Provide a metaview, lifting students into a wider view of the concept. Use another medium (not reading or writing) to connect students' personal knowing to the concept (i.e. visual arts, music, movement, metaphor, etc.) Involve learners in reflective production that blends the emotional and the cognitive.

Dramatization of Mapping.

Objective: To use a dramatization to emphasize the concept of the function as a MAPPING from x to y, and the inverse function as a mapping from y to x.

Activity: You will need two robes, one black and one white, two cardboard squares with a string through them to allow them to be worn around the neck, and two signs, one labeled "X," and the other labeled "Y." On one of the cardboard squares write: f(x) = x + 5, and on the other write: f-1(y) = y - 5. Draw two large chalk circles on the floor of the classroom; label one circle "X" and the other "Y." Choose nine students to participate in the demonstration. One student will be the FUNCTION (dressed in white, and wearing the f(x) = x + 5 square around her neck). One student will be the INVERSE FUNCTION (dressed in black, and wearing the f-1(y) = y - 5 square around his neck). Two of the students will be standing in the "X" circle, and should hold the "X" sign TOGETHER, and the other five students should stand off to the side. No one should be in the "Y" circle. Now the FUNCTION should go to the "X" circle, take the two students with her to the five students standing off to the side, and take away their "X" sign. Then she should bring all seven students to the "Y" circle, and give them a "Y" sign to all hold TOGETHER. This is very important since there are not seven y's, but one y, represented by the seven students. Tell the class that the FUNCTION has mapped the x = 2 into a y = 7. Now have the INVERSE FUNCTION go to the "Y" circle, take the seven students off to the side, take away their "Y" sign and bring the ORIGINAL two students back to the "X" circle and give them back their "X" sign to hold together. Tell the class that the INVERSE FUNCTION had mapped the y = 7 into an x = 2 and furthermore, has undone what the FUNCTION has done. In other words, you started with two students, went through a mapping and an inverse mapping and ended up where you began.

Assessment: Quality of class participation and level of understanding of the concept.