Thursday, May 28, 2015
CCSSM Reflection
Throughout this assignment I have learned a lot more than I honestly thought I would when looking at a bunch of standards. When looking at the two standards that I was assigned specifically I learned just how much they lean towards an inquiry basis. The same is true for the whole set of standards. When watching the other presentations and listening to the examples provided you can see the opportunity for inquiry based math lessons using the common core state math standards. Inquiry based instruction is what we are moving towards so it is positive that the standards work well with that. These standards focus on a deeper level of thinking and being able to explain the reasoning behind your solutions. They encourage students to understand mathematical concepts rather than simply how to plug numbers into a formula. Students are really challenged to think deeper with these standards. I think that these standards are a step in the right direction to not only communize standards across the state, but also to encourage an inquiry based structure in the classroom and more thoughtful students.
Wednesday, May 27, 2015
"Preserving Pelicans with Models That Make Sense" & "Count On It: Congruent Manipulative Displays"
"Preserving Pelicans with Models That Make Sense"
This article talks about model-eliciting activities, specifically an activity relating to pelicans and the concentration of their colonies. An MEA is an activity that allows students to work with models in order to help form their understanding of concepts. In the articles example students were trying to come up with the best way to estimate the number of pelican colonies in an area. Students worked in small groups to come up with the best way to estimate this number.
I think that this kind of activity is very beneficial to student learning if implemented properly. It allows students to share, discuss, and revise their ideas and to really think through a problem situation. I would use this type of activity in many different situations in my own classroom. I personally think that the MEA is best suited to topics that students can relate to the most because it can be very time consuming and involves a lot of thought to carry out.
Moore, T.J., Doerr, H.M., Glancy, A.W., & Ntow, F.D. (2015). Preserving pelicans with models that make sense. Mathematics Teaching in the Middle School, 20(6), 358-364.
"Count On It: Congruent Manipulative Displays"
This article talks about the use of manipulatives. As students we have had plenty of experience working with them to assist in our own learning, but thinking about how to effectively use a manipulative to teach your future students seems less simple. You must make sure that you are properly connecting the concept being taught with the manipulative being used. It is also important to understand that when you start using manipulatives with your students you begin with very concrete examples. The more the students learn the more abstract the manipulatives can be. this article also talks about the importance of guiding students to use manipulatives in their own independent study.
Throughout my personal experience using manipulatives I am able to understand the positives that they can have when working with them. I had never really thought about how difficult it is to incorporate them into a lesson before though. Obviously they help some people but how do you introduce them effectively. I can see my students using all kinds of manipulatives in my classroom, whether it be during a lesson or while working on their homework, as long as the manipulative fits the task at hand. I am a very hands on person and when you have to work through a difficult problem they can be very helpful.
Morin, J., & Samelson, V.M. (2015). Count on it: Congruent manipulative displays. Teaching Children Mathematics, 21(6), 362-370.
This article talks about model-eliciting activities, specifically an activity relating to pelicans and the concentration of their colonies. An MEA is an activity that allows students to work with models in order to help form their understanding of concepts. In the articles example students were trying to come up with the best way to estimate the number of pelican colonies in an area. Students worked in small groups to come up with the best way to estimate this number.
I think that this kind of activity is very beneficial to student learning if implemented properly. It allows students to share, discuss, and revise their ideas and to really think through a problem situation. I would use this type of activity in many different situations in my own classroom. I personally think that the MEA is best suited to topics that students can relate to the most because it can be very time consuming and involves a lot of thought to carry out.
Moore, T.J., Doerr, H.M., Glancy, A.W., & Ntow, F.D. (2015). Preserving pelicans with models that make sense. Mathematics Teaching in the Middle School, 20(6), 358-364.
"Count On It: Congruent Manipulative Displays"
This article talks about the use of manipulatives. As students we have had plenty of experience working with them to assist in our own learning, but thinking about how to effectively use a manipulative to teach your future students seems less simple. You must make sure that you are properly connecting the concept being taught with the manipulative being used. It is also important to understand that when you start using manipulatives with your students you begin with very concrete examples. The more the students learn the more abstract the manipulatives can be. this article also talks about the importance of guiding students to use manipulatives in their own independent study.
