At a time of mushrooming interest in Advanced Placement (AP) tests, a new book, "AP: A Critical Examination of the Advanced Placement Program," assembles studies on how capable the program is of meeting the increasingly diverse expectations held up for it. Growing out of a symposium held at Harvard in 2007, the book focuses on AP science…

Background: Securing appropriate challenge or preventing boredom is one of the reasons frequently used to justify ability grouping of gifted students, which has been shown to have beneficial effects for achievement. On the other hand, critics stress psychosocial costs, such as detrimental effects on academic self-concept (contrast or…

Statistics is a branch of mathematics that involves organization, presentation, and interpretation of data, both quantitative and qualitative. Data do not lie, but people do. On the surface, quantitative data are basically inanimate objects, nothing more than lifeless and meaningless symbols that appear on a page, calculator, computer, or in one's…

In this paper we report on a study of a short-term mathematics program for grade 7-8 gifted students that integrated open-ended mathematics tasks with the arts (poetry and drama) and with technology. The program was offered partially online and partially in a classroom setting. The study sought to investigate (a) students' perceptions of their…

Kruteskii's work on the mathematical abilities of school children is a seminal work on the nature of mathematical ability. However, the task of developing methods for the practical application of his work is still a significant problem in mathematics education. The authors have developed a practical application of Kruteskii's approach to the…

In this study, we used logistic regression to examine how well student background and prior achievement variables predicted success among students attending accelerated and enrichment mathematics courses at a summer program (N = 459). Socioeconomic status, grade point average (GPA), and mathematics diagnostic test scores significantly predicted…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

The purpose of this study was to describe the development of the Hungarian mathematics education system from the first half of the 20th century to the present day. The study focused on educational programs for mathematically talented students in Hungary, since it is the success of these talented students that has earned Hungary such an impressive…

Good teaching is responsive to individual differences, tailoring instruction to meet the needs of individual learners. In gifted education, students need a curriculum that is differentiated (by level, complexity, breadth, and depth), developmentally appropriate, and conducted at a more rapid rate. This collection of essays from experts in the…

Gifted middle school mathematics students often exhibit boundless energy, a desire to exert some degree of control over their learning, and an ability to think logically and abstractly in ways that astound their parents and teachers. Middle school math curriculum that combines guided investigations of real-life problems with product-based…

During 3 field experience visits, 23 elementary preservice teachers implemented mathematical problem-solving tasks with grade 3-6 gifted students. Researchers investigated what the teachers learned about gifted students regarding student characteristics, mathematical problem-solving tasks, and pedagogy. Each teacher completed a pre- and…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…

There are a wide range of provisions to be considered when catering for the mathematically gifted student(s) in the classroom. These include acceleration, enrichment, differentiation, curriculum compacting, mentorships, and competitions. The focus for this article is specifically on the use of competitions as one provision for the education of…

Teachers know their students must struggle and grapple with authentic tasks in order to grow stronger. Classroom teachers of the gifted know that their students cannot advance cognitively without facing relevant and challenging material that demands higher level thinking and reasoning. Therefore, the teacher of gifted mathematics students must…

Differentiating instruction for gifted students can enhance participation, engagement, and mathematical learning for all students. The purpose of this article is to (a) discuss gifted students' perception of their participation to middle school mathematics classrooms; (b) explain how one teacher differentiated a mathematical task to engage all her…