Describes two activities to introduce or extend the concept of the natural number e. Students conduct a lottery using either a table of random numbers or a computer simulation to link experimental probability results to the theoretical probability and to the number e. (MDH)

Described are activities that use a hundred chart to improve student abilities to recognize and describe number patterns, to use variables, to make and informally prove conjectures, and to communicate mathematical ideas to classmates. Included are the directions, four reproducible student sheets, the answers, and extensions. (KR)

Discussed is how the concept of equivalence can relate various segments of a mathematics program and help students develop an appreciation of the unity of mathematics. Activities and examples of equivalence at all grade levels are included. (KR)

Describes and illustrates the Monomial Sums Approach, a graphical learning strategy, facilitated by microcomputer capabilities that allow easy manipulation and exploration of graphical representations of polynomial functions. Reduces emphasis on memorized rules in favor of qualitative understanding of functional behavior, visualization of…

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

Presented are four activities that focus on gathering and interpreting data about pizza as a basis for integrating mathematics, health, and social studies. Reproducible sheets for parents to use with their children, class-activity sheets, and a data sheet are provided. Each activity includes the objective, needed materials, directions, extensions,…

A project in which teams of preservice teachers were grouped with teams of seventh grade students and worked cooperatively on a set of assignments is described. The plan, project, implementation, results, and summary are presented. (KR)

Addresses some concerns about teaching and learning geometry by describing how The Geometer's Sketchpad software program allows for the implementation of many of the recommendations from the National Council of Teachers of Mathematics (NCTM) in the mathematics classroom. Explains the types of activities that can be used with the software and…

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…

As of 2005, 15 states had adopted a broad-based merit aid program, providing a combined $1.2 billion for college students on the basis of academic qualifications. This represents a shift away from a long tradition of need-based aid at the state and federal levels. This article utilizes a Cox proportional hazards model to analyze states'…

Currently, the teaching of retake GCSE mathematics in further education is predominantly teacher-centred and transmission-oriented. This paper argues that this approach is ineffective for students' learning and for their attitudes towards learning and that a student-centred, collaborative approach to learning, where discussion and reflection are…

This paper describes the forms of knowledge used by players of fantasy sports, games where players create ideal sports teams and compete to accumulate points based on professional athletes' statistical performances. Messages from a discussion forum associated with a popular fantasy basketball game were analyzed to understand how players described…

Variability stands in the heart of statistics theory and practice. Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners'…

In this study, the researchers developed the Web-based Probability Explorer (WPE), a mathematical microworld and investigated the effectiveness of the microworld's constructivist learning environment in enhancing the learning of probability and improving students' attitudes toward mathematics. This study also determined the students' satisfaction…

This paper describes research into the beliefs and practices established over time by teachers, who had been engaged in an innovative "mathematical investigations" school program, based on the use of exploratory software. The theoretical framework perceives the teacher as an active mediator of innovation, constructing and reorganizing a…