Module 12
Hey Jess! Hope you're having a great week!
Coordinate Grids
Here is a list of the sites I explored:
http://www.math.com/school/subject3/practice/S3U1L2/S3U1L2Pract.html
This site works well, but I do not really see a need for its use in the classroom, as this activity could be done just as easily on paper. While the school I am in right now provides laptops for all of the students, not all schools do that, so this may be a good site to assign review homework on, but it isn't necessary. It is good practice at identifying coordinates, but there is nothing really added by using technology with this activity as the kids are just typing the letter they find. I would possibly use this in a class, but I would not say it is really necessary to complete these types of activities.
http://www.shodor.org/interactivate/activities/GeneralCoordinates/
This one was very similar to the one above, but it was an actual interactive game, so there was more use of the technological portion. There were two different modes, view mode and guess mode, so the students could switch back and forth based on which level they were at. I could see this being used as a fun review game for homework or if there was extra time in the classroom for coordinate review. It could also be competitive, which often motivates students!
http://www.beaconlearningcenter.com/weblessons/GridGraph/default.htm
I loved this site and would definitely use it in a classroom! It is an interactive map of sorts where the student is helping a virtual character plan a museum visit. Each question about coordinates provides a real life scenario in which this math could be used and it makes it a fun activity for the students to get to the end. This was probably one of my favorite sites I visited.
http://www.shodor.org/interactivate/activities/OrderedSimplePlot/
I liked this site because it allowed students to virtually create their own graph and easily change any mistakes made. They are able to enter the coordinates and see where they are on the graph, so they can play around in all four quadrants. I would definitely use this tool when teaching the four quadrants as the students can easily see where each coordinate lands, but they do not have to continuously erase if errors are made, which makes it much less confusing.
http://mrnussbaum.com/stockshelves
This was another link with a very fun and interactive educational game! I probably would not use this to teach, but would allow students to get on it for review when extra time allowed in class or at home if they wished. It is a fun game for the kids but also serves a purpose. It can also be competitive if multiple students are playing, so I think this is something they would really enjoy.
While technology integration is currently a widely encouraged concept, I think there are definitely plenty of advantages and disadvantages. Technological tools often make things faster and easier for the teacher in the classroom, as there is a lot less set up required and it is easier to correct any error that may occur. It also helps children with skills they will need in the future using and accessing different sites and resources. However, a few of the obvious disadvantages are that technology is known to not work at times, and it can also be distracting to students. If a lesson is planned around technology, it is always good to have a back up plan in mind in case the site crashes or the internet won't work - both of which commonly occur in schools. As for distractions, if every student is on a computer, it can be hard to ensure that they are all doing what they are supposed to be doing. For example, I mentioned earlier that the school I am completing my field work in allows each student to have a laptop. When the teacher has them all doing something on the computer, more often than not we catch at least one student playing a game or messing with the webcam rather than completing the assignment. Obviously this is not supposed to occur, but young students are curious and love to play when they think they can't get caught. This is easier to avoid when you can see the paper on all of their desks.
Did you have trouble opening some of these links? A few told me that the host names were invalid, so I couldn't look through them!
Miras, Reflections, and the Kaleidoscopes
I have never used a Mira before! I wouldn't necessarily call it problematic, but I did run into a little frustration because if it moved at all, things would look different. You can tell a bit in my sketch that I ran into that problem while drawing the face and one of the swing ropes. However, it does provide an excellent example for transformations and what an exact flip would look like. As for what I would take into the classroom, I enjoyed a lot of these activities! One that stuck out to me was the alphabet symmetry. I think that is an excellent way to look for symmetry as the alphabet is something easy that everyone can feel comfortable using. With lines of symmetry, the Mira can be helpful in showing that if an object has a line of symmetry, the flip will look the same. However, with the boy and the swing, there was no line of symmetry, so when it was flipped, he was facing the complete other direction. A Mira would be fun to use in the classroom to help differentiate between reflections, rotations, etc. Would you use a Mira in your classroom? How would you prevent it from moving slightly and distorting the image the students are trying to trace? For me, this was just a slight inconvenience, but I am worried that with younger students, this might really frustrate them.
Case Studies
1. What ideas about measurement do the children in Barbara’s class (case 12) bring to school before they are taught about it?
