Part IV Teaching Mathematics

What we must watch at this level is that children recognize that the notation triggers speech which involves instructions that can be carried out on oneâ&#x20AC;&#x2122;s fingers. The answer is the last thing one says â&#x20AC;&#x201D; the label for the set at rest after the operations have been completed. There may be some children for whom the fascination of their fingers or the games on the array is limited. For these people and the others the Algebricks may serve as an entry into mathematics compatible with their interest in building with a flexible and colorful material. Since the rods are prisms, when they are used in play to make buildings they become involved in a vast number of relationships which have spatial meaning. There is potential for algebraic and numerical meanings in these relationships as well. It is the teacherâ&#x20AC;&#x2122;s responsibility to observe the spontaneous building of each child and note which properties of the rods he is exploring through his staircases, towers, cubes, trains, etc., to extend these activities, and introduce some games which will give the learner an entry into seeing some relationships he may not yet have found on his own. The following are some of the most primitive observations that can be made about the rods:  The set of rods subdivides into subsets whose elements are rods of one color; the rods of each such class are now defined by their distinctive colors.

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The Common Sense of Teaching Mathematics
The Common Sense of Teaching Mathematics

"Since knowing produces knowledge, and not the other way around, this book shows how everyone can be a producer rather than a consumer of m...