I think one of the main ways to make sure kids are being held accountable when using manipulatives is for the teacher to make sure and circulate the room. Obviously this leaves some lag time that the students could get off task or only let one student do the work, so more would probably need to be done. Maybe each student could be held accountable for documenting their work with the manipulatives. Like we did in class with the manipulatives we had to write down what we came up with using the manipulatives. Something like this could be done with the students in our classrooms as well. Another way to hold the students accountable for the manipulative activities is to do one on one evaluations. The teacher could have each student model the activity they were suppose to do for them again in an assessment type format.
I believe that the reason people say "hands-on, minds-on" now instead of just "hands-on" is because of how interactive the manipulatives are now and how much it can help students understand concepts. If the student is working with manipulatives they are more likely to be engaged both physically and mentally rather then if they were doing a worksheet or listening to a lecture. "Hands-on, minds-on" helps recognize how engaged the students are with their activities and hopefully learning even more.
The process standards fit in very nicely with the use of manipulatives. Students must problem solve when working with manipulatives. They may have never seen a particular manipulative before so they must problem solve how to actually use the manipulative and work through the activity. The students will also be using communication as well if they are working with a partner. They will have to communicate their ideas to each other to be able to properly use the manipulatives. Reasoning and proof can also be addressed with the use of manipulatives. The students will need to reason through how they are working with their manipulatives and then prove what they have done works. Connections are also prevalent with the use of manipulatives. It is very easy to incorporate many different content standards with the use of just one manipulative and students will be able to recognize how they all work together. Finally, representation is used with manipulatives by the students representing different problems with their manipulatives.
Tuesday, April 27, 2010
Monday, April 26, 2010
Errors Blog
I think one of the most informative things we did this semester was looking at the Errors in class. It was so helpful to actually sit and look at what a student did and try to figure out what they were really thinking when completing the problem. So many times in school I felt like teachers would just simply mark when I got an answer wrong and never really looked at what I did wrong in my computation. Doing these errors in class I was able to get practice on analyzing students responses. I think this will really help me in my classroom be able to identify what is really going on with my students.
Another helpful thing from these errors was learning different ways to teach my students mathematics. In 107 and 108 we got a taste of the different ways to try and look at the math problems and solve them but I feel like with this we went more in depth. I was able to see even more ways to do math for my students. When trying to teach students the traditional way to do addition or subtraction, if they do not understand it I now have a way to try and help them understand it. I will be able to present these problems to my students in a way that actually makes sense to them so they do not just think of math as a subject they just don't get and can't do. After completing these errors I will be to adapt to my students and accommodate their needs in mathematics.
Another helpful thing from these errors was learning different ways to teach my students mathematics. In 107 and 108 we got a taste of the different ways to try and look at the math problems and solve them but I feel like with this we went more in depth. I was able to see even more ways to do math for my students. When trying to teach students the traditional way to do addition or subtraction, if they do not understand it I now have a way to try and help them understand it. I will be able to present these problems to my students in a way that actually makes sense to them so they do not just think of math as a subject they just don't get and can't do. After completing these errors I will be to adapt to my students and accommodate their needs in mathematics.
Technology Blog
I found the week we spent focusing on technology really interesting. I have worked with Geometer's Sketchpad before but it had been awhile so it was nice to have a refresh of the different kinds of things you can do with it. I think the best part of the Sketchpad is being able to show students the properties of geometric figures. They would be able to actually see how angles stay the same, or lengths stay the same. I feel students will actually understand these concepts better because they will actually be able to see it rather than just telling them this is what it is. I will definitely try to incorporate Sketchpad into my teaching even if it is only using the free preview version. I think all students should be able to utilize this technology.
The calculators we used in class were also really interesting. I had never seen a calculator that was able to do all the different things that calculator was able to do. I think it would be really important to make sure students really understand how to work with fractions. The calculator will be very nice for when students have mastered their understanding of it, but if introduced at the wrong time I think it may hinder there understanding. Obviously though I think that these calculators are very helpful and a good look into what the future will be like for our students.
Another piece of technology we have really utilized in this class is the smart board. I had heard about smart boards before coming to this class but had never seen one actually used before. I think it is an incredible piece of technology because it can make things so interactive for students. I think by having the students actually work on the original document from the computer makes it more exciting for them and like they are really contributing. I'm sure sometime in the future there will even be personal smart boards for every student on their desk.
The calculators we used in class were also really interesting. I had never seen a calculator that was able to do all the different things that calculator was able to do. I think it would be really important to make sure students really understand how to work with fractions. The calculator will be very nice for when students have mastered their understanding of it, but if introduced at the wrong time I think it may hinder there understanding. Obviously though I think that these calculators are very helpful and a good look into what the future will be like for our students.
Another piece of technology we have really utilized in this class is the smart board. I had heard about smart boards before coming to this class but had never seen one actually used before. I think it is an incredible piece of technology because it can make things so interactive for students. I think by having the students actually work on the original document from the computer makes it more exciting for them and like they are really contributing. I'm sure sometime in the future there will even be personal smart boards for every student on their desk.
