Models in Math

The use of models as an instructional tool is to teach abstract and complex concepts.  The focus is on the use of models in the mathematics classroom, although, this course is beneficial to teachers of all disciplines. Students often have a difficult time understanding mathematics and the importance of learning the topic; they simply memorize and implement formulas.

YouTube is a great site to find effective models of mathematical concepts.  You can find videos that involve math above.

Essentially, a model is a tool used to make learning easier by simplifying the target in some way. For example, a science teacher could use a diagram of a solar system to illustrate the proportional size of all the planets. What you are trying to simplify is called a target, and the simplified version is the model. In our example of the solar system, the target is the entire system and the model is the diagram.

There are different types of models you can implement in to the classroom.

Conceptual Models

• Conceptual models illustrate a concept, or "units of thought".  For example, a model could be used to represent a flood. A flood is a concept, because by itself 'flood' does not mean anything, but the category of flood is associated with its appearance, importance, images, personal experiences, and other weather phenomena.

Concrete Models

• The most common type of model is a concrete model. These are "tangible material models that we can generally interpret with relative ease."  A model airplane is concrete model because it is something we can physically touch, and most everyone will know that it symbolizes a real airplane.

Scale Models

• The purpose of a scale model is to look like the object we are representing. A blueprint is a scale model because the shape and size of each room is proportional to each other.

Function Models

• Functional concrete models are intended to represent certain functional relationships of their targets. They have relatively less emphasis on retaining scalar relationships and on accuracy of appearance. A classroom model is an example of a functional model. It is not intended to represent the solar system to scale is a very difficult thing to do in a classroom. Instead, this model's purpose is to illustrate the relative positions and motions of the sun, planet, and moon in relation to each other.

Similes, Analogies, and Metaphors

• These models are often used when it is important to make abstract ideas more concrete.

There are two main components of a model; the target and the analog. The target is the complex item, concept, or idea we are trying to represent. The simpler item, concept, or idea used to explain or the first is known as the analog. The similarities between the objects are the correspondence.

For a model to be effective it must:

• Be engaging for students: if students are engaged throughout the entire activity, they are more likely to understand and think about what they learn from the analogy.
• Require high-level thinking: models are effective when students create models themselves, explore and explain ideas, given time, and express high-level thinking.
• Be familiar and interesting to students: analogies that are familiar to students and connected to familiar things.
• Include multiple models to reinforce the same concept: incorporate several activities, analogies, and discussions.