Reasoning is the process of thinking used to make claims and reach conclusions. It is among the first skills that should be taught to students in mathematics lessons and contributes to the creation and development of mathematical foundations. This study identifies evolution and trends in research on mathematical reasoning over the last four…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

"Talking Points: Discussion Activities in the Primary Classroom" encourages and supports classroom discussion on a range of topics, enabling children to develop the important life-skill of effective group communication. Children who can explain their own ideas and take account of the points of view and reasons of others are in the process of…

This textbook presents the divisions of arithmetic in their natural order. The fundamental operations upon integers, common fractions, decimals, denominate numbers, and numbers expressed by letters, are followed by their applications to business and to various employments. The pupil is taught to develop observation and thought power, rather than…

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

This guide contains classroom-tested problems designed to introduce and reinforce mathematical concepts in a quick, "fun" way. Activities emphasize the logic and reasoning skills needed to build a strong foundation in mathematics. The problems are thinking activities and require only upper elementary level mathematics skills. Activities are…

The purpose of this report is to investigate the range of student responses in three domains--hypothesizing, organizing data, and algebraic generalization of patterns during their work on a spreadsheet-based activity. In a wider context, we attempted to investigate students' utilization schemes of spreadsheets in their learning of introductory…

In this lesson, students identify the question-answer relationship (QAR) for word problems that relate to a graphic or table. They then use the QAR strategy to determine the mathematical and cognitive actions required to answer the word problem. This activity is particularly appropriate for fourth- and fifth-grade students. During two 40-minute…

This book shows the reader how to use Information and Communication Technology (ICT) effectively to enhance the teaching of mathematics in the secondary school. It explains which forms of technology can be used to improve mathematics teaching and learning, how to get started and where to go for further information. The book includes practical…

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter…