The Virtual Grand Tour (VGT) is a paradigm for integrating a presentation of an overview of a larger subject with the possibility of launching at any time an exploratory study of a given sub-topic. The name derives from the paradigm's emulation of those 18th-century travels intended to educate (especially) young, affluent British men; today, with…

Problem solving is seen to lie at the "heart" of mathematics (Cockcroft, 1982). Problem solving is also of great importance to industry that claims many young people leave school and take up jobs without the skills needed to sort out difficulties and problems (Smith Report, 2004). So is problem solving at the heart of mathematics teaching in…

An interdisciplinary course centered on mathematical ideas (involving infinity and geometry) is described. The course was developed by the authors, both mathematicians, as a vehicle for engaging students in learning about mathematical ideas that are rarely found in the general undergraduate curriculum. The course was offered to honors students…

The mathematics education community, in its call for reform, underscores the importance of mathematics instruction emphasizing the use of multiple representations in the presentation of concepts. The focus of the study was how teacher beliefs affect their ability to implement a multiple representations curriculum. The novice instructor's attitude…

"Thinking schools" will be sites of learning for everyone declared the Singapore Prime Minister, Goh Chok and Minister of Education Teo Chee Hean's in 1997 also spoke on the model of "thinking schools, learning nation". Gardner's model was used for the thinking school model in Singapore, in order to develop critical and…

This article describes a valuable lesson that university mathematics faculty members learned from fifth grade and middle school teachers in a professional development workshop. The goal of the workshop was to show how models for whole number operations could be linked to models for rational numbers and to connect the traditional algorithms to the…

The shape and form of effective teacher-pupil talk has recently become the focus of attention within policy guidelines such as the National Numeracy and Literacy Strategies. Prior to this, research on classroom discourse has established that social context plays an important role in determining the quality of teacher-pupil talk since it directs…

Some research studies, many of which used quantitative methods, have suggested that graphics calculators can be used to effectively enhance the learning of mathematics. More recently research studies have started to explore students' styles of working as they solve problems with technology. This paper describes the use of a software application…

Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students…

Elementary education students enrolled in an experimental mathematics course participated in this study. The course is taught using a social constructivist approach and is designed to improve students' mathematical problem-solving ability and deepen their understanding of mathematics. The research question for the present study is as follows: In…

This paper contributes to knowledge about principled action which makes a difference to learners' attainment. We report on the Improving Attainment in Mathematics Project, a project focusing on low-attaining secondary students. The purpose of the project was to introduce innovations in practice through action research with 10 teachers over 2…

Four elementary students with behavior disorders attending a day treatment facility were trained to recruit positive teacher attention. Data on student recruiting and academic productivity were collected across 59 twenty-minute sessions. A multiple baseline across students design demonstrated a functional relationship of recruitment training on…

A classroom intervention employing math racetracks was carried out to teach math facts to two elementary students with learning disabilities. A math racetrack is a drill and practice procedure where known and unknown facts are placed on a sheet of paper like an oval racetrack. The effectiveness of using math racetracks was evaluated with a…

Lecture is a common presentation style that gives instructors a lot of control over topics and time allocation, but can limit active student participation and learning. This article presents some ideas to increase the level of student involvement in lecture. The examples and suggestions are based on the author's experience as a senior lecturer for…

Our primary goal is to design a micro world which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to…