Mathematical Habits of Mind: Mathematical Representations
Mathematical Representations refers to the use of visual, tangible, or symbolic objects or expressions to represent mathematical ideas or relationships. These representations can take many forms, including diagrams, graphs, manipulatives, equations, and computer or calculator displays, and are often used to connect instruction with students' interests and experiences. It is important for students to be exposed to and skilled in using multiple mathematical representations, as this allows them to choose the representation that is most effective for a given context and for their own learning. Using multiple representations can also help students better understand and make connections between different mathematical concepts.
Imagine you are planning a trip to a new city and want to figure out how long it will take to get there by car. You might start by looking at a map to get a sense of the distance between your starting location and your destination. The map provides a visual mathematical representation of the distance, using lines and symbols to show the roads and cities. You might also use a ruler or other tool to measure the distance on the map, providing a numerical mathematical representation of the distance.
Next, you might use a formula mathematical representation to calculate the estimated travel time. This equation would represent the relationship between the distance, speed, and time needed to make the trip. By using this equation and the information about the distance and your planned speed, you can estimate how long it will take to reach your destination.