Tuesday, April 27, 2010
Journal Article Review: Fractions and the funky cookie
Summary:
This article discussed the use of manipulatives, pattern blocks, to help students deepen their understanding of fractions. This was a 5th grade class who received extra help from a math specialist who came in to work with the students according to one agenda; however, their agenda changed as they saw the needs of the students. The specialist realized through the use of guiding questions as they worked with manipulatives that the students needed to understand the concept of fractional parts of a whole item must be of equal size. The teacher used pattern blocks to demonstrate with the use of the "funky cookie" which was a an irregular shape made up of different types of pattern blocks. The teacher asked the students to explain if and how they could share the "funky cookie" between 6 people. They were also asked to construct their own shape that could be shared between 6 people. Through this, the specialist understood that the students needed to understand that in order to share between 6 people, the parts had to be the same size in order to make it equal. The students were able to come to a full understanding of what equal parts of a whole unit meant.
Reflection:
I thought this article was great! Especially after working with pattern blocks in class today in our manipulative activity!! It was helpful to see how the teacher adapted her teaching plans/strategies to fit the students' needs as they arose. It is evident from this article that teachers need to anticipate where the students' thought process are going and how to guide them with the right questions that will be thought provoking and directional to guide them to what they need to know. It is also evident that teachers need to be fluent in their mathematical knowledge and need to have a depth of understanding in math that exceeds that of paper and pencil math so that the teacher can think of more than one strategy to problem solve.
This was a creative approach to help the students come to an understanding and was a great example of running with a teachable moment with the students. I think that this reinforces the benefits of incorporating manipulatives into lessons in order to help students grasp concepts that are difficult to understand. I liked this article a lot and appreciated the way the teacher was flexible in their plans to meet the needs of the students.
Ellington, A. Whitenack, Joy (2010). Fractions and the funky cookie.
Teaching Children Mathematics 16(9), 534-539.
This article discussed the use of manipulatives, pattern blocks, to help students deepen their understanding of fractions. This was a 5th grade class who received extra help from a math specialist who came in to work with the students according to one agenda; however, their agenda changed as they saw the needs of the students. The specialist realized through the use of guiding questions as they worked with manipulatives that the students needed to understand the concept of fractional parts of a whole item must be of equal size. The teacher used pattern blocks to demonstrate with the use of the "funky cookie" which was a an irregular shape made up of different types of pattern blocks. The teacher asked the students to explain if and how they could share the "funky cookie" between 6 people. They were also asked to construct their own shape that could be shared between 6 people. Through this, the specialist understood that the students needed to understand that in order to share between 6 people, the parts had to be the same size in order to make it equal. The students were able to come to a full understanding of what equal parts of a whole unit meant.
Reflection:
I thought this article was great! Especially after working with pattern blocks in class today in our manipulative activity!! It was helpful to see how the teacher adapted her teaching plans/strategies to fit the students' needs as they arose. It is evident from this article that teachers need to anticipate where the students' thought process are going and how to guide them with the right questions that will be thought provoking and directional to guide them to what they need to know. It is also evident that teachers need to be fluent in their mathematical knowledge and need to have a depth of understanding in math that exceeds that of paper and pencil math so that the teacher can think of more than one strategy to problem solve.
This was a creative approach to help the students come to an understanding and was a great example of running with a teachable moment with the students. I think that this reinforces the benefits of incorporating manipulatives into lessons in order to help students grasp concepts that are difficult to understand. I liked this article a lot and appreciated the way the teacher was flexible in their plans to meet the needs of the students.
Ellington, A. Whitenack, Joy (2010). Fractions and the funky cookie.
Teaching Children Mathematics 16(9), 534-539.
Manipulatives Blog
I have come to understand manipulatives more through this class. I cannot remember a time that I used manipulatives in math growing up in school. I am very enthusiastic about using manipulatives in my classroom because I feel that they assist the student in deepening their understanding of mathematical concepts and gives them a visual representation that will further their knowledge. I believe that what you hear, you'll forget; what you see, you'll remember; what you do, you learn. I think that all three of these steps are vital to a students' learning experience, but the latter is often forgotten to be made part of their curriculum.
