Gateways to Advanced Mathematical Thinking A project of Education Development Center Gateways to Advanced Mathematical Thinking was a dual curriculum development/research project funded by the National Science Foundation (DUE 9450731). The development component of the project built a model curriculum module for use with undergraduates, and particularly with preservice teachers, which motivates appreciation for mathematics, focuses on conceptual understanding without sacrificing formal techniques, and makes explicit connections to the high school curriculum. Topics include precalculus methods for solving optimization problems, both exactly and approximately. Another working group of the GAMT project researched student understanding of basic approaches in linear algebra. Students were interviewed with problems designed to show the extent to which they could use reasoning by linearity in algebraic and geometric situations. Gateways to Advanced Mathematical Thinking (DUE 9450731) Al Cuoco, PI Wayne Harvey, Co-PI Optimization Click here to download the entire module (827 K) in pdf format or download individual sections below: Table of Contents and Introduction (207 K) Part1: Geometric Techniques (620 K) Minimizing Distance Maximizing Area Contour Lines Part 2: Algebraic Techniques (620 K) Squares are never negative The Arithmetic Geometric Mean Inequality Part 3: Graphical Techniques (414 K) The Box Problem Samples from the Making Mathematical Connections project Samples from the Making the Connections project For information about more projects for teachers and students of mathematics, visit the websites of EDC's Division of Mathematics Learning and Teaching and Center for Mathematics Education. © Copyright 2003 Education Development Center, Inc. (EDC)