Module Nine

Quick Images Video

I thought the students did well making connections to what they saw and how they remembered what the figure looked liked according to them. When I saw the image at first I thought of the crescent moon shape. The students were able to notice facts about the shape that I only thought of as an after thought. When they began to move the image, I was able to think of banana or a smile, but that was only after they rotated the image. Aubrey, did think of a moon shape?

Shapes and Geometric Definitions

Triangle- Shape that has only 3 straight sides that connect.

Square- Shape that has 4 equal straight sides that connect creating 4 90 degree angles.

Rectangle- Shape that has 4 sides that connect but 2 sides that are parallel are longer than the other 2 parallel sides, also creating 4 90 degree angles.

Parallelogram- Shape that has 4 straight sides that connect where the opposite sides are parallel. Squares and Rectangles are parallelograms.

The definition tells you what the meaning of the word is, whereas the attributes tells us something that is being caused, so with my definitions above I think I may have included some attributes along with the definitions. Aubrey, what do you think about this question, are attributes an extension of  the definition?   I believe that a definition is the explanation of what the meaning of the term is. 

Through the eyes of the students...

The students need to consider not only the number of sides the geometric shape has but also the angles that are created with the shape. They also need to learn about rotations of shapes, many students struggled with the idea that a triangle was still a triangle even if it was drawn on it's side. Even with the rectangle, some students questioned the idea of the shape still being a rectangle since it was drawn differently. The students learned that as they applied the definition they had developed they were able to count the shape as that particular shape, but still would struggle in cases and would try to make sense of how it was that shape within the attributes they discovered. One student mentioned they think it is a triangle, it looks upside down, but then in the same writing says that it kind of doesn't look like a triangle. Children begin to use the definition to create the understanding that they have and while I feel it may have been shallow to start with they start to grasp a deeper understanding the more they use their minds. 

Susannah

I feel like Susannah has an understanding of triangles in general but relates them to the common equilateral triangle and the triangles that don't look the same are causes her to question what type of triangle it is. She states that those (L and R) are not real triangles. Later on Susannah mentions that the triangles are still triangles, but adding that you have to turn them and they need to have 2 slanty sides is a must for the rules. She begins to understand that L and R are triangles, they just look different. 

Evan

Evan chimes in later in the conversation, stating that triangles must have points, and that even if the triangles look stretched out and turned upside down they are still triangles. He has a good understanding that triangles have three sides, three corners and turning the shape doesn't change it. I think his explanation of the points help students grasp a better understanding and him being so sure of turning the shape, I especially liked his connection...if I turn myself, I am still me. Do you think he helped the class?

Natalie

In this case the students are trying to define what a square is and what a rectangle is. The students are struggling with how to separate the two shapes into their own definitions and use the attributes associated to the shapes correctly. Roberto states that a square has four sides, four corners, four angles, and it's a square. Clarisa chimes in with four corners and four angles is the same thing, but nothing was mentioned about the use of it's a square as part of the definition. When Charlie called out, that they are the exact same thing and drew examples it helped the students see that the definitions they we coming up with were not specific enough. Maryanne and Brett have figured out the the definition needs more differentiation to really be able to justify the difference between a square and a rectangle. 

Dolores and Andrea

For Dolores's case they speak of the difficultly they had of seeing differently shaped triangles as triangles since they were heavy exposed to the common equilateral triangle we see for shapes on posters in younger classrooms. They felt like they had to break out of her usual thinking to let new ideas in. In Andrea's case Zachary is also taking about what is in his head and how he has to use his eyes and head in connection to see that the shapes are triangles. It is like they are brain-washed into thinking shapes can only be one way, and the process of ending those misconceptions take time. Misconceptions are a topic we've discussed in Science and I feel like that is what these children are struggling with, standard shapes are introduced at home and in preschool, but these have caused an undesired effect on the students thinking process. 

I now have a new understanding that misconceptions are all around us, since I want to teach in kindergarten, I will ensure that I have many pictures of different shapes inside my classroom. Instead of having the standard shapes, I will post pictures of shapes of varying types and sizes. I will introduce children to shapes that may not be common at that age level, but breaking the misconceptions early is important to harness the definition and attributes of the shapes. Aubrey, what do you think about these case studies? Did they open your eyes to what our children are thinking and how they process definitions and attributes?

Math Activity with Color Tiles

 While creating the 5 sides I did okay, I did not find the two decagon without help from the photo on the page. Naming the shapes was easy, but I did have to remember the name for the 12 sided shape. Aubrey, how successful where you, did you know the names? The funny thing about this activity was that my children had used my colored tiles, and I couldn't find them, so I had picked up the bag  of pentominoes and thought about if I could just use those. But my children found the tiles this morning before school....I thought I was gonna have to go to the lab and borrow some. 

For Further Discussion

Inside my home, my work space is in my bedroom, the room itself is a rectangular shape, the tray ceiling however is an octagon shape. My desk is a rectangle as are my computer screens. I have many things that are circular in shape around me as well, like the CD's, coins and speakers. Shapes are all around us, I have picture frames that are squares and rectangles. When driving my children to school we see circles in the traffic lights, octagons in the stop signs, rectangles in the speed limit signs and so much more.  Triangles are not as common in my home, but I see the yield pedestrian signs while driving. Our world is full of geometric shapes, inviting the students to see this inside a classroom would be a bit of a challenge at first, but I think this concept would open their minds to the shapes all around us. What do you think Aubrey?