Making Physical Models (Manipulatives) For Math Representation

Using Other Nonlinguistic Representations
Making Physical Models. As the name implies, physical models are concrete representations of the knowledge that is being learned. Mathematics and science teachers commonly refer to the use of concrete representations as “manipulatives.” The very act of generating a concrete representation establishes an “image” of the knowledge in students' minds. The following example illustrates this process in the context of a science class.
Mrs. Allison helped her 4th grade class to understand why we see different phases of the moon by presenting a concrete representation of the moon's monthly journey around the earth and its relationship to the sun. For the moon, Mrs. Allison gave each student a white Styrofoam ball and had them stick it on the end of a pencil. For the sun, she used a lamp with the shade removed. She told her students each of them would be the earth.
Mrs. Allison placed the lamp in the middle of the room, pulled down the window shades, and turned off the lights. Then she had each student place the ball at arm's length between the bulb and their eyes, simulating a total solar eclipse, which, she explained, is quite rare. Because the moon usually passes above or below the sun as viewed from Earth, Mrs. Allison then had her students move their moon up or down a bit so that they were looking into the Sun. From this position the students could observe that all the sunlight was shining on the far side of the moon, opposite the side they were viewing, simulating a new moon.