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.…

We have been incrementally adding data-driven methods into the Deep Thought logic tutor for the purpose of creating a fully data-driven intelligent tutoring system. Our previous research has shown that the addition of data-driven hints, worked examples, and problem assignment can improve student performance and retention in the tutor. In this…

This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

This third edition of the best-selling "Mathematics in Nursery Education" provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics learning--number and counting, calculation, pattern, shape, measures and data handling--it summarises the research findings and underlying key concepts…

The second edition of this essential handbook provides a comprehensive, updated overview of the science that informs best practices for the implementation of response to intervention (RTI) processes within Multi-Tiered Systems of Support (MTSS) to facilitate the academic success of all students. The volume includes insights from leading scholars…

This book describes and illustrates learning paths for the mathematical concepts and skills of each grade 8 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about…

This paper proposes a learning based method that can automatically determine how likely a student is to give a correct answer to a problem in an intelligent tutoring system. Only log files that record students' actions with the system are used to train the model, therefore the modeling process doesn't require expert knowledge for identifying…

A description is given of materials produced by the Schools Council Project on Statistical Education. (MK)

New software tools for data analysis provide rich opportunities for representing and understanding data. However, little research has been done on how learners use these tools to think about data, nor how that affects teaching. This paper describes several ways that learners use new software tools to deal with variability in analyzing data,…