Wednesday, April 7, 2010
April Journal Summary #2
Mathematics Teaching in the Middle School. Map Scale, Proportion, and Google Earth. By: Martin Roberge and Linda Cooper
This article talks about how children are able to at a young age realize the relationship between things on a map and their actual size. However, only 23% of middle school students could correctly find the distance between two cities on a map. They believe there is this gap because there is so much focus on just setting up the proportions and not realizing what they are representing. Teachers should focus students' attention on the context of the problem so they can develop an understanding of the relationship between values in a proportion. They had students take aerial maps and find ratios and scales for them. The students looked at baseball fields and football fields. They then extended their map scales to creating proportions. They then wanted students to apply map scale within a proportion to explore new situations. The teacher then placed numerous aerial pictures of famous landforms and asked different questions about the pictures. This activity really helps students to understand the relationship between values as they construct proportions.
I found this article really interesting because I have worked with Google Earth before. Since the teacher got their aerial shots from Google Earth I was interested in how they used them. I also think making the students work through proportions and map scale this way would be very beneficial. I think in math we tend to just give students equations and things to plug different numbers into that they do not understand why they are doing it. By having the students figure out the map scale on their own first, they are able to then understand why we make proportions and where they come from. If students understand where the proportions are coming from hopefully they would be less likely to make mistakes in their scaling. Hopefully we could increase that 23% who do it correctly to about 50%. An adaptation I would maybe make to this activity is to let the students use Google Earth themselves and pick a picture to scale on their own. This way they could know another use of technology and explore a little more on computers.
This article talks about how children are able to at a young age realize the relationship between things on a map and their actual size. However, only 23% of middle school students could correctly find the distance between two cities on a map. They believe there is this gap because there is so much focus on just setting up the proportions and not realizing what they are representing. Teachers should focus students' attention on the context of the problem so they can develop an understanding of the relationship between values in a proportion. They had students take aerial maps and find ratios and scales for them. The students looked at baseball fields and football fields. They then extended their map scales to creating proportions. They then wanted students to apply map scale within a proportion to explore new situations. The teacher then placed numerous aerial pictures of famous landforms and asked different questions about the pictures. This activity really helps students to understand the relationship between values as they construct proportions.
I found this article really interesting because I have worked with Google Earth before. Since the teacher got their aerial shots from Google Earth I was interested in how they used them. I also think making the students work through proportions and map scale this way would be very beneficial. I think in math we tend to just give students equations and things to plug different numbers into that they do not understand why they are doing it. By having the students figure out the map scale on their own first, they are able to then understand why we make proportions and where they come from. If students understand where the proportions are coming from hopefully they would be less likely to make mistakes in their scaling. Hopefully we could increase that 23% who do it correctly to about 50%. An adaptation I would maybe make to this activity is to let the students use Google Earth themselves and pick a picture to scale on their own. This way they could know another use of technology and explore a little more on computers.
April Journal Summary #1
Teaching Children Mathematics. Asmorgasbord of assessment options. By: Kathy Bacon
This article is focused on student-centered classroom assessment. Assessment should support the learning of useful mathematics and provide useful information to both teachers and students. Teachers should look at assessments to see where next to go with their students and should really use assessment as a guide for the next phases of learning. For assessment to really be effective teachers need to use a variety of techniques, understand their goals, and think about what is really being developed. Math should be a progression of learning. Van de Well provided an idea of the different levels of learning and how children should move through the process. Level 0: Visualization, Level 1: Analysis, Level 2: Informal Deduction, Level 3: Deduction, Level 4: Rigor. These levels help to assess a student's level of geometric thinking. An example was then given of three students at different levels of their geometric thinking. Through each child's reasoning the teacher was able to help the student build and go further into their geometric thinking. This article really stresses how assessments should allow creation of products that show their thought process. The assessment option should be thoughtfully matched to the achievement target.
I thought this article gave a lot of insight into assessment. I had never really thought of assessment as a progression. I can see now why it is so important to have insightful assessment for math. One thing about the article I didn't really like was all the examples given. I did not see how they were related or how they showed progression. I wish they would have given more examples of what the students were taught, what the assessment was, and then where the teacher went from there. I would have also liked to see how the teacher analyzed the assessment results a little bit more. Overall, I though the article was helpful in making teachers think more about assessment but I do not think it was presented in the best manner.
This article is focused on student-centered classroom assessment. Assessment should support the learning of useful mathematics and provide useful information to both teachers and students. Teachers should look at assessments to see where next to go with their students and should really use assessment as a guide for the next phases of learning. For assessment to really be effective teachers need to use a variety of techniques, understand their goals, and think about what is really being developed. Math should be a progression of learning. Van de Well provided an idea of the different levels of learning and how children should move through the process. Level 0: Visualization, Level 1: Analysis, Level 2: Informal Deduction, Level 3: Deduction, Level 4: Rigor. These levels help to assess a student's level of geometric thinking. An example was then given of three students at different levels of their geometric thinking. Through each child's reasoning the teacher was able to help the student build and go further into their geometric thinking. This article really stresses how assessments should allow creation of products that show their thought process. The assessment option should be thoughtfully matched to the achievement target.
I thought this article gave a lot of insight into assessment. I had never really thought of assessment as a progression. I can see now why it is so important to have insightful assessment for math. One thing about the article I didn't really like was all the examples given. I did not see how they were related or how they showed progression. I wish they would have given more examples of what the students were taught, what the assessment was, and then where the teacher went from there. I would have also liked to see how the teacher analyzed the assessment results a little bit more. Overall, I though the article was helpful in making teachers think more about assessment but I do not think it was presented in the best manner.
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