Coordinate Grids
http://mathsfirst.massey.ac.nz/Algebra/CoordSystems/Coordinates2D.htm
http://www.beaconlearningcenter.com/weblessons/GridGraph/default.htm
http://www.shodor.org/interactivate/activities/MazeGame/
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell18.swf
https://www.funbrain.com/games/whats-the-point
http://mrnussbaum.com/stockshelves
http://www.math.com/school/subject2/S2U4Quiz.html
http://www.math.com/school/subject3/practice/S3U1L2/S3U1L2Pract.html
I decided to visit all of the websites. However, I was not able to access three of them. Because I want to teach kindergarten, I don't plan on using any of these in my future classroom, but if I am not lucky to get a kindergarten job and I teach an older age, I would use websites from shodor.com and math.com. The activities would be engaging for the students for a certain amount of time, and I think they could reinforce the teaching that the teacher has done. Some of the issues of using these types of technologies are that they are the same unless the programmer makes changes the games will be the same most of the time. But like I mentioned before I think these could be used as a reinforcement to the teachings of the teacher. Aubrey, did you have luck on getting the first two links to work or the graphing applet? I couldn't access those.
Miras, Reflections, and the Kaleidoscopes
I have not used a mira before, but I have to say that it is a pretty cool device. I did find the task difficult if the shapes or letters were too close together. I was having a tough time drawing the lines of symmetry across the middle of the letter instead of just above or below. This is what I came up with for the lines of symmetry in the letters given, I think if a different font were used, H would have 2 lines of symmetry and E would have 1 line. I found the words SAY, WOW, TOMB, and ACT for the challenge of finding a word that has symmetry. Aubrey, how do you think font would change the results? Did this hurt your eyes at all, my astigmatism was going a little crazy.
No Lines of Symmetry
1 Line of Symmetry
2 Lines of Symmetry
3+ Lines of Symmetry
E, F, G, J, K, L, N, P, Q, R, S, Z
A, B, C, D, H, I, M, T, U, V, W, Y
X
O
I have a better understanding of the differences between reflections and transformations along with rotations. I enjoyed the article and the learning and hands-on activity the students did. I will definitely bring the idea of hands-on learning into my future classroom, and I think it would be fun to introduce the students to the ideas of reflections and mirror images.
Case Studies
- The students have an understanding that people are bigger or smaller than each other. They believe that the box is big, mostly because it is bigger than most of them. They also understand that stacking things can be a way to measure something when some of the children recommended using a "measuring tape" to measure they already knew that there is something already made that will tell home tall or big something is.
- In Rosemarie's case the teacher first thought that the students had the correct idea on the measurement of feet concerning the size of the foot, but once the children performed the task on their own, they had a difficult time answering the question of whose foot was the biggest. At the beginning of Dolores's case, the children had the same struggle of measurement and the idea that a bigger foot meant fewer steps. With the guidance and homework assignment that the teacher gave the students, it seems that most of the students were able to finally make the connection.
- Chelsea is understanding the relation to the foot size of Tyler and Chrissy but takes notice that the other measurements should also be the same measurement. Henry has also noticed the difference that the children have given in the measuring of the different lines. They both seem to have an understanding that if the results are similar in measurement on one line, they should be the same for the other lines. These observations relate to Sandra's class because they have the same discrepancy, the students believe that the bigger feet mean bigger numbers, and that is the opposite thought process. I was a bit surprised by the 7th-grade responses, to be honest, I thought that they would have a better understanding of size. What about you Aubrey, did this particular case study surprise you like it did me?
- In both of the case's the students had discovered that using different tools for measurement is important depending on the size of the item. For the 2nd-grade class, some of the students thought that placing a finger on the mark would be okay because "nothing is perfect" however other students disagreed with this and gave other ways to accurately measure the length by "flipping" the ruler if it was not long enough. Some of these students also understood that the smaller marks between the inch marks meant "1/2". The 4th-grade class seemed to understand the precision of measurement, but a few students struggled with the very beginning space on the rulers, but they all seemed to have grasped the idea of the ruler starting at "0" and moving up.
- The unit of measurement and geometry should be introduced in the early school-aged years because as the students progress through the grades what they learn will continue to grow, expand and change in understanding. The kindergarten students are well on their way of building knowledge of measurements, but they still have a lot to learn. They will need to learn that the size of the unit used for measuring gives way to the number of units used, they need to learn measuring tools, and much more. By reviewing the case's we can see that this concept is still needing to be learned in the older grades, so most of these topics will still warrant discussion even if just for a refresher.
For Further Discussion...
