Barger, R.H., & McCoy, A.C. (2009). Sacred cows make the best hamburgers. Mathematics Teacher, 102(6), 414-418.
The main idea of this article was that college mathematics courses should be more interactive and hands-on. Instead of the lecture and practice problems homework system that most courses consist of, Barger and McCoy did research and then tested out their own mathematics course, entitled Contemporary Mathematics, in which they implemented their creative and interactive material. The course is an equivalent of a mathematics general education course, in which most students are not majoring in anything related to the math or science areas. In the article, they highlighted the lessons on volume and surface area. Before starting this class, they noticed that a lot of students mix up the formulas for volume and surface area, proposing that this is because students do not understand the formulas. In this new course, the students built shapes and formulated their own hypotheses of what volume and surface area is and how to find them for different shapes. As was shown through test scores, the students understood mathematics so much more and grades improved. Additionally, Barger and McCoy point out that these interactive methods do not take that much more time than regular lectures and that understanding the formulas is worth much more than the extra time! Thus they concluded that mathematics can be taught in a different and more meaningful way to students in college.
From all my studies of education, I agree that mathematics courses can and should be more interactive. Firstly, the main reason they wanted mathematics courses to be more interactive and hands-on is so that students will understand more. I think this is supported by our study of relational learning in MathEd 117. By working it out and discovering "formulas" on their own, these students are doing relational learning, which will impact their learning and their tests scores. Secondly, this idea is supported from what I have studied in my Theatre Ed classes. "Dramatic learning" is when students are able to take control of their learning, by hands-on activities and the time develop their own ways to learn things. This article supported that type of learning because the students made their own formulas for volume and surface area. Thirdly, Barger and McCoy addressed my one concern - time. They acknowledged this but said the time was not so much more that it overpowered the understanding these students were gaining. Thus, I am sold on this new idea!
Wednesday, March 24, 2010
Thursday, March 18, 2010
Blog Entry #6
Switzer, J. M. (2010). Bridging the math gap. Mathematics Teaching in the Middle School, 15(7), 400-405.
In the article that I read, Switzer's main idea was that effective teaching requires building on previous knowledge. This idea came to him when teachers in the middle schools and high schools in his district could not teach their students because they did not understand the alternative algorithms that these students were doing for basic math. He quickly realized that understanding what students learned in elementary school can help teachers teach students better because they can connect that knowledge to what they will teach them in middle school and high school. The example Switzer used was the concept of partial products. Students in his district had learned the principles behind the distributive property of multiplication over addition (usually represented by the traditional algorithm of FOIL) in elementary school when learning multiplication of two digit numbers. If the algebra teachers realized the alternative algorithm that the students used for basic multiplication, then learning multiplication of polynomials would have been a lot easier. Overall, Switzer concluded to having meetings with all grade levels of teachers in his district so they could become in sync to how students are learning mathematics so they could integrate those alternative ways into their teaching of more advanced mathematics.
I think that Switzer was very perceptive when it came to the needs in his school district and I agree that teachers do need to build not only just on previous knowledge, but on the way that that knowledge was learned. I would say his secondary idea, which was that alternative algorithms are great and can easily be transferred to traditional algorithms if necessary, was also brilliant. When I was reading his article, I felt that it feel right in line with what we have been learning in class. Firstly, in class we have been exploring relational ways of understanding basic mathematics. In this article, he addressed an alternative way of understanding multiplication of double digit numbers, which seemed very relational to me. I had never thought about how the traditional algorithm of this process makes absolutely no sense! I mean, multiply the second number on the bottom with the first two numbers on the top, each separately, then drop a zero down and then multiply the first bottom number with the top two and then add it all up at the end! It has so many rules and steps to remember! The alternative way he talked about was a basis for algebra as well as teaching students the importance of place value with more than one digit numbers. I thought his explanation really illustrated what we have been learning in class about understanding why mathematics is the way it is. Secondly, his ideas would save a lot of time if the teachers did understand exactly how, not just what, the students learned before they got to their classrooms. It would make teaching effective and efficient. So many of the articles we have read don't necessarily have teaching ideas that are both of those things. Lastly, his idea is just very logical! You can't teach students certain principles or algorithms if you don't know how they learned what they know at this point. Having meetings like he did makes sense for the situation he described in his school district, but I am sure there are other ways of making sure upper division teachers are aware of how students learned in the lower division years. Overall, I am very supportive of Switzer's ideas.
In the article that I read, Switzer's main idea was that effective teaching requires building on previous knowledge. This idea came to him when teachers in the middle schools and high schools in his district could not teach their students because they did not understand the alternative algorithms that these students were doing for basic math. He quickly realized that understanding what students learned in elementary school can help teachers teach students better because they can connect that knowledge to what they will teach them in middle school and high school. The example Switzer used was the concept of partial products. Students in his district had learned the principles behind the distributive property of multiplication over addition (usually represented by the traditional algorithm of FOIL) in elementary school when learning multiplication of two digit numbers. If the algebra teachers realized the alternative algorithm that the students used for basic multiplication, then learning multiplication of polynomials would have been a lot easier. Overall, Switzer concluded to having meetings with all grade levels of teachers in his district so they could become in sync to how students are learning mathematics so they could integrate those alternative ways into their teaching of more advanced mathematics.
I think that Switzer was very perceptive when it came to the needs in his school district and I agree that teachers do need to build not only just on previous knowledge, but on the way that that knowledge was learned. I would say his secondary idea, which was that alternative algorithms are great and can easily be transferred to traditional algorithms if necessary, was also brilliant. When I was reading his article, I felt that it feel right in line with what we have been learning in class. Firstly, in class we have been exploring relational ways of understanding basic mathematics. In this article, he addressed an alternative way of understanding multiplication of double digit numbers, which seemed very relational to me. I had never thought about how the traditional algorithm of this process makes absolutely no sense! I mean, multiply the second number on the bottom with the first two numbers on the top, each separately, then drop a zero down and then multiply the first bottom number with the top two and then add it all up at the end! It has so many rules and steps to remember! The alternative way he talked about was a basis for algebra as well as teaching students the importance of place value with more than one digit numbers. I thought his explanation really illustrated what we have been learning in class about understanding why mathematics is the way it is. Secondly, his ideas would save a lot of time if the teachers did understand exactly how, not just what, the students learned before they got to their classrooms. It would make teaching effective and efficient. So many of the articles we have read don't necessarily have teaching ideas that are both of those things. Lastly, his idea is just very logical! You can't teach students certain principles or algorithms if you don't know how they learned what they know at this point. Having meetings like he did makes sense for the situation he described in his school district, but I am sure there are other ways of making sure upper division teachers are aware of how students learned in the lower division years. Overall, I am very supportive of Switzer's ideas.
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