Throughout my personal experience using manipulatives I am able to understand the positives that they can have when working with them. I had never really thought about how difficult it is to incorporate them into a lesson before though. Obviously they help some people but how do you introduce them effectively. I can see my students using all kinds of manipulatives in my classroom, whether it be during a lesson or while working on their homework, as long as the manipulative fits the task at hand. I am a very hands on person and when you have to work through a difficult problem they can be very helpful.
Morin, J., & Samelson, V.M. (2015). Count on it: Congruent manipulative displays. Teaching Children Mathematics, 21(6), 362-370.
Monday, May 25, 2015
"Word Problem Clues" (video)
I think that this lesson was very well thought out and there was a lot of planning behind it. However, I think when implementing this lesson it went in an entirely different direction than previously planned for. In some aspects the lesson ended up being kind of all over the place. The initial intention of the lesson was to use the clues in the word problems to help you figure out the problem. I think that she did a really good job of trying to incorporate this into the lesson, but the students continued to be confused by the problem and I felt she just kept asking the same questions to try and clear up the confusion. I think that the students have a solid foundation of addition and subtraction and strategies to complete both, but they struggle with applying them and little mistakes upon completion.
As the teacher described in the beginning, many of the students, even after the teacher directed portion of the lesson, still wanted to simply add the numbers together and say that was their answer. They weren't focusing on what the problem actually said and meant. I understand why this lesson may not have gone in the intended direction. With more time for examples I think this lesson could have flowed more smoothly. Maybe the teacher could have gone through more examples or strategies together. Some students were beginning to grasp it and possible strategies, but were making mistakes along the way.
Overall, I really like the idea for this lesson. I love the opportunity for students to explain their work and really talk about how they arrived at the answer they came up with. I like the student reflection on their own work and the opportunity for students to reevaluate their work and fix possible mistakes. I think this could have been more beneficial if students had the opportunity to see and walk through correct answers after this lesson so they could compare and learn from their mistakes. This lesson idea is something that I can most definitely see myself using in my own classroom.
As the teacher described in the beginning, many of the students, even after the teacher directed portion of the lesson, still wanted to simply add the numbers together and say that was their answer. They weren't focusing on what the problem actually said and meant. I understand why this lesson may not have gone in the intended direction. With more time for examples I think this lesson could have flowed more smoothly. Maybe the teacher could have gone through more examples or strategies together. Some students were beginning to grasp it and possible strategies, but were making mistakes along the way.
Overall, I really like the idea for this lesson. I love the opportunity for students to explain their work and really talk about how they arrived at the answer they came up with. I like the student reflection on their own work and the opportunity for students to reevaluate their work and fix possible mistakes. I think this could have been more beneficial if students had the opportunity to see and walk through correct answers after this lesson so they could compare and learn from their mistakes. This lesson idea is something that I can most definitely see myself using in my own classroom.
Wednesday, May 20, 2015
Standards Articles
Construct Viable Arguments & Critique the Reasoning (3)
The String Task: Not Just for High School
This article talks about functional thinking or relationships amongst numbers. An experiment was conducted in classrooms grades 3-5 to promote algebra early on in school. The types of problems in this article that were used to teach functional thinking, lent themselves well to working with standard 3. The first problem had to do with cutting a piece of string a number of times. Students had to figure out the relationship between the number of cuts and the number of strings. "Students were encouraged to discuss their mathematical thinking and to use multiple representations to communicate their ideas with their peers… [and] to explain their thinking" (Isler, 285). Students had ample opportunity to talk with other student or the teacher. They came up with a relationship between the two numbers in partners, represented their data with charts and pictures, and explained their reasoning. This worked the same way for the Brady problem. Except this problem was square tables and how many people could sit at each.
Isler, I., Marum, T., Stephens, A., Blanton, M., Knuth, E., & Gardiner, A.M. (2014). The string task: Not just for high school. Teaching Children Mathematics, 21(5), 282-292. Retrieved from http://www.nctm.org/Publications/teaching-children-mathematics/2014/Vol21/Issue5/The-String-Task-Not-Just-for-High-School/
Use Appropriate Tools Strategically (5)
Mapping the Way to Content Knowledge
This article talks about using a content map in order to better understand how to teach subtraction as a preservice teacher. This is an example of how the teacher and the student can benefit from a tool. There are various other examples of tools being used throughout the article. A student is working to solve 70 - 23 and get an answer of 53 using the traditional method. When she repeats the problem again using base-10 block and a hundred chart she gets the problem correct. The particular example of the subtraction content map is something that I have benefited from as a preservice teacher and the other tools described in this article can be beneficial for future students.