The kids were able to use relative terms, like "big" and "very big," and also compare the box to the size of other objects around them. They were able to define their term "big" by comparing it to things, like a tree or King Kong. However, when initially asked how big the box was, none of them used numerical content to describe it. They were able to relate it to other objects, saying it was "big like the light" or half the size of an object in the room. When the teacher went more in-depth with her question relating to measurement, the students were able to recognize that they could use a ruler, but they did not have one so they used baskets instead. Although one basket is not a unit of measurement, they were connecting the idea that the box was the size of multiple baskets.
2. Many children struggle with the idea that the larger the unit, the fewer the number of units needed to cover a length. Go through the cases by Rosemarie (case 13) and Dolores (case 14) to identify how different children are making sense of this issue.
The students' confusion makes sense, and it is something I had never thought about before! If they are taught that larger sizes relate to larger measurements, it would be difficult to understand larger unit sizes relative to smaller amounts of that unit! In Rosemarie's case, the students thought Miriam had the largest foot because she took the largest number of steps. In the beginning, they seemed to understand the concept, making connections to say that our hands are smaller than our feet, but their confusion definitely set in. Miriam was actually the one to point out that the smaller the foot, the more steps would be needed. Can you think of a better way to talk through this type of confusion in the classroom?
3. In Dolores’s case, line 245, Chelsea notices that Tyler and Crissy both measure the width of the basketball court as 62 “kid feet.” Why didn’t everybody measure the width as 62 kid feet? What discrepancy is Chelsea noticing? What is Henry noticing? How are their observations related to the issue that arises in Sandra’s seventh-grade class (case 17)?
The discrepancies can be occurring for many reasons! Everyone has different sized feet, so they would not all get 62 "kid feet." The way that they walk could also influence the number, as they may not all be walking toe to heel. Both Henry and Chelsea are able to realize that if the results are close for one line, they should be for another line as well. In relation to Sandra's class, they both were confused at the relation of bigger feet meaning smaller outcomes. I was surprised that 7th graders would struggle with this!
4. The children in cases by Mabel (case 15) and Josie (case 16) are working out the use of standard tools for measuring length. Specifically, the children in both classes discuss how to place the tool and how to read the number of units. What do the students have to say about these two issues? What do they understand about measuring with accuracy and precision?
Both of the cases seemed to understand the importance of measuring accurately and precisely. In case 15, they were discussing putting their fingers between the rulers, and recognizing that while one finger threw off the measurement by a small amount, more fingers would throw it off by a larger amount. They also were able to recognize that different tools are best for different sizes. In case 16, the students were able to recognize that the extra quarter of an inch could throw off their measurements.
5. By comparing the cases from second, third, fourth, and seventh grades to Barbara’s kindergarten (case 12), can we identify ideas that, by the older grades, are understood by the children and no longer warrant discussion. What are some issues that still lie ahead for Barbara’s students to sort out?
These studies really helped me realize the process students must go through to properly understand measurement. I was surprised that students in middle school were still struggling with the concept of larger units leading to a smaller number outcome. That is something that I never would have thought to cover until seen firsthand. I think the earlier that these concepts are introduced, the easier the students understanding will be. I think things like placing fingers between the rulers no longer warrant prior discussion in older grades, as the 4th graders seemed to understand this clearly. However, if issues like that arise, I think they do warrant discussion to prevent future error and misunderstanding. Barbara's students still have a lot of learning ahead to understand measurement! They seem to grasp the concept of comparing sizes to see what is larger or smaller, but their understanding of units is just beginning.
For further discussion…
A fellow teacher says that he cannot start to teach any geometry until the students know all the terms and definitions and that his fifth graders just cannot learn them. What misconceptions about teaching geometry does this teacher hold?
One big misconception is that vocabulary must come before content. I believe that when teaching anything, but especially geometry, the vocabulary can be learned while learning the content. If the correct vocabulary is used over and over while teaching, practicing, and reviewing the content, the students will understand what it means. I personally think that this is a more helpful way of learning the vocabulary, as they will have examples of when these things occur rather than just broad definitions that they have never seen before.
Now that you’ve had some time to explore the world of geometry, how has your view of the key ideas of geometry that you want your students to work though changed?
These modules have really helped me see past my previous thoughts about geometry. I struggled with it so much in school and I really only thought about shapes when I thought of geometry, but I now see that there is so much more to it and how helpful manipulatives and hands-on activities can be when teaching it. When I was taught geometry, I was forced to memorize vocabulary and do an endless amount of worksheets. I believe that if I had learned it this way in school instead, I could have been much more successful.
