Nets Activity
How could you use a similar activity with students in the classroom? Were you able to complete the activity without too much frustration? What are some anticipated issues while doing this activity with students?
While this activity was a challenge at first, once I cleared my mind and focused on one cut out at a time I was able to correctly identify the seven additional pentominoes that would make the "box." I did have a mistake in placing the bottom on just one of the shapes. It was on one of the octagon pieces, and I just miscalculated it by one square. I knew it was one or the other and I went with the wrong one. I think some students would get easily discouraged while doing this activity, at least at first. I think it would be beneficial to use the Polydons manipulatives that were used in the article so that students could not easily rip the paper. This would work well with students that could visual the changes but could pose difficulties for those that are more hands on. Ensuring that the students understand that having a tough time is okay would be important for my classroom.
Aubrey, did you have any trouble making the connections to the creation of the "boxes"?
Textbook Reading
4. Find one of the suggests applets, or explore GeoGebra and explain how it can be used. What are the advantages of using the computer instead of hands-on materials or drawings?
I decided to look up geogebra.org, and I pretty much got sucked into creating shapes and lines and polygons. You can use this program for a variety of different applications dealing with graphing calculators and geometry. Going into classic mode allows the user to do graphing, 3D shapes, and probability to just name a few things. Using this applet to create geometrical shapes is that if you know what you are doing, you can make the shapes and measurements rather fast. You don't have to necessarily worry about the size of the shape you are drawing about the students. You don't have to hear a student say "I can't draw that shape." Aubrey, what do you think about this program?
2. Briefly describe the nature of the content in each of the four geometric strands discussed in this chapter: Shapes and Properties, Location, Transformations, and Visualization.
Shapes and Properties: this is the content that is associated with both 2- and 3-dimensional shapes, that they learn what they are called and the way the shapes are similar and different. The students can begin to classify the different types of shapes and how the properties of the shapes will connect and be developed.
Location: is the analysis of paths from points on a map by way of using a coordinate system. Grid systems are used to identify locations, Level-1 thinkers the coordinates slides but do not flip or twist, like a reflection over the x- or y-axis. Level-2 thinkers can use logical reasoning, that includes the slope and Pythagorean relationships.
Transformations: these are the changes in the position or size of the shape. This includes slides, flips, turns, and line symmetry at the Level-0 thinkers. But for Level-1 thinkers, it also includes the composition of the transformation, proportional reasoning, and the understanding of tessellations. Level-2 thinkers, use their overall understanding of symmetries and in to build a bridge between the two ideas.
Visualization: creating of mental images and visually understanding the different viewpoints that could be predicted. Level-0 thinkers think about shapes with relation to the way they look. Level-1 thinkers give way to the meaning of properties and connecting the 2- and 3- dimensional shape properties together.
Spatial Readings/Building Plans
Did you find any of these activities challenging? If so, what about the activity made it challenging?
No, I did not find these activities challenging, I enjoyed this type of thinking and was able to get all the answers right on the first try.
Why is it important that students become proficient at spatial visualization?
I almost feel that spatial visualization is almost like thinking outside the box like one cannot be closed minded to the opportunities that could happen if that makes sense at all. Not only that but it helps you view things within our world, such as driving directions, ability to put things together (furniture or puzzles), it is giving the ability to see how something could work while still having the thoughts in your head. Aubrey, does that make sense? I think I have a good bit of spatial visualization.
At what grade level do you believe students are ready for visual/spatial activities? How can we help students become more proficient in this area?
I believe this learning should start as early as possible even before kindergarten when I think of spatial visualization it includes the ideas of putting together puzzle pieces. Encouraging younger children to put puzzles together help their minds work out the proper positions of the pieces. Though they can get frustrated with it, they will develop what they need to as time goes on. By continuing to practice and do things that involve spatial thinking and visualization they will become more open to seeing the larger pictures in their minds.
Tangrams
B1. Start with a parallelogram. Find a way to cut your parallelogram into pieces you can rearrange to form a rectangle.
It took me a few minutes to figure this problem out, I was having trouble with just drawing the line, so I decided to cut it out. Once I did that I was able to see that I had not made a straight enough line to create the rectangle, so I made adjustments.
B5. Start with a trapezoid. Dissect the trapezoid into pieces that will form a rectangle.
I again had trouble finding the right angle to cut the end of the trapezoid off at, I may have better luck when I am not so tired, but these problems were much more difficult for me than the other things we have done in the module. Aubrey, how did you do on this section, I think I need to revisit it to see if I can grasp a better understanding.
For Further Discussion
I decided to go online and shop at Toys R' Us and Amazon.com for this discussion, and I found the following games and toys. Each of these would promote and engage the children in learning about geometric shapes and spatial visualization without any actual teaching going on. By sorting and categorizing most of these shapes the children are learning how to make different shapes work together and how to create things with different geometric shapes. All of these toys are valuable to the children. Aubrey, what do you think? Do my toys fit into the informal recreational geometry ideas?
Today, Aubrey and I met in person to talk about this weeks blog. We both were very successful in the creation of the Nets boxes, Aubrey was able to correctly mark all of the bottoms of the boxes. :) We both figured out how to create the boxes in our heads, and had to resist the urges to pick up the pieces and create the boxes before allowed.
ReplyDeleteI thought Aubrey's explaination of van Hiele's level were accurate and the activities I thought made sense. We both had fun on the GeoGebra website and found it could be useful.
While I did not have any problems with the spatial reasonings, Aubrey struggled. While we were together today I walked her step by step through the process I used to place the train and know how the order of the pictures went. I explained to her that I looked at the "building" layouts and the angles that the sights were being viewed from. I also explained how I knew how the placement of the items would be behind during some views. Though we didn't agree on what age we thought it should be introduced, we both made vaild points.
We both failed at the Tangrams and had difficulty and we both feel like we need more experience with this section to really grasp a better understanding of how to break the tangrams apart to create the new shape. Aubrey mentioned that in her FE the students in her class were able to create the box shape in no time at all. I shared that at first I struggled, but when I stopped and thought about it I was successful. I had also worked into the late night hours completing the blog assignment.
Our toys that we found were similar and we agreed that many of the toys available have different geometric designs in them but most often the children don't realize what they are, but using these "toys" help start the developing concepts of math and geometric designs.
Thanks for meeting up with me today Aubrey, until next time :)