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4A - 4B - 4C - 4D - 4E

Module 4: How the Students See It

B. Frames of Reference

Wizard of Id cartoon
© THE WIZARD OF ID by Johnny Hart and Brant Parker, reproduced with permission from Field Enterprises, Inc.

To understand the Earth looks flat because it is a small part of a very large sphere, 

people need to be able to change their frame of reference from standing on the surface to looking at the Earth from space. 

The Martian Moon Problem

Deimos and Phobos, the two moons of Mars, have phases just as our Moon has. 

For a person observing from the surface of Mars, what is the phase of each moon? 



What are the differences in thinking between the first three and the last three students' answers given by college students. 

Student #1 Answer: “B” Explanation: “I imagined myself on the surface.

Student #2 Answer: “B” Explanation: “My point of view—I just reversed what I saw.”

Student #3 Answer: “B” Explanation: “Put myself on Mars in my imagination.”

Student #4 Answer: “D” Explanation: “Observing shadows on models.”

Student #5 Answer: “D” Explanation: “Moon is moving towards sun.”

Student #6 Answer: “D” Explanation: “Because Phobos is in the direct sunlight and not in front of Mars.”

What are some concepts traditionally introduced in the planetarium that may be difficult for the last three students?

Swiss psychologist and epistemologist Jean Piaget and colleagues 15 studied how people solve problems like the Martian Moon Problem.

The 3 who gave correct explanations could imagine themselves in a different frame of reference. 

The thinking of other 3 was dominated by what they saw directly from their own frame of reference (or by something not relevant to the problem).
Doing concrete experiments can help.

Example: two students face a model Moon  illuminated by a model “Sun,” draw the “Moon,” 

and compare drawings.

Piaget and his colleagues identified 3 levels of intellectual development.

Frames of Reference
Egocentric* Level (starts about age 4)
Can imagine only one’s own point of view.
Concrete Level (starts about age 8 or 9)
Can imagine another viewpoint, but only after a concrete experience.
Formal Level (starts about high school age)
Can imagine a situation from different points of view.

* “Egocentric” here should not imply selfishness.

When a situation is complex, or subject matter unfamiliar, even adults begin at the egocentric level.
E.g. the college students’ responses to the Martian Moon Problem.

Ask questions during a program to find out how people are understanding. 

If you find people are operating at the egocentric level, try presenting the topic from their point of view.

...or move on to other concepts that can be readily communicated egocentrically or concretely in the time available.

In the Wizard of Id cartoon...
Wizard of Id cartoon

At what level is the Wizard reasoning in the second frame?

[Egocentric, Concrete, or Formal?]

At what level is he thinking in the last frame?

Suggest a strategy for communicating the following concept to a concrete level planetarium visitor. 

[Breakout rooms?]
CONCEPT: The two galaxies in these photographs actually have the same spiral shape. 
The galaxy shown at left is viewed from the side, and the galaxy on the right is viewed from above (or below).

(Photographs courtesy of Lick Observatories.) 

Astronomy textbooks use diagrams like the one below to explain the phases of the Moon.

What level of reasoning is required to understand this diagram?

4A - 4B - 4C - 4D - 4E