Analyzing and Modeling Arithmetic Errors

Abstract

Thirty-nine seventh-grade students completed an arithmetic test designed to uncover errors involving misunderstandings of (a) operations with whole numbers, (b) grouping symbols, and (c) rules of precedence (order of operations). Both the students' final answers and the intermediate steps for each test item were analyzed, and models to represent students' behaviors were developed. Certain types of errors were common across students. Errors were found to be closely tied to the format of the test item. Variations in the formats of test items that left the underlying computations unchanged exposed some students' superficial understandings of mathematical concepts.