Poling, L.L., Goodson-Epsy, T., Dean, C., Lynch-Davis, K., & Quickenton, A. (2015). Mapping the way to content knowledge. Teaching Children Mathematics, 21(9), 538-547. Retrieved from http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol21/Issue9/Mapping-the-Way-to-Content-Knowledge/
The String Task: Not Just for High School
This article talks about functional thinking or relationships amongst numbers. An experiment was conducted in classrooms grades 3-5 to promote algebra early on in school. The types of problems in this article that were used to teach functional thinking, lent themselves well to working with standard 3. The first problem had to do with cutting a piece of string a number of times. Students had to figure out the relationship between the number of cuts and the number of strings. "Students were encouraged to discuss their mathematical thinking and to use multiple representations to communicate their ideas with their peers… [and] to explain their thinking" (Isler, 285). Students had ample opportunity to talk with other student or the teacher. They came up with a relationship between the two numbers in partners, represented their data with charts and pictures, and explained their reasoning. This worked the same way for the Brady problem. Except this problem was square tables and how many people could sit at each.
Isler, I., Marum, T., Stephens, A., Blanton, M., Knuth, E., & Gardiner, A.M. (2014). The string task: Not just for high school. Teaching Children Mathematics, 21(5), 282-292. Retrieved from http://www.nctm.org/Publications/teaching-children-mathematics/2014/Vol21/Issue5/The-String-Task-Not-Just-for-High-School/
Use Appropriate Tools Strategically (5)
Mapping the Way to Content Knowledge
This article talks about using a content map in order to better understand how to teach subtraction as a preservice teacher. This is an example of how the teacher and the student can benefit from a tool. There are various other examples of tools being used throughout the article. A student is working to solve 70 - 23 and get an answer of 53 using the traditional method. When she repeats the problem again using base-10 block and a hundred chart she gets the problem correct. The particular example of the subtraction content map is something that I have benefited from as a preservice teacher and the other tools described in this article can be beneficial for future students.
Poling, L.L., Goodson-Epsy, T., Dean, C., Lynch-Davis, K., & Quickenton, A. (2015). Mapping the way to content knowledge. Teaching Children Mathematics, 21(9), 538-547. Retrieved from http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol21/Issue9/Mapping-the-Way-to-Content-Knowledge/
CCSM 3 & 5
Construct Viable Arguments & Critique the Reasoning (3)
This standard focuses on students not only being able to solve problems, but how they get to their solution. Students must explain, support, and defend the solutions to the problems they are attempting to solve. This standard leaves plenty of room for students to justify their process to their classmates, and to explain the steps they took to reach their solution. It allows them to work with others to ensure they are reaching the correct solution, and it also shows that their may not always be one solution to a problem. Creating a classroom where respect for others and their thoughts will help to achieve this standard. Providing an open environment for discussion will be beneficial as well.
Use Appropriate Tools Strategically (5)
This standard helps to create a more hands on and active learning environment in the math classroom. Manipulatives and various other tools can be used during instruction and by students to help deepen their understanding of various concepts. It is possible that a tool can be beneficial in teaching/learning multiple concepts, but it is important to make sure that the tool is assisting in the learning process of your students and that it in fact serves a purpose. A variety of tools should be available and accessible to your students. They should understand how to use each tool, when it is appropriate to use each, and the benefits and limitations of each.
This standard focuses on students not only being able to solve problems, but how they get to their solution. Students must explain, support, and defend the solutions to the problems they are attempting to solve. This standard leaves plenty of room for students to justify their process to their classmates, and to explain the steps they took to reach their solution. It allows them to work with others to ensure they are reaching the correct solution, and it also shows that their may not always be one solution to a problem. Creating a classroom where respect for others and their thoughts will help to achieve this standard. Providing an open environment for discussion will be beneficial as well.
Use Appropriate Tools Strategically (5)
This standard helps to create a more hands on and active learning environment in the math classroom. Manipulatives and various other tools can be used during instruction and by students to help deepen their understanding of various concepts. It is possible that a tool can be beneficial in teaching/learning multiple concepts, but it is important to make sure that the tool is assisting in the learning process of your students and that it in fact serves a purpose. A variety of tools should be available and accessible to your students. They should understand how to use each tool, when it is appropriate to use each, and the benefits and limitations of each.
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