The way in which two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students is described. Carolyn and Elizabeth's approach is to pose several problems of various degrees of difficulty and complexity for each aspect of the…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

Recursion is a programming paradigm as well as a problem solving strategy thought to be very challenging to grasp for university students. This article outlines a pilot study, which expands the age range of students exposed to the concept of recursion in computer science through instruction in a series of interesting and engaging activities. In…

In this paper we report on the sustained research and development work at the AMSTEL Institute of the University of Amsterdam to improve mathematics and science education at primary and secondary school level, which has lead amongst other things to the development of the integrated computer working environment Coach 6. This environment consists of…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for…

The purpose of this study was to examine preservice mathematics teachers' knowledge about common (mis)conceptions and difficulties of elementary students. In addition, it was aimed to investigate preservice teachers' knowledge about the possible sources of these misconception/difficulties, and their suggested strategies to overcome those…

Whether teaching mathematics in a contained elementary classroom, as a specialized math teacher, or as an ELL teacher, this new resource will help meet the needs of English Language Learners. Offering strategies, guidelines, and classroom vignettes, this book demonstrates how to adjust mathematics instruction to make the learning less…

Making math concepts understandable is a challenge--one that is more complex when a classroom includes students with learning difficulties. With this highly practical resource, teachers will have just what they need to teach a critical content area with confidence: research-based strategies that really work with students who have learning…

This article introduces and explains probability games from diverse cultures. Activities are described and teacher-ready materials are included. (Contains 7 figures.)

Difficulties that are encountered by dyslexic undergraduates with their learning and understanding of mathematics are explored. Specific consideration is given to issues arising through mathematical content, its delivery, the procedures and processes of doing mathematics, and its assessment. Particular difficulties, which have emerged through…

This paper describes a modification of a popular TV game show, "American Idol[R]," conducted in an undergraduate calculus course. The focal point of this game show is to get students to interact in competitive self-assessment. Student competition is an effective device to engage students in the learning process. Placing students in the role of…

In this article we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics. The purpose of the activity is to tie together several topics in the context of a "real-world" situation. These topics include: fractals, non-Euclidean geometry, symmetry, and Platonic solids. This activity…

For mathematics teachers who are continually looking for ways in which to engage their students in the learning process, the capabilities offered by technology answer the call. Whether the technology comprises computer based applications or graphics calculators, often boring aspects can be bypassed so that students can work on the "good…

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…