THOUGHT EXPERIMENT LESSON


 
 

 In the "Playing with Abstractions" section of the Beyond Numbers exhibit, visitors are invited to take an imaginary journey in the space that surrounds a mathematical knot.
 
 



  NCTM Standards and/or AAAS Benchmarks addressed:

 Geometry and Special Sense:
Students describe, model, draw and classify shapes, develop spatial sense, recognize and appreciate geometry in their world.

 Mathematics as Communication:
Students reflect and clarify their thinking about mathematical ideas and situations. Students relate their everyday language to mathematical language and symbols.

 Habits of Mind, Communication Skills:
Students learn to describe and compare things in terms of number, shape, texture, size, weight, color, and motion.

VOCABULARY

visualize - to form a mental image

sphere - the outer surface of a round object

hollow - empty (or full of air)

  

INTRODUCTION

In the following activities, students are invited to use their imaginations to explore spatial environments and to use communication skills to describe their explorations. The teacher may choose to use only the first two for younger students or have the students do all three.
 
 

OBJECTIVES

Students will visualize the inside of objects.
 

MATERIALS

shapes - a box, a globe, a donut, and others such as a rope, a bottle, an octahedron
K-3: drawing materials, optional tape recorder to record descriptions 
3-5: pencil and paper for writing descriptions
 
 

PROCEDURE

Tell students that imagination, creativity and visualization help mathematicians in their work.

 Thought Experiment #1:
Have students relax quietly as you read the following: Imagine you are sitting in a chair/on the floor. That's not hard to do because you are sitting. Now you are going to imagine some things you aren't really doing. Imagine that you stand up and walk around. Where do you walk to? [Allow students to describe where they "walk." Encourage them to provide details, using words like "over," "around," "behind," "next to," etc.] Now imagine you can walk on the walls and on the ceiling. As you walk along the walls how do you go to another room? What do you see? [Younger children may tape their responses. Older children may write their responses.] Display the shapes. Ask students which shape is most like their classroom. Have them discuss the reasons for their choice.
 
 
Thought Experiment #2:
Have students relax quietly as you read the following: Imagine you are on the surface of a sphere. That's not hard to do because you are on a sphere -- the earth. Now imagine yourself inside the earth. What is it like? [Allow students to describe what they imagine.] Imagine the earth is a hollow sphere and instead of us being on the outside, we're on the inside. What does it look like? [Younger children may tape their responses. Older children may write their responses.] Display the shapes. Ask students which shape is most like the earth. Have them discuss the reasons for their choice.

 Thought Experiment #3:
Have students relax quietly as you hold up the donut shape and read the following: Imagine you are inside this hollow ring. You start to walk. What kind of scenery do you see? Have students write a story that has the inside of a donut as the setting.
 
 

EXTENSION

Have students attempt to draw or act out their thoughts.
 
 

ASSESSMENT

Student narratives and stories should be judged on their use of sequence, directional words and imagination that relates the object's shapes.		  

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