1. How do you know students deepen their understanding while using manipulatives?
You know the students deepen their understanding while using manipulatives by their interactions and conversations while they are participating in the activity. As the students are working through manipulative activities, they should be talking out their processes and you can usually tell when a student is confused by the look on their faces. The students are more likely to have the "aha!" moment when using manipulatives because they can connect the mathematical ideas that they know in their mind with the experience and visual representation. Students understand more by doing what they are learning.
2. How do you know if the students can transfer their understanding from manipulatives to other situations?
You will be able to know if the students can transfer their understanding from manipulatives to other situations by asking them guiding questions where they will have to think through practical, real world application questions. They will then problem solve and communicate through discussion ways that they can take what they are learning by using the manipulatives and connect it with the real world.
3. How can you assess that understanding or growth?
You can assess their growth by requiring reflection to be a part of their activities. This way, the students will be incorporating the communication process standard and you can easily tell what their thought processes are about math. You can then assess their ability to utilize their mathematical language in an appropriate manner. Their understanding and growth can be assessed by setting up activities that are meaningful to their learning. A teacher can tell if the student is growing and learning based on their interactions with other students in working together using critical thinking skills to problem solve.
4. When students work in groups, how do you hold each youngster accountable for learning?
When students work in groups, I think that it is important that students have individual work to show that they were working and putting forth effort that is acceptable and contributes to their learning. I would have the students document what they are learning as they go through the different activities. I would also have the student not only write about what they are doing (methods), but what they are learning, and also what observations they make along the way. I would then have the students write a synthesis of their information in the form of a reflection that includes conclusions that they reached from their observations and also their thoughts about it.
5. When students work in groups, how do you assess each youngster's depth of understanding?
When students work in groups, their depth of understanding is critical as manipulatives should deepen their understanding, not provide a way to do simply hands on activities without any academic gain. Teachers should pay close attention as they are engaging in the activities and also take time to go around the room to ask the students questions that are thought provoking for the student which will cause them to give more than a surface/product answer. The student should be able to explain the process and make conjectures of how what they are doing relates not only within mathematics, but also interdisciplinary.
6. How are you improving students' problem solving skills with the manipulatives?
Students will need to know how to think critically in problem solving not just in math or in school, but as it relates to their daily lives and futures as professionals. Students learn to problem solve when working with manipulatives because they are activating their mind to think beyond what seems obvious. Students have to use manipulatives to solve problems and this causes the students to learn how to use many approaches and a variety of strategies to solve problems. There is usually more than one way to do things and this is true for problem solving. There is usually more than one way to solve a problem and some ways work better than others. Using manipulatives also helps students to refine their skills of determining the best strategy to problem solve and sometimes through guess and check/trial and error.
7. Why do they say not "hands - on" but "hands - on; minds - on"?
If activities are hands on only, students aren't learning to the depth at which their potential is. Activities need to be thought provoking and engaging of the mind as they work with their hands so that they can correlate knowledge/information to experience. A teacher should ensure that they are promoting equity within the education they are giving to the student in that they need to give the students solid instruction that give the student a firm foundation from which to build upon. If the students don't have good instruction and are given manipulatives, they will end up confused and won't get the max out of what they are supposed to be learning. They won't be able to make the connections and conclusions that are intended for them. Manipulatives must be coupled with strong teaching.
8. How do the process standards relate to the use of manipulatives?
Problem Solving:
Manipulatives incorporates the use of every process standard. Students exercise criticial thinking skills when using manipulatives in that they have to think beyond what is "expected or obvious" to come up with creative solutions. Students use a variety of problem solving strategies to come to a solution. Manipulatives also focuses more on the process rather than the product which is important when it comes to deepening mathematical understanding.
Communication
Students naturally use the process standard of communication when working with manipulatives/activities, especially when working with groups. As the students are encouraged to talk through their mathematical thought processes to reach a solution they are furthering their ability to communicate using the language of math. Their communication skills are sharpened as they engage in discussion and written reflection.
Reason and Proof
Students are asked to give rationale for their thinking when working with these activities. They should be talking through their processes, making conjectures and testing their predictions to see if they have understanding. Students should be working through problems that are meaningful and lend to explanation and justification of their work.
Representation
manipulatives are a great way to incorporate representation. Students can use manipulatives to represent data, mathematical equations, shapes, patterns, etc.
Connections
Students can make connections especially with the real world as they problem solve and work with manipulative activities. They are able to connect mathematical ideas together to see how mathematics is a coherent whole.
