Module 9

Quick Images Video

When I first viewed the shape, I thought it was a crescent shape with a small circle in the middle. When the students began their discussion, they compared to the shape to things it reminded then of. Different answers they gave were the shape was a moon, it was like the letter C, it looked like part of jet ski, and looked like a part of a circle. 

Was you first thought different than the students? If so, how?

Shapes and Geometric Definitions

First, write about your own thinking. 

What are your definitions for these geometric terms? 
Triangle- A three sided shape
Square- Four sided shape with all equal sides
Rectangle- Four sided shape with the two different paralleled side lengths. The first two are short, the other sides are longer. 
Parallelogram- A shape with two sets of parallel sides.

Did you have a hard time coming up with definitions? Were there any harder than others?

What is the difference between a definition and a list of properties or attributes? 
A definition defines the shape, and attributes are used within the definition to describe the shape.

What is the purpose of a definition? 
A definition explains a word. It can also break down the word.

Did you think differently?

Then, examine this set of issues through the eyes of the students. 

What specific issues do the students need to consider in order to make sense of definitions for triangle, square, rectangle, and parallelogram? 
I think students need to familiarize with the shapes and various attributes. If a definition mentions 90 degree angles, the student must be familiar with what that is and look like to know what shape is begin referred to.

What process do the students go through as they learn to apply their definitions? 
They learned how to build their own definitions of each shape first. They described each shape by its attributes and tried to be specific to prevent confusion.

Looking beyond the specific geometric content of this set of definitions, how do children develop a sense of the purpose of definition? 
They honestly are leaning how to use and interpret a definition. This can not only help them in a geometric sense, but can also help them in other subjects and everyday things.

Respond to the following questions:

Follow the thinking of Susannah throughout Andrea's case 19. What does she understand about triangles? What is she grappling with? What ideas or questions does she contribute to the class discussion? What does she figure out by the end of the case? 
The students came up with a few facts:
Triangles have three straight lines. 
If they have wavy or round sides, it is not considered a triangle. 
A triangle must have three points.
The students debated these different facts. They gave various examples why it could be true based on the few triangles they were looking at. All had three points, straight sides, and sides of different lengths. The students also discusses that no matter how you change the position or stretch the shape, it is still the same shape. The student compared himself to the topic.

Now go back and follow the thinking of Evan throughout Andrea's case 19. What does he understand about triangles? What is he grappling with? What ideas or questions does he contribute to the class discussions? What does he figure out by the end of the case? 
Evan understood that if you have a shape and you stretch it, or change its position (rotate or flip), it is still the same shape. Evan compared himself. He said if you flipped him him, or stretched him, he would still be the same person. He even wrote that you can turn a triangle in any direction and still be a triangle.

Consider Natalie’s case 20. What are the students learning about squares and rectangles? What do they still need to figure out? Refer to specific examples from the case to illustrate your ideas. 
They are learning the difference between a square and rectangle. When they listed definitions of both, they have same definitions. They need to make the definition more specific.

Also in Natalie’s case 20, after line 250, the students are working to define the term square. Their conversation is as much about what a definition should be as it is about the particular term square. What does their discussion make clear about definitions? In particular, consider Roberto’s definition (“four sides, four corners, four angles, and it’s a square”) and the other children’s responses in the lines that follow. 
The realized that they need to specify various attributes and facts about shapes in the definition to decrease confusion. If you don't, then some of the definitions sound like the same shape.

In Dolores's case 18 (lines 25-43) and in Andrea's case 19 (lines 162-168), students are talking about what it feels like to make sense of a new idea. Describe their conversations. Refer to specific portions of the text in your discussion. What is your reaction to their comments? 
The students in case 18 mention how a "regular" triangle might feel ",ore like a triangle" than others. This lead me to believe that since students are initially introduced a "regular" triangle, the students need to learn that there are variations to shapes. The initial shape introduced is not the only shape. They definitely are trying to work on their definitions and different attributes of each shape.
Was there a particular students in the cases you followed closely? I enjoyed reading and following Ethan.

Reflect on what you just read and discuss how this will impact what you will do in your future classroom
I really liked the open discussions of the class. The students building on one another's contributions and giving great examples. This is something I would like to do in my classroom. It seemed to have a great outcome.

Math Activity with Color Tiles

When making these shapes, I built off of previously made shapes. I continued to create shapes until I felt I had made them all, and I had. I created the entire set. When I named them, I noticed I had one category a shape short, so I had to recount. I found which one I had miscounted. I forgot to count two sides of one shape.

Did you enjoy this activity? Did you find it difficult? I enjoyed the activity. Would you do this in a classroom?

For Further Discussion

If I were to describe my home, it is made up of various geometric shapes. My walls and floors different shaped quadrilaterals, my floors are hardwood with quadrilaterals, and frames are quadrilaterals. I live in a duplex that creates a dodecagon with our patios sticking out. It is crazy how geometry is everywhere in our lives.