Responding to students' questions is a critical part of teaching mathematics. A particular response may either stifle a student's inquiry or, ideally, stimulate his or her interest in mathematics. Although formulating responses that have the potential to engage students in developing new mathematical insights is challenging, the authors believe…

Music learning and music performance involve all aspects of the individual: cognitive, emotional, social, and psychomotor. John Feierabend shows that music requires a special kind of intellectual process that is unique to the discipline. Brain density reaches its peak in a child's first few years of life; hence, as with language, music learning…

This paper examines research studies that have concluded that elementary school children can learn more difficult and abstract social studies concepts than are taught in the traditional social studies curriculum. Research studies that focus on constraints on cognition, the use of embedded concepts, and understanding knowledge restructuring and…

While many contemporary developmental theorists have avoided taking a stand on the controversial relationship between learning and development, this paper is based on the belief that the notion of "bandwidth of competence," or L. S. Vygotsky's "zone of proximal development," provides a useful framework for considering this…

Nine articles on the young adolescent consider the ability of middle schools to adapt to the needs of their students, the educational implications of preadolescent development, adolescent brain growth and cognitive ability, and the relevance of Piaget's psychology to the middle school. The authors' conclusions include the necessity to identify and…

This paper addresses four of the seven themes of the 2nd International Conference on the Teaching of Mathematics--research, technology, pedagogical innovation, and curricular innovation--from the point of view that learning mathematics is learning. Research from a variety of fields including education, neurobiology, and cognitive psychology…