## 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.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number

Knowledge Being Assessed

6–8

9–12

Select This Item for My Item Bank

59%

64%

64%

57%

60%

61%

56%

66%

62%

53%

54%

61%

57%

54%

56%

52%

54%

53%

52%

50%

Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

6–8

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.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number

Knowledge Being Assessed

6–8

9–12

Select This Item for My Item Bank

61%

77%

58%

69%

35%

38%

31%

29%

25%

27%

17%

14%

Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

6–8

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.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number

Knowledge Being Assessed

6–8

9–12

Select This Item for My Item Bank

75%

79%

72%

80%

68%

75%

68%

76%

37%

44%

#### 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

6–8

9–12

Select This Item for My Item Bank

69%

78%

62%

80%

48%

49%

38%

41%

33%

45%

36%

40%

28%

37%

Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

6–8

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

6–8

9–12

Select This Item for My Item Bank

55%

57%

55%

57%

45%

61%

47%

55%

43%

49%

41%

51%