A study of the explanations used by elementary school students in the interpretation of the fraction concept, and addition and subtraction of fractions

Edmunds, Michael John (1982) A study of the explanations used by elementary school students in the interpretation of the fraction concept, and addition and subtraction of fractions. Masters thesis, Memorial University of Newfoundland.

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Abstract

The purpose of this study was to analyze the explanations given by grade six students in their interpretations of the fraction concept and the addition and subtraction of fractions. -- A series of 52 questions dealing with the fraction concept and the addition and subtraction of fractions were developed, tested, and analyzed. Twenty students were randomly selected and were interviewed and audiotaped. The questions included problems at the physical, pictoral and symbolic levels. Questions were presented using both part of a set interpretation of a fraction and part of a whole interpretation of a fraction. The questions used in the study were of two different types. Type 1 questions were of the form where the number in the set was the same as the denominator. Type 2 questions were of the form where the number in the set was a multiple of the denominator. -- An analysis was carried out to determine the interpretations of the fraction concept and the addition and subtraction of fractions. Where incorrect interpretations were found, they were analyzed to hypothesize their nature and cause. -- There were very few incorrect interpretations of the fraction concept and the addition and subtraction of fractions when the students were given Type 1 questions. The only consistent incorrect interpretation was that three students explained the fraction in terms of a relationship between the parts of a set rather than as a relationship between the parts and the total number in the set. -- There were many incorrect interpretations of the fraction concept and the addition and subtraction of fractions when the students were given the Type 2 questions. The most commonly used incorrect interpretation was an attempt by the students to reduce the Type 2 questions to Type 1 questions. The students explained their procedures as if the questions were Type 1. -- There were very few computational errors made by the students and therefore it was pointless to determine if the errors were systematic. -- The incorrect interpretations were not found to by systematic. Students gave consistent incorrect interpretations to particular questions but they were not consistent in using the same incorrect interpretations for all the questions.

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