In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…

Community college developmental math students (N = 657) from three math levels were asked to place five whole numbers on a line that had only endpoints 0 and 20 marked. How the students placed the numbers revealed the same three stages of behavior that Steffe and Cobb (1988) documented in determining young children's number sense. 23% of the…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

This paper reports selected findings from a study of number sense proficiency of students aged 13 to 16 years in a state in Malaysia. A total of 1756 students, from thirteen schools in a state in Malaysia participated in this study. A majority (74.9%) of these students obtained an A grade for their respective year-end school examinations. The…

Recently, the nature of children's mental number line has received much investigation. In the number line task, children are required to mark a presented number on a physical number line with fixed endpoints. Typically, it was observed that the estimations of younger/inexperienced children were accounted for best by a logarithmic function, whereas…

This essay argues for the importance of quantitative reasoning skills as part of a liberal education and describes the successful introduction of a mathematics-based quantitative skills course at a small Canadian university. Today's students need quantitative problem-solving skills, to function as adults, professionals, consumers, and citizens in…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…

This book provides a comprehensive collection of 66 teaching strategies and ideas to help overcome problems with number, each linked to a specific kind of error described in the related manual. Most of these strategies are classroom-ready and easily implemented. Some are notes for the teacher to read and then plan activities accordingly, and many…

Describes the development, refinement, and validation of a framework for nurturing and assessing multidigit number sense in young children. Major constructs incorporated were counting, partitioning, grouping, and number relationships. The framework was validated through case studies of six first-grade children. (30 references) (MKR)