Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4…

Examines Australian students' conceptions of ordering decimals. Fifty secondary students studied over 12 months showed little change in their misconceptions. Whole number misconceptions are important in earlier years but disappear with time. The fraction misconception persists however, being displayed by approximately 20% of year 10 students. The…

The concept of fractional number was studied with 10- to 12-year-old and 13- to 16-year-old students who were deaf and hard of hearing (n=21) and comparison groups of hearing students (n=26). The deaf and hard-of-hearing students achieved similarly to younger hearing students in overall performance by fraction type and problem solving strategies.…

The purpose of this study was to assess children's and adults' quantitative understanding of fractions in a new and potentially definitive way, and to determine whether this understanding was related to fraction computational skill. Thirty-seven seventh graders and 32 adults (college students) participated in the study. A computation task was used…