Children's understanding of logical and conventional rules in arithmetic algorithms

Abstract

The study examined third graders' ability to distinguish logical from conventional algorithm rules. Third graders performed written addition and subtraction algorithms, answered questions about the amounts exchanged in carrying and borrowing, and evaluated the alterability and relativity of two alternative rules: an alternative conventional rule, involving a conventional aspect of the algorithm (e.g., putting the answer above the problem, rather than below), which does not change the answer, and an alternative logical rule, involving a logical aspect of the algorithm (e.g., adding a carried “ten” to the hundreds column), which produces an incorrect answer. Results indicate that children know that using an alternative logical rule produces a different answer, but many do not judge this answer to be necessarily incorrect. Rather, they judge the correctness of both types of rules, as well as the answers produced by using the rules, to be conventional, and thus under the control of the teacher or other school authorities.