This is MegaMathematics: The Los
Alamos Workbook
By Nancy Casey and Mike Fellows
A collection of classroom lessons in mathematics and computer science. Each lesson contains extensive background material that assumes that the topic of the lesson is new to the teacher. Topics include map coloring, graph theory, knot theory, finite state machines, algorithms, logic and infinity.
(File size is 851KB.)
Description of a series of four lessons in a second grade classroom. Students worked on a problem from graph theory involving dominating sets in a setting designed to promote language development.
(File size is 159KB.)
Description of a classrrom session with high school students. Through a problem in graph theory, students explore notions of precise mathematical language, conjecture, deduction, and proof. The lesson is continuously shaped and restructured by the teacher according to student responses and questions.
(File size is 172KB.)
If mathematics is thought of as a language, how can teachers' experiences with teaching young children to read and write inform their mathematics teaching? Understanding literacy and language acquisition has affected language arts teaching over the last 20 years, and now this understanding is most apt for the elementary school mathematics classroom as well. Everyone would benefit from the creation of a mathematics community where elementary school students, teachers, and professional mathematicians respect and share one another's insights.
(File size is 120KB.)
Computer SCIENCE in the Elementary
School
By Mike Fellows
Description of one mathematician's experiences working in elementary school classrooms. Includes many activities in discrete mathematics and the impact of classroom visits on the mathematician's own research.
(File size is 266KB)
Combinatorially Based Cryptography for Children (and Adults)
By Mike Fellows and Neal Koblitz
Popularizing mathematics for children (and adults) is an important aspect of mathematics education reform. This paper describes how certain notions of modern cryptography can be presented to youngsters using combinatorial constructions. Among the topics discussed are the use of Boolean circuits for bit commitment protocols and hash functions, and the construction of a public key message transmission system using perfect codes in a graph.
(File size is 383KB.)
A classroom structure in which children's individual needs can be considered is necessarily quite complex. It must be flexible with plenty of options so that children can choose to do work that is meaningful to them. Yet if children are simply given a myriad of choices, then told to plan their time and accept responsibility for their learning, the result is likely to be chaos. This essay describes the observations of a researcher who observed how, over a period of 3 months, a second-grade teacher with 16 years experience gradually taught her students how to thrive and learn in a classroom that is flexible, rich, and highly structured.
(File size is 147KB.)
Nancy Casey (casey931@cs.uidaho.edu)