most effective way. I guess, they should determine whether or not it would benefit the students to switch or try to correct what the students have learned to what they believe is the better way.
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