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When first-grade students start addition of whole numbers, they are given sets of objects to combine and count to determine the sum. Most educators agree that beginning students need experience combining group or objects, such as combining two pencils and three pencils to get a group of five pencils. Such activities are needed to give students an understanding of what addition means before moving on to faster — but less meaningful — ways to sum numbers, such as the use of an algorithm or calculator. This approach is based on the learning principle that meaning comes from knowing the things signified by the symbols. Thus, familiar, concrete experience — actual or recalled — should be a first step in the development of new abstract concepts and their symbolization. Though this principle of moving from the concrete to the abstract is extensively used in teaching the addition of whole numbers, it is used much less in teaching the division of fractions. The inevitable result in that a student may be able to use an algorithm by rote to divide fractions, but the skill is useless because it is devoid of meaning.