In class today, Monique and I did three different manipulatives which I thought were good. We did the snap blocks, unifix cubes and pattern blocks. I would have liked to experiment with the other manipulatives but we ran out of time. I really liked the snap blocks because they were so versatile and had many colors. It was easy to find activities that could be incorporated at every grade level with these. I also really liked the pattern blocks as there were a lot of things you could do with them. I thought with the pattern blocks; however, that it could be helpful to have many colors of the same shape (e.g. triangles would have yellow, green, orange, red, blue) so that if a student wanted to do representation of a pie graph for data analysis, it would be less confusing. I do understand that it is also important for them to be the same color. I also appreciated our discussion in class about what to do when students had deficiency in fine motor skills and thought that the suggestions were very good and insightful.
I really have enjoyed learning more about manipulatives in this class and I'm excited to purchase my own and implement them in the classroom.
1. How do you know students deepen their understanding while using manipulatives?
You know the students deepen their understanding while using manipulatives by their interactions and conversations while they are participating in the activity. As the students are working through manipulative activities, they should be talking out their processes and you can usually tell when a student is confused by the look on their faces. The students are more likely to have the "aha!" moment when using manipulatives because they can connect the mathematical ideas that they know in their mind with the experience and visual representation. Students understand more by doing what they are learning.
2. How do you know if the students can transfer their understanding from manipulatives to other situations?
You will be able to know if the students can transfer their understanding from manipulatives to other situations by asking them guiding questions where they will have to think through practical, real world application questions. They will then problem solve and communicate through discussion ways that they can take what they are learning by using the manipulatives and connect it with the real world.
3. How can you assess that understanding or growth?
You can assess their growth by requiring reflection to be a part of their activities. This way, the students will be incorporating the communication process standard and you can easily tell what their thought processes are about math. You can then assess their ability to utilize their mathematical language in an appropriate manner. Their understanding and growth can be assessed by setting up activities that are meaningful to their learning. A teacher can tell if the student is growing and learning based on their interactions with other students in working together using critical thinking skills to problem solve.
4. When students work in groups, how do you hold each youngster accountable for learning?
When students work in groups, I think that it is important that students have individual work to show that they were working and putting forth effort that is acceptable and contributes to their learning. I would have the students document what they are learning as they go through the different activities. I would also have the student not only write about what they are doing (methods), but what they are learning, and also what observations they make along the way. I would then have the students write a synthesis of their information in the form of a reflection that includes conclusions that they reached from their observations and also their thoughts about it.
5. When students work in groups, how do you assess each youngster's depth of understanding?
When students work in groups, their depth of understanding is critical as manipulatives should deepen their understanding, not provide a way to do simply hands on activities without any academic gain. Teachers should pay close attention as they are engaging in the activities and also take time to go around the room to ask the students questions that are thought provoking for the student which will cause them to give more than a surface/product answer. The student should be able to explain the process and make conjectures of how what they are doing relates not only within mathematics, but also interdisciplinary.
6. How are you improving students' problem solving skills with the manipulatives?
Students will need to know how to think critically in problem solving not just in math or in school, but as it relates to their daily lives and futures as professionals. Students learn to problem solve when working with manipulatives because they are activating their mind to think beyond what seems obvious. Students have to use manipulatives to solve problems and this causes the students to learn how to use many approaches and a variety of strategies to solve problems. There is usually more than one way to do things and this is true for problem solving. There is usually more than one way to solve a problem and some ways work better than others. Using manipulatives also helps students to refine their skills of determining the best strategy to problem solve and sometimes through guess and check/trial and error.
7. Why do they say not "hands - on" but "hands - on; minds - on"?
If activities are hands on only, students aren't learning to the depth at which their potential is. Activities need to be thought provoking and engaging of the mind as they work with their hands so that they can correlate knowledge/information to experience. A teacher should ensure that they are promoting equity within the education they are giving to the student in that they need to give the students solid instruction that give the student a firm foundation from which to build upon. If the students don't have good instruction and are given manipulatives, they will end up confused and won't get the max out of what they are supposed to be learning. They won't be able to make the connections and conclusions that are intended for them. Manipulatives must be coupled with strong teaching.