Coordinate Grids
Here is a list of the sites I explored:
http://www.math.com/school/subject3/practice/S3U1L2/S3U1L2Pract.html
This site works well, but I do not really see a need for its use in the classroom, as this activity could be done just as easily on paper. While the school I am in right now provides laptops for all of the students, not all schools do that, so this may be a good site to assign review homework on, but it isn't necessary. It is good practice at identifying coordinates, but there is nothing really added by using technology with this activity as the kids are just typing the letter they find. I would possibly use this in a class, but I would not say it is really necessary to complete these types of activities.
http://www.shodor.org/interactivate/activities/GeneralCoordinates/
This one was very similar to the one above, but it was an actual interactive game, so there was more use of the technological portion. There were two different modes, view mode and guess mode, so the students could switch back and forth based on which level they were at. I could see this being used as a fun review game for homework or if there was extra time in the classroom for coordinate review. It could also be competitive, which often motivates students!
http://www.beaconlearningcenter.com/weblessons/GridGraph/default.htm
I loved this site and would definitely use it in a classroom! It is an interactive map of sorts where the student is helping a virtual character plan a museum visit. Each question about coordinates provides a real life scenario in which this math could be used and it makes it a fun activity for the students to get to the end. This was probably one of my favorite sites I visited.
http://www.shodor.org/interactivate/activities/OrderedSimplePlot/
I liked this site because it allowed students to virtually create their own graph and easily change any mistakes made. They are able to enter the coordinates and see where they are on the graph, so they can play around in all four quadrants. I would definitely use this tool when teaching the four quadrants as the students can easily see where each coordinate lands, but they do not have to continuously erase if errors are made, which makes it much less confusing.
http://mrnussbaum.com/stockshelves
This was another link with a very fun and interactive educational game! I probably would not use this to teach, but would allow students to get on it for review when extra time allowed in class or at home if they wished. It is a fun game for the kids but also serves a purpose. It can also be competitive if multiple students are playing, so I think this is something they would really enjoy.
While technology integration is currently a widely encouraged concept, I think there are definitely plenty of advantages and disadvantages. Technological tools often make things faster and easier for the teacher in the classroom, as there is a lot less set up required and it is easier to correct any error that may occur. It also helps children with skills they will need in the future using and accessing different sites and resources. However, a few of the obvious disadvantages are that technology is known to not work at times, and it can also be distracting to students. If a lesson is planned around technology, it is always good to have a back up plan in mind in case the site crashes or the internet won't work - both of which commonly occur in schools. As for distractions, if every student is on a computer, it can be hard to ensure that they are all doing what they are supposed to be doing. For example, I mentioned earlier that the school I am completing my field work in allows each student to have a laptop. When the teacher has them all doing something on the computer, more often than not we catch at least one student playing a game or messing with the webcam rather than completing the assignment. Obviously this is not supposed to occur, but young students are curious and love to play when they think they can't get caught. This is easier to avoid when you can see the paper on all of their desks.
Did you have trouble opening some of these links? A few told me that the host names were invalid, so I couldn't look through them!
Miras, Reflections, and the Kaleidoscopes
Case Studies
1. What ideas about measurement do the children in Barbara’s class (case 12) bring to school before they are taught about it?
The kids were able to use relative terms, like "big" and "very big," and also compare the box to the size of other objects around them. They were able to define their term "big" by comparing it to things, like a tree or King Kong. However, when initially asked how big the box was, none of them used numerical content to describe it. They were able to relate it to other objects, saying it was "big like the light" or half the size of an object in the room. When the teacher went more in-depth with her question relating to measurement, the students were able to recognize that they could use a ruler, but they did not have one so they used baskets instead. Although one basket is not a unit of measurement, they were connecting the idea that the box was the size of multiple baskets.
2. Many children struggle with the idea that the larger the unit, the fewer the number of units needed to cover a length. Go through the cases by Rosemarie (case 13) and Dolores (case 14) to identify how different children are making sense of this issue.
The students' confusion makes sense, and it is something I had never thought about before! If they are taught that larger sizes relate to larger measurements, it would be difficult to understand larger unit sizes relative to smaller amounts of that unit! In Rosemarie's case, the students thought Miriam had the largest foot because she took the largest number of steps. In the beginning, they seemed to understand the concept, making connections to say that our hands are smaller than our feet, but their confusion definitely set in. Miriam was actually the one to point out that the smaller the foot, the more steps would be needed. Can you think of a better way to talk through this type of confusion in the classroom?
