Shadows are fascinating! They come in a wide variety of shapes and sizes. Sometimes you see them, sometimes you don't. When they do appear, you can't pick them up, nor can you weigh them. Shadows change shape and direction at different times of the day.
“How can my children possibly be expected to do problem solving when they are only beginning to learn to read and to do basic arithmetic computation?” This is often the lament of primary-school teachers when urged to include problem solving in their mathematics programs. Developing problem-solving skills is often equated with training children to solve arithmetic word problems, but problem olving has a much broader meaning. It is not only possible for young children to become problem solvers but also, primary mathematics instruction can be organized to help develop problem-solving skills.
Among the most popular “math materials” found in elementary school classrooms are commercially available attribute materi als such as attribute blocks. Using these materials children of all ages can be actively involved in many enjoyable activities that help to develop classification skills, vocabulary, and logical reasoning ability. Any number of different activities arc possible for the entire class, small groups, or individual children.
In recent years school mathematics programs have included an increasing emphasis on probability and statistics. Many of the activities suggested in these programs offer wonderful opportunities to involve students in active learning experiences in which they perform experiments using a variety of manipulative materials (e.g., coins, spinners, dice, and cards). These activities are highly motivational and certainly lend themselves to the use of manipulative materials. However, all too often such activities tend to become supplementary or enrichment experiences that are quite limited in scope and isolated from the rest of the school mathematics program, and the connection between using manipulative materials and learning basic mathematical concepts is weak.
Very often, in planning to teach mathematics, we first decide what concepts and skills we will stress and then choose activities and materials that can be used to help develop those concepts and skills. We might decide to use plastic counters for basic ideas about number, or an abacus for teaching place value, or assorted geometric figures to teach shapes. We recognize the need for the child to develop these ideas through experiences with concrete materials.
NCTM's development of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and the recent companion document, Professional Standards for Teaching Mathematics (NCTM 1991), is an extraordinary achievement. At a time when many agree that we urgently need change in mathematics education, these sets of standards project an exciting vision of what mathematics learning can be and how all students can develop “mathematical power.” They establish a broad framework to guide reform efforts and challenge everyone interested in the quality of school mathematics programs to work collaboratively to use them as a basis for change. How will we meet this challenge? The Editorial Panel believes that translating that vision into reality at the elementary school level will be possible only if elementary school teachers are involved in taking leadership roles as agents of change.
Board games can be recreational and fun to play. They can also provide many opportunities for developing number concepts, drilling in basic skills and number facts, and teaching movement along the number line. If children are taught to make their own games, additional skills of planning, ordering, and making and testing rules can be developed. The actual games may reftect content studied in other curriculum areas, hobbies, stories, contemporary problems, and individual interests.
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