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Manipulatives use in teaching Mathematics

Manipulatives use in teaching Mathematics

Manipulatives (blocks, rods, bean sticks, etc.) are commonly used in mathematics education. In recent years, a number of websites have been developed that contain "virtual" versions of some of these manipulatives. The references given below provide information about some of these websites.

It appears that there may be a fine dividing line between a concrete manipulative and a virtual manipulative. For example, does it make any difference in student learning whether a physical spinner is used to generate data, or whether a computerized spinner (that may well look the same) is used?

One of the most important general developments in science in recent years has been the idea of Computational Science. Thus, we now have Computational Biology, Computational Chemistry, etc. (The same idea applies to other disciplines, and these other disciplines have had varying levels of success in incorporating IT within their basic fabric.) And, as might be expected, Computational Mathematics is now an important branch of mathematics. The essence of Computational "XXXX" (name a discipline) is the development and use of mathematical models that can be implemented on a computer. Thus we have 1) The "real thing."; The mathematical model.; and 3) The Computational Model (simulation). This has deep educational ramifications, both in math education and in each other discipline. In brief summary:

1. Math education needs to include both math modeling and computer implementation of math models (computer simulations). This needs to be taught/learned in a manner that transfers to disciplines outside of math.

2. Each discipline needs to be examined from the point of view of the math modeling and computer simulation that has become and/or is becoming an integrated component of the discipline. Thus, each teacher of a specific discipline needs to help students learn current and potential roles of math modeling and computer simulation to represent and help solve the problems of the discipline.

Consideration of these factors has led to the appropriate use of manipulatives at specific grade levels. The Middle Grades Mathematics Project (Lappan, Fitzgerald, Phillips, Shroyer, & Winter, 1986), for example, is an activity-based mathematics program in which such manipulatives as tiles, cubes, geoboards, dice, and counters are used. Here the students continually explore by building, drawing, and discussing various "challenge situations."

Manipulatives have, unfortunately, been implemented more slowly at the secondary level. As a result, research on their effectiveness at this level ...

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