8. How do the process standards relate to the use of manipulatives?
Problem Solving:
Manipulatives incorporates the use of every process standard. Students exercise criticial thinking skills when using manipulatives in that they have to think beyond what is "expected or obvious" to come up with creative solutions. Students use a variety of problem solving strategies to come to a solution. Manipulatives also focuses more on the process rather than the product which is important when it comes to deepening mathematical understanding.
Communication
Students naturally use the process standard of communication when working with manipulatives/activities, especially when working with groups. As the students are encouraged to talk through their mathematical thought processes to reach a solution they are furthering their ability to communicate using the language of math. Their communication skills are sharpened as they engage in discussion and written reflection.
Reason and Proof
Students are asked to give rationale for their thinking when working with these activities. They should be talking through their processes, making conjectures and testing their predictions to see if they have understanding. Students should be working through problems that are meaningful and lend to explanation and justification of their work.
Representation
manipulatives are a great way to incorporate representation. Students can use manipulatives to represent data, mathematical equations, shapes, patterns, etc.
Connections
Students can make connections especially with the real world as they problem solve and work with manipulative activities. They are able to connect mathematical ideas together to see how mathematics is a coherent whole.
In class today, Monique and I did three different manipulatives which I thought were good. We did the snap blocks, unifix cubes and pattern blocks. I would have liked to experiment with the other manipulatives but we ran out of time. I really liked the snap blocks because they were so versatile and had many colors. It was easy to find activities that could be incorporated at every grade level with these. I also really liked the pattern blocks as there were a lot of things you could do with them. I thought with the pattern blocks; however, that it could be helpful to have many colors of the same shape (e.g. triangles would have yellow, green, orange, red, blue) so that if a student wanted to do representation of a pie graph for data analysis, it would be less confusing. I do understand that it is also important for them to be the same color. I also appreciated our discussion in class about what to do when students had deficiency in fine motor skills and thought that the suggestions were very good and insightful.
I really have enjoyed learning more about manipulatives in this class and I'm excited to purchase my own and implement them in the classroom.
Saturday, April 17, 2010
Thursday, April 15, 2010
Errors
I was glad to have done this activity in class this semester. It was so interesting to see students' work and their thought processes. I realized through this activity that I learned just like these students -- a set of rules and regulations without knowing why the rules worked. It is important to be able to see where students are messing up in their math work as a result of a wrong understanding about their mathematical processes.
I felt that this was a very helpful activity to prepare me to be an excellent educator because I have more of an understanding of how and why students think the way they do. It's amazing how learning math in the way that "it has always been done" gives a faulty foundation in math.
I really appreciated when we would work through a problem and then use manipulatives to show how the problem worked because it helped me to visualize and comprehend why rules that I have been taught worked.
I learned not to teach students shortcuts, use manipulatives as much as possible, and to show the processes, explain why they work, and the product and not just the product.
TECHNOLOGY BLOG:
I think I've used technology more in this class than in all of my other classes. I am so thankful to have had the opportunity to implement technology into my learning experience as a future educator. It is overwhelming when I think about how technologically advanced this next generation is whom I will be teaching. I am still nervous about using the smart board in the classroom, but before this class, I had never come in contact with one, so I feel like I am at a point where I am comfortable enough to play around with it and figure it out whereas before I wasn't at all. I feel like I've grown a lot in my understanding in how it works and also in understanding the importance of it in the classroom as it gets the students to actively engage in learning.
I've noticed that I have learned a lot about formatting Word documents because of the different requirements in our assignments in ETE 339 as well. I've never used a Google document before and the thought of it scared me a little, but I create them all of the time. I also use them outside of school in my organization for things such as sign up sheets and brainstorming ideas sheets. This tool is so handy to have in collaborating with others to accomplish a common task/goal.
I remember the calculators that I had in high school and I thought that they were technologically advanced and I graduated in 2000. As we looked at the calculators in class and went through the various activities yesterday, I was amazed that one could do so many things on a calculator and that they had become so versatile. I never would have dreamed that a calculator could set up a data table, find the lcd, gcd, etc.
These things goes to show that technology has come such a long way and should be implemented in the classroom. If you would have asked me in January if I was excited to use technology in the classroom, unfortunately, I would have responded the same as most teachers today that they didn't know enough about it to use it effectively. I think that at least now, though I'm not an expert in technology, have gotten enough exposure to it and the possibilities within the classroom that technology can be used that I am excited to try it out in my own class. I know that I will be learning as I go, but teachers are life long learners anyway. I am glad that I had the opportunity to experiment and practice with technology in this class. I feel that I've grown a lot in this area.
