Module 8

Quick Images:

Once you've viewed the video, discuss on your blogs what you noticed about their responses. You should also consider how you saw the shape and how your perspective compared to the way the students described what they saw.

I found this video to be very interesting because when I was watching the shape be shown I had the same response that one little boy had in that “he just remembered the shape.”  I watched the shape and did not make a connection to it I just remembered the visual of it and knew what to draw.  Many students made connections to real life objects.  Students gave responses such as: “it looked like a moon”, “it looked like a C”, “it looked like a banana”, “it looked like a boat”, and “it looked like a melon”.  Students were able to look at the shape and then think of an object it reminded them of; even if it was an object they had to rotate.  The teacher would allow the students to show her how they related the picture to the object they named by having them to come to the overhead and maneuver the object to show the rest of the class.  I thought it was neat also that the one little boy named the shape by its actual name which was a “crescent”.  Another thing I found interesting was when he mentioned that there were two points that helped in drawing the picture one at the top and one at the bottom with two curved sides.  I found that to be interesting as his way of looking at the picture.  It was a neat activity to see to understand how students learn because as I mentioned I just remembered a visual image without anything to compare it with or remember it by and was able to draw it but these students had in depth reasons as to how they remembered the shape.  I would like to try this in the classroom just to see the way that my students think about things.

Case Studies: Shapes:

These case studies were very interesting for me to look at to see the way that the children thought about different things.  Looking at Andrea’s case it was a neat way to watch how the students viewed triangles.  Susannah had a hard time grasping that triangles that don’t look like “real triangles” (which I took as what appeared as 3 equal sides) could not possibly be triangles.  After hearing suggestions from different classmates about what a triangle was she finally agreed with one idea suggested by classmate Will that a triangle can have “two slanty sides”.  Evan who was in this case as well seemed to understand what a triangle was the best to me.  He knew that a triangle had points at their ends and were not curvy.  He also suggested a triangle is made up of three sides.  He shared an idea with the class that “no matter how you turn him, he is still Evan.”  This was interesting to me because it was a very valid point.  A triangle is made up of three straight sides that connect and no matter how you maneuver it, it remains a triangle.

Natalie’s case was more to me about definitions and how they need to be exact.  Students were describing squares and rectangles pretty much as the same thing being: “four sides, four corners, and it’s a square.”  That is not true not all shapes that fit that description are a square.  A rectangle fits that description but its parallel sides are the same size.  This case showed me the importance of giving detailed and correct definitions but also made me think that giving visuals would help students to better understand ideas and concepts.

In looking over Dolores’s and Andrea’s cases it was evident that the students were talking about how to make sense of a new idea.  The students in Andrea’s case said something very well when he said “we have to make our eyes and our heads meet.”  He suggests that we have to look outside of just what we already know or what we are seeing and connect the two to have a better understanding of a concept or idea.  In Delores case study a student suggest that “we have to be open to look further” which suggest that sometimes the ideas we have are not always right and we have to keep our minds open to learning new things.

In my classroom I hope to be able to lead my students in a direction that does not get them confused.  I hope to be able to give my students concrete definitions and examples of terms that they can carry with them throughout their years.  I also want to be able to teach my students to have an open mind when learning because things can change and ideas can be elaborated on as well.  I myself as the teacher have to keep an open mind when teaching because I can be introduced to new teaching strategies or new methods of learning that I am unaware of.  I found these case studies to be a lot of help and very interesting.

For further discussion:

If geometry is the mathematics that describes the world we live in, that means geometry is everywhere around us. Use the language and concepts of geometry to describe your own world your home, your workplace, your possessions, your daily commute or other travels. 

As I am laying in bed writing this blog I am going to describe my room using geometrical terms:

• The room is shaped like a SQUARE.
• The mirror is shaped like an OVAL.
• The walls make up 4 RIGHT ANGLES.
• The TV is a RECTANGLE that has 4 RIGHT ANGLES.
• The window has PERPENDICULAR LINE SEGMENTS forming window panes.
• The green chair has INTERSECTING LINE SEGMENTS.
• The desk chair has SPHERE shaped wheels.
• The fan has a 3-D CIRCLE and a 2-D CIRCLE on it.  
• The dresser is a RECTANGLE made of smaller RECTANGLES, SQUARES, and CIRCLES.
• The pin board is one big SQUARE made up of 4 smaller SQUARES.
• The bed is a RECTANGLE.
• I am sure there are many more but I wanted to list the major things that stick out to me.

Geometry really is all around us and you don't think about it until you actually sit there and look around.  I feel like now whenever I am in a new place I am going to be looking around to see the different geometric things.