Pendleton, K.L. (2010). Investigating the randomness of numbers. Mathematics Teacher, 103(5), 364-370.
In this article, Pendleton writes about the need to test the randomness of samples using statistical methods that are well known to those who study statistics. He explains that it is hard to test the randomness of a large sample, but fairly simple to test the randomness of a small sample. He goes through two tests to use in testing randomness. In the first you compare the sample mean with its population, and in the second you compare the sample's distribution with that of its population. He explains how these tests could be used in a classroom to teach finding the mean and standard deviation. Pendleton says testing samples for randomness will add to more confidence in the results found.
I agree that random samples should be tested for randomness. Nearly every time I read or hear the results of a study that included a random sample I can't help but wonder how random the sample was and how they can be sure of that it is. This article explained how such things can be tested and how they will add validity to results, and I believe this to be true. I also agree that it would be beneficial to do an activity such as this in a statistics classroom because students could pick random students from within their own classroom and then test the randomness of it. This would be teaching them to find the mean and standard deviation in a way that is more real to them.
Friday, March 26, 2010
Friday, March 19, 2010
Blog Entry #6
Gilbert, M.J., & Coomes, J. (2010). What mathematics do high school
teachers need to know. Mathematics Teacher, 103(6), 418-423.
Through research done with several different teachers and their classrooms, this conclusion was reached, "How teachers hold knowledge may matter more than how much knowledge they hold." Several points were made within this article to support that teachers deep understanding of a small amount of mathematical knowledge is more beneficial to their students than having large, but shallow, amounts of mathematical knowledge. It is vital that teachers have this deep understanding of the material that they are teaching to their students so that the teacher will be able to quickly recognize and even anticipate student misconceptions and errors. The sooner a teacher acknowledges a student misconception and corrects it, the better. If a students misconception is not properly realized and corrected, then they will take that incorrect information with them into their future mathematics learning. It is vital that teachers not only know how to answer the questions they ask their students, but that they will be able to understand several different solutions to any mathematical question they ask. If they do not have this understanding, then they may not be able to notice and fix students' errors. Having this understanding of why a student made a certain mistake will provide the teacher with the opportunity to guide the student to developing more careful thought processes that will prevent them from making that mistake in the future.
I agree with the main point made in "What Mathematics do High School Teachers Need to Know?" because of three reasons. First, I have had several experiences that support that teachers need to have a deeper understanding of what they are teaching. I cannot count the number of times that I, or another student in my class, has asked a question of our teacher wherein the teacher gives an answer, but they do so without addressing the question asked because they did not understand what the student was asking in the first place. They had simply assumed they knew and had continued from there. Second, I have had experiences wherein I was attempting to teach a mathematics principle to someone else and have been unsuccessful. I was unsuccessful because I did not have a deep enough understanding of the material that I was trying to teach, so I could not recognize their misconceptions and correct them. Third, the article gives excellent examples from the classrooms that were studied of numerous representations and misconceptions that students gave/had about one problem. If the teacher had not been able to first interpret the different solutions given, and then realize what precisely it was that the student had made an error on, they would not correct the student on the precise point that the student didn't understand and although the student might be shown how to get the right answer, they could still have that misconception. For these reasons I feel that it is more important for a teacher to have a deep understanding of a small amount of mathematical knowledge, rather than a shallow understanding of a large amount of mathematical knowledge.
teachers need to know. Mathematics Teacher, 103(6), 418-423.
Through research done with several different teachers and their classrooms, this conclusion was reached, "How teachers hold knowledge may matter more than how much knowledge they hold." Several points were made within this article to support that teachers deep understanding of a small amount of mathematical knowledge is more beneficial to their students than having large, but shallow, amounts of mathematical knowledge. It is vital that teachers have this deep understanding of the material that they are teaching to their students so that the teacher will be able to quickly recognize and even anticipate student misconceptions and errors. The sooner a teacher acknowledges a student misconception and corrects it, the better. If a students misconception is not properly realized and corrected, then they will take that incorrect information with them into their future mathematics learning. It is vital that teachers not only know how to answer the questions they ask their students, but that they will be able to understand several different solutions to any mathematical question they ask. If they do not have this understanding, then they may not be able to notice and fix students' errors. Having this understanding of why a student made a certain mistake will provide the teacher with the opportunity to guide the student to developing more careful thought processes that will prevent them from making that mistake in the future.
I agree with the main point made in "What Mathematics do High School Teachers Need to Know?" because of three reasons. First, I have had several experiences that support that teachers need to have a deeper understanding of what they are teaching. I cannot count the number of times that I, or another student in my class, has asked a question of our teacher wherein the teacher gives an answer, but they do so without addressing the question asked because they did not understand what the student was asking in the first place. They had simply assumed they knew and had continued from there. Second, I have had experiences wherein I was attempting to teach a mathematics principle to someone else and have been unsuccessful. I was unsuccessful because I did not have a deep enough understanding of the material that I was trying to teach, so I could not recognize their misconceptions and correct them. Third, the article gives excellent examples from the classrooms that were studied of numerous representations and misconceptions that students gave/had about one problem. If the teacher had not been able to first interpret the different solutions given, and then realize what precisely it was that the student had made an error on, they would not correct the student on the precise point that the student didn't understand and although the student might be shown how to get the right answer, they could still have that misconception. For these reasons I feel that it is more important for a teacher to have a deep understanding of a small amount of mathematical knowledge, rather than a shallow understanding of a large amount of mathematical knowledge.
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