I felt that this was a very helpful activity to prepare me to be an excellent educator because I have more of an understanding of how and why students think the way they do. It's amazing how learning math in the way that "it has always been done" gives a faulty foundation in math.
I really appreciated when we would work through a problem and then use manipulatives to show how the problem worked because it helped me to visualize and comprehend why rules that I have been taught worked.
I learned not to teach students shortcuts, use manipulatives as much as possible, and to show the processes, explain why they work, and the product and not just the product.
TECHNOLOGY BLOG:
I think I've used technology more in this class than in all of my other classes. I am so thankful to have had the opportunity to implement technology into my learning experience as a future educator. It is overwhelming when I think about how technologically advanced this next generation is whom I will be teaching. I am still nervous about using the smart board in the classroom, but before this class, I had never come in contact with one, so I feel like I am at a point where I am comfortable enough to play around with it and figure it out whereas before I wasn't at all. I feel like I've grown a lot in my understanding in how it works and also in understanding the importance of it in the classroom as it gets the students to actively engage in learning.
I've noticed that I have learned a lot about formatting Word documents because of the different requirements in our assignments in ETE 339 as well. I've never used a Google document before and the thought of it scared me a little, but I create them all of the time. I also use them outside of school in my organization for things such as sign up sheets and brainstorming ideas sheets. This tool is so handy to have in collaborating with others to accomplish a common task/goal.
I remember the calculators that I had in high school and I thought that they were technologically advanced and I graduated in 2000. As we looked at the calculators in class and went through the various activities yesterday, I was amazed that one could do so many things on a calculator and that they had become so versatile. I never would have dreamed that a calculator could set up a data table, find the lcd, gcd, etc.
These things goes to show that technology has come such a long way and should be implemented in the classroom. If you would have asked me in January if I was excited to use technology in the classroom, unfortunately, I would have responded the same as most teachers today that they didn't know enough about it to use it effectively. I think that at least now, though I'm not an expert in technology, have gotten enough exposure to it and the possibilities within the classroom that technology can be used that I am excited to try it out in my own class. I know that I will be learning as I go, but teachers are life long learners anyway. I am glad that I had the opportunity to experiment and practice with technology in this class. I feel that I've grown a lot in this area.
Monday, April 12, 2010
Journal Article Review:
It is important that teachers are familiar with technology applications that are available to learners so that they can implement them within the classroom to enhance the learning of their students. The use of technology allows students to have feedback immediately so that they know what they understand and what they need to work on. It is also an interactive approach to learning and allows students to have a visual representation. These programs have the ability to be customized and can even have bilingual options which helps English Language Learners.
The article gives multiple examples of different uses of technology in a lesson. The outcomes of using technology in teaching are very positive. I appreciated this article because I find myself to be one of those people who doesn't like technology all that well. It is good for me to be able to see the benefits and different applications that are available for learning. I can see myself using this in my classroom.
The article gives multiple examples of different uses of technology in a lesson. The outcomes of using technology in teaching are very positive. I appreciated this article because I find myself to be one of those people who doesn't like technology all that well. It is good for me to be able to see the benefits and different applications that are available for learning. I can see myself using this in my classroom.
Journal Article Review: Supporting Language Learners
In this article, several techniques were discussed to become more effective in teaching English Language Learners. ELL's are becoming increasingly prevalent in the United States and teachers need to teach with awareness in order to provide an education that is equitable. The techniques that were discussed were: using advanced organizers, developing student's vocabulary, using visual cues, adjusting teacher talk, promoting low-anxiety classrooms, and using predictable routines. The authors of this journal also expressed the need for teachers to keep high expectations on these students because they will rise to the challenge and meet expectations.
I thought that this article was very helpful because it gave practical examples of how to help these students to get a quality education. All students have the right to learn, so it is our responsibility as teachers to ensure that students are able to engage within the classroom just like the other students. I will definitely take the information given in this article and keep it for future reference as it had excellent suggestions.
I thought that this article was very helpful because it gave practical examples of how to help these students to get a quality education. All students have the right to learn, so it is our responsibility as teachers to ensure that students are able to engage within the classroom just like the other students. I will definitely take the information given in this article and keep it for future reference as it had excellent suggestions.
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