Gateways to Advanced Mathematical Thinking (GAMT)
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Michelle Manes; Education Development Center, Inc. (EDC)  
The goal of this project is to research the ways in which high school and college mathematics students come to acquire flexible understandings of essential concepts needed for analytic and algebraic thinking. Integral to this research effort is the development of model curriculum materials that motivate appreciation for mathematics, focus on conceptual understanding without sacrificing formal techniques, and introduce students to finite, infinite, discrete, and continuous processes and their interactions. Investigate The Box Problem and The Burning Tent Problem. Abstracts of project papers, some with Sketchpad sketches or Mathematica notebooks, include: The Interplay between Algebraic and Geometric Thinking: The Case of Determinants; Revealing the Faces of Abstraction; Constructing the Complex Numbers; Linear and Functional Thinking; Trends in the Organization and Content of Linear Algebra Courses; Visualizing Simultaneous Equations and Cramer's Rule with Dynamic Geometry Software; A Step Towards Understanding Undergraduates' Approaches to Linear Algebra: The Case of the Dot Product.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles, Documents/Sketches/Galleries, Mathematica, Geometer's Sketchpad 
Math Topics:  Basic Algebra, Linear Algebra, Imaginary/Complex Numbers, Euclidean Plane Geometry, Logic/Foundations 
Math Ed Topics:  Curriculum/Materials Development, Pedagogical Research, Psychological Research 
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