Key Idea: Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and oral and written descriptions can be used to represent objects, events, and processes in the real world.

Students are expected to know that:

  1. The term model refers to a representation of something in the real world.
  2. Models can represent objects.
  3. Models can represent events or processes.
  4. Geometric figures, diagrams, sketches, and maps can be used as models.
  5. Number sequences and graphs can be used as models.
  6. Oral and written descriptions can be used as models.

Boundaries:

  1. Students are not expected to know that simulations are examples of models.
  2. Students are not expected to know that mathematical statements or symbolic equations are examples of models.
Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

Grades
6–8
Grades
9–12

MOM005

Only physical objects can be modeled; events and processes cannot be modeled (Grosslight et al., 1991).

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MOM002

A model is always a three-dimensional object. Therefore, pictures, diagrams, graphs, written descriptions, abstract mathematical or conceptual models are not models (Grosslight, et al., 1991).

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Frequency of selecting a misconception was calculated by dividing the total number of times a misconception was chosen by the number of times it could have been chosen, averaged over the number of students answering the questions within this particular idea.