Counting PrinciplesOnline version Match the counting principles with the description. by Christine Mulgrave-King 1 Stable Order Principle 2 The Order-Irrelevance Principle 3 The Cardinal Principle 4 One-to-One Correspondence Principle 5 The Abstraction Principle Students recite a number-name list in a fixed order, e.g. start with 'one' and count 'two, three, ..., seven, and so on. In other words, students engage in rote-counting This principle means that the list of words used must be in the same repeatable order. For example, it is always 1,2,3,4,5 and not 1,2,4,5,3. Students understand that the order in which objects are counted has no effect on the total number of objects, and the quantity of a group of objects remains constant even when the objects are rearranged. Five objects are arranged in a line, rectangular array, a circle or scattered, but not matter what, we only have 5 things. It does not really matter whether the counting procedure is carried out from left to right, from right to left or from somewhere else, so long as every item in the collection is counted once and only once. Whatever is the number of objects in the group, the final number that is called out represents the quantity of that set of objects. A child needs to appreciate that the final number name is different from the earlier ones in that it not only ‘names’ the final object, signaling the end of the count, but also tells you how many objects have been counted. Each object is assigned a unique number-name, based on one-to-one correspondence between each object and the number-name. Students model numbers with the objects in collections or sets. Students realize that counting can be applied to any set, to objects of different attributes (e.g., buttons of different colors, toys of different sizes) or non-visual things such as sounds and actions. Students apply all the principles of counting.
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