Early Fraction Learning [Paperback]

Early Fraction learning is centrally of interest to studentsand researchersin mathematics education, tackling as itdoes one of that discipline's most vexing problems: why arefractions so difficult to learn and to teach?Early Fraction learning is centrally of interest to studentsand researchersin mathematics education, tackling as itdoes one of that discipline's most vexing problems: why arefractions so difficult to learn and to teach?1. Introduction.- References.- 2. Pre-fraction Concepts of Preschoolers.- Method.- Problem Descriptions and Rationales.- Results.- Problem 1: Skipping Ropes.- Problem 2: Sharing the Crackers.- Problem 3: Sausages.- Problem 4: Swapcards.- Discussion.- References.- 3. Dimensions of Young Childrens Conceptions of the Fraction One Half.- Theory.- Method.- Problem Descriptions.- Results.- Accuracy of Responses: One-half (Candysticks and Jellybabies).- Procedures Used.- Accuracy of Responses: Sharing (Snakes and Crackers).- Procedures Used.- Procedures Used by Most Accurate Children: One-half.- Procedures Used by Most Accurate Children: Sharing.- Case of John (4,11): A Strong Halver.- Case of Julie (5,3): A Weak Halver.- Case of Jamie (5,3): A Strong Sharer.- Case of Lisa (5,5): A Weak Sharer.- Discussion.- References.- 4. The Social Origins of Pre-fraction Knowledge in Three Year Olds.- Method.- Development of the Interview Plan.- Description of the Interview Tasks.- The Parent Questionnaire and Interview.- Results.- Performance on the Sharing Tasks.- Performance on the Recognition Tasks.- Data from the Parent Interview.- Relationships Between Sharing Competence and Home Factors.- General Discussion.- References.- 5. Higher Order Thinking in Young Childrens Engagements with a Fraction Machine.- The Copy Cat Fraction Machine.- Method.- Results.- Copy Cat Performance.- Counting Performance.- Relationships Between Copy Cat Performance and Counting.- The Case of Jayme and One-third.- Discussion.- References.- 6. Fractions as Operators and lCë