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## Inconsistencies in the Teaching of Arithmetic in the Elementary Grades

In order to introduce the subject matter in this article the following truefalse test is given for the reader. It is suggested the reader take this test and attempt to rationalize each answer in Ianguage suitable for elementary grade pupils. Preserve your test answers and compare them and your discussions of the items with those of the author which will be printed in the next issue.

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## Geometry in the elementary grades: a comparative study of Greek mathematics education

Can concepts of geometry be taught effectively to students in the elementary grades? This most interesting question has been asked by instructors, educators, and parents who are concerned with instruction on the elementary level. At present very little geometry is taught in the elementary school, although some basic concepts are taught on the junior high level. The full consideration of geometry is usually reserved for the second year of high school.

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## Arithmetic in Upper Elementary Grades

The most effective learning procedures emphasize meaning and understanding. A modern program in arithmetic aims to develop meanings so that the child perceives purpose and logic in what he is taught. When the learner can see the reasons for the uses or applications of the arithmetic that is being studied, he will be able to understand more clearly and more efficiently use the number relationships involved. This program makes use of children's experiences, a growing readiness for learning, a step-by-step course in arithmetic, and a continuous review of skills. It also guides the child to become increasingly aware of the place numbers have in the world in which he lives, such as in science or business, and provides him with opportunities to apply his newly-learned concepts in arithmetic to these everyday problems of community living.

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## Slide Rules for the Upper Elementary Grades

THE PUBLIC PRESSURE to produce more scientists will quicken the interest in mathematics. The publicity given to sputnik, the shot truly heard around the world, will resound from the kindergarten through the university. The resulting changes which will undoubtedly occur in the curriculum will have to be evaluated by educators at some future date. But to one who has taught in both public schools and teacher education institutions, it seems apparent that much good will obtain from greater emphasis on mathematics and science. Certainly educators have taken a great deal of criticism (justly given) from lay critics about our mathematically illiterate graduates from both high school and college. In fact, if they are deficient in mathematics on leaving high school, the colleges contribute to this deficiency rather than lessen it. This may happen in one of two ways. First, if they are forced into required college mathematics for which they are unprepared they fail or muddle through thereby increasing their frustrations toward mathematics; or secondly, they avoid mathematics entirely and are four years further removed from it on graduation.

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## An enrichment program for elementary grades

A continued concern of teachers is that of adjusting instruction to meet the varying abilities of pupils within a classroom. Cincinnati initiated a program in 1959–60 to provide opportunity for able children in arithmetic in Grades 3–6 to proceed at a rate commensurate with their ability. Generally, two groups moving at different rates a re formed within the class.

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## Flow charts for the elementary grades

The following relay games in arithmetic are suggested as an introduction to flow charts and as practice in the fundamental operations. These games may be adapted for use at any elementary or secondary level.

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## The metric system in the elementary grades

We are all interested in a better education for our children, a better education in less time and with less expenditure of effort and of the teacher's time. Educators say that they are not emphasizing the study of the metric system until industry makes the change, and industry says that it cannot change because all the help is educated in the use of the English system—a vicious circle if there ever was one; for the metric system has been the legal system of measure for 100 years, is used extensively in this country, is destined to become the only system of measure in this country, and is the language of measure throughout the world.

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## Mathematics in the Elementary Grades: The Soviet Experience

In the Soviet Union, a complete ten-year education is free and compulsory for everyone. All Soviet schools teach the same mathematics curriculum for all ten years. The first three years comprise the primary schooling with classes conducted by one teacher. Teaching is done by subject specialists beginning in the fourth grade.

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## Investigations: Developing Algebra-'Rithmetic in the Elementary Grades

The “Investigations” department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.

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## Research into Practice: Developing Algebraic Reasoning in the Elementary Grades

Direct modeling with concrete objects can be a powerful problem-solving strategy for young children (Chambers 1996). However, as problem situations become more complex. the value of more powerful strategies becomes apparent. An algebraic approach in which students first describe the problem using an unknow n in an equation and then solve for the unknown (Lesh, Post, and Behr 1987) is one such strategy.