3. In Dolores’s case, line 245, Chelsea notices that Tyler and Crissy both measure the width of the basketball court as 62 “kid feet.” Why didn’t everybody measure the width as 62 kid feet? What discrepancy is Chelsea noticing? What is Henry noticing? How are their observations related to the issue that arises in Sandra’s seventh-grade class (case 17)?
The discrepancies can be occurring for many reasons! Everyone has different sized feet, so they would not all get 62 "kid feet." The way that they walk could also influence the number, as they may not all be walking toe to heel. Both Henry and Chelsea are able to realize that if the results are close for one line, they should be for another line as well. In relation to Sandra's class, they both were confused at the relation of bigger feet meaning smaller outcomes. I was surprised that 7th graders would struggle with this!
4. The children in cases by Mabel (case 15) and Josie (case 16) are working out the use of standard tools for measuring length. Specifically, the children in both classes discuss how to place the tool and how to read the number of units. What do the students have to say about these two issues? What do they understand about measuring with accuracy and precision?
Both of the cases seemed to understand the importance of measuring accurately and precisely. In case 15, they were discussing putting their fingers between the rulers, and recognizing that while one finger threw off the measurement by a small amount, more fingers would throw it off by a larger amount. They also were able to recognize that different tools are best for different sizes. In case 16, the students were able to recognize that the extra quarter of an inch could throw off their measurements.
5. By comparing the cases from second, third, fourth, and seventh grades to Barbara’s kindergarten (case 12), can we identify ideas that, by the older grades, are understood by the children and no longer warrant discussion. What are some issues that still lie ahead for Barbara’s students to sort out?
These studies really helped me realize the process students must go through to properly understand measurement. I was surprised that students in middle school were still struggling with the concept of larger units leading to a smaller number outcome. That is something that I never would have thought to cover until seen firsthand. I think the earlier that these concepts are introduced, the easier the students understanding will be. I think things like placing fingers between the rulers no longer warrant prior discussion in older grades, as the 4th graders seemed to understand this clearly. However, if issues like that arise, I think they do warrant discussion to prevent future error and misunderstanding. Barbara's students still have a lot of learning ahead to understand measurement! They seem to grasp the concept of comparing sizes to see what is larger or smaller, but their understanding of units is just beginning.
For further discussion…
A fellow teacher says that he cannot start to teach any geometry until the students know all the terms and definitions and that his fifth graders just cannot learn them. What misconceptions about teaching geometry does this teacher hold?
One big misconception is that vocabulary must come before content. I believe that when teaching anything, but especially geometry, the vocabulary can be learned while learning the content. If the correct vocabulary is used over and over while teaching, practicing, and reviewing the content, the students will understand what it means. I personally think that this is a more helpful way of learning the vocabulary, as they will have examples of when these things occur rather than just broad definitions that they have never seen before.
Now that you’ve had some time to explore the world of geometry, how has your view of the key ideas of geometry that you want your students to work though changed?
These modules have really helped me see past my previous thoughts about geometry. I struggled with it so much in school and I really only thought about shapes when I thought of geometry, but I now see that there is so much more to it and how helpful manipulatives and hands-on activities can be when teaching it. When I was taught geometry, I was forced to memorize vocabulary and do an endless amount of worksheets. I believe that if I had learned it this way in school instead, I could have been much more successful.
Hey Megan! Hope you're doing well! I really liked exploring the links, some were troublesome but the ones I did look at were very interesting! My favorites were the ones I posted about, you made really great points about the ones you shared! I think the usage of a Mira would depend on grade level, as you mentioned it could be really frustrating for younger students. I am not familiar with Miras so I would need to work with them more in order to have a better idea how to prevent those errors :) For the case study, I think Miriam did a great job with her explanation, as you mentioned. I mentioned in my blog I think the adult vs kid foot portion could've definitely been an eye opener. To answer your question, I could have a child with smaller feet come up and measure something, then me measure it, to show students bigger feet does not yield a bigger measurement. Seeing this big of difference in foot size may help students visualize it much better. I also really liked the points you made about misconceptions and vocabulary coming before content, great post Megan!!
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