Turtle Escapes the Plane: Some Advanced Turtle Geometry

Since the LOGO Turtle took his first step he has been mathematically confined to running around on flat surfaces. Fortunately the physically intuitive, procedurally oriented nature of the Turtle which makes him a powerful explorer in the plane is equally, if not more apparent when he is liberated to tread curved surfaces. This paper is aimed roughly at the High School level. Yet because it is built on intuition and physical action rather than formalism, it can reach such "graduate school" mathematical ideas as geodesics, Gaussian Curvature, and topological invariants as expressed in the Gauss-Bonnet Theorem

Student Science Training Program in Mathematics, Physics and Computer Science

During the summer of 1976, the Massachussetts Institute of Technology Artificial Intelligence Laboratory sponsored a Student Science Training Program in Mathematics, Physics and Computer Science for high ability secondary school students. This report describes, in some detail, the style of the program, the curriculum and the projects the students undertook

Can research on science learning and instruction inform standards for science education?

We contrast the current science education reform effort with the reforms of the 1960s and suggest how the current effort could be enhanced. We identify insights from recent research that we believe can inform the reform process, in particular, to reach all science students and also impart a cohesive view of science. We propose an ldquoalternative modelsrdquo view of scientific explanation and show how this view would contribute to reforms of (1) course goals, (2) social aspects of science learning, (3) instructional practices, and (4) roles for technology

Transitions in Mathematics Education

International audienceThis book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education