Goodman, T. (2010) Shooting free throws, probability, and the golden ratio. Mathematics Teacher, 103(7), 482-487.
In this entry, Goodman is emphasizing the effectiveness of using real world application type of problems to help students in their math classes. His entry focuses more on a possible use of math outside the classroom, free throw shooting probability, than it does on using the situation to teach a concept. Goodman writes his article describing the process he and his students used to calculate the probability of a basketball player, Paige, making free throws in various situations: first in a "one and one" where Paige only shoots the second shot if she makes the first, second if she shoots both shots regardless of the outcome of the first, and third if there are three free-throws taken. They used the same process with t charts and graphs and writing equations using season percentage, p, as a basis. Once they determined Paige's probability, they applied the same methods and came up with a table for multiple athletes with different initial shooting percentages. Goodman concludes that this type of applicational situation allows students the opportunity to expand their understanding of mathematics and obtain a greater knowledge of the concept.
I agree with Goodman's thinking that contextual situations are beneficial for student learning and ultimate understanding. In all of my experience both attending math class and tutoring peers in them, the biggest road block for students' understanding is their doubt in themselves. They loose the motivation to try to understand a difficult concept because they don't see how it will benefit their life in the future. Goodman's example of free throw shooting proves the importance of having a basic knowledge of math and also the options available when more math knowledge is obtained. This topic is something all types of people can relate to and it is useful, especially in sports. I think more activities using this type of application can only benefit students.
Thursday, March 25, 2010
Monday, March 22, 2010
Blog Entry 6
Hunt, J. (2009) Prime or composite? Mathematics Teacher, On Math, 1-5.
This article focused on the importance of understanding prime and composite numbers and their factors. Hunt emphasizes that having a basic knowledge of these concepts is a necessity before students advance into middle school and higher math education. She describes her method of teaching these concepts to her class: using rectangle area, a factor game, and then a homework project. She first utilized a KWL chart and had the students list everything they remembered about factors and prime/composite numbers. They discussed student responses and together came up with a definition for the term factor. Hunt then gave her students colored pencils and graph paper and had her students use their new knowledge of factors to find different ways to form rectangle areas ranging from 1 to 30. After this activity, from student observation, the class established a meaning for prime and composite numbers. Hunt then reinforced this idea with a factor game played with partners on the computer. To end the lesson, she assigned a homework project, giving each student a different area of bathroom floor and each individually was supposed to figure out all possible floor plans to achieve that area.
I agree with Hunt's emphasis on understanding factors and her way of teaching them to her class. I really like how she balanced the amount of information she gave to the students and the amount they had to come up with on their own. She provided guidance after class discussion so that the students had a firm understanding of each concept, but the students had to think first and basically came upon the definitions themselves. Through the use of multiple activities to present the concept, Hunt reinforced the material multiple times in her students brains. This is a very useful practice from my personal experience, the more ways I see a concept, the more it sticks in my brain. I also thought, from her description, this method made very good use of time. The students were actively engaged for the whole class period and all the material planned on being covered was covered. I think this is a creative and effective way to teach this baseline information to students.
This article focused on the importance of understanding prime and composite numbers and their factors. Hunt emphasizes that having a basic knowledge of these concepts is a necessity before students advance into middle school and higher math education. She describes her method of teaching these concepts to her class: using rectangle area, a factor game, and then a homework project. She first utilized a KWL chart and had the students list everything they remembered about factors and prime/composite numbers. They discussed student responses and together came up with a definition for the term factor. Hunt then gave her students colored pencils and graph paper and had her students use their new knowledge of factors to find different ways to form rectangle areas ranging from 1 to 30. After this activity, from student observation, the class established a meaning for prime and composite numbers. Hunt then reinforced this idea with a factor game played with partners on the computer. To end the lesson, she assigned a homework project, giving each student a different area of bathroom floor and each individually was supposed to figure out all possible floor plans to achieve that area.
I agree with Hunt's emphasis on understanding factors and her way of teaching them to her class. I really like how she balanced the amount of information she gave to the students and the amount they had to come up with on their own. She provided guidance after class discussion so that the students had a firm understanding of each concept, but the students had to think first and basically came upon the definitions themselves. Through the use of multiple activities to present the concept, Hunt reinforced the material multiple times in her students brains. This is a very useful practice from my personal experience, the more ways I see a concept, the more it sticks in my brain. I also thought, from her description, this method made very good use of time. The students were actively engaged for the whole class period and all the material planned on being covered was covered. I think this is a creative and effective way to teach this baseline information to students.
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