Constancy of Errors to Basic Facts in the Fundamental Operations in Arithmetic

Abstract

This study was made to determine the constancy of an error to a basic fact in the four fundamental operations in arithmetic. There is some experimental evidence to indicate that many errors made in arith metic are sporadic and due to chance rather than to a faulty knowledge. An error due to chance is known as a chance error and it is not constant. An error due to a faulty knowledge should be persistent and constant. A test containing only one response to a combination would not differen tiate between a sporadic and a constant error. One of the first studies to show that an error is not always constant was made by Brueckner and Ewell.1 This study used fractions instead of basic combinations. The results indicated that at least three examples of the same type had to be offered in a test to see if an error were constant. Brueckner2 further showed that errors to examples in division of fractions from a test taken six different times were largely due to chance. The senior writer3 showed that a multiplication fact in division had to occur at least three times before the effect of chance could be determined in diagnosing the results. Ruch showed that a pupil's score made on a test of basic facts in addi tion is a variable. He arranged the one hundred addition facts in random sequences on five different forms and gave these tests to thirty pupils in Grade III. There was not one case in which a pupil made the same score on all of the five forms.4 This variation must have been due to chance errors. The investigation reported in the following pages is a more ex haustive study than that reported by Ruch for each of the four funda mental operations.