Investigating connections between fractional competence and algebraic reasoning in the middle years

Abstract

To succeed in mathematics, middle-years’ students must move from additive to multiplicative thinking and from arithmetic calculations to generalised algebraic reasoning. This thesis’ focus on fractions gives insight into 607 middle-years students’ solution strategies and the potential to prompt algebraic thinking and reasoning as they attempted two paper and pencil assessments: The Fraction Screening Test (FST) and the Algebraic Thinking Questionnaire (ATQ). Analysis of the results has revealed that students exhibit many previously reported misconceptions. For example, students ordered fractions by size of denominator or by the difference between the numerator and denominator (gap thinkers)...