Topic: Models

Below is a list of key ideas related to Models. For each key idea, you will find a list of sub-ideas, a list of items, results from our field testing, and a list of student misconceptions. After clicking on a tab, click on it again to close the tab.

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

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).

36%

43%

MOM005

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

37%

36%

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.

A model of something is similar to but not exactly like the thing being modeled.

Students are expected to know that:

  1. A model represents (brings to mind) one or more aspects of the thing being modeled.
  2. While a model represents one or more aspects of the thing being modeled, it does not represent all aspects of the thing being modeled.
Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

Grades
6–8

Grades
9–12

MOM003

A model should look like the object, event, or process it is modeling (with the possible exception that it can be smaller). Therefore, a diagram or graph could be considered a model only if it bore a physical resemblance to what is being represented (Grosslight et al., 1991; Penner et al., 1997; Treagust, et al. 2002; Schwartz & White, 2005).

41%

30%

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.

Models are useful for thinking about real-world objects, events, and processes.

Students are expected to know that:

  1. Someone may use a model to think about (i.e. to visualize or imagine and to reason with or reflect upon) objects, events, and processes in the real world (phenomena).
    Examples:
    • Objects: Earth (how much is covered by land vs. water), Moon (how cratered it is), Sun, Earth-Moon-Sun System (relative sizes, relative distances, etc.)
    • Events: Eclipse, Earthquake, tsunami, car crash, election, battle
    • Processes: erosion, presidential campaign, chemical reaction, car assembly, plant growth
  2. Use of models makes it possible to observe phenomena that would be difficult or impossible to observe in the real world. For example, a phenomenon could happen very slowly, very quickly, on a very small scale, or on a very large scale. The phenomenon could also be too complex, too expensive, or too dangerous to observe directly.
  3. Use of models makes it possible to illustrate abstract aspects of a phenomenon (e.g. arrows to represent forces).
  4. Use of models makes it possible to ignore some features of a phenomenon being considered so that there is less to keep track of. This allows the exclusion of features that are believed to be irrelevant in how the phenomena behave (e.g. food web diagrams do not show how predators catch and consume their prey, point masses in a physics problem do not show the actual size and/or shapes of the objects they represent). Whether or not a given feature turns out to be irrelevant depends upon the purpose of the model and how well understood the phenomenon is.
  5. A model may be modified as it is being used based on new information about the phenomenon it represents or based on new thinking about what features of the phenomenon are important to represent in the model.

The usefulness of a model in thinking about objects, events, and processes depends on how closely its behavior matches key aspects of what is being modeled.

Students are expected to know that:

  1. Judgments about the usefulness of a model are/should be based on how closely its behavior matches key aspects of what is being modeled (rather than on how attractive it is).
  2. The key aspects of the referent that need to be represented accurately in the model depend upon the purposes of the model.
  3. The only way to judge the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number

Knowledge Being Assessed

Grades
6–8

Grades
9–12

Select This Item for My Item Bank

MO066004

In order to accurately represent what would happen to a real human in a car crash, crash test dummies should be about as strong and sturdy as a real human body is.

69%

78%

MO061003

If a student is studying how long it would take a spaceship to go between different planets in the solar system, his model should accurately represent the relative distances between the planets, but does not need to accurately represent other aspects of the solar system.

62%

80%

MO065004

An architect does not need to create a 3D model of his house design if his 2D plans show everything that is needed in order to build the house.

48%

49%

MO060002

Whether a globe or a wold map is a better model of the earth depends on the task they will be used for.

38%

41%

MO062002

If a student makes a model of the solar system to think about how long it would take a spaceship to travel between the planets, it is essential for him to accurately represent the relative sizes of and distances between the planets, but it is not essential that he makes the model of each planet look like the planet it represents.

33%

45%

MO063004

If a student wants to make a model of the solar system to think about how long it would take a spaceship to travel between the planets, it is essential to accurately represent the relative sizes and distances, but it is not essential to make each model planet look like the planet it represents.

36%

40%

MO093001

28%

37%

Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

Grades
6–8

Grades
9–12

MOM006

The more a model is similar to what is being modeled (particularly with respect to physical similarities), the better the model is (AAAS Project 2061, n.d.).

50%

41%

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).

16%

15%

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.

There is no guarantee that ideas based solely on a model are correct.

Students are expected to know that:

  1. Since a model is not identical to the object, event, or process it represents, it may look or behave differently than what it is representing.
  2. The only way to find out how adequately a model represents the behavior of a real world phenomenon is to check and see if the real world phenomenon behaves the way the model predicts it will behave.
  3. If a model and the phenomenon it represents behave differently, one or more significant aspects of the phenomenon are not being represented accurately, or are not being represented at all. Changing which aspects of the phenomenon are represented accurately (and which are not) may lead to a model that behaves more like the phenomenon behaves.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number

Knowledge Being Assessed

Grades
6–8

Grades
9–12

Select This Item for My Item Bank

MO068003

If a student makes a drawing of how he thinks evaporation works and it turns out it was incorrect, he should make a new version that more accurately represents what he now knows about evaporation.

55%

57%

MO094001

A model can predict the behavior of the object it represents (e.g. how a roof will perform in a rainstorm), but the predicted behavior may not be exactly the same as the object’s actual behavior because a model is never exactly the same as the object it represents.

55%

57%

MO095001

A model can predict the behavior of the object it represents (e.g., a car crashing into a wall), but the predicted behavior of the object may not be exactly the same as the actual behavior of the object because a model is never exactly the same as the object it represents.

45%

61%

MO069004

If a student makes a drawing of how he thinks people see in the dark and it turns out it was incorrect, he should make a new version that more accurately represents what he now knows about how people see in the dark.

47%

55%

MO067003

Even if an engineer makes a good model of an airplane and discovers that it can fly well in the rain, she still cannot be absolutely certain that the real airplane will fly well in the rain unless she actually flies it in the rain.

43%

49%

MO070004

A model of an object can be used to predict how an object will behave, but the prediction may not be the same as the actual behavior of the object because a model is never exactly like the object it represents.

41%

51%