Teaching the Values of Coins
Drum, Randell L., Petty, Wesley G., Jr., Teaching Children Mathematics
Teaching about coins can be a frustrating experience for many primary teachers. Teaching the names of the coins is not the problem. Instead, teaching about the values of coins is difficult.
Many teachers try to use memorization techniques for teaching monetary objectives related to values. Memorization, however, is a poor method of teaching or learning. The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) recommends a de-emphasis on rote memory as a teaching and learning technique.
For teaching measurement objectives, including those related to monetary value, the Curriculum and Evaluation Standards endorses the use of manipulative materials and the development of concepts. These criteria, however, emphasize an even more crucial problem with teaching about coins at the primary level: the coins, although concrete models of themselves, are nonproportional in relation to their values. This situation means that the coins are abstract models when they are used to teach their values.
Using coin models that are proportionately sized according to the value of each coin becomes the solution to the problems that teachers have had with teaching about money. Proportionate models simplify instruction related to monetary values by presenting it on a concrete level. Pictures of the values represented by the coins are created in the minds of the students. For example, the true relationship between the value of a dime and the value of a penny is visually represented, since the dime-value model is ten times the size of the value model for a penny. Furthermore, the model for the value of a quarter is the same size as the combined models for the values of two dimes and a nickel or any other combination of coins that has the same value as a quarter. These and other value relationships involving coins and sets of coins are much more easily understood when they are shown with the value models.
Creating Proportionate Models to Represent the Values of Coins
The values of coins are measured in cents. Therefore, a proportionate model representing the unit value of a cent, as well as models for the values of each coin, is needed when teaching about money. Figures 1-5, which can be enlarged and used as blackline masters, are the basic models needed. The models are based on a square shape. The actual size of the basic square is not important; 1 find that a 20-cm-by-20-cm square is easy to create and use with students.
Note the shape of the regions representing the quarter [ILLUSTRATION FOR FIGURE 5 OMITTED]. Each comprises two and one-half columns out of the ten within the basic square. This shape is essential to ensure that the models can be used to teach objectives that involve establishing relationships among values.
The Professional Standards for Teaching Mathematics (NCTM 1991) recommends that the mathematical concepts emphasized should be connected to daily living. Because the half-dollar coin is not commonly circulated today, I do not find it necessary to teach about it. A proportional model for the half-dollar coin could be produced easily.
Teaching the Values of Coins and Their Relative Values
Teachers should use normal coin models, such as the coins themselves or plastic versions of them, to introduce each coin by name. The proportionately sized value models of the coins should then be substituted as manipulatives representing the coins as the instruction progresses to objectives related to values.
Teaching the values of coins requires showing the worth of each coin in cents. This instruction is done by placing cutouts representing the values of each coin on top of the cent model. The number of cent units covered by a coin model represents the value of the coin. See figure 6 as an example representing the placement of the nickel model over the cent model. The nickel model covers five of the cent models, so the nickel has a value of five cents. …