Teaching students what the definitions and terms within the realm of geometry are important, but we must introduce and show our students learning through doing. If we wait until the students know all the terms of geometry, we would never be able to teach them the intricate details that geometry holds. This misconception of the students knowing the definitions is what is holding our students back. Engaging the students in activities that allow them to learn and explore for themselves will help the students learn how the definition fits the word, it creates a long-lasting "bond" to the knowledge that they can learn. Waiting to introduce things will just hurt the students as they progress in school, open their minds to the concepts now so they can build and make connections.
Geometry is much more than I had originally posted about, the key ideas I spoke about included shapes, perimeter, area, and knowing the different angles. I hadn't realized that spatial knowledge was such an integral part of geometry, or that coordinate grids where included. After discussing all the information we have the last few weeks, I have learned much more about geometry, and I am more aware of the content knowledge, and a little less scared of the word geometry.
|
No Lines of Symmetry
|
1 Line of Symmetry
|
2 Lines of Symmetry
|
3+ Lines of Symmetry
|
|
E, F, G, J, K, L, N, P, Q, R, S, Z
|
A, B, C, D, H, I, M, T, U, V, W, Y
|
X
|
O
|
- The students have an understanding that people are bigger or smaller than each other. They believe that the box is big, mostly because it is bigger than most of them. They also understand that stacking things can be a way to measure something when some of the children recommended using a "measuring tape" to measure they already knew that there is something already made that will tell home tall or big something is.
- In Rosemarie's case the teacher first thought that the students had the correct idea on the measurement of feet concerning the size of the foot, but once the children performed the task on their own, they had a difficult time answering the question of whose foot was the biggest. At the beginning of Dolores's case, the children had the same struggle of measurement and the idea that a bigger foot meant fewer steps. With the guidance and homework assignment that the teacher gave the students, it seems that most of the students were able to finally make the connection.
- Chelsea is understanding the relation to the foot size of Tyler and Chrissy but takes notice that the other measurements should also be the same measurement. Henry has also noticed the difference that the children have given in the measuring of the different lines. They both seem to have an understanding that if the results are similar in measurement on one line, they should be the same for the other lines. These observations relate to Sandra's class because they have the same discrepancy, the students believe that the bigger feet mean bigger numbers, and that is the opposite thought process. I was a bit surprised by the 7th-grade responses, to be honest, I thought that they would have a better understanding of size. What about you Aubrey, did this particular case study surprise you like it did me?
- In both of the case's the students had discovered that using different tools for measurement is important depending on the size of the item. For the 2nd-grade class, some of the students thought that placing a finger on the mark would be okay because "nothing is perfect" however other students disagreed with this and gave other ways to accurately measure the length by "flipping" the ruler if it was not long enough. Some of these students also understood that the smaller marks between the inch marks meant "1/2". The 4th-grade class seemed to understand the precision of measurement, but a few students struggled with the very beginning space on the rulers, but they all seemed to have grasped the idea of the ruler starting at "0" and moving up.
- The unit of measurement and geometry should be introduced in the early school-aged years because as the students progress through the grades what they learn will continue to grow, expand and change in understanding. The kindergarten students are well on their way of building knowledge of measurements, but they still have a lot to learn. They will need to learn that the size of the unit used for measuring gives way to the number of units used, they need to learn measuring tools, and much more. By reviewing the case's we can see that this concept is still needing to be learned in the older grades, so most of these topics will still warrant discussion even if just for a refresher.
Hey Traice:
ReplyDeleteIt was nice to talk to you on the phone for a little bit this afternoon. I can't remember if the ones I chose were the first two or not, I scrolled through and chose based on if it looked interesting. In the font symmetry activity I tried with the Mira and it was very difficult so I ended up doing it without it mostly. I tried each letter with the Mira first. My eyes did hurt a little after the module was done. If the font changed to something a little more curvy, it would be harder to see where the symmetry lines would be.
In the case study I could see the younger kids being confused but I think I was surprised that the 7th graders didn't get it. Maybe they didn't have much practice with measurement. I know my kids think that their age is their clothing size, and I have to tell them that may not always be true. This was a good module and I learned a lot about how students see measurement and that we can't assume that they've been exposed to different scenarios but we can provide them new experiences to help them along the way.
Aubrey,
ReplyDeleteI had never used a mira before either but I found it to be a pretty cool tool. I found the symmetry on the alphabet very challenging because using the mira as a reflection showed that not all of the letter are actually symmetrical. Curvy line font would be very very difficult in my opinion.
I agree with your observation that we cannot assume that students have been previously exposed to a math concept, or any concept really. In my FE class we have a newer student who is currently struggling with most of the math that is being taught because she was not taught it in her previous school.
Math in general is so much more than most people think. If you ask the average adult what math is, I assume you'd get answers like, "adding numbers", "pointless with today's technology", or maybe something along the lines of "numbers, shapes, and that is about it". While we as current students and soon be teachers have learned math is so so much more than that, even geometry is more than what I originally thought.
Hope that doctor gave you good news...and you get to feeling better soon! Let me know if you need anything :)