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Manipulatives
Posted:
Apr 10, 1995 4:55 PM


I agree with Linda Coutts that working with manipulatives can become as rote as other excercises, and certainly one would not want to become "dependent" on them in the sense that you had to carry them around with you. I do have a couple of other thoughts about manipulatives, however.
1. Too often they are contrived and become an end in themselves  their connections to the mathematics they are to represent just never really get made.
2. Where well used, however, they can enable students to visualize the mathematics they are doing in ways that pushing symbols around does not do. I think that a student who is dependent on *visualizing* pattern blocks when working with fractions probably has a far better sense of what is going on then the student who has just learned some procedures.
For older kids  When I teach trig, I give my students large unit circles on graph paper with a radius of ten graph units of .1 each. They approximate the coordinates of the points on the circle at the intersections of the radii at pi/6, pi/4, ... etc and write these on the circle. From then on they can visualize the important symmetries by referring to the circle and they use the circle on tests and in doing work involving trig for several years afterward. For these kids the unit circle is a manipulative  they depend on it, not for values (they have calculators for these if necessary) but for visualizing and understanding the nature of circular functions. A kid who doesn't happen to have her circle available will often sketch it quickly when working on a problem  which is exactly how I would hope she would think
Joan Reinthaler Sidwell Friends School



